Top-Higgs Associated Production involving {\boldmath A 0 , H 0 } with Mass at 300 GeV
TTop-Higgs Associated Production involving A , H with Mass at 300 GeV George W.-S. Hou ∗ †
National Taiwan University ‡ E-mail: [email protected]
We advocate two Higgs doublet model without Z symmetry, and focus on the extra top Yukawacouplings ρ tt and ρ tc . We show that A and H bosons are still allowed at 300 GeV mass, where cg → tA , tH can lead to tt ¯ c same-sign top, or top-assisted di-Higgs th h signatures, resp. Asbonus material, we explore the constraint provided by current 4-top search, but advocate directsearch for triple-top generated by cg → tH / A → tt ¯ t for H , A above t ¯ t threshold, and offersome insight on the mild but intriguing “excess” found by CMS in gg → A → t ¯ t at 400 GeV. European Physical Society Conference on High Energy Physics - EPS-HEP2019 -10-17 July, 2019Ghent, Belgium ∗ Speaker. † Work done in collaboration with Masaya Kohda and Tanmoy Modak. ‡ Home institute. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - ph ] O c t + S -lite George W.-S. Hou
1. Introduction: 2HDM without Z In 1977, Glashow and Weinberg gave [1] the “edict” of Natural Flavor Conservation (NFC):only one Yukawa matrix per mass matrix for two Higgs doublets. This eliminated the worriesof Flavor Changing Neutral Higgs (FCNH) couplings. It arises automatically in supersymmetry,where one doublet couples to u -type quarks, the other couples to d -type quarks, which is two Higgsdoublet model (2HDM), type II, usually implemented by a Z symmetry.Citing the Cheng-Sher pattern [2] of √ m i m j to control FCNH couplings, we pointed out [3]that t → ch or h → t ¯ c , where h is the lightest neutral scalar, are the best probes for such couplings.The paper also stressed that the Cheng-Sher pattern reflects the emergent fermion mass and mixinghierarchies, and called it Model III to distinguish from usual 2HDM I & II that invoke Z symmetry.With observation of h ( ) in 2012, a second doublet is now highly plausible, and it is imperativethat we undertake experimental search. Thinking back [4] towards the 1991 proposal for t → ch search, the ansatz of √ m i m j is seen as a “scaffold”, and one should take the 2 × ρ ct is constrained by flavor physics tobe rather small [5], and ρ cc should not be much larger than λ cc = √ m c / v < .
01, where v = ρ tc and ρ tt can be O ( ) , where ρ tc can induce t → ch decay, but modulated by the h – H mixing angle cos ( β − α ) . From here we see that FCNHcouplings for h can be suppressed by h – H mixing.With emergent “alignment”, that cos ( β − α ) (called cos γ from now on) appears to be rathersmall because h is rather close to the SM Higgs boson, we understand the non-observation sofar of the t → ch , t → uh and h → µτ decays are manifestations of alignment. A discussionsynthesizing mass-mixing hierarchy and approximate alignment as replacement of NFC can befound in Ref. [6]. We shall refer to 2HDM without Z , i.e. with extra Yukawas, as g2HDM.In our previous EPS-HEP proceedings [7], we emphasized that the extra Yukawa couplings ρ tt and ρ tc , naturally O ( ) and complex, could drive [8] electroweak baryogenesis (EWBG). The ρ tt coupling is the robust driver, but if it is less than a few %, then an O ( ) ρ tc with near maximalphase can be a backup option. The present report arose from our invited talk [9] at Moriond QCD2018, where we used a diagram from our 1997 study of cg → tA [10] that gives same-sign topsignature. Expecting this lighter A case to be ruled out by LHC data, to our surprise, we found [11]the answer in the negative: an A as light as 300 GeV is still viable! Replacing A by H , the CP even exotic scalar, we explore the viable parameter space for top-assisted di-Higgs production [12]via cg → tH → th h . As bonus material, we further discuss [13] the 4-top search constraint ontriple-top, and mention an “excess” at 400 GeV [14] in scalar t ¯ t resonance search by CMS. cg → tA → tt ¯ c : allowed for m A ∼
