Update of global Two-Higgs-Doublet model fits

Journal of High Energy Physics, May 2018

Abstract We perform global fits of Two-Higgs-Doublet models with a softly broken ℤ2 symmetry to recent results from the LHC detectors CMS and ATLAS, that is signal strengths and direct search limits obtained at \( \sqrt{s}=8 \) TeV and \( \sqrt{s}=13 \) TeV. We combine all available ATLAS and CMS constraints with the other relevant theoretical and experimental bounds and present the latest limits on the model parameters. We obtain that deviations from the so-called alignment limit β − α = π/2 cannot be larger than 0.03 in type I and have to be smaller than 0.02 in the remaining three types. For the latter we also observe lower limits on the heavy Higgs masses in the global fit. The splittings between these masses cannot exceed 200 GeV in the types I and X and 130 GeV in the types II and Y. Finally, we find that the decay widths of the heavy Higgs particles cannot be larger than 7% of their masses if they are lighter than 1.5 TeV.

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Update of global Two-Higgs-Doublet model fits

Accepted: May Update of global Two-Higgs-Doublet model ts Debtosh Chowdhury 0 1 2 3 4 5 6 Otto Eberhardt 0 1 2 6 E-mail: 0 1 2 6 0 F-91405 Orsay Cedex , France 1 F-91128 Palaiseau Cedex , France 2 Piazzale Aldo Moro 2 , I-00185 Roma , Italy 3 Centre de Physique Theorique, Ecole Polytechnique 4 Laboratoire de Physique Theorique, Universite Paris-Sud 5 Istituto Nazionale di Fisica Nucleare , Sezione di Roma 6 Parque Cient co, C/Catedratico Jose Beltran , 2, E-46980 Paterna , Spain We perform global ts of Two-Higgs-Doublet models with a softly broken strengths and direct search limits obtained at p Beyond Standard Model; Higgs Physics - s = 8 TeV and p Z2 symmetry to recent results from the LHC detectors CMS and ATLAS, that is signal s = 13 TeV. We combine all available ATLAS and CMS constraints with the other relevant theoretical and experimental bounds and present the latest limits on the model parameters. We obtain that deviations from the so-called alignment limit = =2 cannot be larger than 0:03 in type I and have to be smaller than 0:02 in the remaining three types. For the latter we also observe lower limits on the heavy Higgs masses in the global t. The splittings between these masses cannot exceed 200 GeV in the types I and X and 130 GeV in the types II and nd that the decay widths of the heavy Higgs particles cannot be larger than 7% of their masses if they are lighter than 1:5 TeV. 1 Introduction 2 Model 3 Constraints and tting set-up 4 h signal strengths 5 Heavy Higgs searches 6 Combination of all constraints 7 Conclusions A.1 H and A decays to tt A.2 H and A decays to bb A.3 H and A decays to A.4 H and A decays to A.5 H and A decays to Z A.6 H decays to ZZ or W W A.7 H decays to hh A.8 A decays to hZ A.9 H+ decays A Detailed description of the direct Higgs searches B Prior dependence of the massive parameters 1 Introduction The discovery of a new scalar resonance with a mass around 125 GeV [1, 2] in the Run 1 phase of the Large Hadron Collider (LHC) has paved the way for new directions in highenergy particle physics. Analyzing the properties of this particle has suggested strong evidence that it is the Higgs boson of the Standard Model (SM), i.e. a scalar CP-even state which has SM-like couplings to the other particles. Currently the combined analysis based on the Run 1 (7 and 8 TeV) LHC data shows that its couplings with the vector bosons are found to be compatible with those expected from the SM within a 10% uncertainty, whereas the coupling to the third generation fermions (top, bottom quarks and the lepton) is compatible within an uncertainty of 15 20% [3]. Thus the current status of the Higgs properties still allows to explore new interpretations of the observation coming from new physics of di erent underlying structures. { 1 { 2HDM has two Higgs doublets in contrast to the single Higgs doublet in the SM. This extension of the Higgs sector leads to the existence of ve scalar bosons, namely a heavy and light CP-even Higgs boson, H and h, a CP-odd Higgs boson, A, and a pair of charged Higgs bosons, H . Whether the scalar boson observed in the Run 1 of LHC is a part of an extended Higgs sector is an outstanding question and is at the cynosure of attention of the current Run 2 (13 TeV) phase of the LHC. The questions we ask is: which parts of the 2HDM parameter space are favoured after possible nal states at the LHC: besides the fermionic nal states tt, bb, + , tb and + they include gauge bosons ( , Z , ZZ, W +W ) and Higgs particles (hh, hZ, HZ, AZ) as the decay products of a heavy resonance. So far, these searches for heavy resonances have remained elusive in the ATLAS and CMS data, and thus the measurements put model-independent 95% C.L. upper limits on the production cross section times branching ratios for di erent production processes and decay modes. In the present work, we assess the status of all four types of softly broken Z2 symmetric 2HDM with natural avour conservation when all the experimental constraints coming from the latest LHC data are taken into account. We confront these with the theoretical constraints on these models (positivity, stability and next-to-leading order unitarity). Furthermore, we perform global Bayesian ts to all relevant constraints on these models, which also include electroweak precision and avour observables, and highlight the complementarity between them. This paper is organized as follows: the 2HDM is de ned in section 2. In section 3 we list all relevant constraints and explain the tting set-up. The results are presented in the subsequent sections, rst taking into account only the Higgs signal strengths in section 4 and the direct searches in section 5, before combining them with the other constraints in section 6. We conclude in section 7. In appendix A we show the details of our implementation of the direct Higgs searches and in appendix B we explain how we treat the prior dependence of the massive parameters. 