2HDM Charged Higgs Boson Searches at the LHC: Status and Prospects
22HDM Charged Higgs Boson Searches at the LHC:Status and Prospects
Stefano Moretti ∗ School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ, United KingdomE-mail: [email protected]
We review status and prospects of searches for the charged Higgs boson of 2-Higgs DoubletModels of all Yukawa types at the Large Hadron Collider.
Prospects for Charged Higgs Discovery at Colliders3-6 October 2016Uppsala, Sweden ∗ Speaker. 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). http://pos.sissa.it/ a r X i v : . [ h e p - ph ] D ec HDM H ± Searches@LHC
Stefano Moretti
1. Introduction
Following the discovery of a neutral Higgs boson (herafter denoted by h ) at the Large HadronCollider (LHC) in July 2012 [1, 2], the quest for new physics Beyond the Standard Model (BSM)must account for a Electro-Weak Symmetry Breaking (EWSB) dynamics governed by the Higgsmechanism. As the discovery of the h state corresponds to that of the last 1/4 of a (complex) doubletHiggs field , it makes sense to investigate BSM scenarios which embed such specific Higgs fields.With this in mind, it is clear that the simplest BSM realisation of an EWSB scenario based onthe Higgs mechanism is the one afforded by 2-Higgs Doublet Models (2HDMs) [3], wherein twoHiggs fields, Φ and Φ , are introduced. On the one hand, these scenarios allow for the existenceof a SM-like Higgs state (alignment limit), in accordance with the experimental findings of theATLAS and CMS collaborations [4, 5]. On the other hand, they offer a variety of new Higgs statespotentially accessible at the LHC, i.e., another CP-even field ( H ), a CP-odd one ( A ) as well as,most notably, a charged pair ( H ± ).The production and decay rates of the latter would depend upon specific details of the underly-ing 2HDM [6], especially the Yukawa interactions. Since such an extended Higgs sector naturallyleads to Flavour Changing Neutral Currents (FCNCs), these would have to be suppressed [7, 8].This is normally achieved by imposing discrete symmetries in modeling the Yukawa interactions.The purpose of this write-up is to review status and prospects of searches for 2HDM H ± statesat the LHC. In doing so, we borrow several elements from a recent review touching on the sametopic [9]. The plan of this note is as follows: in Sect. 2 we describe the H ± interactions within the2HDMs and list theoretical and experimental contraints. Sects. 3 and 4 cover present and future H ± studies at the CERN collider, respectively. Finally, we conclude in Sect. 5. H ± Couplings in 2HDMs
We limit ourselves to studying the softly Z -violating 2HDM potential, which reads [9] V ( Φ , Φ ) = − (cid:110) m Φ †1 Φ + m Φ †2 Φ + (cid:104) m Φ †1 Φ + h . c . (cid:105)(cid:111) + λ ( Φ †1 Φ ) + λ ( Φ †2 Φ ) + λ ( Φ †1 Φ )( Φ †2 Φ ) + λ ( Φ †1 Φ )( Φ †2 Φ )+ (cid:104) λ ( Φ †1 Φ ) + h . c . (cid:105) . (2.1)Apart from the term m , this potential exhibits a Z symmetry, ( Φ , Φ ) ↔ ( Φ , − Φ ) or ( Φ , Φ ) ↔ ( − Φ , Φ ) . (2.2)The most general potential contains in addition two more quartic terms, with coefficients λ and λ ,and violates the Z symmetry in a hard way [6]. The parameters λ – λ , m and m are real. Thereare various bases in which this potential can be written, often they are defined by fixing propertiesof the vacuum state. The potential (2.1) can lead to CP violation, provided m (cid:54) =
0. Upon EWSB,of the 8 degrees of freedom of Φ and Φ , 3 are absorbed as scalar polarisations of the W ± and Z gauge vectors while the remaining 5 appear as physical Higgs states ( h , H , A and H ± ). In fact, 3/4 of it were discovered at the S p ¯ p S in the form of the W ± and Z bosons. HDM H ± Searches@LHC
Stefano Moretti
Model d u (cid:96) I Φ Φ Φ II Φ Φ Φ X Φ Φ Φ Y Φ Φ Φ Table 1:
The most popular Yukawa interactions for 2HDMs. Here, Φ and Φ refer to the Higgs doubletcoupled to the particular fermion. With all momenta incoming, we have the H ∓ gauge couplings [6]: H ∓ W ± h : ∓ ig ( β − α )( p µ − p ∓ µ ) , H ∓ W ± H : ± ig ( β − α )( p µ − p ∓ µ ) , H ∓ W ± A : g ( p µ − p ∓ µ ) . (2.3)Here, tan β is the ratio of the Vaccum Expectation Values (VEVs) of the 2 doublets Φ and Φ ,which is typically defined between 1 and ∼ m t / m b . Further, α is the mixing angle in the CP-even Higgs sector, its range being π , e.g., [ − π / , π / ] . The strict SM-like limit corresponds tosin ( β − α ) =
1, however, the experimental data from the LHC [4, 5] allow for departures from it.