300 GeV
Without a Z symmetry, the coupling of A to fermions is (no cos γ suppression) i √ ∑ F = u , d , e sgn ( Q F ) ρ Fi j ¯ F iL F jR A + h . c ., (2.1)where i , j = , , ( Q F ) = + −
1) for F = u ( F = d , e ), and ρ F are3 × cg → tA production [10], we con-sidered [11] a light A in the range 200 GeV < m A <
340 GeV, i.e. below t ¯ t threshold, allowing1 + S -lite George W.-S. Hou
200 220 240 260 280 300 320 340012 m A ( GeV ) | ρ t c | c γ = ρ bb = ρ cc = ρ ττ = CMS ( CRW ) ATLAS ( SRtte μ ) ( σ )
80 fb -
150 fb -
300 fb -
600 fb - -
200 220 240 260 280 300 320 340012 m A ( GeV ) | ρ t c | c γ = ρ bb = ρ cc = ρ ττ = CMS ( CRW ) ATLAS ( SRtte μ ) ( σ )
300 fb -
600 fb - - Figure 1: [left] 2 σ exclusion and [right] 5 σ discovery for | ρ tc | by SS tt for various (cid:82) L dt at 14 TeV, withSRtt e µ of ATLAS cc → tt search (blue/dark) and CRW of CMS t ¯ tt ¯ t search (purple/light) overlaid. A → t ¯ c + ¯ tc to be dominant. However, to avoid the A → Zh constraint from ATLAS [15] andCMS [16], we assume | ρ tt | (cid:28) gg → A , even though the AZh gauge coupling is cos γ ,or alignment, suppressed. This means our discussion can be extended somewhat to beyond the t ¯ t threshold. Note that one still has the ρ tc -driven EWBG [8] even in this case. To simplify discus-sion, in the following numerics we set all ρ Fi j = ρ tc , and assume the alignment limitwhere c γ =
0, so that B ( A → t ¯ c ) = H , H + bosons are treated as somewhat heavier.Assuming ρ tc =
1, the cross section for cg → tA at 14 TeV is 1 fb for m A at 200 GeV, and1.3 fb for 340 GeV after selection cuts. For the same-sign top plus jet (SS tt ) signature, i.e. same-sign di-lepton plus jets, the main background is t ¯ tW production. ATLAS has a dedicated qq → tt search [17] in various signal regions (SRs), where we find SRtt e µ , or e µ final state from bothtops decaying semileptonically, giving the best limit on ρ tc . On the other hand, the most relevantconstraint comes from the t ¯ tt ¯ t search for CMS, which has been recently updated to 137 fb − [18], orfull Run 2 data, from an earlier analysis [19] based on 2016 data. Based on the number of leptons,jets or b -tagged jets, CMS defines eight SRs plus two control regions (CRs) for background. Wefind CRW for t ¯ tW background gives the best limit. In the left panel of Fig. 1 we give the 2 σ exclusion limits for various integrated luminosities, and the 5 σ discovery reaches are given in theright panel. For comparison, we overlay the constraints from SRtt e µ of ATLAS cc → tt search [17]from Run 1, and CRW ( t ¯ tW control region) of 4-top search by CMS [18] with full Run 2 data. Notethat this plot is an update of our published work [11] based on the earlier CMS PAS.It should be clear that there is a lot of room for improving the SS tt search, but the constraintfrom full Run 2 4-top search is pretty good. However, a dedicated search would be better. It isalso interesting to note that cg → tA → tt ¯ c might be discovered at 5 σ level for ρ tc around 0.6 withfull Run 2 plus Run 3 data. The HL-LHC could push down to smaller ρ tc values, although it maybecome less pertinent for EWBG. This highlights the value of a timely dedicated search.We find it mildly surprising that a relatively light A at or below t ¯ t threshold with FCNH cou-pling ρ tc is not yet ruled out by LHC data. Direct search – which probes EWBG! – is encouraged. In this and the next section, we skip the discussion of near degenerate A and H bosons. See original papers. + S -lite George W.-S. Hou cg → tH → th h : allowed for m H ∼
300 GeV
If in fact the H is the lighter exotic scalar, one should consider cg → tH , again assuming | ρ tt | (cid:28)
