Forward-backward asymmetry as a discovery tool for Z′ bosons at the LHC

Journal of High Energy Physics, Jan 2016

The Forward-Backward Asymmetry (AFB) in Z′ physics is commonly only perceived as the observable which possibly allows one to interpret a Z′ signal appearing in the Drell-Yan channel by distinguishing different models of such (heavy) spin-1 bosons. In this paper, we revisit this issue, showing that the absence of any di-lepton rapidity cut, which is commonly used in the literature, can enhance the potential of the observable at the LHC. We moreover examine the ability of AFB in setting bounds on or even discovering a Z′ at the Large Hadron Collider (LHC) concluding that it may be a powerful tool for this purpose. We analyse two different scenarios: Z′-bosons with a narrow and wide width, respectively. We find that, in the first case, the significance of the AFB search can be comparable with that of the ‘bump’ search usually adopted by the experimental collaborations; however, in being a ratio of (differential) cross sections, the AFB has the advantage of reducing experimental systematics as well as theoretical errors due to PDF uncertainties. In the second case, the AFB search can outperform the bump search in terms of differential shape, meaning the AFB distribution may be better suited for new broad resonances than the event counting strategy usually adopted in such cases.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP01%282016%29127.pdf

Forward-backward asymmetry as a discovery tool for Z′ bosons at the LHC

Received: May Forward-backward asymmetry as a discovery tool for Z0 bosons at the LHC Elena Accomando 0 1 2 5 6 Alexander Belyaev 0 1 2 5 6 Juri Fiaschi 0 1 2 5 6 Ken Mimasu 0 1 2 3 6 0 Harwell Science and Innovation Campus , Didcot, Oxfordshire, OX11 0QX U.K 1 Falmer , Brighton, BN1 9RH U.K 2 University Rd, Southampton, SO17 1BJ U.K 3 School of Physics and Astronomy, University of Sussex 4 Particle Physics Department, STFC, Rutherford Appleton Laboratory 5 School of Physics and Astronomy, University of Southampton , High eld Campus 6 LHC @ 13 TeV The Forward-Backward Asymmetry (AFB) in Z0 physics is commonly only perceived as the observable which possibly allows one to interpret a Z0 signal appearing in the Drell-Yan channel by distinguishing di erent models of such (heavy) spin-1 bosons. In this paper, we revisit this issue, showing that the absence of any di-lepton rapidity cut, which is commonly used in the literature, can enhance the potential of the observable at the LHC. We moreover examine the ability of AFB in setting bounds on or even discovering a Z0 at the Large Hadron Collider (LHC) concluding that it may be a powerful tool for this purpose. Hadronic Colliders - width, respectively. We nd that, in the rst case, the signi cance of the AFB search can be comparable with that of the `bump' search usually adopted by the experimental collaborations; however, in being a ratio of (di erential) cross sections, the AFB has the advantage of reducing experimental systematics as well as theoretical errors due to PDF uncertainties. In the second case, the AFB search can outperform the bump search in terms of di erential shape, meaning the AFB distribution may be better suited for new broad resonances than the event counting strategy usually adopted in such cases. 1 Introduction 2 Bounds on the Z0-boson mass 3 The forward-backward asymmetry 3.1 The reconstructed AFB 3.2 On the di-lepton rapidity cut 4 The role of AFB in Z0 searches: narrow heavy resonances 4.1 Z0 models with AFB centred on peak 4.2 Z0 models with shifted AFB 5 The role of AFB in Z0 searches: wide heavy resonances 6 On the robustness of AFB against PDF uncertainties 7 Conclusions 1 Introduction Heavy neutral Z0-bosons arise in a number of theories that extend the Standard Model (SM) gauge group by adding an extra U( 1 ) symmetry. The most common Z0-boson benchmark models can be divided in three main classes: E6 models, Generalized Left-Right (GLR) symmetric models and Generalized Standard Models (GSM), see, e.g., the reviews in [1, 2] and references therein. All of these models predict a relatively narrow width for the Z0bosons, with Z0=MZ0 lying in the 0:5{12% range. The lowest Z0=MZ0 value is realised in the E model from the E6 class while the biggest value appears in the Q-model belonging to the GSM class. Experimental searches for a heavy Z0-boson at the LHC are usually interpreted in the context of the Sequential Standard Model (SSM), which is part of the GSM class [3]. This benchmark scenario just includes one extra neutral vector boson with couplings to fermions identical to those of the corresponding SM Z-boson and no mixing with the neutral Electro-Weak (EW) SM bosons. Being nothing but a heavier copy of the SM Z-boson, this Z0-boson is characterized by a narrow width: Z0=MZ0 ' 2:8%, including the Z0-decay into top-antitop pairs above threshold. Dedicated search strategies therefore assume that the new heavy resonance is narrow and can be described by a Breit-Wigner line-shape, standing over the SM background, when looking at the invariant mass distribution of the Z0-boson decay products. In this way, the new physics signal is thought to have a well de ned peaking structure, concentrated in a small interval centred around its mass. On the basis { 1 { of this assumption, the 95% Con dence Level (C.L.) upper bound on the cross section is derived and limits on the mass of the Z0-boson are extracted within the above mentioned benchmark models. In the case of a narrow width Z0 scenario, even interference e ects can be accounted for without substantially altering the described experimental approach [4, 5]. However, the narrow width hypothesis is quite strong, even if well motivated. There exist counter examples of theories where the predicted Z0-boson is characterized by a large width. For example, this can be realized in Technicolor [6] scenarios, Composite Higgs Models [7] or in more generic setups where the Z0-boson couples di erently to the rst two fermion generations with respect to the third one [8, 9] or else interacts with the SM gauge bosons in presence of mixing [10], so that large Z0 =MZ0 values are induced by the section within these two scenarios we refer to ref. [16] and references therein. Both processes might give rise to an excess of events spread over the SM background. In this `e ectively' non-resonant case, the experimental analyses are essentially counting experiments: an excess of events sought out of an estimated SM background. To make the analyses more robust, the same background is often estimated with multiple data-driven methods. Kinematical cuts are then optimized in order to maximize the discovery/exclusion potential at the LHC. Despite this, as one can understand, this analysis can be fragile. The experimental results heavily rely on a good understanding and control of the SM background, as the new physics signal is not expected to have a de nite shape. The choice of the control region, needed to de ne the functional form of the SM background to be used in the regions where there might be some signal, is not trivial. Interference e ects between a new physics signal and the SM background can indeed a ect the low scale region of the distribution in the invariant mass of the Z0-boson decay products, proving the assumption that the control region is new physics free to be simply false. Under these premises the experimental analyses could get quite complicated. On the one hand, the possible presence of wide objects could in fact deplete the `new physics free' region, owing to an increase of the interference e ects driven by the large width. On the other hand, the wide Z0-bosons could easily escape detection in the bump searches due to the same interference e ects combined with the absence of a resonant peaking structure in, e.g., the di-lepton invariant mass distribution. All of this can conspire to make the discovery of a wide Z0 very problematic. The importance of such e ects has been highlighted in refs. [4, 5, 17]. The same level of complication arises when searching for heavy charged W 0-bosons as described in { 2 { refs. [5, 17, 18]. For that search, which also relies on a counting strategy as no Breit-Wigner can appear owing to the presence of the neutrino in the leptonic Drell-Yan channel, the CMS collaboration recently included the interference e ects between the extra W 0 and the SM W -boson [19, 20]. In this paper, we focus on the Z0-boson search and study the potential of a second observable, complementary to the di-lepton invariant mass used by default, in order to maximize the sensitivity to new massive Z0 objects, either narrow or broad. The variable we analyse is the Forward-Backward Asymmetry (AFB). In the literature, this observable is usually advocated in the second stage of the data analysis process to interpret experimental results after a possible discovery of a new spin-1 particle using a standard bump hunt. The AFB can be used to disentangle di erent models with Z0-bosons and nail down the underlying theory. This procedure relies on the assumption that the new heavy Z0boson is characterized by a narrow width and it would be discovered via the bump search. Our purpose is to show that the AFB can be used not only for interpreting a possible discovery but also in the very same search process. We show that the AFB observable can be associated to the default resonance search to improve and/or extend the discovery potential for both narrow and wide Z0s. Focussing on AFB, we aim at establishing the methods needed to study Z0-boson production at the CERN LHC in the Drell-Yan channel, giving rise to