Prospects for 2HDM charged Higgs searches
PProspects for 2HDM charged Higgs searches
M Krawczyk , S Moretti , P Osland , GM Pruna , R Santos , Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland School of Physics and Astronomy, University of Southampton, Highfield, Southampton SO171BJ, United Kingdom Department of Physics and Technology, University of Bergen, Postboks 7803, N-5020Bergen, Norway Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Centro de F´ısica Te´orica e Computacional, Faculdade de Ciˆencias, Universidade de Lisboa,Campo Grande, Edif´ıcio C8 1749-016 Lisboa, Portugal, Instituto Superior de Engenharia de Lisboa - ISEL, 1959-007 Lisboa, PortugalE-mail:
[email protected], [email protected], [email protected],[email protected], [email protected]
Abstract.
We discuss the prospects for charged Higgs boson searches at the LHC, withinthe two-Higgs-doublet models (2HDM). The 2HDM is generally less constrained than thecorresponding sector of the MSSM, but there are still severe theoretical and experimentalconstraints that already exclude significant regions of the naive parameter space. Explicitsearches in the H + → τ + ν and H + → t ¯ b channels are further restricting parts of the 2HDMparameter space.
1. Introduction
The discovery of the Higgs particle [1, 2] raises the obvious question of whether there are moreHiggs-like particles. While the simplicity of the minimal Standard Model is very attractive, thereare well-known issues that remain to be understood. So far, searches for additional neutral Higgsbosons have found nothing up to a mass of the order of 1 TeV (see, for example, Ref. [3]).The charged-Higgs sector of the 2HDM has many features in common with the MSSM, butit is a priori less constrained. The mass is essentially unknown, but constrained relative to otherparameters of the model. Compared to the MSSM, there is more room for a wide range ofmasses. In particular, the charged Higgs boson mass could a priori be rather different from theneutral Higgs masses.In the next section we shall introduce some basic notation, and review the most importantconstraints. Then, in the following sections we will separately discuss three mass ranges. Insection 3 we discuss the light-mass case, where a top quark may decay to a charged Higgs boson, t → H + b . In section 4 we discuss the intermediate mass region, where the charged Higgs bosonis too heavy to be produced via top decay, but where the Model II is excluded by the b → X s γ constraint, up to of the order of 480 GeV [4] . In section 5 we consider still higher masses, wherethe b → X s γ constraint does not apply. For a complementary review, see Ref. [6]. A recent study concludes that this limit is even higher, at 570 GeV [5]. a r X i v : . [ h e p - ph ] M a r . Model review The 2HDM is a simple extension of the SM, described in detail in Refs. [7, 8].
We decompose the SU(2) doublets as follows:Φ a = (cid:18) ϕ + a ( v a + η a + iχ a ) / √ (cid:19) , a = 1 , v a real. The ratio between these is denoted tan β = v /v , and plays an important role in the parametrization of the model.The potential is written as V (Φ , Φ ) = − (cid:110) m Φ † Φ + m Φ † Φ + (cid:104) m Φ † Φ + H.c. (cid:105)(cid:111) + λ † Φ ) + λ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + λ (Φ † Φ )(Φ † Φ )+ 12 (cid:104) λ (Φ † Φ ) + H.c. (cid:105) + (cid:110)(cid:104) λ (Φ † Φ ) + λ (Φ † Φ ) (cid:105) (Φ † Φ ) + H.c. (cid:111) . (2.2)In many studies, the terms with λ and λ are left out, in order to control flavour-changingneutral interactions.The spectrum consists of three neutral Higgs boson (the lightest one is here assumed to be thediscovered one, at 125 GeV), and a charged pair, H ± . If CP is conserved, there are two CP-evenones ( h and H , arising from η and η in Eq. (2.1)), and an odd one ( A , arising, together withthe neutral Goldstone boson, from χ and χ ). If, on the other hand CP is not conserved, theywill mix to mass eigenstates H , H and H , with H being the lightest one.The Yukawa interactions can be written as −L Yukawa = Q L Φ a F Da D R + Q L (cid:101) Φ a F Ua U R + L L Φ a F La L R + H.c. , a = 1 , (cid:101) Φ a = iσ Φ ∗ and Q L and L L are left-handed quark and lepton doublets, whereas D R , U R and L R are the corresponding right-handed fields.Different choices for the F a define different “Models”: Model I is defined by Φ (and onlyΦ ) coupling