2 Model The Two-Higgs-Doublet model with a softly broken Z2 symmetry is characterized by the following scalar potential: V = m121 y1 1 + m222 y2 2 m122( y1 2 + y2 1) + 12 1( y1 1 )2 + 12 2( y2 2 ) 2 + 3( y1 1)( y2 2) + 4( y1 2)( y2 1) + 12 5 ( y1 2 )2 + ( y2 1 h )2i ; (2.1) { 2 { Yb;1 = Yl;1 = 0 Yb;2 = YbSM= sin Yl;2 = YlSM= sin Yb;2 = Yl;2 = 0 Yb;1 = YbSM= cos Yl;1 = YlSM= cos Yb;1 = Yl;2 = 0 Yb;2 = YbSM= sin Yl;1 = YlSM= cos Yb;2 = Yl;1 = 0 Yb;1 = YbSM= cos Yl;2 = YlSM= sin Type X (\lepton speci c") Type Y (\ ipped") 2 are the two Higgs doublets. While writing the potential we have assumed that the scalar potential is CP conserving. Instead of the eight potential parameters from eq. (2.1) we will use the physical parameters in the rest of this article. They consist of the vacuum expectation value v, the CP-even Higgs masses mh and mH , the CP-odd Higgs mass mA, the mass of the charged Higgs, mH+, the two diagonalization angles and the soft Z2 breaking parameter m212. Assuming the observed scalar of mass and , 1.6 TeV, that is beyond the region where the 125 GeV scalar was found. Moreover, we trade the angles and with and tan , since these combinations can be directly related to physical observables. All SM parameters were xed to their best- t values [34, 35]. Neglecting the rst two generations of quarks and the rst generation of the leptons, the Yukawa part of the 2HDM Lagrangian reads as follows: LY = YtQLi 2 2tR Yb;1QL 1bR Yb;2QL 2bR Yl;1LL 1lR Yl;2LL 2lR + h:c: Here, l stands for or . In the above Lagrangian, by convention the top quark only couples to 2; its Yukawa coupling is related to the SM value YtSM by Yt = YtSM= sin . With an unbroken Z2 symmetry in the Yukawa sector, there are only four possibilities through which the Higgs elds couple to the bottom quark and the leptons at tree-level, if we assume that the leptons couple to the same doublet. They are commonly called type I, type II, type X or \lepton speci c" and type Y or \ ipped". In table 1 we categorize the corresponding Yukawa coupling assignments. 3 Constraints and tting set-up Our statistical analysis of the 2HDM is a Bayesian t, in which the following priors are used for the previously de ned parameters: 1:1 0 ; log(tan ) 1:7 (equivalent to 0:08 tan 50); strength Value tth ZZ ggF ZZ VBF W W ggF W W VBF ggF VBF W W Wh Wh W W Zh Zh W W tth tth bb Wh bb Zh bb tth pp -0.25 -0.14 -0.26 -0.16 -0.37 1 0 0 1 1 1 0 0 1 -0.21 -0.25 -0.26 -0.16 -0.37 1 0 0 0 1 1 1 0 0 0 0 1 -0.47 1:4 1:4 -0.25 1:9 3:5 -0.47 0.1. The colours in the rst column indicate the decay category in gures 1 and 2. Extreme tan values outside the chosen prior are expected to be excluded due to the absence of strong 2HDM e ects in certain avour observables (see e.g. reference [36]); the aforementioned interval is a very conservative estimate. The only implicit assumption we make is that the 125 GeV scalar is the light CP-even Higgs particle of the 2HDM and that the other scalars should be heavier, yet in LHC reach. The focus of this article is on LHC Higgs observables, that is h signal strengths and searches for H, A and H+. Most details of the implementation of the corresponding observables can be found in our last article [31]. The modi cations to this will be explained in the following. { 4 { For the signal strengths, we de ne production, where \production" stands for the ggF, VBF, Vh, Zh, Wh, tth or pp production channels of the h, while \decay" denotes the subsequent h decay products , ZZ, W W , 1 For the last one, only upper limits are available; we assign to this signal strength a central value of 0 and adjust the Gaussian error such that the likelihood distribution has the 95% limit at the value provided by the experimental collaborations. All h couplings are calculated at leading order: while the fermionic decays and the bosonic decays to W W and ZZ are possible at tree-level, we apply one-loop expressions for the decays into nal states including massless bosons (that is gg, and Z ) [37]. A list of the available experimental signal strength values from LHC Run 1 and 2 can HJEP05(218)6 be found in the tables 2 (ATLAS and CMS combination for Run 1), 3 (ATLAS numbers for Run 2) and 4 (CMS measurements for Run 2). For the Run 2 data, we also list the corresponding integrated luminosities L. The numbers for the correlations in table 2 can be found in the mentioned document. For Run 2, ATLAS provides correlations only for the combination of the and ZZ decays; observing very similar numbers in the corresponding Run 1 data, we assume identical correlations for the and ZZ nal states. The correlation between tth tth was extracted from gure 17 in [42]. (We assume that the V V nal state therein is dominated by W W .) Also the CMS correlations in table 4 were reconstructed from the signal strength contours (or cross section times branching ratio contours) in the plane of VBF vs. ggF production. In section 4 we discuss the individual impact of the signal strengths on the 2HDM parameters, ordered by the decay products. Concerning the direct searches for the heavy CP-even, the CP-odd and the charged Higgs, we have updated the number of used LHC analyses from 16 in [31] to 50 Run 1 and 2 measurements in the present article. We calculate the product of the production cross section [105{114] and the branching ratio [115, 116] of a speci c decay, compare it with the experimental bounds, we assign Gaussian likelihoods with a central value of 0 to the ratio of the theoretical value and the observed upper limit of method agrees with the treatment of the upper limit of the Z signal strength mentioned above and coincides with our approach in [31] under the assumption that the observed upper limit does not deviate from the expected one. With no evidence for such a deviation in any of the searches, this approximation seems to be justi ed. The experimental input from Run 1 and 2 can be found in tables 5, 6 and 7. These analyses comprise a large variety of searches for heavy resonances decaying into fermionic or bosonic states: bb, and Z limits can be applied to both, the CP-even and CP-odd Higgs bosons; signatures with a pair of massive bosons or AZ in the nal state can exclusively stem from H decays at tree-level in the 2HDM, while a CP-odd resonance decaying to one h or H and one Z is interpreted as A; nally, the searches for charged Higgs particles were performed looking B. In order to B . This for the instance ( nal states tb or . If the branching ratio into a speci c nal state | like for )(bb) | is included in the upper limit, we list it in the table. If the nal state is not included in the B limits, but its information is needed to distinguish it from other searches, we write it in square brackets. The secondary decay products of one particle are 1In order to improve readability, we drop charge or conjugation labels when there is no ambiguity. { 5 { strength ggF VBF Vh tth ZZ ggF ZZ VBF ZZ Vh ZZ tth W W VBF W W Wh W W tth tth bb Vh bb tth pp Z pp -0.29 -0.22 -0.29 -0.22 1 0 1 0 1 -0.31 amount of data. For instance, the latest CMS results of the searches for an H decaying via ZZ into two leptons and two neutrinos are available only for mH > 600 GeV. Lighter mH scenarios will be constrained using an older publication based on an integrated luminosity of 2:3 fb 1 . Also for the upper limits on H ! hh ! (bb)(bb) by CMS and on H+ ! tb by ATLAS we apply di erent searches depending on the masses. For gg ! X ! , CMS combined their 8 and 13 TeV data; the limits are given for the 13 TeV production cross section. A detailed discussion of how the di erent searches constrain the 2HDM can be found in section 5, where we show the results ordered by the decay products. Apart from the discussed tree-level Higgs observables the 2HDM scalars can also contribute to the quantum corrections of other observables, the most important ones being the electroweak precision observables, the b ! s branching ratio and the mass di erence { 6 { strength ggF VBF Vh tth