1. Besides the discussion above, a new signature would be H → h h , leading to cg → tH → thh [12], or top-assisted di-Higgs production. Given the general interest in di-Higgs searchat the LHC, this sounds interesting in its own right.The CP -even scalars h , H and CP -odd scalar A couple to fermions by − √ ∑ F = u , d , e ¯ F iL (cid:20)(cid:0) − λ Fi j s γ + ρ Fi j c γ (cid:1) h + (cid:0) λ Fi j c γ + ρ Fi j s γ (cid:1) H − i sgn ( Q F ) ρ Fi j A (cid:21) F jR + h . c ., (3.1)where λ F are the usual diagonal Yukawa matrices, and we take c γ = cos γ , s γ = sin γ as shorthand.We see that in the alignment limit of c γ →
0, couplings of h become diagonal, i.e. approach SMYukawa couplings, while H , A couple via extra ρ F Yukawa matrices. We again exploit the ρ tc coupling of H for its associated production with top.To discuss Hhh coupling, we need to consider the Higgs potential, which we assume is CP -conserving ( CP violation only through Yukawa). It can be written in the Higgs basis as [6] V ( Φ , Φ (cid:48) ) = µ | Φ | + µ | Φ (cid:48) | − ( µ Φ † Φ (cid:48) + h . c . ) + η | Φ | + η | Φ (cid:48) | + η | Φ | | Φ (cid:48) | + η | Φ † Φ (cid:48) | + (cid:20) η ( Φ † Φ (cid:48) ) + (cid:0) η | Φ | + η | Φ (cid:48) | (cid:1) Φ † Φ (cid:48) + h . c . (cid:21) , (3.2)where all parameters are real, v arises from the doublet Φ via µ = − η v , while (cid:104) Φ (cid:48) (cid:105) = µ >
0. The “soft-breaking” parameter is eliminated by a second minimization condition, µ = η v , which reduces the total number of parameters to nine [6], just one more compared to2HDM II. For c γ small but not infinitesimal, one has c γ (cid:39) −| η | v m H − m h , (3.3)where another relation connects the proximity of m h to η v . One finds approximate alignment i.e.small c γ can be attained [6] without requiring η , η to be small, which is an important check forthe prerequisite of O ( ) Higgs quartics for sake of first order electroweak phase transition [8].The
Hhh coupling is the coefficient of the λ Hhh Hh term derivable from Eq. (3.2), λ Hhh = v (cid:20) c γ s γ η + c γ ( c γ − ) η + s γ ( − c γ ) η + s γ c γ η (cid:21) (cid:39) c γ v (cid:20) m H v − η + ( s γ ) c γ η + O ( c γ ) (cid:21) , (3.4)where η = η + η + η , and the second step follows for small c γ , which shows that λ Hhh → c γ →
0. To enhance cg → tH → thh , sizable λ Hhh is needed, and η < η and η − can be expressed [6, 12]in terms of m h , m A , m H , m H + , µ , all normalized to v , as well as the mixing angle γ , but η and η do not enter scalar masses. We do not go into the details [12] here, but with v =
246 GeV and m h =
125 GeV fixed, in the following numerics, we scan over µ ∈ [ , ] GeV, η ∈ [ , ] , η ∈ + S -lite George W.-S. Hou
Figure 2: λ Hhh vs m H and c γ plots for the scan points that pass perturbativity, tree-level unitarity andpositivity through 2HDMC, where | η i | < T parameter constraint is also imposed. η η η η η η η η m H ± m A m H | λ Hhh | µ v (GeV) (GeV) (GeV) (GeV)1 0.287 3.00 − .
188 2.04 − . − . − .
172 0.557 303 481 280 97 1.612 0.294 2.78 0.269 2.10 − . − . − .
21 0.633 340 518 304 104 1.773 0.309 2.98 − .
017 2.42 − . − . − .
301 0.881 363 536 354 123 2.18
Table 1:
Parameter values for three benchmark points. [ − , ] , m H ∈ [ , ] GeV, m H + ∈ [ , ] GeV, m A ∈ [ , ] GeV with m H < m A , m H + ,and γ values that satisfy c γ ∈ [ , . ] . We identify η − with Λ − of 2HDMC [20], which we useto enforce perturbativity (conservatively impose | η i | < σ error of T parameter constraint are plotted in Fig. 2, wherethe horizontal dashed line drawn at | λ Hhh | ∼
70 GeV is to illustrate that λ Hhh can be sizable over afinite parameter region. Note that the condition m H < m A , m H + forbids the decays H → AZ , H ± W ∓ .From the scan points, we select three favorable benchmark points for m H (cid:46)
350 GeV, with λ Hhh around or slightly above 100 GeV, as given in Table 1. All three benchmark points corresponds to c γ = .
