Charged fermions below 100 GeV

Journal of High Energy Physics, May 2018

Abstract How light can a fermion be if it has unit electric charge? We revisit the lore that LEP robustly excludes charged fermions lighter than about 100 GeV. We review LEP chargino searches, and find them to exclude charged fermions lighter than 90 GeV, assuming a higgsino-like cross section. However, if the charged fermion couples to a new scalar, destructive interference among production channels can lower the LEP cross section by a factor of 3. In this case, we find that charged fermions as light as 75 GeV can evade LEP bounds, while remaining consistent with constraints from the LHC. As the LHC collects more data, charged fermions in the 75–100 GeV mass range serve as a target for future monojet and disappearing track searches.

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Charged fermions below 100 GeV

HJE Charged fermions below 100 GeV Daniel Egana-Ugrinovic 0 1 3 6 7 Matthew Low 0 1 3 4 7 Joshua T. Ruderman 0 1 2 3 5 7 Geneva, Switzerland 0 New York , NY 10003 , U.S.A 1 Einstein Drive , Princeton, NJ 08540 , U.S.A 2 Theoretical Physics Department , CERN 3 Stony Brook , NY 11794 , U.S.A 4 School of Natural Sciences, Institute for Advanced Study 5 Center for Cosmology and Particle Physics, Department of Physics, New York University , USA 6 C.N. Yang Institute for Theoretical Physics, Stony Brook University 7 We revisit the How light can a fermion be if it has unit electric charge? lore that LEP robustly excludes charged fermions lighter than about 100 GeV. We review Beyond Standard Model; Supersymmetric Standard Model - LEP chargino searches, and nd them to exclude charged fermions lighter than 90 GeV, assuming a higgsino-like cross section. However, if the charged fermion couples to a new scalar, destructive interference among production channels can lower the LEP cross section by a factor of 3. In this case, we nd that charged fermions as light as 75 GeV can evade LEP bounds, while remaining consistent with constraints from the LHC. As the LHC collects more data, charged fermions in the 75{100 GeV mass range serve as a target for future monojet and disappearing track searches. 1 Introduction 2 3 4 5 A review of LEP limits on higgsinos Simpli ed model for charged fermions LEP limits on the simpli ed model LHC limits on the simpli ed model 5.1 5.2 5.3 5.4 5.5 Invisible decays of the Higgs Monojet searches Disappearing track searches Other LHC searches Combined LEP and LHC limits 6 Conclusions A Validation of LHC analyses A.1 Monojet searches A.2 Disappearing track searches Higgs, they may also be relevant for understanding the electroweak phase transition [6{8]. The LHC is now sensitive to charginos with masses of hundreds of GeV [9{16]. As more data are collected, heavier states will come into reach. Signi cant attention has been devoted towards maximizing the mass reach for new electroweak fermions (see for example refs. [17{35]). However, it is also important to be mindful of any gaps in the exclusion limits at lower masses, to make sure that new physics is not missed during the march to higher masses. The conventional view is that LEP sets the strongest bounds on electroweak fermions lighter than about 100 GeV, while the LHC probes higher masses. The clean environment bounds on fermions lighter than half the maximum center-of-mass energy, p of LEP, plus the robust production mechanism through s-channel =Z, implies powerful s = 209 GeV. Photons from initial state radiation (ISR) can be tagged, and therefore detection does not { 1 { require energetic decay products from the new fermions. There has developed a sort of folk bound : it is commonly believed that LEP robustly excludes fermions with unit charge lighter than about 100 GeV. Indeed, most LHC searches for charginos only display bounds above 100 GeV [9, 11{16, 36{45],1 and many theory studies of charginos also only consider masses above 100 GeV. In this work, we explore fermions with unit electric charge and masses between mZ =2 and 100 GeV. We limit ourselves to study charged fermions in the higgsino gauge representation and call these fermions charginos, both if they are part of the MSSM or if they arise in a more generic, possibly non-supersymmetric, context. We critically examine the robustness of the LEP-II bounds on charginos. We do not consider the region below mZ =2, where the Z boson can decay to the new fermions, leading to powerful constraints from LEP-I [51{54]. The LEP SUSY working group combined limits from the 4 experiments: ALEPH, DELPHI, L3, and OPAL (\ADLO" combination). A combined limit excludes charginos with masses below 103.5 GeV [55], however this bound relies on a restrictive set of assumptions: ( 1 ) wino-like production cross section, (2) gaugino-uni ed relation between the bino and wino mass (implying a large splitting between the chargino and lightest neutralino), and (3) decoupled sneutrinos. There is also a combined limit applied to the regime of small splitting between the chargino and neutralino [56], excluding charginos lighter than 92.4 GeV (91.9 GeV) for higgsino (wino)-like cross sections, respectively. In this work, we review the LEP bounds, including newer searches not included in the LEP SUSY working group combination, and we nd that charginos with a higgsino-like cross section are excluded in the range mZ =2 to approximately 90 GeV. In gure 1, we compare the cross section of higgsino-like charginos to two bounds from LEP. Note that although we nd a bound of about 90 GeV, the higgsino cross section is always within an order one factor of the bound for all masses above mZ =2. If the cross section can be reduced, the bound may be signi cantly weakened. We consider a deformation of the minimal model, illustrated in gure 2, where the cross section is reduced. A new scalar has a Yukawa coupling with the charged fermion and the electron, such that t-channel exchange of the scalar destructively interferes with the usual s-channel diagram. The dashed curve in gure 1 shows how the fermion's cross section is reduced, for a particular choice of the scalar mass and the strength of its Yukawa interaction. As we will describe below, we nd that the t-channel scalar can reduce the LEP-II limit on charginos from about 90 GeV to about 75 GeV. We nd that this gap survives current searches at the LHC. A previous study identi ed a window of light charginos that decay to leptons through displaced vertices and survive LEP searches [58], however this gap has now been closed by LHC searches for displaced leptons [59]. Previous