ZZ ggF ZZ VBF ZZ Vh,h ZZ Vh,l ZZ tth W W ggF pp ggF VBF tth bb VBF bb Vh bb tth pp W W VBF+Vh 1:11 0:5 2:3 2:2 1:20 0:06 0 0 0 1:02 0:89 1:17 0:84 1:11 0:72 3:7 1:2 0:19 0:7 0:19 0:6 1:1 0:9 0:22 1:03 2:85 2:78 1:19 0:27 0:67 0:44 0:89 0:35 0:58 2:5 0:4 0:81 1:0 1 -0.32 1 -0.43 1 -0.24 -0.32 1 -0.43 1 -0.24 1 in the Bs meson system. While the implementation into HEPfit was already explained in [31], we updated the experimental values [35, 117, 118]. Also for the treatment of theoretical constraints we refer to [31], with two exceptions: we do not apply any constraints arising from the renormalization group evolution and de ne our model at the electroweak scale. And for the next-to-leading order unitarity bounds we chose the most conservative approach that appeared reasonable to us, namely requiring that the real and imaginary parts of the S-matrix eigenvalues should be between 0:5 and 0:5 and between 0 and 1, respectively. Moreover we impose perturbativity by discarding scenarios for which the one-loop contribution to these eigenvalues exceeds the tree-level term in magnitude. { 7 { Channel Experiment 2 2b [100;900] [90;1000] [90;1000] [90;1000] [90;1000] [65;600] [200;1600] [200;1200] [140;1000] [140;1000] [300;1500] [300;1500] [145;1000] [270;1100] [260;1100] [260;1000] [300;1000] [220;1000] [220;1000] [225;600] [220;350] [130;1000] [130;1000] [180;1000] [180;600] [200;600] [180;600] rst column, we assign a label and colour to each search, which correspond to the ones in gures 6 to 12. Details of production and decay modes are given in the second column. The third column contains the corresponding reference. The mass ranges, for which the corresponding limits on are given, and the integrated luminosity the searches are based on, can be found in the fourth and fth column. The CMS Run 1 limits of the di-photon channel are included in their Run 2 bounds. V V refers to either W W or ZZ. C8V V provides signal strength limits. A8hh contains information B about the decays of hh to 4b, 2 2b, 2 2b and 2 2W . { 8 { A13 C13 2HDM. For an explanation, see the description below table 5. In the last column, we additionally highlight an underlying integrated luminosity of around 3, 13 or 36 fb 1 in red, yellow or green, respectively. { 9 { HJEP05(218)6 Channel Experiment Mass range [TeV] 2HDM. For an explanation, see the description below table 5. As numerical set-up we use the open-source package HEPfit [119], interfaced with the HJEP05(218)6 release candidate of the Bayesian Analysis Toolkit (BAT) [120]. The former calculates all mentioned 2HDM observables and feeds them into the parallelized BAT, which applies the Bayesian t with Markov chain Monte Carlo simulations. 4 h signal strengths In this section we show the impact of the h signal strengths on the 2HDM parameters. The ts were done with the most up-to-date experimental inputs; for a comparison with the status before EPS-HEP 2017, see [ 121 ]. The di erences in the Z2 symmetry assignment to the fermions result in a type dependent treatment of their couplings to the light Higgs boson. The signal strength of the process with a given initial state i producing an h which decays to the nal state f can be written as if = ri rf f0 P rf0 BSM(h ! f 0) ; (4.1) where rx is the ratio of the 2HDM and the SM partial width of an h decaying into x and BSM(h ! x) is the corresponding SM branching ratio. From this equation one can see that every signal strength depends on the 2HDM h couplings of all decay products. In gure 1 we show the individual impact of the signal strengths with a speci c nal state on the plane as well as their combination in all four types of Z2 symmetry. We have tried to adopt the colouring scheme from gure 14 of the Run 1 combination [3]. All contours delimit the regions allowed with a probability of 95.4%. The upper limit on pZp is included in the combination, but not shown separately as its e ect In type I all fermions have the same relative coupling to h: rtt = rbb = r = r )]2. This can only deviate signi cantly from 1 if tan is not close to the alignment limit =2. In these regions, the di= is photon signal strengths are the most constraining ones, see the upper left panel of gure 1. For larger tan values, the ZZ and W W signal strengths become the most important constraints. In the combined t to all signal strengths, the largest possible deviation of from =2 is 0:26 at 95.4% if we marginalize over all other parameters. The upper right panel of gure 1 shows t results with the same inputs for type II. Here, the relative down-type fermion and lepton couplings to h are di erent from the vs. tan plane in all four 2HDM types. We show the 95.4% posterior probability contours for individual ts to data from h decays to , bb, , , W W and ZZ in red, cyan, purple, orange, blue and green, respectively. The resulting 95.4% regions of the combined ts to all signal strengths are the black-bordered grey areas. top coupling, and thus the fermionic signal strengths yield more powerful constraints. But also the signal strengths with a bosonic nal state become stronger because of the modi cations of the loop coupling rgg and the fermionic couplings in the denominator of eq. (4.1). Especially the W W and ZZ signal strengths constrain to be very close to =2; the largest deviation from the alignment limit in the one-dimensional t to all signal strengths is 0:055 at 95.4%. The so-called \wrong-sign" solution for the fermionic couplings, which is represented by the lower \branches" of the individual W W , ZZ, bb and signal strength ts for tan > 3 and < 1:5, can (cannot) be excluded in the combined t to all signal strengths with a probability of 95:4% (99:7%). These scenarios have also been shown to be incompatible with the assumption that the 2HDM of type II is stable under a renormalization group evolution up to O(1) TeV [31, 122]. In type X, the h couplings of the down-type quarks agree with the ones of the top quark, but the leptonic couplings are like in type II. Consequently, the contour of the bb decays in the lower left panel of gure 1 has a similar shape as the one of type I, while the and decays behave more like in type II for large tan for < =2. For tan the latter two are the dominant signal strengths. For very large tan , the wrong-sign solution of the fermion couplings is allowed at 95:4%. However, no larger deviations of from =2 than 0:069 are allowed at the 95:4% level if we combine all signal strength information and marginalize over all other parameters. Finally, the type Y t can be found in the lower right panel of gure 1. Like in type II, has to be very close to the alignment limit with the bosonic signal strengths being the strongest constraints. But like in type X, the wrong-sign coupling of the fermions cannot be completely excluded at 95:4% in the t combining all signal strengths, although it is only possible for very large tan . In this type's combined t and marginalizing over the other As compared to the status before EPS-HEP 2017 [121], the W W , and bb signal