169 ( s γ = − . ρ tc = . B ( H → hh ) between 23% to 24%. Note that the ρ tc and c γ values are consistent with t → ch bounds. The H → t ¯ c + ¯ tc branching fraction is around 70%.With these three benchmark points, we study the signature of cg → tH → b (cid:96) ν + b [12].Imposing lepton, missing E T cuts and requiring at least 5 jets (with at least 4 b -tagged), the main t ¯ t Single- t t ¯ th t t ¯ tW t ¯ tZ Others(fb) (fb) (fb) (fb) (fb) (fb) (fb)1 6.70 1.01 1.01 0.016 0.022 0.234 0.0072 7.42 1.01 1.12 0.019 0.022 0.262 0.0083 7.94 1.52 1.14 0.024 0.020 0.268 0.008
Table 2:
Background cross sections after selection cuts at √ s =
14 TeV. A second set of benchmarks as well as more discussions are given in Ref. [12]. + S -lite George W.-S. Hou background cross sections are given in Table 2. For benchmark 1, 2, 3, we find signal cross sectionsof 0.396, 0.38, 0.288 fb, total background cross sections of 9.00, 9.86, 10.92 fb, and significanceof 3.2, 2.9, 2.1 (7.2, 6.6, 4.8) for 600 (3000) fb − , respectively. We see that, though H → hh needsfinite h - H mixing as well as O ( ) extra Higgs quartics, as it now stands, the thh or top-assisteddi-Higgs signature has non-negligible discovery potential at the LHC.
4. 4t on Triple-Top; and “Excess” in A → t ¯ t at 400 GeV? In this section we present some “bonus” material from our more recent work [13] on 4-topconstraints on g2HDM, and insight on some t ¯ t news.One peculiarity of Nature is that, while SM single-top and t ¯ t enjoy the sizable cross sectionsat 14 TeV of roughly 0.2 and 0.6 nb, respectively, triple-top cross section at roughly 2 fb [21] iseven smaller than 4-top production at just above 10 fb. As such, the ATLAS and CMS experimentshave been pursuing 4-top search, where CMS has recently updated their previous result based on36 fb − [19] to full Run 2 data of 137 fb − [18], clearly zooming in on 4-top cross section mea-surement (epitomized by the measured central value agreeing with theory projection). However,the search for triple-top has been bypassed.We have focused so far on a lighter A or H , i.e. below t ¯ t threshold, which are actually spin-offsfrom our earlier triple-top work. For H and A above t ¯ t threshold, we proposed [22] two years agothe process cg → tH , tA → tt ¯ c , tt ¯ t , where the same-sign top signature arises from decay to t ¯ c via ρ tc , while the triple-top signature arises from H , A → t ¯ t decay via ρ tt . Assuming ρ tc (needed forproduction) and ρ tt are O ( ) , the triple-top cross section can be larger than 4-top, extending evento pb. In the classic argument that a suppressed SM effect makes the New Physics search morecompelling, we have urged all along a targeted, direct search for triple-top at the LHC.Skipping the details [13], we plot in Fig. 3 the constraints from CMS 4-top search, where SR8is from 36 fb − [19], while SR12 is from 137 fb − [18], for two m A values, treating it as the lighterexotic boson. One sees that the constraint has barely improved when the data has increase four- - - - - ρ tt ρ t c c γ = ρ bb = ρ cc = ρ ττ = S R S R m A =
400 GeV - - - - ρ tt ρ t c c γ = ρ bb = ρ cc = ρ ττ = m A =
500 GeV
Figure 3:
Constraints on ρ tc and ρ tt for A alone case [13], from SR8 (purple/light) of Ref. [19], and SR12(red/dark) of Ref. [18], for [left] m A =
400 GeV and [right] 500 GeV. + S -lite George W.-S. Hou fold. This is largely because for SR12 at 137 fb − , CMS has fixed to 4-jets, hence tuned towards4-top measurement and giving less improvement on constraining triple-top!An inadvertent encounter further strengthens our point. To understand the constraint from gg → A / H → t ¯ t , we noticed [13] the mention of an “excess” (CMS wording) – but neither in Ab-stract, nor Introduction, nor in Summary – in CMS-PAS-HIG-17-027, though “deviation” appearedin abstract of arXiv version [14]. To quote roughly: “a signal-like excess for the pseudoscalar hy-potheses (largest) at 400 GeV, Γ / Γ tot = σ local (1.9 σ look-elsewhere)”, where we do notquote the CMS plots that illustrate the deviation. This study has traditionally been viewed bytheorists as difficult [23], due to the peak-dip nature of interference with SM t ¯ t background.Several points are worthy of note [13]: • The 400 GeV “signal” for A → t ¯ t is consistent with ρ tt (cid:46) . ρ tc (cid:46) . H and H + are at 500 and 550 GeV, respectively. • It should be emphasized that 1.9 σ global significance should be “below radar”, but sinceATLAS pioneered the t ¯ t scalar resonance search [24] with Run 1 data (although with m t ¯ t starting at 500 GeV), it would be interesting to see an ATLAS update with Run 2 data, andneedless to say, the full Run 2 result for both ATLAS and CMS. • The “excess” of CMS, though for pseudoscalar A , could actually arise from scalar H ,because with fully imaginary Yukawa coupling ρ tt , the H could mimic the A in the triangletop loop of gg → H production (see Ref. [25] for a brief discussion, for H admixture in h ).