di-lepton pairs in the nal state: pp ! l+l with l = e; . This production process is particularly clean and thus represents the golden channel for Z0-boson discovery at the LHC. The paper is organized as follows. In section 2, we derive current and projected bounds for Z0 model benchmarks for the LHC at 8 and 13 TeV, respectively, for the models presented in ref. [1]. In section 3, we discuss the role of the forward-backward asymmetry within the Z' physics, its reconstruction and statistical uncertainty. We also discuss the e ect of a rapidity cut on the di-lepton system upon the signal signi cance. This cut is commonly implemented in order to increase the e ciency in guessing the quark direction in pp collisions, which is needed to reconstruct the AFB observable. The drawback of applying it is a decrease of the number of signal events with the consequent depletion of the AFB signi cance. The outcome is that this stringent cut can be relaxed for the range of Z0-boson masses which we will be looking for in the next LHC run. In section 4, we discuss the role of the AFB in searches for narrow width Z0-bosons and systematically analyse Z0 model benchmarks confronted with AFB and bump searches. We will show that the signi cance from the AFB can be comparable with that obtained from the cross section studies over the same invariant mass distribution of the di-lepton system. In this scenario, the advantage of using the AFB observable would consist in minimizing the systematics, as the AFB is a ratio of (di erential) cross sections. Moreover, the two observables (cross section and asymmetry) could be of mutual support to make the claim of a possible new physics discovery more robust, if the bump search itself would provide only mild evidence for a Z0 state. In section 5, we analyse the role of AFB in searches for wide Z0 particles. We consider two benchmark models which predict a wide Z0-boson with ratio Z0 =MZ0 of the order of several tens of percent. In this case, again, the AFB can be complementary to the resonance { 3 { search and have a distinctive line shape contrary to the invariant mass distribution of the cross section, which could well mimic the background shape. That is, the latter would only give rise to an excess of events evenly spread over the SM background, which is of di cult interpretation and in many cases of di cult measurement owing to uncertainties in the background modelling. In section 6, we discuss the Parton Distribution Function (PDF) uncertainties at the energy scale where we expect to nd new Z0-bosons at the LHC. Our nding is that, even if the design luminosity L = 300 f b 1 is reached at the LHC Run II, the AFB can play an important role in the narrow (and wide) Z0-boson hunt. The reason is that, even if a striking new physics signal with low statistical error were to be found in the bump search, its theoretical interpretation could be very poor owing to the severe indeed much bigger than the statistical one and the gap grows with incresing luminosity. In this case, the AFB measurement could be of valuable help. We show in fact that the AFB error is dominated by statistics, as the PDF uncertainties largely cancel in the ratio between cross sections, so it can only improve with the luminosity. Finally, in section 7 we summarize and conclude. 2 Bounds on the Z0-boson mass In this section, we re-derive the existing bounds on the mass of the Z0-boson from the aforementioned benchmarks models as obtained by, e.g., the CMS collaboration, after the 7, 8 TeV run with about 20 f b 1 of accumulated luminosity, assuming a narrow width. These can be found in ref. [16]. After con rming current CMS limits obtained under the above assumption, we further present those obtained by taking into account the full width e ect as well the intereference corrections. Finally, we produce projected limits for LHC Run 2. Z; ! e+e ; + trigger e ciency. We therefore start by scanning over the thirteen benchmark models predicting a Z0boson characterized by a narrow width ( Z0 =MZ0 5%) summarized in ref. [1], and extract the limits on MZ0 by making use of the 95% C.L. upper bound on the Z0-boson production cross section in Drell-Yan, (pp ! Z0 ! e+e ; + ). In order to reduce systematic uncertainties, the experimental analysis normalizes the Z0-boson production cross section in Drell-Yan to the SM Z-boson cross section on peak. As shown in gure 1, the 95% C.L. upper bound is indeed given on the ratio R = (pp ! Z0 ! e+e ; + )= (pp ! ). The use of this ratio R in fact cancels the uncertainty in the integrated luminosity and reduces the dependence on the experimental acceptance and We calculate this ratio, R , at the Next-to-Next-to-Leading Order (NNLO) in QCD using the WZPROD program [21{23] (which we have adapted for Z0 models and new PDF sets [1]) and the CTEQ6.6 package [24]. Similar computations have been performed in ref. [17], albeit within a di erent kinematical setup. There, the R ratio is evaluated at NLO+NLL using RESUMMINO. The NNLO QCD contributions give rise to a K-factor which depends on the energy scale, thus we fully take into account such a dependence. The NNLO prediction for the SM Z; production cross section, (pp ! Z; ! l+l ) with { 4 { (a) (b) ! l+l ) with l = e; . The combined analysis of the di-muon and di-electron channels has been produced by the CMS collaboration with a data sample collected at the 8 TeV LHC, corresponding to an integrated luminosity of 20.6 and 19.7 f b 1 respectively [16]. Theoretical predictions for the class of the E6 models are superimposed to extract the corresponding Z0-boson mass limits. As described in the text, in order to match theoretical predictions and experimental results, the optimal cut on (pp ! Z0 ! l+l )= (pp ! the invariant mass of the di-lepton pairs has been implemented: for ELHC = 8 TeV. (b) Same as (a) for the other two classes of GSM and GLR models. M = jMll MZ0 j 0:05 ELHC l = e; , in the mass window of 60 to 120 GeV is 1.117 nb. With all these ingredients at hand, we compute R as a function of the mass of the new heavy Z0-boson, MZ0 , and derive the corresponding limits for all benchmark models. Figure 1(a) shows the bounds on all E6 models, while gure 1(b) displays the results for the remaining two classes of models, GLR and GSM. As previously mentioned, traditional experimental analyses work under the hypothesis that the signal has a Breit-Wigner line shape and performs the analysis in a restricted search window around the hypothetical mass of the Z0-boson. This approach is theoretically motivated by the benchmark models, all predicting a narrow width Z0-boson, and by the will to perform as model independent an analysis as possible. One should stress that the CMS analysis makes use of a dedicated cut on the invariant mass of the di-lepton pairs: jMll MZ0 j 0:05 ELHC where ELHC is the collider energy. This cut was designed so that the error in neglecting the (model-dependent) Finite Width (FW) and interference e ects (between ; Z; Z0) is kept below O(10%) for all models and for the full range of allowed Z0 masses under study, following the recommendations of [4, 5]. This procedure thus continues to allow for a straightforward interpretation of the extracted mass bounds in the context of any theory predicting a narrow Z0-boson. At this stage of our own analysis, we work under the very same setup, for validation purposes, with the notable exception that we allow for the aforementioned FW and interference e ects, unlike the experimental results which assume the so-called Narrow Width Approximation (NWA), wherein the (narrow) Z0 is actually produced on-shell. Table 1 summarizes the bounds we obtain. They reproduce the CMS limits very well in general, within the accuracy { 5 { GLR L S I N R B LR Y SM Q T3L with an extra U 0( 1 ) gauge group predicting a new heavy neutral boson characterized by a narrow width. From left to right, the columns indicate the MZ0 limit in GeV within the E6, GLR and GSM class of models. of 1{2%. The only slight exception is the Q-model in the GSM class where our limit, based on the present analysis accounting for full width and interference, is di erent from the CMS one by about 5%. This is well in line with expectations, as this model is the one yielding the largest width. But let us set the stage in some more detail. In gure 2 we show the behaviour of the new physics signal for two representative scenarios: the E model ( gure 2(a)) and the SSM benchmark scenario ( gure 2(b)). The solid line represents the full new physics signal, that is, Z0-boson production and decay including the interference with the SM background. The dashed line gives instead the pure Z0-boson signal, neglecting the interference. (As evident from the plots, in both cases we allow for FW e ects of the Z0-boson.) As one can see, the shape of the distribution in the invariant mass of the dilepton system is quite model dependent o peak due to the presence of large interference e ects. The sign of the interference is not de ned a priori. It can be either positive, like in the majority of the E6 models, or negative, like in the two other classes of GLR and GSM models. In addition, its magnitude can be quite sizeable. For a detailed description of the behaviour of the interference between the new Z0-boson and the SM background we refer to refs. [4, 11], where the models with maximal constructive and destructive interference have been identi ed. The o peak tail of the signal distribution in the di-lepton invariant mass is thus highly model dependent in the low mass region, leading to either an excess or a depletion of the total number of expected events as compared to the SM background, according