strengths have become more constraining; the latter changed drastically due to additionally released data. In type II, a small spot of the \wrong sign" branch around tan = 3 and = 1 was allowed at the 95:4% before summer 2017 and has disappeared now. The two angles and de ne all tree-level couplings of fermions and bosons to the light Higgs h, but the loop couplings to gluons and photons are more complicated. In order to analyse their allowed ranges, we show the rgg vs. r plane in gure 2. Apart from the individual ts to the di erent nal states and their combination like in gure 1, we also add the contours from a t to only Run 1 and only Run 2 data, respectively. The relative one-loop couplings read like this: 8 rgg = <rtt = rbb in type I and X, h : rtt gtgF + rbb gbgF + prttrbb( ggF t ggF i gbgF ) = ggF in type II and Y, r = prV V F1( W ) + P f prff Ncf ef2 F1=2( f ) + 23mm2H2h+ chH+H F0( H+ ) 2 F1( W ) + P f Ncf ef2 F1h=2( f ) 2 Here, the SM gluon-fusion production cross section is ggF whereas its pure top and bottom loop contribution are denoted as gtgF and gbgF , respectively. Their values were calculated with HIGLU [106]. For the di-photon coupling, we follow the notation of [37], in which the loop functions F1, F1=2 and F0 are de ned in eq. (2.17) and i = 4mi2=m2h. Ncf and ef denote the colour factor and the electric charge of the fermion f , respectively. The triple Higgs coupling chH+H can be found after eq. (5) of [18]. In all types, the combined t to all signal strengths is dominated by the bosonic decays. While the mainly delimit r , rgg is constrained also by the measurements. The maximal deviation of r (rgg) from its SM value is roughly 30% (20%). The wrong-sign solution for the fermion couplings can be seen in type II, X and Y: the regions for rgg > 1 in gure 2 contain the lower branches of gure 1. For type II, it has been shown that the wrong-sign couplings feature increased rgg and reduced r [12]. In the lower right panel of gure 2, this \second solution" is visible between 1:1 and 1:2 for rgg as spikes in the W W , ZZ and contours for large r as well as in the combined in the plane of the relative one-loop couplings of the h to gluons and photons. While the colours of the shaded contours with solid borders correspond to the ones in gure 1, the Run 1 and Run 2 combinations are bounded by the dark green and brown dashed contours, respectively. signal strength t in both r directions. Comparing all Run 1 signal strengths with all Run 2 signal strengths, one can see that generally the Run 2 data is more constraining in all types. However, the Run 1 signal strengths prefer a smaller rgg and thus determine the upper limit of the gluon coupling ratio in the combined t to all signal strengths. This can be seen in the types II and Y. The run time for ts with 120 million iterations was 230 80 CPU hours for the di-photon nal state and 70 20 CPU hours for the other single channels. 5 Heavy Higgs searches The detailed analysis of the individual direct searches can be found in A. Here we only want to discuss the impact of the relevant combined decay categories. The narrow width approximation will be applied throughout this section; we will comment on its validity at the end of the next section. In gure 3 we show the available parameter space for 2HDM masses and angles from the t where the heavy Higgs searches are taken into account. The region inside the various coloured patches are disfavoured by the corresponding search category denoted in the legend. The central areas inside the solid grey line mark the 95.4% allowed regions when all heavy Higgs searches are considered in the t, including also CAZ and CHZ . In the panels 8 8 in the rst row the black dashed lines mark the limit from the t to theory constraints only. The combination of all H/A/H+ searches is represented by the orange/blue/green dashed contours. The channels described in the previous sub-sections which are not constraining or very weakly constraining in this mass vs. angles plane are not shown in the gure. From the rst row of gure 3 we can see that the region around = =2 remains unconstrained in all four types of 2HDMs when all the heavy Higgs searches are taken in account. From moderate to high masses, the di-Higgs channels dominate the excluded regions in all four types whereas H ! , H ! and H ! V V are the most important constraints below the hh threshold. In type I and X, the nal exclusion region is mainly dominated by the heavy Higgs to two light Higgs channel, while in type II and Y this is only true if > =2; for < =2 the nal constraint is weak except for 250 GeV. Although the di-photon searches alone disfavour mH . 600 GeV for regions ' =2 this region is allowed when considering all the heavy Higgs searches in the t. The H ! V V decays only are susceptible to the tan . 1 region and for mH & 800 GeV in all four types; this again is an e ect of ne-tuning. In the displayed mH vs. tan ranges, all the H searches become ine ective for mH & 1000 GeV in type II and Y, whereas in type I and X the tan . 1 regions remain inaccessible even if the heavy Higgs mass is as large as 1500 GeV. This is an e ect of the combination of all heavy Higgs searches, in which scenarios with small tan are sampled less by the tter. This feature is not worrisome, because these regions are also suppressed by the avour observabels as we will show in the next section. In the pseudoscalar mass vs. tan planes we see that the di-photon channel constrains low tan and mA up to 600 GeV for all four types. The A ! hZ channel can exclude tan values up to 10 and mA almost as heavy as 1000 GeV in all four types. The exclusion also applies for the large tan regions in the types II and Y. The next most important channel for the pseudoscalar searches in type II is the A ! channel, which e ciently excludes high tan regions for mA as large as 1000 GeV. In type X this channel is susceptible to tan . 20 and mA . 400 GeV. The exclusion from this channel is weaker for type I and Y. The contour for all pseudoscalar searches is mainly dominated by the hZ channel in type I and Y, and a combination of hZ and in type II and X. Combining all the pseudoscalar Higgs searches the present data constrain certain regions where mA . 1000 GeV. For type X, the mA < 400 GeV region remains available only if tan & 10. In the same mass regions a very narrow range of intermediate tan remains accessible for type II when all constrains are taken into account. The bound on large pseudoscalar masses is similar to the heavy Higgs case when all constraints are taken into account. The main channel which constrains the charged Higgs mass is H+ ! tb. The exclusion region of this channel is shown in red in the last row of gure 3. From the gures we see that the present searches for the charged Higgs mass can only constrain the regions with searches with a probability of 95.4% by the central area inside the grey solid line. We compare them with the areas excluded by searches in various nal states represented by the coloured patches. The areas inside the coloured dashed lines correspond to the exclusion at 95.4% when all H searches (orange), all A searches (dark blue) and all H+ searches (dark green) are considered. In the rst row the limits from theory constraints are shown by black dashed lines. tan . 