studies have considered charged scalars, below 100 GeV, that are not excluded by LEP [60{62]. The rest of this paper is organized as follows. In section 2, we review LEP searches and nd that a charged fermion, with a higgsino-like cross section, is bounded to be heavier than about 90 GeV. In section 3, we introduce the simpli ed model that we use to study 1A few LHC searches, mainly from ps = 7 TeV, do show bounds on masses below 100 GeV [10, 46{50]. { 2 { HJEP05(218) (black solid), and charged fermion pair production cross section, F +F , allowing for t-channel interference (black dashed). In the t-channel diagram shown in gure 2, the coupling is set to = 0:5 and the singlet mass to mS = 110 GeV. The light and dark red lines are the LEP limits on the pair production cross section +H H from [56] and [57], respectively. The limits in this gure assume higgsino-like decays, and a chargedneutral mass splitting of m = 2:7 GeV. e+ e , Z F + F pair production at LEP. The s-channel production is xed by the fermion's quantum numbers, while the t-channel production depends on the scalar's mass and the strength of the Yukawa interaction between the charged fermions and the scalar. the e ect of t-channel interference on the chargino bounds. In section 4, we discuss LEP-II limits in the presence of t-channel interference. Then, in section 5, we evaluate the limits from LHC searches for monojets, multileptons, and disappearing tracks. Section 6 contains our conclusions. We include an appendix that describes the validations of our simulations for recasting LHC searches. 2 A review of LEP limits on higgsinos We start by providing a brief summary of LEP limits on the pure higgsino model. The pure higgsino model corresponds to an extension of the Standard Model with a vector-like pair of color-neutral, SU(2)W doublet fermions with hypercharge Y = 1=2. We assume that discrete symmetries prevent mixing between the new doublet fermions and Standard { 3 { HJEP05(218) e+ e , Z + H H + fu + H + 0 H higgsinos decays (center and right). fu; fd stand for Standard Model up or down type quarks or leptons. Both the cross section and branching ratios are xed by the higgsino's quantum numbers and the chargino and neutralino masses. Model leptons. At the renormalizable level, all of the new doublet fermion interactions are set by their quantum numbers. The spectrum of the higgsino system contains one charged and one neutral Dirac fermion: the chargino, , and the neutralino, H H 0 . At dimension- ve, the masses of H and 0H may be split by the Weinberg operator (in the MSSM this mass splitting arises from the mixing among the higgsinos, winos, and bino). At one-loop, there is an additional irreducible contribution to the mass splitting from infrared e ects. In the range H 50 GeV m 100 GeV, this radiative splitting monotonically increases from 206 MeV to 256 MeV [63]. In this work, we assume that the neutral fermion is the lightest component of the doublet and is stable. At LEP, charginos are pair produced via s-channel diagrams mediated by gauge bosons and they decay through W bosons into quarks, leptons or pions, as shown in gure 3. The decays may be two or three-body, depending on the chargino-neutralino mass splitting. Since all interactions are xed by the higgsino's quantum numbers, the properties of the higgsino system, including the chargino lifetime and branching ratios, are completely determined by the chargino and neutralino masses. LEP performed several searches for charged higgsinos heavier than half the Z boson mass. The searches may be divided into di erent categories depending on the charginoneutralino mass splitting m m H m 0 ; H (2.1) which controls both the typical momentum of the nal state particles and the chargino lifetime [66]. The region m > 3 GeV is covered by conventional searches looking for charginos promptly decaying into leptons and jets. For 320 MeV < m < 3 GeV, the most e ective searches require a photon from ISR as well as other detector activity from the chargino's decay products. For m < m < 320 MeV the chargino lifetime is greater than 1 cm, and dedicated searches for disappearing tracks and large impact parameters set the strongest limits. Finally, for mass splittings below the charged pion mass, m < m the chargino quickly becomes collider-stable and is probed by heavy stable charged particle (HSCP) searches. According to [56], the combination of the above searches leads to a lower limit on the chargino mass of m > 92:4 GeV. H { 4 { Prompt decays Displaced decays m m Search ADLO conventional 3 GeV 3 GeV m 320 MeV m 10 GeV (prompt) m m 320 MeV (displaced) 320 MeV m 5 GeV reference. Above, ` stands for leptons (e; ; ), j for jets, ISR for initial state radiation (of a photon), and HSCP for heavy stable charged particles. The searches included in the ADLO combination are speci ed in parentheses. They include a combination of the analyses using a subset of the full dataset, up to 2001, for conventional searches and using the full dataset, up to 2002, for \low DM" compressed searches. We further break down the ADLO compressed searches into \prompt" and \displaced" depending on the chargino-neutralino mass splitting, which xes the chargino lifetime. The ADLO combination also reports limits on HSCP searches for m m , which we do not use in this work. Instead, we recast the OPAL HSCP search [71], which provides stronger limits. None of the OPAL searches in the table are included in the ADLO combination, and they are all performed with the full luminosity. The last column indicates the charged-neutral higgsino mass splitting covered by each reference. To understand this limit in more detail, we reanalyze a selection of LEP results, which we summarize in table 1. These results include the ADLO results, which are a combination of the ALEPH, DELPHI, L3, and OPAL limits, and additionally, results published afterwards individually by the OPAL collaboration. The results of our analysis are shown in gure 4. Most regions of the chargino H neutralino parameter space are excluded by more than one search, so each region is labeled by the search that leads to the strongest limit at that point in parameter space. We nd that charged higgsinos are excluded up to at least 100 GeV, except in two well-de ned regions. In the rst region, the mass splitting is large, m & 60 GeV. In this case, for m 0 . 25 GeV, the limit on the chargino mass degrades to 96 GeV because the signal kinematics resemble the background from W boson pair production. The second region with weaker limits occurs when the chargino and neutralino are compressed, but the chargino is not collider-stable, namely m . m . 