to the sign of the interference. Furthermore, it is clear that the fully integrated cross section for the complete new physics signal, that is, Z0-boson production and decay including the interference with the SM background, is not always a uniquely de ned variable. In the SSM, and more generally in all GSM and GLR models, the signal can manifest itself as a negative correction to the di erential cross section (solid line) at low masses. Similarly, the fully integrated cross section for the pure Z0-boson production and decay, neglecting the interefences, can also give an incorrect picture. Taking into account the low mass tail of the invariant mass distribution can overestimate the Z0-boson signal by a large factor. For a SSM Z0 with mass MZ0 = 3 TeV, we have that the fully integrated cross section for the pure signal is Z0 = 0:17 f b while the complete signal cross section, integrated in the mass window where it is positive de nite, is equal to Z0 + Interference = 0.06 f b. In this case, taking into account the unphysical tail (which in the SSM is in reality washed out by the destructive interference) leads to an overestimate the Z0 signal by a factor of 3 and consequently the { 6 { HJEP01(26)7 0.1 D V e T f 0.05 0.04 ' ZΣ0.03 ITN0.02 Σ0.01 0.00 3 3 Model = E6-Ψ s = 8 TeV M Z ' = 3 TeV Model = GSM-SSM s = 8 TeV M Z ' = 3 TeV 4 4 5 5 HJEP01(26)7 from the Z0-boson production and decay in the Drell-Yan channel: pp ! e+e . the E model. The solid line shows the complete new physics contribution to the invariant mass We consider distribution, that is the Z0 signal plus the interference with the SM background. The dashed line represents instead the pure Z0 signal, neglecting the intereference. The inset plot displays the ratio between the interference contribution and the pure Z0 signal. All curves have been produced for the 8 TeV LHC. No cuts are applied. (b) Same for the SSM benchmark scenario. { 7 { extraction of more stringent, erroneous limits. In essence, a shape analysis of the signal over the full invariant mass region is very challenging. Thus, the de nition of the observable to be used to interpret the data and extract the mass bounds on the hypothetical Z0-boson must indeed be appropriately chosen. However, thanks to the approach recommended in [4, 5], all such extreme e ects are avoided and, in the instance, we can conclude that our code for the simulation of DrellYan processes which might receive a contribution from a narrow Z0-boson exchange, pp ! ; Z; Z0 ! l+l (l = e; ), has been validated against the CMS results. In short, by nally taking into account the published acceptance e ciency corrections (A ), we can indeed reproduce the above mentioned extracted bounds on the Z0-boson mass by self-consistently evaluating signal and background. In doing so, we have applied Poisson statistics for computing the signi cance, de ning a 5 observation as a discovery and excluding new physics up to 2 when deriving limits on MZ0 . Here, 5 ( 2 ) observation means a new physics e ect at the level of 5( 2 ) standard deviations away from the expected number of events within the SM. With these de nitions and using the abovementioned code, in gures 3 and 4, we now project discovery and exclusion potential of the upgraded LHC, which will run at 13 TeV. The rst two plots show the LHC discovery potential for the E6 models ( gure 3(a)) and for the remaining two classes GLR and GSM ( gure 3(b)). The discovery reach that we nd is in accordance with the results published in the Snowmass white paper [25] and references therein. Figures 4(a) and 4(b) display instead the LHC exclusion potential for E6, GSM and GLR models, respectively. In deriving these results, we stress that we have included the A factor extracted by the analyses performed by CMS at the 8 TeV LHC, thereby implicitly assuming that no signi cant departures in this respect occur at the upgraded CERN machine. These projections are valid only for narrow width Z0-bosons for which the optimal observable is the invariant mass of the di-lepton system, used in the standard bump search performed by the experimental collaborations. From the above plots, one can conclude that the 13 TeV run of the LHC should be able to discover a Z0-boson with mass up to about 4500 GeV and 5600 GeV within the E6 and GSM/GLR class of models, respectively. If nothing is found, the exclusion limits will be pushed up to 5300 GeV and 6400 GeV for an E6 Z0-boson and a GSM/GLR Z0-boson, respectively. considered thirteen models. These projections have been obtained for the design value of the integrated luminosity: L = 300 f b 1. search using traditional methods. This concludes the section on the state-of-the-art of narrow width Z0-bosons and their 3 The forward-backward asymmetry In this section, we de ne the forward-backward charge asymmetry (AFB) and discuss its role in Z0-boson searches other than the interpretation of an observed resonance. In the literature, the AFB has been long exploited to help disentangle the various theories predicting an extra heavy neutral boson and tracing back the Lagrangian parameters (see, { 8 { u eqR 02.1000 it the GSM and GLR classes of models. 5 contours as a function of Z0-boson mass and luminosity. We perform a combined analysis over pairs and assume the A factor given by CMS at the 8 TeV LHC. (b) Same for n n v v the GSM and GLR classes of models. 2 contours as a function of Z0-boson mass and luminosity. We perform a combined analysis over pairs and assume the A factor given by CMS at the 8 TeV LHC. (b) Same for Class U 0( 1 ) Models boson mass from direct searches at the forthcoming Run II of the LHC at 13 TeV. We assume the original design value for the integrated luminosited: L = 300 f b 1 . We consider thirteen di erent models with an extra U 0( 1 ) gauge group predicting a new heavy neutral boson characterized by a narrow width. From left to right, the columns indicate the MZ0 limit in GeV within the E6, GLR and GSM class of models. { 9 { for example, [26{28] and references therein). This is not an easy task and the sensitivity of AFB measurements to new physics like additional Z0-bosons has therefore received a lot of attention in the past years. For Drell-Yan processes, AFB is de ned from the angular distribution d d cos l 1 / 4 3 spin, col i X X 2 Mi = 2 X Pi Pj[(1 + cos2 l)CSij + 2 cos lCAij] (3.1) where l is the lepton angle with respect to the quark direction in the di-lepton centerof-mass frame (CM), which can be derived from the measured four-momenta of the dicontribution to the angular distribution linear in cos l. In eq. (3.1), p lepton system in the laboratory frame. The AFB is indeed given by the coe cient of the s^ is the invariant mass of the di-lepton system, and Pi and Pj are the propagators of the gauge bosons involved in the process. At tree-level, the Drell-Yan production of charged lepton pairs is mediated by three gauge bosons: the SM photon and Z-boson and the hypothetical Z0boson. These three vector boson exchanges all participate in the matrix element squared. We thus have: Pij Re[Pi Pj] = (s^ Mi2)(s^ Mj2) + Mi iMj j (s^ M 2)2 + M 2 2 i i i (s^ Mj2)2 + Mj2 j2 where Mi and i are the mass and width of the gauge bosons involved and i; j = f ; Z; Z0g. Finally, the factors CSij and CAij in the angular distribution given in eq. (3.1) are coe cients which are functions of the chiral quark and lepton couplings, qLi=R and eiL=R, to the i-boson with i = f ; Z; Z0g: CSij = (qLiqLj + qRiqRj)(eiLejL + eiRejR); CAij = (qLiqLj qRiqRj)(eiLejL eiRejR): (3.2) (3.3) (3.4) (3.5) (3.6) One can conveniently compute the forward (F) and backward (B) contributions to the total cross section integrating over opposite halves of the angular phase space: d^F = d^B = Z 1 Z 0 d^ d^ 0 d cos l 1 d cos l d cos l = d cos l = s^ s^ X X 192 i;j i 192 i;j i Pij 1 + ij 34 CSij + CAij ; Pij 1 + ij 3 S 4 Cij CAij ; where i and j sum over the mediating resonances, f ; Z; Z0g. From the above expressions one can immediately see that the total cross section, = F+ B, depends uniquely on the parity symmetric coe cient CS. Conversely, the di erence between forward and backward cross sections, F B, preserves only the contribution proportional to the parity antisymmetric coe cient CA. This is the term which is related to the AFB. One can thus de ne the AFB as the di erence between forward and backward cross sections normalized to the total cross section: ^ = d^F + d^B = s^ 72 X i;j i Pij 1 + ij Cij ; S AFB = d^F d^F + d^B d^B = s^ Z0; ZZ0; Z0Z0. In the light of the above discussion, the total cross section and AFB depend on di erent combinations of Z0-boson couplings to ordinary matter. For that reason, the AFB can give complementary information about the structure of such couplings when compared to the total cross section. This feature has motivated several authors to study the potential of the AFB observable in interpreting a possible Z0-boson discovery obtained in the usual resonance hunt as in refs. [26, 27, 29, 30]. Our point is that AFB can also be a powerful tool to search for new physics. 