1 and mH+ . 1000 GeV in all four types. The inclusion of all the searches in the t yields stronger constraints in the mH+ vs. tan plane than the t to all charged Higgs searches only. In type II and Y this is due to the H ! hh ! 4b searches, which are particularly sensitive to large tan and disfavour certain regions featuring tan type I and X it is more di cult to pinpoint one particular channel for the seeming exclusion of tan values up to 2 for charged Higgs masses above 1 TeV, but in the next section we see that these bounds can be relaxed once we take into account also other constraints. 6 Combination of all constraints After discussing the individual e ects of the h signal strengths and the searches for H, A and H+ on the 2HDM, we want to confront these constraints with the other bounds on the parameters. In gure 4 we copy the information about all heavy Higgs searches gure 3 in the mass vs. angle planes, and add the bounds from signal strengths and theoretical constraints to the mH vs. planes and the impact of the avour observables to the planes with tan . Finally, the global t to all constraints is represented by the grey regions. The signal strength bounds do not depend on the masses of the heavy Higgs particles; their limits on di er for each type, see section 4. The theory conditions force the 2HDM's into the alignment limit for mH > 600 GeV, decoupling the heavy Higgs particle from physics around the electroweak scale. The type dependence of this e ect is negligible as it only enters via sub-leading Yukawa terms in the beta function parts of the NLO unitarity conditions. Besides the obvious consequences for certain constellations of mH and , the combination of the signal strengths with the theory constraints also disfavours large values of tan . This is because extreme values for the latter result in a destabilization of the unitarity conditions [31]. Speci c combinations of the 2HDM angles can still ful l the theoretical constraints, but these solutions are highly ne-tuned and thus have a low posterior probability. The avour constraints have been discussed many times in the literature; the summary is that in all types the Bs mass di erence sets lower limits on tan (at least for masses within the reach of the LHC), while the branching ratio of b ! s processes enforces mH+ & 580 GeV at 95% C.L. in type II and Y [124]. In combination with theory and electroweak precision bounds, these limits on the charged Higgs mass can be translated to lower limits on the neutral masses. (The individual impact of ST U will be explained below as it is not visible in these two-dimensional projections of the parameter space.) The combination of all constraints is more intricate than the naive superposition of all individual bounds. First of all, we should mention that it also depends on the prior we choose for the masses: while the direct experimental observables depend on the masses of the heavy Higgs bosons, the theoretical bounds and the loop-induced e ects are only sensitive to the mass squares. Since we want to combine both, we need to decide whether we want to use a at prior for the masses or the mass squares. A detailed discussion can be found in appendix B. The contours we show here are a superposition of a t with at mass priors and a t with at mass square priors in order to be as conservative as possible. In the mH vs. planes of type I and X, the combination of signal strengths and theory only leave a very small strip around the alignment limit of = =2. Heavy Higgs searches additionally exclude mH < 380 GeV in type X. The reason for this are not only with a probability of 95.4% in light grey and compare them with the areas excluded by various sets of bounds: the 95.4% contours of heavy Higgs searches (dark grey), avour observables (yellow) and h signal strengths (pink) as well as the 99.7% limits from theory constraints (purple). the H ! searches as observed in gure 3, as they are similar to the bounds in type I, but mainly it is an interplay of the strong bounds of the A searches for low tan and the above-mentioned exclusion of large tan due to signal strengths and theory, which together disallow mA < 400 GeV. This bound translates to a limit on mH using the unitarity and electroweak precision constraints, since these bounds delimit the mass splittings, see below. Also in the type II and Y planes we see a lower limit of mH > 550 GeV, which in this case derives from the lower bound on mH+ from the b ! s measurements and the fact that the mass di erence mH mH+ cannot be too large. The absolute maximal deviation of from =2 is 0.03 in type I and 0.02 in the types II, X and Y. (This corresponds to 1 sin( ) < 5 10 4 and < 2 10 4, respectively.) In the mH vs. tan planes one can see that the ne-tuning for large tan scenarios disfavours these regions and pushes the allowed contours towards smaller values of tan . Only in type I and for mH < 350 GeV, the heavy Higgs searches have a visible impact on this plane, excluding tan . 2:5. More or less the same holds for mA vs. tan , where in type I tan < 3 is excluded by direct A searches if mA < 350 GeV. We already mentioned above that in type X, the interplay between ne-tuning and A searches sets a lower limit of 400 GeV on mA. Having a look at the mH+ vs. tan planes, one can see the lower bounds on the charged Higgs mass in type II and Y from b ! s , which we quantify to be 600 GeV in our t. Also here, we observe that large tan values are disfavoured and the posterior regions are shifted towards small tan . The t only to electroweak precision data does not exclude any region in the twodimensional mass vs. angle projections in gure 4. What it does constrain are the mass di erences between H, A and H+. That is why in gure 5 we show the di erence between the pseudoscalar and charged Higgs mass, once depending on the H mass (left column) and once against the mH mH+ di erence. In the mA mH+ vs. mH planes the dominant constraints come from the theory bounds, at least in the decoupling limit mH > 600 GeV. The ST U pseudo-observables are stronger if mH < 600 GeV and mH+ > mA. In type I, they yield a lower bound on mA mH+ in the global t for mH < 250. If we look at the mA mH+ planes, we observe that here the oblique parameters are the strongest constraint on mA mH+ if the charged Higgs mass is larger than mH . Combining all constraints and marginalizing over all other parameters, we obtain the following ranges for the mass di erences allowed with a probability of 95%: mH mA [GeV] mH mH+ [GeV] mA mH+ [GeV] We can thus exclude the decays H ! H+H , H ! AA, H ! H+W as well as H ! AZ in all four types with a probability of 95%. For all heavy Higgs search limits, we implicitly assumed the narrow width approximation. In