3 GeV. This region of parameter space is covered by ISR assisted searches and searches for large impact parameters or disappearing tracks. In this region, the limit on the charged higgsino mass degrades 90 GeV, as discussed in the introduction. This is the absolute lower limit that we nd on the charged higgsino mass, and is approximately consistent with the limit m > 92:4 GeV reported by the ADLO combination [56]. The limits presented in gure 4 rule out most of the parameter space with charginos below 100 GeV, but are speci c to the pure higgsino model. In the introduction we pointed out that O( 1 ) modi cations to the pure higgsino production rates may lead to considerably weaker limits. In the following sections, we investigate quantitatively how the limits on charginos change when the basic assumptions of the pure higgsino model are relaxed. { 5 { gion (left) and in the compressed region (right). In the uncompressed region the strongest limits are set by the OPAL multilepton search [65] and by ADLO searches for promptly decaying higgsinos [55]. H The range m 50 GeV is not covered by the OPAL multilepton search, so we rely exclusively on the ADLO combination. In the compressed region, the space from 3 GeV m 10 GeV is mainly covered by a combination of the ADLO conventional and ADLO \low DM" prompt searches, as well as by the OPAL multilepton search. The OPAL and ADLO ISR assisted searches [56, 57], set bounds in the regions 320 MeV m 3 GeV and 320 MeV m 5 GeV, respectively. In the region m m 320 MeV, the chargino decays within the detector, and we rely exclusively on the ADLO combination, which contains dedicated searches for kinked tracks and large impact parameters. The region m m is covered by the OPAL HSCP search [71], which applies to particles with a decay length 3 m. The black dashed line indicates the one-loop radiative chargino-neutralino mass splitting. 3 Simpli ed model for charged fermions In this section, we consider a minimal extension of the pure higgsino model to illustrate how simple deviations from this model modify the LEP phenomenology. We add to the Standard Model a pair of color-neutral, vector-like doublet fermions F and F with hypercharges Y = 1=2 and Y = 1=2, respectively, as in the pure higgsino model. The charged and neutral components of the doublets are de ned as F = F 0 ! F ; F = F + ! F 0 : (3.1) We refer to the fermions F as charginos to indicate that they have unit charge and are part of an SU(2)W doublet, even though our simpli ed model is non-supersymmetric. Consider now introducing a real scalar singlet S, which couples to the doublet F and the electron doublet Le. Up to dimension- ve, the Lagrangian contains the operators, L mF F F + m2S S2 + 2 1 (F H)(F Hc) + LeF S + h:c: + V (H; S): (3.2) { 6 { We require the potential, V (H; S), to be minimized at the origin of the eld space of S, so that it does not condense. This model does not violate lepton number, as can be seen by assigning F and F electron numbers of 1 and 1, respectively. Individual lepton avor numbers are also preserved, implying that the model is safe from avor constraints. Additional renormalizable interactions beyond the ones in eq. (3.2) are easily forbidden by imposing discrete and continuous global symmetries. Such symmetries forbid mixing of the new doublets with Standard Model fermions and stabilize the lightest component of the singlet-doublet sector. The only dimension- ve term we include is the Weinberg operator, which is responsible for splitting the neutral and charged components of the SU (2)W doublets at tree-level.2 The couplings and are generically complex, but for simplicity we set the phases to zero and do not study the CP -violating phenomenology. Without loss of generality, we work in the basis where mF 0 and 0. In addition to the scalar singlet with mass mS, the model contains one charged Dirac fermion with mass mF = mF and one neutral Dirac fermion with mass mF 0 . The mass splitting between the charged and neutral fermions is v 2 2 m mF mF 0 = + mrad ; (3.3) or mS ! 1). For mF where the Higgs condensate is v = 246 GeV and mrad is positive and accounts for the radiative splitting of the doublet. We assume that mF > mF 0 . The model in eq. (3.2) is very similar to the pure higgsino model, but the Yukawa interaction, LeF S, leads to two important modi cations to LEP phenomenology. First, the pair production rate of F at LEP is modi ed with respect to the pure higgsino case, since a new t-channel singlet-mediated contribution interferes destructively with the schannel gauge-mediated contribution. The diagrams contributing to the production cross section are shown in gure 2. To show the e ect of this interference, in gures 5 and 6 we plot the LEP F pair production cross section normalized to the charged higgsino cross section, as a function of the coupling and the singlet mass mS for mF = 75 GeV. We see that over a wide range of couplings and masses, the LEP pair production cross section is reduced with respect to the pure higgsino case (which is recovered in the limits ! 0 = 75 GeV, the absolute minimum is obtained for = 0:5 and mS = 81 GeV, at which point the cross section is reduced to a factor of 0:3 of the cross section when = 0. This minimum is indicated by the red cross in gure 6. The second e ect of the singlet-doublet Yukawa interaction is to alter the decay branching fractions and lifetime of the charged fermion. When mS > mF , as we assume for the rest of this work, the scalar singlet mediates a new three-body decay mode, shown in gure 7 (right panel). In gure 8 (left panel), we show the branching fractions into quarks, leptons, and pions as a function of the coupling , and in gure 8 (right panel) as a function of the charged-neutral fermion mass splitting m. Since the new Yukawa interaction 2The Weinberg operator (F H)(F Hc) may be obtained from integrating out a heavy complex singlet with electron number coupling to the bilinears F H and F Hc at tree-level. Note that in this case the operator (F F )(HyH), which may not be forbidden by continuous and discrete symmetries respected by the interactions in eq. (3.2), is not generated. { 7 { F +F , at LEP within our simpli ed model, normalized to the charged higgsino pair production cross section . The cross section is shown as a function of the coupling for xed singlet mass mS = 150 GeV (left), and as a function of the singlet mass mS for xed coupling = 0:5 (right). In both cases, the charged fermion mass is set +H H to mF = 75 GeV. Cross