3.1 The reconstructed AFB The AFB is obtained by integrating the lepton angular distribution forward and backward with respect to the quark direction. As in pp collisions the original quark direction is not known, one has to extract it from the kinematics of the di-lepton system. In this analysis, we follow the criteria of ref. [31] and simulate the quark direction from the boost of the dilepton system with respect to the beam axis (z-axis). This strategy is motivated by the fact that at the pp LHC the di-lepton events at high invariant mass come from the annihilation of either valence quarks with sea antiquarks or sea quarks with sea antiquarks. As the valence quarks carry away, on average, a much larger fraction of the proton momentum than the sea antiquarks, the boost direction of the di-lepton system should give a good approximation of the quark direction. A leptonic forward-backward asymmetry can thus be expected with respect to the boost direction. In contrast, the subleading number of di-lepton events which originate from the annihilation of quark-antiquark pairs from the sea must be symmetric. As a measure of the boost, we de ne the di-lepton rapidity yll = ln 1 2 E + Pz E Pz (3.8) where E and Pz are the energy and the longitudinal momentum of the di-lepton system, respectively. We identify the quark direction through the sign of yll. In this way, one can de ne the reconstructed forward-backward asymmetry, from now on called AFB. Namely, we have de ned AFB using the l reconstructed angle, which is the angle between the nal state lepton and the incoming quark direction in the center-of-mass of the di-lepton system. As the AFB reconstruction procedure relies on the correlation between the boost variable, yll, and the direction of the incoming valence quark, it is therefore more likely to pick up the true direction of the quark for higher values of yll. Increasing the probability of identifying the direction of the quark would lead to an observed value of AFB that is closer to the `true' value of AFB if one were able to access the partonic CM frame. The tradeo occurs in the reduction of statistics which impacts the signi cances the other way. The general de nition of signi cance S between predictions of an observable O with uncertainty O from two hypotheses is S = jO1 O2j : p O12 + O2 2 The statistical uncertainty on the AFB is given by AFB = s 4 F B L ( F + B)3 = r (1 A2FB) L = r (1 N A2FB) ; where L is the integrated luminosity and N the total number of events. One can thus see that the signi cance is proportional to the root of the total number of events. Imposing a stringent cut on the boost variable, yll, would then improve the reconstructed AFB guiding it towards its true line shape, but it will decrease the statistics. In the next subsection, the subtle balance between line shape gain and statistics loss in maximizing the signi cance via the di-lepton rapidity cut will be discussed in detail. 3.2 On the di-lepton rapidity cut As discussed in the previous section, since the true quark direction is not known in pp collisions, at the LHC one has to extract it from the kinematics of the di-lepton system. In this paper, the valence quark direction is approximated by the boost direction of the l+l pairs with respect to the beam axis, that is given by the sign of the di-lepton rapidity yll de ned in eq. (3.8). The correctness of this assignment as a function of yll has been studied in ref. [31] for di-lepton events with invariant masses above 400 GeV. In this section, we further analyse this issue by investigating the energy scale dependence of the probability of getting the true quark direction via the sign of yll. In gures 5(a) and 5(b), we plot the fraction of events with the correctly assigned direction for up-quarks and down-quarks, respectively, as a function of jyllj for di erent invariant mass windows of the di-lepton system. The fraction of correctly assigned events increases with the rapidity, con rming the results presented in literature [31]. The additional information contained in gure 5 is that such an increase depends on the energy scale. For di-lepton invariant masses of TeV order the probability of getting the true quark direction becomes more than 80% for a rapidity cut jyllj 0:8. For higher invariant masses, beyond the present Z0-boson limits of O(3 TeV), the same probability can be obtained by imposing a lower rapidity cut: jyllj 0:35. Moreover, up-quarks and down-quarks respond di erently to the jyllj cut. The probability of getting the correct direction is higher for up-quarks than for down-quarks, at xed jyllj value. In gure 6, the fraction of correctly assigned events is shown as a function of the invariant mass for ve di erent cuts on the magnitude of the di-lepton rapidity, jyllj. This time, we consider the average over up and down-quarks. From here, one can see that, in searching for extra Z0-bosons with masses larger than O(3 TeV) the jyllj cut is not mandatory. The true direction of the quark is indeed correctly guessed more than 70% of the times, even if no cut is applied on the di-lepton rapidity. This means that, at HJEP01(26)7 ] 90 1.5 | yuu¯ | (a) Muu¯ range [TeV] 5 < Muu¯ < 13 4 < Muu¯ < 5 3 < Muu¯ < 4 2 < Muu¯ < 3 1 < Muu¯ < 2 103 the 13 TeV LHC via the boost direction of the di-lepton system, given by the sign of the di-lepton rapidity yll, as a function of the modulus jyllj = jyuuj for six di erent invariant mass windows scanning from 500 GeV to 5000 GeV and beyond. Lower plot: di erential luminosity as a function of jyllj for the correctly assigned quark pair (dashed-line) and for the full sample (solid line). (b) Same as (a) for valence down-quarks. high di-lepton invariant masses, we should be able to observe a lepton asymmetry with a well approximated shape even without imposing ad hoc cuts. As we discuss in the next two pages, the advantage of not imposing a jyllj-cut would be twofold: preserving a small statistical error on that shape, owing to the much larger acceptance one should have in absence of the jyllj cut (see gures 7 and 8), and working with an event sample avour independent up to a large extent (see gure 8). This latter feature would guarantee a more model independent procedure, as the di erent Z0 models have obviously di erent couplings of the extra gauge boson to up and down-quarks. Let us start to clarify these two points. We address rst the statistical/acceptance issue. In order to quantify the delicate balance between AFB line shape and statistical error, in the upper plot of gure 7 we show the shape of the reconstructed lepton asymmetry, AFB, within the SM as a function of the di-lepton invariant mass for a set of di erent cuts on jyllj. We compare the results to the true AFB, where the direction of the valence quark is taken directly from the Monte Carlo (MC) event generator. In the lower plot of gure 7, we display the acceptance as a function of the same variable Mll for the same set of jyllj cuts. Comparing the two plots, one can see that AFB tends to the true AFB with increasing the jyllj cut, but at the same time the acceptance heavily decreases. In particular, for masses above 2.5 TeV, if we apply the stringent cut jyllj 0:8 used in literature, the number of events goes down by a factor of 3 while the gain in shape is only about 20% of the true AFB value. With increasing mass, the acceptance decreases indeed more rapidly with the jyllj cut. To visualize how the above features impact the AFB sensitivity to new physics, in gure 8 we compare the reconstructed AFB observable predicted by three representative 0.6 0.5 0.4 B ∗F A0.3 0.2 0.1 0.0 100 ) 80 %60 ( 40 A20 Rapidity cut 13 TeV LHC via the boost direction of the di-lepton system, given by the sign of the di-lepton rapidity yll, as a function of the di-quark (or di-lepton) invariant mass for ve di erent cuts on the di-lepton rapidity. Lower plot: di erential luminosity as a function of the di-lepton invariant mass for the correctly assigned quark pair (dashed-line) and for the full sample (solid line). Here we average on both up and down-quarks. A∗FB, | yee| cut acceptance; LHC @ 13 TeV, L =300 fb−1 True AFB No cut | yee| > 0.2 | yee| > 0.4 | yee| > 0.8 | yee| > 1.2 0 500 1000 1500 2000 2500 invariant mass within the SM at the 13 TeV LHC with a total integrated luminosity L = 300 f b 1 for a set of di erent rapidity cuts on the di-lepton system. In the legend, jyeej corresponds to jyllj de ned in the text. The black line represents the true AFB for comparison. Lower plot: acceptance as a function of the di-lepton invariant mass for the same set of di-lepton rapidity cuts as above. versus the jyllj Z0-models (E , EI and GLR{LR) with the SM expectation at the 13 TeV LHC with total integrated luminosity L = 100 f b 1. As a new physics signal, we consider a hypothetical Z0-boson with mass MZ0 = 3 TeV. To quantify the e ect of the di-lepton rapidity cut on the signi cance either in searching for new physics via AFB or in distinguishing between di erent Z0 models, we show results for the commonly used jyllj 0:8 setup ( gure 8(d)) 0:4 ( gure 8(c)) and no cut ( gure 8(b)) scenarios. We further display, in 3200 3400 3600 0.4 )e 0.2 u (rT 0.0 FB−0.2 A −0.4 −0.6 −01.85 . if10 n ig5 S 0.6 0.4 results are for the LHC at p imposed: jyllj plot (b) with jyllj models for a Z0-boson with mass MZ0 = 3 TeV. The results are for the LHC at p as predicted by the SM (black), the E (orange), the EI (magenta) and the GLR{LR (purple) L = 100 f b 1. Lower plot: the signi cance in distinguishing models is displayed. The double colour in each bin visualizes the two compared models. (b) Reconstructed forward-backward asymmetry as a function of the di-lepton invariant mass as predicted by the SM (black), the E (orange), the EI (magenta) and the GLR{LR (purple) models for a Z0-boson with mass MZ0 = 3 TeV. The s = 13 TeV and L = 100 f b 1 . No cut on the di-lepton rapidity is 0. Lower plot: the signi cance in distinguishing models is displayed. (c) Same as 0:4. (d) Same as plot (b) with jyllj 0:8. gure 8(a), the ideal situation represented by the true forward-backward asymmetry, AFB. As one can see, imposing a strong di-lepton rapidity cut helps in recovering the true shape and magnitude of the forward-backward asymmetry. However, the consequent decrease