a simultaneous t to all constraints except for these direct search limits we nd that with a probability of 95% the decay widths of H, A and H+ never exceed 5:5% of the mass of the particle in the types II and Y. For masses below 1 TeV the maximal decay widths are less than 3:5% in these two types. In type I and X and for yield =m < 3:5% (< 5%) if m < 1 TeV (< 1:5 TeV). Only the ratio = H; H+ the ts A=mA can reach 7% for mA 550 GeV, but in the decoupling limit mA > 600 GeV similar bounds apply as for H and H+. We would like to stress here that all these 95% limits are maximally Figure 5. In the mA mH+ vs. mH (left panels) and mA mH+ (right panels) planes we show the allowed regions by various sets of constraints: the heavy Higgs searches, the oblique parameters and the avour observables determine the 95.4% allowed contours in dark grey, light blue and yellow, respectively. For the theoretical constraints, the 99.7% regions are given by the purple shaded areas. We superimpose the 95.4% probability combination from the global t to all observables in light grey. allowed values and that in a typical 2HDM scenario the widths are signi cantly smaller. Therefore we conclude that the narrow width approximation is a reasonable choice for 2HDM scenarios. { 19 { Finally, addressing the last variable of our chosen parametrization, we also observe limits on the soft Z2 breaking parameter m212. The upper limits strongly depend on the maximally allowed physical Higgs masses and are around (1 TeV)2 in all types. Due to the lower mass limits on the physical Higgs particles in the types II, X and Y, we also observe that m212 is limited from below, the respective minimal values being (280 GeV)2, (170 GeV)2 and (240 GeV)2. Only in type I an unbroken Z2 symmetry is still compatible with all constraints. The run time for the global ts to all constraints with 240 million iterations was 130 CPU hours. Conclusions HJEP05(218)6 550 7 j In all four 2HDM types with a softly broken Z2 symmetry we have presented global ts to the most recent data. Focussing on the latest measurements from LHC, we have showed explicitly how the individual signal strengths a ect the leading order h couplings at tree-level and at oneloop level. Combining all information about the signal strengths, we nd that the quantity =2j cannot exceed 0.26, 0.055, 0.069 and 0.056 in the types I, II, X and Y. The one-loop couplings of the h to gluons and photons cannot di er by more than 20% and 30%, respectively, relative to their SM values. In order to systematically discuss the searches for H, A and H+, we have categorized them according to their decay products and have compared the exclusion strength of the single available ATLAS and CMS analyses on the production cross section times branching ratio, depending on the masses. We have then combined all decay categories and have showed their impact on the 2HDM masses and mixing angles. For mH below 1 TeV we observe strong bounds on \extreme" values for the angles, that is if is very di erent from the alignment limit =2 or if tan is smaller than 1 or larger than 10. The exact limits depend on the model type and mH . Also the LHC searches for pseudoscalars severely constrain the 2HDM parameters: for mA < 1 TeV, the lower limits on tan reach values of around 10 in the types I and X. In the types II and Y, these limits are weaker, but there are also mass dependent upper limits. The bounds from charged Higgs searches are less constraining in comparison; nevertheless, they also start to be stronger than the indirect constraints in the regions with low mH+ and low tan . Finally, we have confronted the LHC h signal strengths and heavy Higgs searches with all other relevant indirect constraints from theory and experiment. In detail, we have showed how stability and unitarity constraints and B physics observables set mass dependent limits on the 2HDM angles and on the di erences between the heavy Higgs masses, while electroweak precision data only a ect the latter. We have compared all di erent sets of constraints and have showed the results in the mass vs. angle planes as well as in the mA mH+ vs. mH ( mH+) planes for all four types of Z2 symmetric 2HDM's together with the simultaneous t to all constraints. In this global t we nd the following 95% probability limits on the 2HDM parameters marginalizing over all other parameters: j II and Y, mH > 700 GeV, mA > 750 GeV, mH+ > 740 GeV and m212 > (240 GeV)2, =2j cannot be larger than 0:03 in type I and 0:02 in the other types. In type while we observe lower mass limits of mH > 450 GeV, mA > 500 GeV, mH+ > 460 GeV and m212 > (170 GeV)2 for type X. For the latter, it is the rst time that a statistically signi cant lower limit on the massive parameters has been observed in a global t for the analyzed mass ranges. Also, if we discard particularly ne-tuned scenarios, only the following ranges for tan are allowed for masses below 1:6 TeV: [0.93; 10.5] in type I, [0.93; are no strict bounds and have to be taken with a grain of salt. Moreover, we can put type dependent upper limits of order of 100 GeV on the di erences between mH , mA and mH+, and thus kinematically exclude all decays of H or A into another heavy Higgs particle. As a consequence, the decay widths of H and H+ cannot exceed 5:5% of their mass in all types, at least as long as we consider masses below 1:5 TeV. While in the types II and Y we see a similar limit for the A decay width, it can amount to up to 7% of mA in the types I and X. Acknowledgments We thank Enrico Franco, Ayan Paul, Maurizio Pierini and Luca Silvestrini for useful discussions. The ts were run on the Roma Tre Cluster. We are grateful for the availability of these resources and especially want to thank Antonio Budano for the support. We also thank Jose Miguel No and Ken Mimasu for giving us a hand with the implementation of the H ! AZ and A ! HZ search limits. This work was supported by the European Research Council under the European Union's Seventh Framework Programme (FP/20072013) / ERC Grant Agreement n. 279972, by the Indo-French Center for Promotion of Advanced Research/CEFIPRA (Project no. 5404-2) and by the Spanish Government and ERDF funds from the European Commission (Grants No. FPA2014-53631-C2-1-P and SEV-2014-0398). A Detailed description of the direct Higgs searches In the following, we will scrutinize the impact of the searches for heavy Higgs particles in all four types of a 2HDM with a softly broken Z2 symmetry, ordered by their decay products. First we will address the fermionic decays to tt, bb and and the loop induced decays with and Z in the nal state. The searches for signals in these channels apply to both, H and A bosons. After that, we will turn towards the H speci c decays into two massive vector bosons or two h bosons and the A speci c channel with an h and a Z nal state. Finally, the decays of a charged Higgs to and tb will be discussed. The limits CAZ and CHZ on the decays H ! AZ and A ! HZ were only used in the 8 8 combination of all