sections are obtained from [72]. F +F , at LEP within our simpli ed model, normalized to the charged higgsino pair production cross section as a function of the coupling and singlet mass mS, for mF = 7+H5 GHeV. The red cross indicates . The cross section is shown the point of maximal s and t-channel interference, at which the cross section is minimal. Cross sections are obtained from [72]. couples the fermion doublets to electrons, larger values of this interaction increase the branching fraction to electrons. This modi cation to the branching ratios results in more electron-rich decays, which alter the LEP search e ciencies relative to the pure higgsino case. Moreover, the singlet-mediated decay mode increases the charged fermion width (for xed masses). This e ect is particularly strong for mass splittings below the pion threshold. For example, for m = 100 MeV and mF the decay length from 57 to 3 m. = 80 GeV, increasing from 0 to 1 lowers F + decays. fu; fd stand for Standard Model up or down type quarks or leptons. The decays through a W (left) or the two body decays into (center) are set by the fermion's quantum numbers, while the singlet-mediated decay width (right) and the scalar singlet mass mS. In the singlet-mediated diagram, both F 0 e and F 0 e nal states are possible. decay branching fractions as a function of the coupling mF 0 = 3 GeV (left), and as a function of the mass splitting for coupling = 0:5 (right). In both cases, the charged fermion mass is mF = 75 GeV and the scalar singlet mass is mS = 110 GeV. Decays into the charged pion are matched to decays into up and down quarks at m = 0:9 GeV. Decay widths are obtained from [63, 73]. UV completions. We conclude this section by brie y commenting on some possible UV completions of our simpli ed singlet-doublet model. One motivation for this is the fact that the electroweak-scale mass of the scalar singlet within our simpli ed model is not technically natural. This is easily remedied by, for instance, promoting the scalar to be part of a chiral super eld in a supersymmetric setup. The singlet-doublet model is a simpli ed version of the wino-bino-sneutrino system. In the MSSM with decoupled higgsinos, the lightest chargino is wino-like. At LEP, s-channel production proceeds via gauge-mediated diagrams, while the interfering t-channel diagram is mediated by the electron sneutrino. Destructive interference due to the sneutrinomediated diagram modi es the charged wino production rates at LEP, and weakens the limits. As an example, consider taking the bino, wino, and higgsino masses to be M1 = 300 GeV, M2 = 95 GeV, and = 500 GeV, with tan = 2. In this case, the lightest neutralino and chargino are wino-like, with a chargino mass m = 82:4 GeV and a chargino neutralino mass splitting m = 0:5 GeV. With a decoupled sneutrino, the chargino production cross section is = 5:35 pb and the chargino is excluded by the ADLO com W { 9 { bination [56], which sets a 2 pb limit on the cross section. Taking m~e = 85 GeV reduces the wino production cross section by more than a factor of 6, = 0:81 pb, so the limits in [56] are avoided. Di erently from our simpli ed model, in this scenario there are a plethora of additional states with electroweak charges at the electroweak scale, including a 105 GeV left-handed selectron and 500 GeV higgsinos. While the selectron and higgsinos in this example are beyond LEP reach, a careful analysis of LHC multilepton and monojet searches is required to decisively test the possibility of light charginos in this supersymmetric context. We leave a detailed study of the wino-sneutrino system for future work. An alternative UV realization of our simpli ed model is to consider the MSSM extended HJEP05(218) by a complex scalar singlet charged under electron number. The scalar singlet can then couple to the higgsinos through a superpotential interaction, LeHuS, where Hu is the uptype Higgs super eld and S has been promoted to a super eld. In this theory, the charged higgsinos would play the role of the fermions F in our simpli ed model. If the fermion partners of the singlet eld are heavy, the discussion would be similar to the one in this work, but with a complex scalar in the e ective theory providing the t-channel interference in gure 2 instead of a real scalar. 4 LEP limits on the simpli ed model In the previous section, we found that a simple modi cation to the pure higgsino benchmark scenario, namely the addition of a singlet scalar, can lead to signi cant di erences in the production rates and decay branching fractions relevant for LEP searches for charginos. In this section, we reanalyze LEP limits in the context of our simpli ed model. Due to the modi ed branching ratios, the relative composition of nal states is di erent in the simpli ed model compared to the pure higgsino model. As a result, the overall search e ciency is di erent in the simpli ed model than in the benchmark models considered in the experimental searches. We take a conservative approach to setting limits meaning that we only set limits from experimental searches that can be reliably recast. When insu cient information about a search is available we do not set limits using that search, however, we do show the would-be limits under speci ed assumptions. We make use of the di erent searches as follows. The OPAL multilepton search [65] sets bounds on the chargino pair production cross section times branching fraction squared into electrons, muons, and hadronically-decaying taus. The search assumes lepton avor universality, which is violated in our simpli ed model since the singlet S mediates three-body decays into electrons only (see gure 7). The e ciencies of electrons and muons are similar, and higher than that of hadronicallydecaying taus [65]. Consequently, the search e ciency in our simpli ed model should be larger than in the avor universal scenario, since decays to electrons are enhanced. There is not enough information presented by OPAL to determine the e ciencies for separate nal states, so we conservatively apply the OPAL limit by assuming the same overall e ciency for leptonic nal states, despite the higher e ciency expected in our simpli ed model. (from the simpli ed model of section 3), set by the searches in = 0:5 and the scalar singlet mass to mS = 110 GeV. All the searches included present limits for the pure higgsino, so we present limits for our simpli ed model by conservatively estimating the e ciencies, as explained in section 4. For comparison, we also show in hatched regions the excluded space that one would obtain assuming the same