of the number of events is so substantial that the signi cance diminishes drastically with increasing the jyllj cut. In addition, and here we address the second point previously anticipated, the implementation of the jyllj cut accentuates the avour dependence of the results or, in other words, the model dependence of the analysis. As the probability of guessing the correct direction of the quark in the reconstruction procedure of the AFB as a function of the jyllj cut depends on the type of quark (up and down-quarks react di erently to the cut gure 5), the reconstructed AFB shows an increased model dependence in its response to the jyllj cut. To exemplify this concept, let us take the third bin from the left in gure 8. There ( gure 8(a)), the E and EI models are degenerate as far as the true asymmetry is considered. When we compare the reconstructed asymmetry, we see that the two models are not degenerate any more in that bin. The splitting increases with the jyllj cut, as the two models react di erently to such a cut, having di erent couplings of the corresponding Z0-boson to up- and down-quarks. In order to minimize the presence of model dependent elements in the analysis, it is thus advisable not to include the di-lepton rapidity cut. Hence, in the following. we will be working in a setup where we do not impose The role of AFB in Z0 searches: narrow heavy resonances The AFB is the observable where the e ects of the interference between new physics and SM background are maximal. In the Drell-Yan processes, these e ects are of course present also in the total cross section. They are readily seen in both cases in the di-lepton invariant mass. As mentioned repeatedly, constraining the search window for new physics within the interval jMll MZ0 j 0:05 ELHC guarantees that nite width and interference e ects are below the O(10%) level when compared to the complete new physics signal. Such e ects are instead an intrinsic part of the AFB and dominate its dynamics. For such a reason, the AFB is an intrinsically model dependent variable and in literature has therefore been traditionally considered for disentangling di erent models predicting a spin-1 heavy neutral particle. Its role has therefore been cornered so far to the interpretation of a possible Z0-boson discovery obtained via the default bump search. In this paper, we aim to show that AFB can also be used for searches, directly, as a primary variable alongside the cross section itself. In this section we focus on Z0-bosons characterized by a narrow width. This is the most common kind of particle predicted by theories with an extra U 0( 1 ) gauge group. This is also the scenario mostly studied in literature. The experimental searches for such an object are tailored on this expectation and the corresponding results coming from the data collected at the 8 TeV LHC have been summarized in section 2. With respect to the `AFB search', the Z0 models can be divided into two categories: Z0 models with AFB centred on the Z0-boson mass and Z0 models with shifted AFB. In the next two subsections, we discuss their properties in turn. 4.1 Z0 models with AFB centred on peak In this subsection, we discuss models where the AFB is peaked on the Z0-boson mass. These models belong to the E6 class of theories which predict new narrow width spin-1 resonances. In the literature, it is known that such models contain one extra neutral gauge boson whose width cannot exceed a few percent of its mass: Z0 =MZ0 5%. Even the inclusion of new Z0-boson decay channels into exotic states would not change this estimate. We rst compare the shape of the AFB distribution as a function of the di-lepton invariant mass, Mll, with the di erential cross section in the same variable. In gure 9, eTVD 1 dΣ 0.01 d dΣ 0.01 d s = 13 TeV. No cut on the di-lepton rapidity is imposed: jyllj the EI model. (d) Same as plot (b) within the EI model. the E model for a Z0-boson with mass MZ0 = 3 TeV. The results are for the LHC at p (b) Reconstructed forward-backward asymmetry as a function of the di-lepton invariant mass as model for a Z0-boson with mass MZ0 = 3 TeV. The results are for the LHC at 0. (c) Same as plot (a) within we show results for two representative E6 models: E and EI . We consider a hypothetical Z0-boson with mass MZ0 = 3 TeV. In gures 9(b) and 9(d), we display both the true and the reconstructed AFB within the two chosen E6 models with and without taking into account the interference between the extra Z0-boson and the SM background. As one can see, the role played by the interference is extremely important. The AFB shape is drastically modi ed by getting its peak heavily accentuated. In contrast, the invariant mass distribution is almost interference free if the jMll MZ0 j 0:05 ELHC cut is imposed, gures 9(a) and 9(c) for the two representative E6 models. In interpreting the experimental data coming from AFB measurements it is then mandatory to include the interference, no matter what kinematical cut is applied. In terms of signi cance, the search for narrow width Z0 models with AFB centred on the Z0 mass is summarized in gure 10 for the two representative models E and EI . Within the E model, the true AFB would give rise to a signi cance slightly lower than that one coming from the usual bump search, as shown in gure 10(a). The reconstruction procedure of the AFB depletes this result but still the two signi cances from cross section Σ HJEP01(26)7 s = 13 TeV and L = 300 f b 1. (b) Same as (a) for the EI model. model for a Z0-boson with mass MZ0 = 3 TeV. The red line represents the signi cance corresponding to the invariant mass distribution. The blue and green lines show the signi cance extracted by an ideal measurement of true and reconstructed AFB, respectively. The results are and AFB are comparable over the full di-lepton invariant mass range. Figure 10(b) shows that the EI model is more accessible through the AFB than the cross section. There, indeed, the signi cance from the true AFB is a factor two bigger than the signi cance coming from the bump search. Once again, the AFB reconstruction pollutes the ideal result. The signi cance from the reconstructed AFB gets reduced, but its value remains anyhow only slightly lower than that one coming from the resonance search. The EI model is not unique in this respect, also the ES model shares the same property. Similar trends are shown by all models belonging to the E6 class of theories and do not change when a more realistic setup is considered. Implementing the acceptance cuts extracted by the CMS analysis at the 8 TeV LHC (PT (l) 25 GeV and (l) 2:5 with l = e; ), the shape of the reconstructed AFB, AFB, including error bars would in fact appear as in gure 11. The signi cances coming from the AFB and the cross section are indeed equivalent in magnitude, if only the statistical error is included. We thus expect that the use of the AFB observable, when associated to the default resonance search, could improve the discovery potential of new narrow width Z0-bosons. Further, being a ratio of di erential cross sections, the reconstructed AFB could help in minimizing the systematical errors thus rendering the measurement much more accurate. This is in particular the case when we should be in presence of an evidence for a new Z0-boson in the resonance search at the 3{4 sigma level. In these conditions, one could not claim the discovery of a new gauge boson just looking at the resonant peak in the di-lepton invariant mass distribution. However, if a signal of similar strength were to be discovered in an independent observable, the suggestion of the possible presence of new physics would turn into a robust claim. This is the role that the AFB would play. In gure 12, we plot the di erential cross section and AFB as a function of in the di-lepton invariant mass, and EI models, at the forthcoming Run II of the LHC at 13 TeV Mll = ps^, within the E with L = 30 f b 1, that is the integrated luminosity which should be collected at the end SM 0 0.5 1 3 3.5 4 0 0.5 1 3 3.5 4 ]V10−1 10−5 10−6 12 in 6 g iS3 1.5 √sˆ [TeV] 2 2.5 1.5 √sˆ [TeV] 2 2.5 (c) −0.5 −11.02 f. 9 in 6 g iS3 1.5 √sˆ [TeV] 2 2.5 1.5 √sˆ [TeV] 2 2.5 (d) SM E6(I), M= 3 TeV SM E6(I), M= 3 TeV 0 0.5 1 3 3.5 4 0 0.5 1 3 3.5 4 model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. The results are for . Acceptance cuts are imposed (see text). The lower for the LHC at p plot shows the signi cance. (b) Binned AFB as a function of the di-lepton invariant mass within the E model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. The results are . Acceptance cuts are imposed (see text). In the lower plot, the blue histogram shows the binned signi cance while the green area indicates the total signi cance integrated over that invariant mass region. (c) Same as (a) for the EI model. (d) Same as (b) for the EI model. of 2016. There, a new physics evidence at barely 4 sigma in the bump search could be reinforced by the simultaneous measurement of the reconstructed AFB, showing a signal at the 2-sigma level. 