to all fermions, whereas in Model II the d -type quarks and charged leptons coupleexclusively to Φ , whereas u -type quarks couple exclusively to Φ . This is similar to the structureof the MSSM [9]. These coefficients F a are proportional to the quark (and lepton) masses, asrequired by the Higgs mechanism. The implications for the charged-Higgs coupling are that theywill consist of two parts, one with a left-handed and the other with a right-handed projector,one proportional to the down-type mass, the other to the up-type mass. The different modelsgive different combinations of projectors and mass factors. For example, for Model II andthird-generation quarks we have (with all fields incoming) H + b ¯ t : ig √ m W V tb [ m b (1 + γ ) tan β + m t (1 − γ ) cot β ] ,H − t ¯ b : ig √ m W V ∗ tb [ m b (1 − γ ) tan β + m t (1 + γ ) cot β ] , (2.4)where g is the SU(2) coupling and V the CKM matrix.There are also Models X and Y, which are basically variants of Models I and II, with differentleptonic couplings. .2. Important constraints A recent summary of theoretical and experimental constraints can be found in Ref. [10]. Thetheoretical constraints include positivity, unitarity and perturbativity, whereas the experimentalones arise from low-energy phenomena, such as various B -meson decays where the existence ofa charged Higgs boson would contribute additional effects, as well as precision measurements atLEP constraining radiative corrections related to the electroweak bosons W and Z .Among the constraints coming from B -meson decay, the B → X s γ decay, which isexperimentally well measured and in the SM dominated by a one-loop diagram involving the W + will in the 2HDM Model II also get a contribution from H + exchange. Careful analyses ofthis effect have led to a mass bound M H ± > ∼
480 GeV [4] (recently updated to M H ± > ∼
570 GeV[5]), largely independent of tan β .The relevant LEP precision data, derived from the vacuum polarization, or radiativecorrections to the W and Z self-energies are usually quantified in terms of the parameters S , T and U [11, 12, 13]. If the charged Higgs is heavy, the smallness of T [14] imposes strongconstraints on the allowed splitting between M H ± , M H and M A [15, 16].
3. The low-mass region, M H ± < ∼ m t In the low-mass region, where the H + can be produced via t decay, Model II and Model Y areexcluded by the B → X s γ constraint. For Model I, all Yukawa couplings are proportional tocot β . Thus, the sensitivity is larger at low tan β .The LHC experiments have already set very strong bounds on the branching ratio for t → H + b , assuming the decay H + → τ + ν [17, 18]. These bounds effectively exclude somerange of low values of tan β , as illustrated in Fig. 1, where the region above the dashed bars isexcluded by the two experiments at the 95% CL.
80 90 100 110 120 130 140 150 160 - - - [GeV] – H M = 1 b tan = 3 b tan = 10 b tan ATLASCMS ) nt -> + BR(H · b) + Model I: BR(t -> H
Figure 1.
Product of branching ratios, BR( t → H + b ) × BR( H + → τ + ν ), for Model I, andthree values of tan β , as indicated (solid). The figure is adapted from Ref. [10], showing also8 TeV exclusion limits from ATLAS [17] (dashed, blue) and CMS [18] (dashed, red).It is seen that in the low-mass region, only Model I with high values of tan β , tan β > ∼ O (5)is still allowed.Model X is like Model I in its couplings to quarks, and would thus have the same branchingratio for t → H + b . However, the leptonic coupling is proportional to tan β rather than cot β .Thus, at low values of tan β the exclusion in Model X is somewhat less severe than in Model I.In this mass region, assuming the H + → W + A/H and H + → W + h rates to be negligible(due to phase space and couplings, respectively), we can approximate the H + → τ + ν branchingatio as BR( H + → τ + ν ) (cid:39) Γ( H + → τ + ν )Γ( H + → τ + ν ) + Γ( H + → c ¯ s ) . (3.1)In Model I, with both rates proportional to cot β , the branching ratio is independent of tan β and of the order of 0.7 [10], whereas in Model X the rate Γ( H + → τ + ν ) is instead proportionalto tan β and the branching ratio quickly approaches unity. Thus, the deterioration in exclusionreach from Model I to Model X is rather modest.In the decay of t → H + b , one has also searched for H + → c ¯ s [19], but the Model I branchingratio is lower by a factor ∼ / τ ν channel.