e ciencies as in the pure higgsino scenario. In the uncompressed region, limits are obtained from the OPAL multilepton search [65] and the ADLO combination with promptly-decaying higgsinos [55]. In the compressed region, limits are obtained from the ADLO conventional combination [55], ADLO \low DM" combination [56], OPAL multilepton, OPAL ISR assisted, and OPAL HSCP searches [57, 65, 71]. The black dashed line indicates the one-loop radiative charged-neutral mass splitting. The OPAL ISR assisted search [57] and ADLO combination with prompt decays [55, 56] set limits on the charged fermion pair production cross section assuming three body decays through a W ( ) or two body decays into a charged pion, with rates xed by the higgsino quantum numbers. Due to S-mediated decays into electrons, in our simpli ed model the W ( ) and decay modes are diluted with respect to the pure higgsino case by a common factor, so we simply dilute the reported limits on the cross section by this common factor squared. This choice is again conservative, since it does not take into account the gain in e ciency due to the additional electrons in the nal state. In the case of the ADLO combination with searches for kinked tracks or for large impact parameters [56], estimating the e ciencies is more challenging, since they depend on both the decay branching fractions and the chargino lifetime. For these searches, we only present for reference the limits that one would obtain by (crudely) assuming the same e ciencies as in the pure higgsino case. In section 5, we recast LHC searches for disappearing tracks to provide a more reliable bound in the case of displaced decays. Finally, the OPAL HSCP search [71] covers the very small mass splitting region with collider-stable charginos. In this case, we simply use the reported pure higgsino cross section limits by rescaling by the fraction of events where both charged fermions have a ight distance longer than 3 m, as required by the search. The resulting limits, for coupling = 0:5 and singlet mass mS = 110 GeV, are presented in gure 9, where di erent colors represent the searches leading to the strongest limit on the pair production cross section at each point. The hatched regions show the would-be limits by assuming that the e ciencies are unchanged between the pure higgsino model and the simpli ed model. From gure 9 (left panel), we see that in the uncompressed region, m 10 GeV, the absolute LEP limit on the charged fermion mass is mF 77 GeV. The weakest end of the limit is achieved for mF 0 . 5 GeV. In this region, multilepton searches lose sensitivity due similarity between the kinematics of the signal and the W +W background. In gure 9 (right panel), we show the limits in the compressed region, m First, we note that we cannot set reliable bounds in the region m m due to our inability to reliably recast kinked track and large impact parameter searches at LEP. The hatched region indicates the would-be limit (crudely assuming higgsino-like e ciencies) and rules out charginos up to 75 GeV. In the highly compressed region, which is covered by HSCP searches, m m , the limit on charginos is mF & 92 GeV, which is weaker than in the pure higgsino case due to the smaller charged fermion lifetime, as discussed in the previous section. For promptly decaying fermions, m & 300 MeV, we see from gure 9 (right panel) that there are a couple of small gaps in coverage in the range mZ =2 mF These gaps are at the interface between the region of validity of di erent searches. They occur due to unphysical discrete jumps due coarse binning in the excluded cross section reported by the corresponding LEP references, and we expect them to be excluded if more ne-grained limits were provided. In addition, these gaps will be covered by LHC searches (see section 5). Disregarding these small gaps, we nd that the absolute limit on charginos within our simpli ed model is mF & 73 GeV. The weakest end of the limit is achieved for m 2 3 GeV, a mass splitting region which is covered by ISR assisted searches. Note that including the hatched regions does not change our conclusions. Finally, we brie y comment on electroweak precision tests. In the renormalizable theory, since the fermion doublets do not couple to the Higgs, there is no one-loop contribution to the S, T , and U parameters [63]. On the other hand, at the renormalizable level the extended oblique parameters, V , W , and X, are nite at one loop [74]. To set limits, we obtain the one-loop V , W , and X parameters using Package-X [75, 76] and perform an electroweak t as in [58]. We nd a 95% CL limit on the charged fermion mass mF 54 GeV, which is independent of coupling and singlet mass mS at one-loop. In addition to the oblique analysis, we also check non-oblique precision electroweak limits. First, we check the impact on the Bhabha scattering, e+e ! e+e , cross section at LEP. In our model, the Bhabha scattering cross section is modi ed at one-loop by box diagrams with F and S in the loop. To set limits, we calculate the amplitudes with FeynCalc [77, 78] and the one-loop integrals with Package-X. We then perform a full t to the measured Bhabha scattering cross section for 7 LEP center of mass energies and 15 scattering angle bins including full correlations reported in [79]. Additional limits are set by Z-pole observables, namely by the Z decay width to electrons and the leptonic e ective weak mixing angle. In our model, these observables are also modi ed at one-loop by diagrams with charged fermions F and a scalar singlet S in the loop. We obtain the amplitudes as above and we set limits by directly comparing with [80] and [81]. The Bhabha scattering and Z-pole non-oblique limits depend strongly on the singlet-doublet Yukawa coupling and the doublet fermion and scalar singlet masses. We nd that all of the parameter space presented in gure 9 is allowed. For reference, xing the fermion doublet masses at mF = 75 GeV and scalar singlet mass mS = 110 GeV, we nd that couplings of 1:5 are excluded by the precision Bhabha scattering analysis at 95% CL, while the strongest limit from Z-pole observables comes from the leptonic e ective weak mixing angle, which excludes improve on the current limit on the leptonic e ective weak mixing angle by at least one HJEP05(218) order of magnitude [82{84] which is enough to decisively probe all the parameter space for our charged fermions up to mF = 100 GeV. 5 LHC limits on the simpli ed model In the previous section, we concluded that LEP rules out charginos within our simpli ed model with mass mF mass mF the impact of searches from the LHC. 77 GeV in the uncompressed region, m 10 GeV, and with 73 GeV in the compressed region, m 10 GeV. In this section, we discuss There are a number of searches that can be used to probe charginos at the LHC. Since the fermion doublets F; F couple to the Higgs via the Weinberg operator, invisible Higgs decays set constraints which we discuss in section 5.1. In the compressed region, the charged fermions may decay leaving little-to-no activity in the detector, and can be probed by monojet searches, presented in section 5.2. For even smaller mass splittings, the charged fermions may lead to kinked or disappearing tracks, as discussed in section 5.3. Other LHC searches leading to weaker limits are mentioned in section 5.4. Finally, the combination of LEP and LHC searches is shown in section 5.5. 