heavy searches; their impact on the mA vs. mH plane is found to be weak if we marginalize over all other parameters. The grey shaded regions in the plots in this section depict the prediction of the 13 TeV B for the corresponding channel without applying any theoretical or experimental constraints on the model; in other words they correspond to our full priors. The black dashed lines delimit the full available posterior ranges of the B for the corresponding channel HJEP05(218)6 when only the theoretical constraints de ned in the section 3 have been used in the t. The areas within the various coloured solid lines depict the 95:4% probability posterior ranges of B after imposing the experimental constraints from the LHC for a particular measurement. The legend of each plot refers to the channels described in tables 5, 6 and 7. The horizontal coloured lines on the top of the panels mark the mass ranges analyzed at the LHC for each of the searches denoted in the legend. In the following plots the posterior prediction of B after considering a particular direct search replicates the prior behaviour unless it deviates from rest of the posteriors for the same channel. In other words, the direct searches only have a visible impact on the 2HDM parameters if their contour is lower than the other coloured contours. Otherwise, they represent the 95.4% probability contours of the prior distributions. Also the lower lines of the searches mostly show the priors and do not pose any signi cant lower limit on B . Since we want to combine all information about a speci c heavy Higgs decay into one gure, we have to \project" the actual measurement onto a B value which we consider searches, the contours of the A13 as common denominator of the decay. For instance, the searches H ! hh comprise a large spectrum of nal state signatures (like 4b or W W ). So we decided to predict the possible values of (pp ! H) B(H ! hh) from the information of the search limits involving further h decays. In other words, we divide the actually tted quantity by the branching ratios of the h decays if necessary, in order to obtain the bare (pp ! H) B(H ! hh). This is why the same model independent search limit can have varying e ects and the exclusion curves are not necessarily the same for the di erent 2HDM types. In our example of the H ! hh 2 2W channel will be the same in all four types, because the information about the h decays was removed by the ATLAS collaboration, who provide (pp ! H) B(H ! hh) limits. On the other hand, the impact of C123b2 will look di erent in all types, because the h ! bb and h ! decays are included in the CMS limits. The ts to the single experiments in this section took 60 7 CPU hours with 120 million iterations. A.1 H and A decays to tt For H and A masses heavier than two top quarks the decay to tt is the dominant in the 2HDM, at least for moderate values of tan . Unfortunately, a possible signal strongly interferes with the tree-level background process gg ! tt. The only available experimental limits of an analysis which takes into account this interference is [123] for the 2HDM of type II. Its limits, however, constrain only a small region for tan 1 and mH=A 500 GeV, which has been excluded by indirect constraints. Therefore, we do not take into account this direct measurement. A.2 H and A decays to bb The direct search for H ! bb decay does not put any constraint on B in all four 2HDM types considered in the analysis. In gure 6 one can see that theoretical constraints provide a suppression of B by roughly an order of magnitude compared to the t without any constraint in type I and X. Similar to the previous case, pseudoscalar decaying to bb searches do not provide any stronger constraint on B than the t with theory constraint alone in all four types. For this search, theory constraints alone restrict B by at least one order in magnitude with respect to the t without any constraints in the parameter space analyzed for all the types. This suppression is more dominant in type II and Y compared to the other two cases. In type II and Y, in the regime mA . 600 GeV the A ! bb search from Run 1 suppresses B compared to the t without any constraints but it remains sub-dominant or at most of similar strength to the t with theory constraint alone. A.3 H and A decays to In the upper panel of gure 7 we show that the H ! searches suppress the B limit by at least one order of magnitude compared to the t with theory constraints alone in the regime where the heavy Higgs mass is below 250 GeV. In this regime the strongest constraint comes from Run 1 data and the suppression of types I and Y. Theory constraints alone restrict B is more pronounced in the B by roughly an order of magnitude compared to the t without any constraints for type I and Y, whereas in type II and X, theory constraints raise the lower limit of B for mH > 500 GeV. This can be understood as a sensitivity of the t to ne-tuned scenarios with extreme tan values, which are disfavoured in a t to the theoretical bounds. From the t without any constraints in the lower panel of gure 7 we see that the predicted ranges of B for the pseudoscalar decaying to are quite narrow for type II and X compared to the other two 2HDM types. The theory constraints yield a suppression by at least one order of magnitude for B compared to the t without any constraints 10 5 . in the types I and Y whereas for type II and X the theory constraints push up the lower limit on B by one order of magnitude compared to the t without any constraints for mA > 350 GeV. The direct search limits for A ! suppress B by roughly one to two orders of magnitude compared to the t with theory constraints alone for all the types except for type Y as long as mA . 300 GeV. In type Y, the experimental upper limits on B are stronger than the theoretical ones for pseudoscalar masses between 200 and 400 GeV, in type II even up to 1 TeV. Scenarios with very light A and B values between B . 10 pb seem also to be excluded at 95% by the prior. However, since we have no experimental data on this region, this prior dependence is not an issue here. A.4 H and A decays to The theory constraints on H=A ! suppress B by one to three orders of magnitude compared to the t without any constraints in all four 2HDM types, see gure 8. Direct searches for a heavy CP-even Higgs decaying to two photons constrain order of magnitude compared the t with theory constraints for mH . 250 GeV in all types. The searches in the di-photon decay channel of a pseudoscalar Higgs yield a suppression of B by one to three orders of magnitude compared to the t with theory constraints for mA . 