4.2 Z0 models with shifted AFB In this section, we discuss narrow width Z0 models where the AFB has a shifted peak, that is, not centred on the Z0-boson mass. These models belong to the GLR class. The same behaviour is also displayed by the SSM scenario taken as benchmark model by the LHC experimental collaborations. SM SM 0 0.5 1 3 3.5 4 0 0.5 1 3 3.5 4 −0.5 −1.04 1.5 √sˆ [TeV] 2 2.5 (d) 3 3.5 4 ]V10−1 1 S 101 100 10−5 10−6 4 .3 if 1.5 √sˆ [TeV] 2 2.5 (c) SM E6(I), M= 3 TeV SM E6(I), M= 3 TeV 0 0.5 1 3 3.5 4 0 0.5 1 results are for the LHC at p model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. The s = 13 TeV and L = 30 f b 1. Acceptance cuts are imposed (see text). The lower plot shows the signi cance. (b) Binned AFB as a function of the di-lepton invariant mass as predicted by the E results are for the LHC at p model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. The s = 13 TeV and L = 30 f b 1. Acceptance cuts are imposed (see text). In the lower plot, the blue histogram shows the signi cance bin by bin while the green area indicate the total signi cance integrated over that invariant mass region. (c) Same as (a) for the EI model. (d) Same as (b) for the EI model. In principle, the reconstructed AFB could reveal the presence of a new spin-1 particle at energy scales lower than its mass, as the shape of this observable as a function of the di-lepton invariant mass is accentuated at mass scales smaller than MZ0 . This behaviour is shown in gure 13(b) where we plot the reconstructed AFB versus Mll = s^ for the representative model GLR{LR. We consider a new Z0-boson with mass MZ0 = 3 TeV. As p one can see, the peak of AFB is shifted on the left-hand side of the physical Z0-boson mass and it appears at around 2.6 TeV. This feature is interesting. However, the signi cance is quite low as shown in gure 13(b), owing to the poor statistics in that region. For Mll values around the physical mass of the Z0-boson, which are statistically relevant, the SM GLR(LR), M= 3 TeV SM GLR(LR), M= 3 TeV 0 0.5 1 ]V10−1 10−5 10−6 15 f.12 in 9 ig 6 S3 2 √sˆ [TeV] 2.5 √sˆ [TeV] 2.5 (c) √sˆ [TeV] 2.5 (d) SM GSM(SM), M= 3 TeV SM GSM(SM), M= 3 TeV 0 0.5 1 The results are for the LHC at p predicted by the GLR{LR model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. . Acceptance cuts are included (see LHC at p text). (b) Binned AFB as a function of the di-lepton invariant mass as predicted by the GLR{LR model for a Z0-boson with mass MZ0 = 3 TeV. Error bars are included. The results are for the s = 13 TeV and L = 300 f b 1. Acceptance cuts are included (see text). (c) Same as (a) for the Generalized Sequential SM, GSM {SM . (d) Same as (b) for the GSM {SM model. signi cance coming from AFB is always much smaller than the signi cance obtained via the measurement of the di erential cross section, displayed in gure 13(a). For these kind of models, the AFB observable is therefore not particularly appropriate for Z0 searches. The same conclusion holds for the SSM (see gures 13(c) and 13(d)). Hence, this benchmark model is not an advisable playground for studying the bene ts of using the AFB in searching for new Z0-bosons. 5 The role of AFB in Z0 searches: wide heavy resonances In this section, we discuss the role of the reconstructed AFB, AFB, in searches for a new Z0-boson characterized by a large width. Such a heavy and wide particle is predicted by 0.8 0.6 (b) 100 0 0.5 1 3 3.5 4 0 0.5 1 3 3.5 4 Error bars are included. The results are for the LHC at p predicted by the GSM {SM model for a Z0-boson with mass MZ0 = 1:5 TeV and Z0 =MZ0 = 80%. cuts are included (see text). (b) Binned AFB as a function of the di-lepton invariant mass as predicted by the GSM {SM model for a Z0-boson with mass MZ0 = 1:5 TeV and Error bars are included. The results are for the LHC at ps = 13 TeV and L = 300 f b 1. Acceptance Z0 =MZ0 = 80%. cuts are imposed (see text). di erent models. A benchmark scenario for experimental analyses is the wide version of the SSM described in ref. [10]. The proposal is to have a heavy copy of the SM neutral gauge boson, Z, with same couplings to ordinary matter and SM gauge bosons. Owing to the Z0-boson decay into SM charged gauge bosons, whose rate grows with the third power of the Z0-boson mass, the total width of the new heavy particle can be in principle quite large: Z0 =MZ0 ' 50% and above. In reality, a word of caution should be spent at this point. The triple Z0W W coupling is governed by the mixing of the extra Z0 with the SM Z-boson. The actual size of this Z Z0 mixing is strongly constrained by the ElectroWeak Precision Tests (EWPT), see ref. [3] for a review on these bounds. In this paper, we neither address this issue nor the validity of the wide SSM. We simply take this model as a popular framework that is representative of a wide Z0-boson. In this context, we thus consider the Z0 width as a free parameter. Under this assumption and for a Z0 =MZ0 ratio of several tens of percent, the invariant mass distribution of the two nal state leptons does not show in the cross section a resonant (or peaking) structure around the physical mass of the Z0-boson standing sharply over a smooth background, but just a shoulder spread over the SM background. This result is plotted in gure 14(a), where we consider a Z0-boson with mass MZ0 = 1:5 TeV and width Z0 =MZ0 = 80%. As the line shape of the resonance is not well de ned and these parton level results could be worsened by detector smearing e ects giving rise to an even broader spectrum, the AFB observable could help to interpret a possible excess of events. The results are shown in gure 14(b). There, one can see that the AFB shape could be visible at the 2 level. A framework, theoretically more grounded than the wide SSM, which predicts a heavy and broad Z0-boson is the so-called non-universal SU( 2 ) model [8, 9]. In this theory, the third generation of fermions is subjected to a new SU( 2 ) dynamics di erent from the usual interaction advocated by the SM. On the contrary, the rst two families of fermions only feel the SM weak interaction. Owing to the non universality of the gauge interactions, di erent consequences appear in this model. The CKM matrix is not unitary anymore, although the unitarity violation is suppressed by the heavy scale of the new physics. Also, Flavour Changing Neutral Currents (FCNCs) can generally show up. In addition and of primary interest for this paper, a new spectrum of gauge bosons emerges in the model. These new vector bosons can be either narrow or wide. The only constraint on the model parameters comes from the EWPTs which bound the Z0-boson to have a mass MZ0 constraints on mass and couplings of the heavy Z0 boson are actually correlated. Usually, they are presented as a two-dimensional contour plot. For the details of the analysis of direct and indirect limits on this model we refer to [9] and references therein. Within this framework, we consider the wide Z0-boson case with MZ0 = 5:5 TeV and Z0 =MZ0 = 20%. This setup ful lls both the limits quoted in ref. [9] and the direct limits coming from direct searches at the 8 TeV LHC [16]. The latter analysis performed at the LHC has been optimized for searches of new physics with no resonant peaking structure. The outcome is that there are no events for di-lepton invariant masses above 1.8 TeV. We have taken this limit into account when evaluating the Z0-boson mass and width. This model is a very good playground to test whether the AFB can be used as a primary variable in searches for wide objects. In this case, in fact, the new physics signal appears as an excess of events spread over the SM background. Almost no line shape is present in the di-lepton invariant mass distribution usually measured. Searches are performed relying on a pure counting strategy, a procedure which does not allow much interpretation of the hypothetical signal. The exploitation of the reconstructed AFB could help in this respect. In gure 15, we compare the Z0-boson spectrum (15(a)) and the reconstructed AFB (15(b)) as functions of the di-lepton invariant mass. As one can see in gure 15(a), the cross section spectrum at parton level is already very broad. Its slope might be lost or mistaken in the SM background normalization. Even if, in the best case, a plateau would be visible over the SM background, its interpretation would be very di cult. The same degree of di culty would appear in interpreting the depletion of events in the low invariant mass region. In principle such a depletion, due to the negative interference between the extra Z0-boson and the SM background, could give rise to a huge signi cance as shown in gure 15(a) (lower plot). However, the experimental tting procedure for this kind of scenarios is not fully settled yet. Severe uncertainties could a ect the functional form chosen to simulate the SM background in the data-driven approach, as the new physics e ects might invade the low mass spectrum that is instead commonly assumed to be new physics free. The same would happen for the alternative procedure based on the Monte Carlo (MC) estimate of the SM background, as this approach relies on the normalization of the MC prediction to the data around the peak of the SM Z-boson and on the existence of a new physics free control region at low invariant masses. Moreover, even in the ideal case in which all errors were under control, the interpretation of such evidence would be quite complicated, having no de ned shape at all. In this context, the Forward-Backward Asymmetry can be of some help. Figure 15(b) shows that the AFB observable has a sharper 1.0 0.8 sˆ [TeV] TH1, M= 5.5 TeV 10−6 L = 300 f b 1. Acceptance cuts are imposed (see text). L = 300 f b 1 Z0 =MZ0 ' 20%. Error bars are included. The results are for the LHC at p as predicted by the non-universal SM (NU SM) for a Z0-boson with mass MZ0 = 5:5 TeV and . Acceptance cuts are imposed (see text). (b) Binned AFB as a function of the and Z0 =MZ0 ' 20%. Error bars are included. The results are for the LHC at p di-lepton invariant mass as predicted by the NU SM for a Z0-boson with mass MZ0 = 5:5 TeV line-shape which can reveal the presence of a spin-1 particle beyond error bars. Such a shape is quite shifted at low energy scales though, compared to the Z0-boson mass. Hence, its extraction should