5.1 Invisible decays of the Higgs The Weinberg operator in eq. (3.2) leads to an e ective dimension- ve coupling between the Higgs and the neutral fermions F 0; F 0 where the second equality uses eq. (3.3) at tree-level. The charged fermion does not couple to the Higgs. The invisible decay width of the Higgs to the neutral fermion is ghF 0F 0 = v = 2 m v ; = mh 2 8 ghF 0F 0 1 4m2F 0 m2 h 3=2 : (5.1) (5.2) The current limit on the Higgs invisible width is BRh!inv 0:24 [85, 86], and rules out most of the parameter space with mF 0 mh=2, except when mF and mF 0 are very compressed (since the compression also suppresses the couplings to the Higgs). The corresponding limits are shown in gure 10. 5.2 In the compressed region of 300 MeV m 10 GeV, the decay products of the charged fermion are soft and therefore challenging to detect at the LHC. In this region, fermion pair production (F +F , F +F 0, F F 0, and F 0F 0) results in a signal with missing energy and little-to-no hadronic or leptonic activity in the detector. This topology is constrained by LHC searches that look for large missing energy along with an ISR jet, namely monojet searches. For splittings below 300 MeV the decays are no longer prompt, and dedicated searches for displaced objects become e ective. There are 13 TeV monojet searches from both ATLAS [87] and CMS [88] with about 36 fb 1 of data. Here, for simplicity, we just recast the CMS search, which is representative of both (but sets stronger limits due to an apparent downward uctuation). This search selects events by de ning 22 exclusive E= T regions, from E= T = 250 to 1400 GeV. The leading jet is required to have a transverse momentum of pT 100 GeV and a pseudorapidity of 2:5. A pT cut on leptons, taus, photons, and b-jets is imposed, and minimum angles are required between the four leading jets. In order to recast the CMS monojet search, we perform a Monte Carlo Simulation. We implement our simpli ed model with FeynRules [89] and simulate events at leading order with Madgraph5 aMC@NLO [90], using the nn23lo1 PDF dataset [91]. We use Pythia8 [92] to simulate the parton shower, and Delphes 3 to perform the detector simulation using the CMS detector card [93]. Jets are clustered using the anti-kT algorithm [94] with jet radius R = 0:4. We match up to three jets using the MLM matching scheme [95] with a matching scale of 50 GeV. In appendix A, we describe the validation of our simulaton. For the signal, we generate a sample of fermion pair production events. We set limits using the CLs method [96], and combine the limits from the di erent missing energy bins by making use of the bin with the best expected limit at each point in the model parameter space. The resulting limits for coupling = 0:5 and singlet mass mS = 110 GeV are presented in gure 10. The limits are mostly driven by the low missing transverse energy bins, E= T 590 GeV, for which the errors are already close to being dominated by systematics. We note that the limits are roughly independent of in the compressed region. This is because monojets searches are sensitive to prompt decays, and therefore the only e ect of the Yukawa coupling is to change fermion branching ratios, to which the monojet searches are not sensitive. 5.3 Disappearing track searches As the charged-neutral splitting goes below 300 MeV, the decay length of the charged fermion becomes macroscopic. At the LHC, there are a number of searches that target various decays lengths. Roughly speaking, decay lengths of O(mm) are probed by searches for displaced vertices, O(cm) are probed by searches for kinked or disappearing tracks, and O(m) are probed by searches for heavy stable particles. Displaced vertex searches do not set the dominant limit anywhere in our parameter space, because they tend to require energetic particles originating from the displaced vertex [97], and are therefore not relevant when the charged and neutral fermions are compressed. Heavy stable particle searches will be discussed in section 5.4. The most recent search for disappearing tracks was performed by ATLAS at 13 TeV with 36:1 fb 1 of data [98]. (The most recent disappearing track search from CMS was at 8 TeV [99].) The search looks for the partial track of a chargino, which decays mid- ight to 0 . The outgoing pion or lepton is very soft, since its momentum is set by m, and is typically not seen, which means the chargino track appears to end abruptly. In addition to the disappearing track, this search requires an ISR jet for triggering. We recast the disappearing tracks search using the following procedure. Using Madgraph5 aMC@NLO, we simulate pair production events at leading order and compute the e ciency to select an event with a disappearing track as a function of the lifetime of the charged fermion and its mass (see appendix A for a more detailed description). We then compute the expected number of events as a function of lifetime and mass and compare to the 95% CL excluded number from ATLAS. The results are shown in gure 10. The disappearing tracks search excludes chargino masses below 100 GeV for mass splittings between 100 and 300 MeV, for our benchmark point of mS = 110 GeV and For splittings smaller than 100 MeV, the charged fermion decay length becomes long enough that the majority of charged fermions do not decay within the tracker. For splittings larger than 300 MeV, most of the charged fermions decay before they reach the tracker. Note that m = 300 MeV corresponds to c 1 cm for our benchmark point, which is naively too short to leave a particle track. However, the large production cross section and sizable = 0:5.3 2 5, imply that limits can be set using the exponential tail relevant boost factor, of the decay distribution. 