There are various “Types” of Yukawa interactions, all of them can lead to the suppression ofFCNCs at the tree-level, assuming some vanishing Yukawa matrices. The most popular is Type-II,in which up-type quarks couple to one ( Φ ) while down-type quarks and charged leptons couple tothe other scalar doublet ( Φ ). They are presented schematically in Tab. 1, wherein the symbols u , d and (cid:96) refer to up-, down-type quarks and charged leptons of any generation, respectively.Explicitly, for the charged Higgs boson in Type-II, we have for the coupling to, e.g., the thirdgeneration of quarks [6]: H + b ¯ t : ig √ m W V tb [ m b ( + γ ) tan β + m t ( − γ ) cot β ] , H − t ¯ b : ig √ m W V ∗ tb [ m b ( − γ ) tan β + m t ( + γ ) cot β ] . (2.1)For other Yukawa models the factors tan β and cot β are substituted according to Tab. 2. The 2HDM is subject to various theoretical constraints. First, it has to have a stable VEV[10, 11, 12, 13, 14], which leads to so-called positivity constraints for the potential [10, 15, 16], V ( Φ , Φ ) > | Φ | , | Φ | → ∞ . Second, we should be sure to deal with a particular vacuum (aglobal minimum) as in some cases various minima can coexist [17, 18, 19].2 HDM H ± Searches@LHC
Stefano Moretti d u (cid:96) I − cot β + cot β − cot β II + tan β + cot β + tan β X − cot β + cot β + tan β Y + tan β + cot β − cot β Table 2:
Yukawa couplings for 2HDMs without tree-level FCNCs normalised to the SM vertices.
Other types of constraints arise from requiring tree-level unitarity and perturbativity of theYukawa couplings [20, 21, 22, 23, 24]. In general, these constraints limit the absolute values of the λ parameters as well as M H ± (which should not be beyond ≈
700 GeV) and tan β (both at very lowand very high values). This limit is particularly strong for a Z symmetric model [19, 25, 26]. The EW precision data, parametrised in terms of the so-called S , T and U parameters [27,28, 29, 30, 31, 32, 33], provide important constraints on 2HDMs [34]. Furthermore, the muonmagnetic moment [25, 35, 36, 37] and the electric dipole moment of the electron [38, 39] limit thecharged Higgs sector of 2HDMs. However, B -physics constraints are the strongest ones emergingfrom low-energy observables. The key ones include B → τν τ ( X ) , B → D τν τ , D s → τν τ , B → X s γ , B − ¯ B mixing.The ratio R b ≡ Γ Z → b ¯ b / Γ Z → had would also be affected by Higgs exchange and, while the contri-butions from neutral Higgs bosons are negligible, those from charged ones are sizable [40]. Indeed,LEP and Tevatron have given limits on the H ± mass and couplings, for charged Higgs bosons in2HDMs. At LEP a lower mass limit of 80 GeV that refers to the Type-II scenario for BR ( H + → τ + ν )+ BR ( H + → c ¯ s ) = ( H + → τ + ν ) = ( H + → c ¯ s ) = H ± → W ± A with A → b ¯ b ,which is not negligible in Type-I, leads to the corresponding M H ± limit of 72.5 GeV (95% CL) if M A >
12 GeV [41].A summary of the discussed constraints (e.g., for the 2HDM-II) performed by the “Gfitter”group [42] is presented in Fig. 1. The strongest limit comes from B → X s γ and the recent inclusionof higher-order effects push the M H ± constraint up to around 480 GeV [43] (see also Ref. [44]).