enable one to help the discovery of a new vector boson with very high mass. In short, here, the AFB measurement could become particularly useful at the edge of the LHC discovery limits, when new particles can be too heavy and broad to be easily detected via a standard resonant peak search. The aforementioned scenarios are in fact particularly challenging for experimentalists. The non-resonant analyses of wide objects have been performed by searching for a smooth deviation from the SM background. The number of events above a given lower cut on the di-lepton invariant mass is compared with the total number of expected background events. An optimal minimum mass threshold is chosen to maximize the sensitivity to new physics. Clearly, such an analysis depends quite strongly on the SM background estimate. Usually, the simulated background is normalized to the event number in a mass window of 30 GeV around the Z-boson mass. A control region is then selected at higher di-lepton invariant masses in order to perform a data driven modelling of the SM background and recast it in a functional form easy to implement in the likelihood used for extracting the limit on the Z0-boson mass. The method is based on the assumption that the control region is new physics free. But, this is not the case for wide Z0-bosons. In these scenarios, the interference between the extra Z0-boson and the SM ; Z is so sizeable that it can invade the control region. Being absolutely model-dependent, it can be either constructive or destructive. In any case, it would change accordingly the shape of the di-lepton spectrum. If the interference is negative, it would led to a depletion of events at low mass scales on the left-hand side of the Z0-boson resonance. This is exactly the example shown in gures 14 and 15 corresponding to the SSM and non-universal SU( 2 ) scenarios, respectively. If not correctly interpreted, these interference e ects could induce one to underestimate the SM background with the consequence of overestimating the extracted mass bounds. Having all these uncertainties to deal with, the support of a second observable like the AFB is strongly recommended for the non-resonant analyses. 6 On the robustness of AFB against PDF uncertainties In this section, we discuss how robust the shape of the forward-backward asymmetry is against the theoretical uncertainties on the PDFs. We further compare the systematic error induced by the PDF uncertainty on the di erential cross section and on the reconstructed AFB. For the determination of the PDF uncertainty we follow [32] and references therein. Here, we just highlight the key points of the procedure. We compute the Hessian PDF uncertainty for our two observables: di-lepton invariant mass distribution and reconstructed AFB. For Hessian PDF sets, both a central set and error sets are given. The number of error sets is twice the number of eigenvectors. For the CTEQ6.6 PDF that we use, the number of error sets is equal to 40. For a given observable X we de ne X i to be the value of the variable using the PDF error set corresponding to the \ " direction for the eigenvector i. The symmetric error on the variable X is then given by: X = 1 uuv XN t 2 i=1 Xi j2: With this de nition, we are now ready to compute the PDF uncertainty on any observable X or any function f (X). For the di erential cross section, X = , we can thus apply eq. (6.1) directly. For the forward-backward asymmetry, the computation is slightly more involved since AFB is a ratio of (di erential) cross sections. In this case, we consider as independent variables the forward and backward (di erential) cross sections, F and B, so that the observable AFB = f ( F; B). According to eq. (6.1), the PDF uncertainty on F and B is given by: F = 1 uuv XN t 2 i=1 j Fi Fi j2 ; B = 1 uuv XN t 2 i=1 j Bi Bi j2: In the Hessian approach, the correlation of the PDF degrees of freedom of any two independent observables, X and Y , is expressed by the quantity cos given in ref. [32] and reported here below: cos 1 Y i=1 Xi )(Yi+ Yi ): The quantity cos characterizes whether the PDF degrees of freedom of X and Y are partially or fully correlated (cos = 1), fully anti-correlated (cos 1) or uncorrelated (6.1) (6.2) (6.3) (cos = 0). Such a quantity enters in the de nition of the PDF uncertainty on any function of two variables, f (X; Y ), as shown in the formula here below (see also ref. [32]): In our case, we have veri ed that the two independent observables, X = Y = B, are fully correlated for all analyzed Z0 models (cos ( F; B) = 1) being evaluated at the same energy scale when computing AFB as a function of the di-lepton invariant mass. Under this condition, by applying the error chain rule as in eq. (6.4), we get (6.4) F and AFB = 1 2 AFB ) 2 F F B : B (6.5) The sign appearing in the above formula is crucial for the AFB. It indeed clearly shows that there is a partial cancellation of the PDF error on the reconstructed AFB due to the fact that this observable is a ratio of (di erential) cross sections. Compared to the di erential cross section, the AFB is then more robust against PDF uncertainties. This is shown in gure 16 where we compare the e ect of PDF and statistical errors on the shape of the di-lepton invariant mass distribution of the cross section and AFB for two reference models, EI and E . As one can see, the behaviours of cross section and AFB are opposite. The di erential cross section in the di-lepton invariant mass is dominated by the PDF error on-peak and in the low invariant mass region. In the region around the peak and for invariant masses below the TeV region, the PDF uncertainty is a factor 2 bigger than the statistical error. On the contrary, the AFB is always dominated by the statistical error: on and o -peak. Moreover, the PDF uncertainty is quite reduced owing to the minus sign in eq. (6.5). The shape of the AFB is thus not a ected by the PDF error, so this observable is theoretically well de ned. In the light of these results, we can revisit gures 11 and 12 which compare di erential cross section and AFB for two representative E6 models and for two luminosity regimes: L = 300 f b 1 and L = 30 f b 1 respectively. These two regimes are representative of the next two years data taking (L = 30 f b 1) and of the design high luminosity Run II (L = 300 f b 1). We stated previously that in the low luminosity regime the AFB could help interpreting the data. As illustrated in gure 12, the AFB signi cance could be in fact comparable to that found using the cross section from a binned mass distribution. In case of an early discovery with a few events, the evidence of new physics from the bump search alone would be insu cent to demonstrate the presence of a new Z0. But, it could be reinforced by a further comparable evidence in the independent variable AFB, leading to a much more robust result. The role of AFB in searching for new Z0-bosons is not con ned to support a not fully convincing evidence in the usual bump search at low statistics. In this section, the main message is that, even after the high luminosity objective is achieved for the current LHC Run II, the AFB may provide additional evidence of new physics and be very useful in the interpretation of the origin of this new physics. As stated above, this time the reason is the PDF's uncertainty which will dominate the theoretical error on the prediction of a new Z0-boson appearing as a resonant peak in the di-lepton invariant mass distribution. V e G 10-26000 100 D 1 V e G Σd10-4 ` s d 10-26000 2.0 1.5 3000 3000 (c) 4000 5000 6000 0.10000 2000 3000 4000 5000 6000 0.5 *AFB 0.0 D -0.5 D -0.5 AFB* ± DPDF AFB* ± DSTAT AAAFFFBBB*** ±± DDPSTDAFT 3500 Model = E6- Χ model for a Z0-boson with mass MZ0 = 3 TeV. The results are for the LHC at p . The solid line shows the central value, the dotted line the PDF uncertainty. results are for the LHC at p s = 13 TeV and L = 300 f b 1 The inset plot displays the ratio between PDF and statistical errors. (b) AFB as a function of the di-lepton invariant mass as predicted by the E model for a Z0-boson with mass MZ0 = 3 TeV. The . The dotted lines show the PDF error band, while the dashed lines de ne the statistical error band. (c) Same as (a) for the EI model. (d) Same as (b) for the EI model. To be more quantitative, we take gures 11(a) and 11(c). There, owing to the decreased statistical error when compared to gures 12(a) and 12(c), we have an a priori statistical signi cance S ' 12 around the peak of the binned cross section which would allow to claim for a new physics discovery. However, the total theoretical error does not improve much with L, being dominated by PDF's uncertainties. Indeed, in this case, the PDF error would be two times the statistical one (see gure 16). The capability of interpreting the results of an experiment is thus signi cantly reduced by PDF's uncertainties in the bump search. This result should be compared with the outcome from an AFB measurement, which is shown in gures 11(b) and 11(d). Here, owing to the higher luminosity, the experimental signi cance is about S ' 7 (including only the statistical error). Such an increase with L would be moreover followed by a proportional reduction of the theoretical error that in this case is purely dominated by statistics. Up to a large extent, the AFB is therefore a PDF 0.30 0.25 FB0.15 A D HJEP01(26)7 DΣ Σ20 PDFs Error Stat. Error 3000 3500 5000 5500 s = 13 TeV and L = 300 f b 1 MZ0 j 0:05 ELHC) as a function of MZ0 as predicted by the E , EI , GLR{LR and GSM{SM models. The results are for . Solid lines represent the PDF uncertainty, dashed ones the statistical error. (b) AFB integrated around the Z0-boson mass (jMll MZ0 j 0:05 ELHC) as a function of MZ0 as predicted by the E , EI , GLR{LR and GSM{SM models. The results are s = 13 TeV and L = 300 f b 1. Solid lines represent the PDF uncertainty, dashed safe observable. For these reasons, even if the large-x PDF's uncertainties are considerably improved in the future, it is likely that an AFB measurement will prove to be useful evidence in any claims of Z0 discoveries using the LHC data. Of course, one needs to consider the energy scale dependence of the PDF errors, if no re tting procedure is employed. In gure 17(a), we plot PDF and statistical errors on the total cross section integrated around the mass of the Z0-boson. We integrate in the window 5% ELHC around the hypothetical MZ0 where interference and nite width e ects can be neglected. In evaluating the statistical error, we assume the design value for the luminosity: L = 300 f b 1. We then vary the value of MZ0 to see how statistical and PDF errors change in magnitude. We consider four theoretical frameworks: E , EI , GLR{LR and SSM. The gure shows that, up to roughly a 4 TeV scale, the cross section is dominated by the PDF uncertainty. In contrast, the asymmetry integrated in the same peak region is heavily dominated by the statistics for all possible Z0 masses, as shown in gure 17(b). The strong dependence of PDF's central values and errors on the di-lepton invariant mass or energy scale also suggests that using as observable the ratio between the Z0-boson cross section and the on-peak SM Z-boson cross section R , might not be entirely PDF safe. The two cross sections are indeed a few TeV a part. As a consequence, the quantitity cos , measuring the correlation between the two variables, is not anymore equal to one as in the AFB case. Therefore, a cancellation analogous to that one in eq. (6.5) could not happen easily. This is another argument in favor of exploring the AFB as a search variable. 7 Conclusions In this paper we have considered the scope of using AFB, the forward-backward asymmetry, in Z0-boson searches at the LHC in the di-lepton channel, i.e., via Drell-Yan production and decay. Such a variable has traditionally been used for diagnostic purposes in presence of a potential signal previously established through a standard resonance search via the cross section. In this respect, we have shown that not imposing the commonly used cut on the di-lepton rapidity (jYllj > 0) would improve the discrimination between di erent Z0 models. In addition, based on the observation that it is a ected by systematics less than cross sections (being a ratio of the latter), we have studied the possibility of using AFB for such a purpose for a variety of Z0 models, E6, GLR, GSM, embedding either a narrow or wide resonance. The focus was on determining whether such a resonance could be su ciently wide and/or weakly coupled such that a normal resonance search may not fully identify it and, further, whether the AFB could then provide a signal of comparable or higher signi cance to complement or even surpass the scope of more traditional analyses. In both high (L = 300 fb 1) and low (L = 30 fb 1) integrated luminosity scenarios, we have found promising results. In the case of narrow width Z0-bosons, we have proven that the statistical signi cance of the AFB search can be comparable with the usual bump search. This makes it a useful observable in Z0 searches. In case of an early discovery at low luminosity, an AFB measurement could indeed valuably support an evidence in the bump search which by itself could otherwise be not robust enough. At the design high luminosities of the LHC Run II, the statistical signi cance of an observed bump type of structure can be large. However, the knowledge of the predicted (di erential) cross section in any particular Z0 model is subject to the large-x PDF errors. The current knowledge of PDFs is such that this results in large uncertainties. The AFB on the other hand bene ts from the partial cancellation of the PDF's uncertainties on cross sections, being a ratio of the latter, making it much more insensitive to PDF's errors. This increases the importance of AFB measurements in the interpretation of any observations. In the case of wide Z0-boson, the AFB search could have a better sensitivity than the cross section studies thanks to a more peculiar line-shape and lower systematic and PDF uncertainties. In essence, here, AFB in speci c regions of the invariant mass of the reconstructed Z0-boson could be sensitive to broad resonances much more than the cross section, wherein the broad distribution of the signal seemingly merges with the background. Further, we have emphasised the fact that the AFB distribution mapped in di-lepton invariant mass can present features amenable to experimental investigation not only in the peak region but also signi cantly away from the latter. We have explored the above phenomenology for all the benchmarks under study as well as assessed and used the optimised strategy for AFB reconstruction. Acknowledgments We are grateful to Patrik Svantesson for stimulating discussions at the early stage of the project. This work is supported by the Science and Technology Facilities Council, grant number ST/L000296/1. All authors acknowledge partial nancial support through the NExT Institute. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. { 29 { [arXiv:0801.1345] [INSPIRE]. 456 (1999) 68 [hep-ph/9903476] [INSPIRE]. [3] J. Erler and P. Langacker, Constraints on extended neutral gauge structures, Phys. Lett. B the LHC: Interference and Finite Width E ects in Drell-Yan, JHEP 10 (2013) 153 HJEP01(26)7 [arXiv:1304.6700] [INSPIRE]. signals from the 4D Composite Higgs Model at the LHC, JHEP 04 (2013) 152 [8] Y.G. Kim and K.Y. Lee, Direct search for heavy gauge bosons at the LHC in the nonuniversal SU( 2 ) model, Phys. Rev. D 90 (2014) 117702 [arXiv:1405.7762] [INSPIRE]. [9] E. Malkawi and C.P. Yuan, New physics in the third family and its e ect on low-energy data, Phys. Rev. D 61 (2000) 015007 [hep-ph/9906215] [INSPIRE]. [10] G. Altarelli, B. Mele and M. Ruiz-Altaba, Searching for New Heavy Vector Bosons in pp Colliders, Z. Phys. C 45 (1989) 109 [Erratum ibid. C 47 (1990) 676] [INSPIRE]. [11] J. Erler, P. Langacker, S. Munir and E. Rojas, Z0 Bosons at Colliders: a Bayesian Viewpoint, JHEP 11 (2011) 076 [arXiv:1103.2659] [INSPIRE]. [12] N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE]. [13] N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344] [INSPIRE]. [14] E. Eichten, K.D. Lane and M.E. Peskin, New Tests for Quark and Lepton Substructure, Phys. Rev. Lett. 50 (1983) 811 [INSPIRE]. [15] E. Eichten, I. Hinchli e, K.D. Lane and C. Quigg, Super Collider Physics, Rev. Mod. Phys. 56 (1984) 579 [INSPIRE]. proton-proton collisions at p 092 [arXiv:1410.4692] [INSPIRE]. [16] CMS collaboration, Search for physics beyond the standard model in dilepton mass spectra in s = 8 TeV, JHEP 04 (2015) 025 [arXiv:1412.6302] [INSPIRE]. [17] T. Jezo, M. Klasen, D.R. Lamprea, F. Lyonnet and I. Schienbein, NLO + NLL limits on W 0 and Z0 gauge boson masses in general extensions of the Standard Model, JHEP 12 (2014) [18] E. Accomando, D. Becciolini, S. De Curtis, D. Dominici, L. Fedeli and C. Shepherd-Themistocleous, Interference e ects in heavy W 0-boson searches at the LHC, Phys. Rev. D 85 (2012) 115017 [arXiv:1110.0713] [INSPIRE]. s = 8 TeV, CMS-PAS-EXO-12-011 (2015) [INSPIRE]. [20] CMS collaboration, Search for physics beyond the standard model in nal states with a lepton and missing transverse energy in proton-proton collisions at ps = 8 TeV, Phys. Rev. D 91 (2015) 092005 [arXiv:1408.2745] [INSPIRE]. (2002) 403] [INSPIRE]. HJEP01(26)7 quark mass e ects, Phys. Rev. D 69 (2004) 114005 [hep-ph/0307022] [INSPIRE]. White Paper, in Community Summer Study 2013: Snowmass on the Mississippi. (CSS2013), Minneapolis, MN, U.S.A., July 29{August 6 2013 [arXiv:1309.1688] [INSPIRE]. 77 (2008) 115004 [arXiv:0801.4389] [INSPIRE]. hep-ph/9504216 [INSPIRE]. [arXiv:0904.2534] [INSPIRE]. [1] E. Accomando , A. Belyaev , L. Fedeli , S.F. King and C. Shepherd-Themistocleous , Z0 physics with early LHC data , Phys. Rev. D 83 ( 2011 ) 075012 [arXiv: 1010 .6058] [INSPIRE]. [2] P. Langacker , The Physics of Heavy Z0 Gauge Bosons, Rev. Mod. Phys . 81 ( 2009 ) 1199 [4] E. Accomando , D. Becciolini , A. Belyaev , S. Moretti and C. Shepherd-Themistocleous , Z0 at [5] E. Accomando et al., W 0 and Z0 searches at the LHC , PoS(DIS 2013 ) 125 [INSPIRE]. [6] A. Belyaev , R. Foadi , M.T. Frandsen , M. Jarvinen , F. Sannino and A. Pukhov , Technicolor Walks at the LHC, Phys. Rev. D 79 ( 2009 ) 035006 [arXiv: 0809 .0793] [INSPIRE]. [7] D. Barducci , A. Belyaev , S. De Curtis, S. Moretti and G.M. Pruna , Exploring Drell-Yan energy using pp collisions at p [21] R. Hamberg , W.L. van Neerven and T. Matsuura , A Complete calculation of the order s2 correction to the Drell-Yan K factor , Nucl. Phys. B 359 ( 1991 ) 343 [Erratum ibid . B 644 [22] W.L. van Neerven and E.B. Zijlstra , The O( s2) corrected Drell-Yan K-factor in the DIS and MS scheme, Nucl. Phys. B 382 ( 1992 ) 11 [Erratum ibid . B 680 ( 2004 ) 513] [INSPIRE]. [23] R. Hamberg , T. Matsuura and W. van Neerven , Total cross sections for Z- and W[24] S. Kretzer , H.L. Lai , F.I. Olness and W.K. Tung , CTEQ6 parton distributions with heavy [26] M. Carena , A. Daleo , B.A. Dobrescu and T.M.P. Tait , Z0 gauge bosons at the Tevatron,


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP01%282016%29127.pdf

Elena Accomando, Alexander Belyaev, Juri Fiaschi. Forward-backward asymmetry as a discovery tool for Z′ bosons at the LHC, Journal of High Energy Physics, 2016, 127, DOI: 10.1007/JHEP01(2016)127