5.4 Other LHC searches As can be seen in gure 10, in the uncompressed region, the invisible Higgs limits close the parameter space left open by LEP while in the compressed region monojet searches, and disappearing track searches work together to constrain some of the parameter space. There are a number of other searches at the LHC that can be used to constrain the simpli ed model for chargino masses below 100 GeV. We mention them brie y in this section. Multilepton searches look for one or more charged leptons. Dedicated searches in the compressed region using an ISR jet have been performed by both ATLAS and CMS [10, 16, 41], but still the minimal lepton pT required in these searches is at least 3:5 GeV (for muons at CMS) and more typically 5 10 GeV. For this reason, these searches do not outperform LEP searches for chargino masses below 100 GeV and mass splittings below 3 GeV. This expectation is con rmed by the latest ATLAS results [10], which do not improve on the 90 GeV LEP charged higgsino bound at small mass splittings. Multilepton searches at LHC are most e ective when the leptons are hard and they set limits in the uncompressed region m 10 GeV, but as discussed above, the only space 3The limits do depend on , but only very weakly. Increasing leads to a shorter decay length, leading to an overall shift of the limits towards lower mass splittings. From = 0 to 1, the limits on m only change by . 40 MeV. uncovered by LEP searches in the uncompressed region is already excluded by invisible Higgs searches. For O(cm) decay lengths, the disappearing track searches are the most sensitive, while for longer decay lengths, HSCP searches become the most sensitive. The HSCP searches performed by LEP constrain cross sections at the 0:01 pb 1 level, which is far below the cross section in our simpli ed model within the range of masses that we consider. Since HSCP searches at the LHC cover approximately the same range of m as the LEP searches, we do not recast HSCP searches from the LHC. Finally, as pointed out in section 5.1, note that the charged fermions in our simpli ed model do not couple to the Higgs at tree-level. As a consequence, there is no one-loop diagram with charged fermions F modifying the h ! rate, and no signi cant limits on our simpli ed model may be set with current measurements of the Higgs to diphoton branching fraction. The combined LEP and LHC limits are shown in gure 10, where we indicate with colors the LHC limits, while the LEP limits discussed in section 4 are shown in gray. From the left panel in gure 10 we see that the uncompressed region, m 10 GeV, is completely excluded up to mF = 100 GeV by a combination of LEP results and the constraint on the Higgs invisible width, where in the plot we highlight in red the region which is exclusively ruled out by the Higgs invisible width constraint. In the right panel of gure 10 we present the limits in the compressed region, m 10 GeV. In red, blue, and green we show LHC constraints from the Higgs invisible width, monojet, and disappearing track searches, respectively. Some parts of parameter space are excluded by both LHC and LEP, and here we simply overlap LHC constraints on top of LEP constraints. In the uncompressed region, the Higgs invisible width constraints do not lead to any signi cant improvement with respect to LEP limits, since the couplings of the Higgs to the neutral fermion are suppressed by the small charged-neutral mass splitting (see eq. (5.1)). On the other hand, the combination of LHC monojet and disappearing track searches cover the region m m 300 MeV, which is hard to exclude reliably with published data from LEP displaced searches as discussed in section 4. In addition, for m 300 MeV, monojet searches at LHC cover most of the small gaps for charged fermion masses mF . 63 GeV left out by our LEP exclusion in gure 9. From gure 10 we conclude that the absolute limit on the chargino mass within our simpli ed model is mF 73 GeV, and is not improved with respect to the absolute LEP limit. The lower end of this limit is obtained in the compressed region, with mass splittings of a couple of GeV. In the uncompressed region, m 10 GeV, the combination of available LEP and LHC limits rule out charginos in our simpli ed model up to at least mF = 100 GeV. The limits are summarized in table 2. We conclude the discussion by brie y commenting on the future projected sensitivity from the LHC (with 300 fb 1). As shown in gure 10, the remaining window is in the compressed region, where disappearing tracks searches and monojet searches are the most constraining. The existing disappearing track search already excludes masses up to (from the simpli ed model of section 3), set by LEP and by the LHC, in the uncompressed region (left) and in the compressed region (right). The coupling is set to = 0:5 and the scalar singlet mass to mS = 110 GeV. The LEP limits are the same as in gure 9 but here are indicated in gray, while LHC limits are colored. In the uncompressed region, the strongest limits are obtained from LEP and from LHC constraints on invisible Higgs decays. In the compressed region, the strongest limits are obtained from LEP and from LHC monojet and disappearing track searches. The black dashed line indicates the one-loop radiative charged-neutral mass splitting. LEP LEP+LHC m m 10 GeV 10 GeV mF mF 76 GeV 73 GeV mF mF for the simpli ed model of section 3. LEP limits are obtained from the searches in table 1, while LHC limits consider constraints on the Higgs invisible width [85, 86], disappearing track [98], and monojet [88] searches. 100 GeV, but in a limited range of m. The limits from these searches lose sensitivity steeply as a function of decay length, as discussed in section 5.3. Near m the decay length scales like ( m)3, so that an eight-fold improvement on the lifetime only improves the m reach by a factor of about 2. Consequently, extrapolating current searches to 300 fb 1, we estimate that the limit will improve moderately, by Other projections have also been made [28, 32]. Monojet searches, on the other hand, cover a wide range of m values, but only extend to 65{78 GeV in charged fermion mass (depending on m). A number of projections have been performed [19{23, 26, 30{32, 100] and typically estimate the reach for higgsinos to extend to 100{200 GeV. These estimates, however, are strongly dependent on the assumed systematics, making it hard to say conclusively whether or not monojet searches, with the high luminosity data, will be su cient to cover the remaining parameter space below 100 GeV. In this work, we surveyed the limits on charginos with