3. Current LHC Status
Fig. 2 shows the typical BRs of the H ± state in the standard 2HDMs in the case of a light( M H ± < m t ) and heavy ( M H ± > m t ) state, for two representative masses. From these plots, it isclear that in the former mass region the τν decay is the best one to pursue, given its cleanliness(e.g., in comparison to cs ) in the highly QCD-polluted environment of the LHC and its relativelyhigh rates, though also note the role of cb in Type-Y. In the latter mass interval, it would appearthat tb and/or W ± h / H can play a significant role (again, alongside τν , which remains relevant inthe Type-II and X). In fact, both tb and W ± h / H lead to the same signature, W ± b ¯ b , as t → bW + and h / H → b ¯ b , so that it is indeed this inclusive mode that ought to be maximised to improve searches3 HDM H ± Searches@LHC
Stefano Moretti
Results and Discussion 46 β tan
10 20 30 40 50 60 70 [ G e V ] ± H M LEP 95% CL exclusion
68% CL exclusion from MC toy95% CL exclusion from MC toy99% CL exclusion from MC toy=1) dof ,n χ∆
95% CL for Prob( =2) dof ,n χ∆
95% CL for Prob( β tan
10 20 30 40 50 60 70 [ G e V ] ± H M β tan
10 20 30 40 50 60 70 [ G e V ] ± H M LEP 95% CL exclusion
95% CL excluded regions R ) γ s X → (B B ) ντ → (B B ) ν De → (B B ) / ντ D → (B B ) ν µ → π ( B ) / ν µ → (K B ) ν µ → (B B Combined fit (toy MC) β tan
10 20 30 40 50 60 70 [ G e V ] ± H M Figure 14:
Exclusion regions in the (tan β, M H ± ) plane. The top plot displays the 68%, 95% and 99% CLexcluded regions obtained from the combined fit using toy MC experiments. For comparison the 95% CLcontours using Prob(∆ χ , n dof ) for n dof = 1 and n dof = 2 are also shown (see discussion in text). Thebottom plot shows the 95% CL excluded regions from the individual constraints given in Table 5, and thetoy-MC-based result from the combined fit overlaid. Figure 1:
Exclusion regions of the 2HDM-II over the [tan β , M H ± ] plane at 95% CL. [Fig. 14 from [42].] in the heavy M H ± region [45], which are notoriously difficult because of the QCD noise. Noticethat, in the plot, M H ± = M A , so that H ± → W ± A decays are forbidden. However, one could swap H ↔ A and obtain a similar decay pattern. Indeed, this decay (for a very light A state, which ispossible unlike the corresponding H case) can play a key role at the LHC Run 2 in a Type-I 2HDM(as we shall see later). Concerning H ± production dynamics, this is dominated by the subprocesses gg , q ¯ q → b ¯ bH + W − ( gg largely dominating over q ¯ q at the LHC), see Fig. 3 These contain both t ¯ t production and decay (relevant for M H ± < m t , Fig. 3a) as well H ± Higgs-trahlung (relevant for M H ± > m t , Fig. 3b) topologies.