600 GeV for all four types considered. In the types II and Y, we observe again that certain intermediate B regions for low mA are disfavoured by the prior. B by roughly one four 2HDM types (top: H, bottom: A). For details, see text. B vs. mH=A planes for the four 2HDM types (top: H, bottom: A). For details, see text. in the B vs. mH=A planes for the four 2HDM types (top: H, bottom: A). For details, see text. in the B vs. mH=A planes for the H and A decays to Z We see from the top panel in gure 9 that for H ! Z , theory constraints suppress by one to four orders of magnitude compared to the t without any constraints for all types. In all four types, direct search for this channel does not provide any constraint on B except for a very small window below mH ' 250 GeV, but it remains sub-dominant compared to the t with theory bounds. Similar to the heavy CP-even Higgs case, theory constraints yield a suppression of by one to two orders of magnitude for the decay A ! Z compared to the t without any constraints in all four types. Direct searches for this channel provide a suppression of by an order of magnitude compared to the t with theory constraints in the mass window B B B 250 . mA . 350 GeV in all four types. Again, some parts of the masses are disfavoured by the prior in the types II and Y. B region for light A A.6 H decays to ZZ or W W The heavy Higgs decays to massive gauge bosons can be divided into searches for ZZ and W W , but the relative coupling of H to two vector bosons V V = ZZ; W W is universal and type independent. However, the production of the H di ers between the types. We show the H ! ZZ channels in the upper panel of gure 10 and the searches for H ! W W as well as the combined searches for H ! V V in its lower panel. The B are constrained by the theoretical bounds in the decoupling limit, where mH > 600 GeV. The direct LHC searches for this channel yield a strong suppression of B by one to three orders of magnitude compared to the t with theory constraint in the mass regime 150 . mH . 800 GeV (150 . mH . 700) for the ZZ (W W ) channel. For the ZZ searches the mH . 250 GeV region is constrained by Run 1 data whereas Run 2 data determine the dominant limits for the rest of the region. For the W W searches, Run 1 data dictate the limit until mH ' 600 GeV and the high mass range is dominated by Run 2 data. Additionally the CV V search for H ! V V severely constrains 8 B in the 200 . mH . 250 GeV region for type II and Y. A.7 H decays to hh In the upper panel of gure 11 we show that for the H decaying to two h bosons, theory constraints already yield a strong suppression of constraints in all four types. Direct searches suppress B compared to the t without any B by at most one order of magnitude compared to the t with the theory constraints in the mass range 200 . mH . 600 (500) GeV in type I and X (type II and Y). The main constraints stem from Run 1 data and the Run 2 searches for hh resonances decaying to two photons and two bottom quarks. Although di erent searches at Run 1 and Run 2 continue to constrain the channel up to mH ' 1200 GeV, they remain sub-dominant to the limit from the t to the B for this theory constraints. A.8 A decays to hZ The searches for A decaying into hZ are shown in the of gure 11; more precisely, they are projected onto the B vs. mA planes in the lower panel B of the decay to (bb)Z. As B vs. mH=A planes for the (bottom) in the B vs. mH planes for the four 2HDM types. For details, see text. B vs. mH=A planes for the four 2HDM types. For details, see text. compared to the t without any constraints, theory constraints e ectively are important in the decoupling limit in all types as well as for mA . 300 GeV in type I and X. Direct searches for this channel yield a strong suppression (one to three orders of magnitude) of B compared to the t with theory constraints for all four types as long as mA . 800 GeV. In all types, the strongest bounds come from searches in the A ! hZ ! (bb)Z channel; in type X we additionally observe that the A ! hZ ! ( )Z limits yield the most important constraints for mA between 200 GeV and 300 GeV. A.9 H+ decays At the present, charged Higgs decaying into does not provide any constraint on the 2HDM's under consideration, see the upper panel of gure 12. The theory constraints yield a suppression of B by roughly one order of magnitude as compared to the t without any constraint for all types but type X as well as for all types if the charged Higgs decays into tb (lower panel of gure 12). In the latter case, the direct searches from Run 1 B in (Run 2) provide even stronger limits on only small di erences between the 2HDM types. B between 180 GeV and 600 GeV (1 TeV), with B Prior dependence of the massive parameters In this appendix we discuss the prior dependence of our analysis when all the constraints have been taken into consideration. In gure 13 we compare the allowed parameter space in the mass versus angles planes and the mass di erence versus mass (di erence) planes from the t with at mass priors (blue solid and dashed curves) with the t with at mass square priors (red solid and dashed curves). At a rst glance one can see that the t with at mass square priors prefers high mass regions and raises the lower limit on the masses by O(100) GeV compared to the t with at mass priors. It is well known that Bayesian statistics do not provide a unique rule to determine the prior distribution and in general the posterior distribution is a prior dependent quantity. A thumb rule would be to choose a at prior for the parameter on which the observables depend linearly. For example, if an observable quadratically depends on a particle mass, one would choose a at mass square prior. Unfortunately, in the 2HDM the theoretical and indirect experimental constraints depend on the mass squares, whereas the direct experimental observables dependent on the masses. Not having su ciently constraining data makes assigning the mass priors in the t with all constraints is a delicate task. This would not be problematic if the observables were measured with a high precision; in fact, we can see that in the types II and Y the di erence between the two priors are considerably smaller as there are strong lower mass limits. In order to be as conservative and prior independent as possible, we decided to combine the 95.4% regions for both priors: the light grey contours for the ts with all constraints in gures 4, 5 and 13 are obtained by superimposing a t with at mass priors and a t with at mass square priors. The corresponding numerical results mentioned in section 6 are based on the more conservative t; for instance, the limits for masses and mass di erences were extracted from the t with at mass priors, while the upper limits on the decay widths were larger in the ts using at mass square priors. (top) and H+ ! tb (bottom) in the B vs. mH+ planes for the four 2HDM types. For details, see text. planes, in the mH vs. planes (corresponding to gure 4) and in the mA vs. mH and mA mH+ vs. mH mH+ planes (corresponding to gure 5), from top to bottom. 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. { 33 { [1] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. 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Debtosh Chowdhury, Otto Eberhardt. Update of global Two-Higgs-Doublet model fits, Journal of High Energy Physics, 2018, 161, DOI: 10.1007/JHEP05(2018)161