5. Conclusion
With one scalar doublet completed, a second doublet seems rather likely. With
No New Physics seen so far, we should check our
Presumptions . From this angle, we advocate 2HDM without Z ,which permits extra Yukawa couplings such as ρ tt and ρ tc , and should be checked experimentally.With ρ tt → ρ tc driving EWBG, we find relatively light A below t ¯ t threshold could give tt ¯ c signature of same-sign top, which is not yet ruled out; relatively light H below t ¯ t thresholdcould give th h or top-assisted di-Higgs signature. These signatures should be searched for.Above t ¯ t threshold and with finite ρ tt , while experiments are zooming in on 4-top, we continueto advocate direct search of 3-top. Stumbling on the “excess” in A → t ¯ t as reported by CMS, wenote that this could arise from g2HDM, even from H origin!In conclusion, the exotic scalars of an extended Higgs sector may be sub-TeV in mass, and farricher and more complex than we are used to think. References [1] S. L. Glashow and S. Weinberg, Phys. Rev. D , 1958 (1977).[2] T. P. Cheng and M. Sher, Phys. Rev. D , 3484 (1987). At CMS PAS level, SR12 in fact gave worse constraint than SR8. + S -lite George W.-S. Hou[3] W.-S. Hou, Phys. Lett. B , 179 (1992).[4] K.-F. Chen, W.-S. Hou, C. Kao and M. Kohda, Phys. Lett. B , 378 (2013).[5] B. Altunkaynak, W.-S. Hou, C. Kao, M. Kohda and B. McCoy, Phys. Lett. B , 135 (2015),[6] W.-S. Hou and M. Kikuchi, EPL , 11001 (2018).[7] G. W.-S. Hou, PoS EPS -HEP2017 , 444 (2017).[8] K. Fuyuto, W.-S. Hou and E. Senaha, Phys. Lett. B , 402 (2018).[9] See http://moriond.in2p3.fr/QCD/2018/WednesdayMorning/Hou.pdf.[10] W.-S. Hou, G.-L. Lin, C.-Y. Ma and C.-P. Yuan, Phys. Lett. B , 344 (1997).[11] W.-S. Hou, M. Kohda and T. Modak, Phys. Lett. B , 212 (2018).[12] W.-S. Hou, M. Kohda and T. Modak, Phys. Rev. D , 055046 (2019).[13] W.-S. Hou, M. Kohda and T. Modak, Phys. Lett. B , 134953 (2019).[14] A.M. Sirunyan et al. [CMS Collaboration], arXiv:1908.01115 [hep-ex].[15] M. Aaboud et al. [ATLAS Collaboration], JHEP , 174 (2018).[16] A.M. Sirunyan et al. [CMS Collaboration], Eur. Phys. J. C , 564 (2019).[17] G. Aad et al. [ATLAS Collaboration], JHEP , 150 (2015).[18] A.M. Sirunyan et al. [CMS Collaboration], arXiv:1908.06463 [hep-ex].[19] A.M. Sirunyan et al. [CMS Collaboration], Eur. Phys. J. C , 140 (2018).[20] D. Eriksson, J. Rathsman and O. Stål, Comput. Phys. Commun. , 189 (2010).[21] V. Barger, W.-Y. Keung and B. Yencho, Phys. Lett. B , 70 (2010).[22] M. Kohda, T. Modak and W.-S. Hou, Phys. Lett. B , 379 (2018).[23] See e.g. M. Carena and Z. Liu, JHEP , 159 (2016); and references therein.[24] M. Aaboud et al. [ATLAS Collaboration], Phys. Rev. Lett. , 191803 (2017).[25] W.-S. Hou, M. Kohda and T. Modak, Phys. Rev. D , 075007 (2018)., 075007 (2018).