100 200 300 400 500 600 - [GeV] – H M ( I ) nt tb (I,X)(I)(X) cs ( I ) ( X ) nt hW (I,X)HW (I,X))=0.7 a - b sin(
100 200 300 400 500 600 - [GeV] – H Mtb (II,Y)(Y) (II) ( II ) nt ( Y ) nt c b ( Y ) cs ( Y ) hW (II,Y)HW (II,Y))=0.7 a - b sin( = 3 b Branching ratios for tan
100 200 300 400 500 600 - [GeV] – H M ( I ) nt (X) nt cs ( I ) ( X ) nt HW (I)tb (I) H W ( X ) )=1.0 a - b sin(
100 200 300 400 500 600 - [GeV] – H M (II) nt (II) nt cb (Y)cs (Y) tb (II)tb (Y) H W ( II ) H W ( Y ) )=1.0 a - b sin( = 30 b Branching ratios for tan
Figure 2:
Charged-Higgs branching ratios vs M H ± , for tan β = h and H (125 GeV and 130 GeV) for Type-I/X (left) and -II/Y (right) with sin ( β − α ) = . M H ± = M A . Fig. 4 shows LHC Run 1 (7 and 8 TeV) limits on the model independent production times BR4
HDM H ± Searches@LHC
Stefano Moretti a gg bt ¯ bH + W − (i) gg bt ¯ t ¯ bH + W − (ii) q ¯ q bγ,Z,g t ¯ t ¯ bH + W − (iii) gg H j ¯ tt b ¯ bH + W − (iv) b gg b ¯ b ¯ t W − H + Figure 3:
Feynman diagrams for the processes gg , q ¯ q → b ¯ bH + W − . rates for the light and heavy H ± range using the τν decay mode from both ATLAS and CMS whilefor the tb mode (only applicable to the M H ± > m t case) see Fig. 5. Some Run 2 analyses also existat present, though they do not significantly improve upon the results shown here.Furthermore, H ± properties can also be accessed indirectly, through either limits (on any state)or measurements (of the SM-like one, e.g., H ± can enter in h → γγ and Z γ decays) in the wholeHiggs sector. Using HiggsBounds [49] and
HiggsSignals [50], constraints on the [cos ( β − α ) , tan β ] plane can be drawn for all 2HDMs, as shown in Fig. 6. Figure 4:
ATLAS (top) and CMS (bottom) upper limits on BR ( t → H + b ) × BR ( H + → τ + ν τ ) (left) and σ ( pp → t ( b ) H + ) × BR ( H + → τ + ν τ ) (right) rates. [Fig. 7 of [46] (ATLAS) and Fig. 8 of [47] (CMS).]
4. Future LHC Prospects
While further investigation of the H ± → τν and tb modes is warranted for Run 2, as intimated,additional interesting possibilities will be offered by the cb (in Type-Y) and W ± A (in Type-I) chan-nels in the low M H ± (and M A ) range. The case for exploiting the former (also with a view atmeasuring tan β ) was already made in [51] and has now lead (in CMS) to competitive (with τν )limits (see Fig. 7) while the latter (also sensitive to α ) was recently advocated in [53] (see Fig. 8).5 HDM H ± Searches@LHC
Stefano Moretti
Figure 5:
ATLAS (left) and CMS (right) upper limits on the σ ( pp → t ( b ) H + ) × BR ( H + → t ¯ b ) rate. [Fig. 6of [48] (ATLAS) and Fig. 10 of [47] (CMS).] t a n ( β ) cos( β−α )E2HDM Type-I excluded/allowed regions t a n ( β ) cos( β−α )E2HDM Type-II excluded/allowed regions t a n ( β ) cos( β−α )E2HDM Type-X excluded/allowed regions t a n ( β ) cos( β−α )E2HDM Type-Y excluded/allowed regions Figure 6:
Green ∗ (Red × ): allowed (excluded) regions from LEP, Tevatron and LHC experiments at 95%CL in all the 2HDMs. The solid, dashed and dotted curve display the contour for ∆ χ = m h =
125 GeV and m H = m H ± = m A =
5. Conclusions
In summary, several charged Higgs production and decay channels afford the LHC with sen-sitivity to various Yukawa structures of a 2HDM. Herein, current limits from direct H ± searchesexclude significant portions of parameter space. Yet, for the future, the combination of both estab-lished and new (fermionic and bosonic) decays of (both light and heavy) charged Higgs states willoffer one the possibility of both discovery and separation of a specific 2HDM scenario.6 HDM H ± Searches@LHC
Stefano Moretti (GeV) + H m
90 100 110 120 130 140 150 ) = c fi + b ) w i t h B ( H + H fi % C L on B ( t Expected (stat. only)Expected s – Expected s – Expected Observed
CMS
Preliminary (8 TeV) -1 m Combined e+
Figure 7:
CMS upper limit on the BR ( t → H + b ) × BR ( H + → c ¯ b ) rate. [Fig. 14c of [52].]
20 40 60 80 100 120 100 120 140 160 180 200 m A ( G e V ) m H + (GeV) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 B R ( H + → W A ) Figure 8: BR ( H ± → W ± A ) in the 2HDM-I mapped over the [ m H ± , m A ] plane for M h =
125 GeV, sin ( β − α ) =
1, tan β = M H =
300 GeV. [The yellow region is excluded by LHC data at 95% CL.]
Acknowledgements
This research is supported in part through the NExT Institute and by the grantH2020-MSCA-RISE-2014 no. 645722 (NonMinimalHiggs).
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