masses ranging from mZ =2 to 100 GeV. We reviewed LEP limits on chargino pair production, and found that charged higgsinos with masses below 90 GeV are excluded. To study limits on fermions with unit charge in a more general scenario, we introduced small modi cations to the pure higgsino case in the context of a simpli ed model. If a singlet scalar couples to the charged fermions and electrons, then the production cross section is reduced, due to destructive interference, and decay branching fractions are modi ed. We showed that for our simpli ed model, LEP only excludes fermions with unit charge belonging to an SU(2)W doublet up to 73 GeV. We also discussed LHC limits on such low mass \charginos". We discussed a combination of searches, including Higgs precision measurements, monojet, multilepton, displaced decay, and HSCP searches. For our simpli ed model, we found that the LHC, with current statistics, is unable to improve on the overall LEP limit on the mass of charginos. The most challenging topology to probe at the LHC corresponds to the compressed region, where charginos decay leaving little-to-no energy deposition in the detector and limits rely mostly on monojet searches. Our results lead to several questions which remain to be addressed. First, it would be interesting to identify the broader class of models with light fermions with unit charge which are consistent with current data. In this work, we explored charged fermions as part of an SU(2)W doublet, but a similar analysis may be carried out for other representations. In the case of SU(2)W singlets, fermions with unit charge may evade LEP bounds due to tchannel interference in the production cross section, as in this work. In the case of SU(2)W triplets, LEP bounds may also be relaxed with t-channel interference, but we point out that the increased pair production cross section at LHC with respect to the SU(2)W doublet case should lead to stronger limits from monojet and multilepton searches. It would be interesting to study the embedding of these models into full UV completions. The case of SU(2)W triplets is particularly interesting, since it corresponds to the case of the charged wino in the MSSM, where interference in LEP pair production arises through an electron sneutrino. Finally, a careful analysis of the systematics and limit projections at both the LHC and future colliders targeting the low mass region is needed. Future e+e colliders, such as FCC-ee, could de nitively test the existence of fermions with unit charge below 100 GeV. As more data are collected, LHC searches will tend to be optimized for higher mass signals that come into reach. It is important to be mindful of gaps in exclusion limits, and to identify light particles that are still allowed. Light particles can serve as a target for future searches, but often require a careful analysis in order to separate from backgrounds. We have found that charged fermions as light as 75 GeV may have evaded both LEP and the LHC, so far, and therefore serve as a target for future LHC searches. Acknowledgments The authors would like to thank Kyle Cranmer, Jared Evans, Ayres Freitas, Andy Haas, Philip Harris, Patrick Meade, Carlos Wagner and Jose Zurita and for useful discussions. E= T (GeV) 250 280 310 340 370 280 310 340 370 400 NCMS 79700 45800 27480 17020 10560 0:68 0:64 0:73 0:64 0:72 MC 0:016 0:02 0:027 0:033 0:044 NCMS 49200 24950 13380 7610 4361 0:70 0:76 0:72 0:83 0:88 MC 0:03 0:43 0:57 0:082 0:11 our simulation, MC. The reported uncertainties are statistical uncertainties from our simulation. The work of D.E.U. is supported by PHY-1620628, M.L. acknowledges support from the Institute for Advanced Study, and J.R. is supported by NSF CAREER grant PHY-1554858. M.L. would like to acknowledge the Mainz Institute for Theoretical Physics (MITP) and the Aspen Center for Physics, which is supported by National Science Foundation grant PHY1607611, for their hospitality and support while part of this work was being completed. A A.1 Validation of LHC analyses Monojet searches We validate our monojet analysis by generating events, applying a detector simulation, implementing the monojet selection, and comparing the resulting number of events to the number of events reported by CMS [88]. The CMS search was performed at 13 TeV and used an integrated luminosity of 35:9 fb 1 . We compare a sample of Z( ) + j events and a sample of W ) + j events which have similar kinematics to our signal. The events are generated at leading order using Madgraph5 aMC@NLO [90] with MLM matching up to 3 jets, showered with Pythia8 [92], and processed through Delphes 3 [93]. The ratio between the number of events predicted by our simulation and the number of events found by CMS is de ned to be MC = NMC : NCMS (A.1) The estimation given by CMS, NCMS, is data-driven and therefore accounts for contributions beyond leading order. In table 3 we report the values of MC found using the ve lowest E= T bins. Across these bins we nd a variation of 8% in Z( ) + j and 18% in W ) + j. The deviation of MC from unity by several tens of percent is expected since we generate our events at leading order while the CMS estimation is data-driven so automatically includes contributions from all orders. A.2 Disappearing track searches The ATLAS disappearing track search that we recast was performed at 13 TeV with an integrated luminosity of 36:1 fb 1 [98]. We parametrize the e ciency to select an event containing a disappearing track by event which we factorize, roughly following the parametrization . χ ± [ ] ATLAS 13 TeV result [98] (blue) and from our simulated events with e ciencies applied according to eq. (A.2) (red). of ATLAS, as event = track selection; (A.2) where track, the track e ciency, indicates the e ciency to reconstruct a chargino as a disappearing track and selection, the selection e ciency, indicates the e ciency for the event to be selected. We compute the track e ciency in Monte Carlo. The events are generated with Madgraph5 aMC@NLO for a range of charged fermion masses. The distribution of decay lengths of the charged fermion is speci ed by the kinematics of the event and by the charged fermion's lifetime. In each event, the charged fermions are decayed and assigned a track e ciency taken from gure 4 of [98]. Our calculation of track is thus a function of charged fermion mass and lifetime. 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Daniel Egana-Ugrinovic, Matthew Low, Joshua T. Ruderman. Charged fermions below 100 GeV, Journal of High Energy Physics, 2018, 12, DOI: 10.1007/JHEP05(2018)012