4. The intermediate-mass region, m t < ∼ M H ± < ∼ GeV
Also in the intermediate-mass region, Model II and Model Y are excluded by the B → X s γ constraint. But in contrast to the low-mass region, the charged Higgs boson can not be producedvia top decay. A variety of production mechanisms are involved. In the 5-flavour scheme , where b quarks are considered parts of the proton and have non-zero distribution functions, the relevantpartonic processes are g ¯ b → H + ¯ t, gg → H j → H + W − . (4.1)Two comments are here in order: • As indicated, the production can proceed via a neutral Higgs boson in the s -channel. Werecall the relevant couplings (all fields incoming) 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 ) , (4.2)where p µ and p ∓ µ refer to the momenta of the neutral and charged scalars. Experimentaldata [3] favour the alignment limit, wherecos( β − α ) → . (4.3)Thus, in this limit only the heavier Higgs bosons ( H and A ) can play a role here. Allowingfor CP non-conservation (considering H rather than h ) does little to modify this conclusion. • In Model I (and Model X) all couplings of the H + to quarks are proportional to cot β .Thus, the production cross section decreases with increasing values of tan β .This is different from the MSSM, which has a Model II structure, and where the crosssection has a minimum for intermediate values of tan β , of the order of (cid:112) m t /m b .As suggested by Eq. (4.1), the kinematics may allow for s -channel resonant effects in theproduction [21]. However, the smallness of T does not allow for a large mass splitting between H ± , H and A . This restricts the possible resonant enhancement.Likewise, there are various possible decay modes: H + → τ + ν, H + → W + h, (or H + → W + H ) , H + → t ¯ b (4.4) For a complete discussion on the flavour scheme choice in inclusive charged Higgs production associated withfermions see IV.3.2 of [20] and references therein. s mentioned above, the H + → W + h vanishes in the alignment limit. For the more generalcase, allowing for CP violation, the relevant coupling is given by H ∓ W ± H : g ± i cos α sin( β − α ) + sin α ]( p µ − p ∓ µ ) . (4.5)Here, α = α + π/ α are two of the rotation angles describing mixing of the neutral Higgsfields [22]. A non-zero value of α would indicate CP violation.The decay H + → W + h (or H + → W + H ) requires some deviation from the alignment limit,whereas H + → W + A and H + → W + A are limited by phase space. Thus, in practice, thechannels H + → τ + ν and H + → t ¯ b are the most relevant ones, with the latter dominating by atan β -independent factor of the order of ( m t /m τ ) . τ ν channel The tau channel benefits from being rather “clean”, and interesting limits have been obtained.Considering as an example, the case M H ± = 300 GeV, we note that both ATLAS and CMSobtain a 95% CL bound σ · BR( H + → τ + ν ) ≤ (0 . − .
17) pb at 8 TeV [17, 18]. A recent ATLASresult at 13 TeV is 0.41 pb. This is to be compared with the model expectation for the crosssection and the branching ratio. Approximate 14 TeV cross sections are quoted in Table 1 for afew tan β values. Accurate values depend on the masses of the heavier neutral states. Barringany significant decay to W + h , the relevant branching ratio is given by ( m τ /m t ) ∼ − . It isseen that the theoretical expectation is far below the current experimental limit. Table 1.
Experimental limits on σ · BR( H + → τ + ν ) [pb] at 8 and 13 TeV together withModel I cross sections [10] at 14 TeV, multiplied by a branching ratio taken to be 10 − .Three intermediate values of M H ± are considered, and for the theory cross sections we take( M , M ) = (500 , β = 1, 14 TeV 1 . × − . × − . × − tan β = 3, 14 TeV 1 . × − . × − . × − tan β = 30, 14 TeV 1 . × − . × − . × − Furthermore, as long as the relevant search region is around tan β = 1, there is no significantdifference between Model I and Model X, so Model X is no more and no less affected by theexperimental bounds on this channel than Model I. t ¯ b channel While the H + → t ¯ b channel suffers from high QCD background rates, sophisticated analyseshave started to constrain these models. 8 TeV exclusion limits from CMS are shown in Fig 2and reproduced in Table 2, together with preliminary ATLAS results at 13 TeV and theoreticalexpectations for three values of tan β . For this channel, assuming BR( H + → t ¯ b ) = 100%, wefind that low values of tan β are excluded. On the other hand, σ (tan β = 30) ∼ − pb, whichis well below the exclusion limit. The charged-Higgs production cross section roughly scales with the glue-glue luminosity, which in the massrange 200-400 GeV increases by factors of 4–5 from 8 to 13 TeV. [GeV] + H m
200 250 300 350 400 450 500 550 600 [ pb ] + H s % C L li m i t on -1
10 110
Observed s – Expected median s – Expected median (8 TeV) -1 CMS b t fi + , H + (b)Ht fi pp final states ll , h tm +jets, l ) = 1b t fi + Assuming B(H
Figure 2.
CMS upper limit on σ ( pp → t ( b ) H + ) for the combination of the µτ h , (cid:96) + jets and (cid:96)(cid:96) (cid:48) final states assuming BR( H + → t ¯ b ) = 100%. [Reprinted with kind permission from JHEP andthe authors, Fig. 10 of [18].] Table 2.
Experimental limits on σ · BR( H + → t ¯ b ) [pb] together with Model I cross sections[10] multiplied by a branching ratio taken to be 1. Three intermediate values of M H ± areconsidered, and for the theory cross sections we take ( M , M ) = (500 , β = 1, 14 TeV 11 . .
46 2 . β = 3, 14 TeV 1 .
41 0 .
882 0 . β = 30, 14 TeV 1 . × − . × − . × − We conclude that in this intermediate mass region the search in the H + → t ¯ b is startingto constrain the model. Since a hadronic final state is considered in this search, there is nodifference between Model I and Model X.
5. The high-mass region,
GeV < ∼ M H ± The high-mass region is distinguished by all Yukawa models being allowed, and also all decaymodes listed in Eq. (4.4).In distinction from the low- and intermediate-mass regions discussed above, we now need toconsider also the Model II cross sections. Cross sections are quoted for both models in Table 3[10]. Note that the cross sections for the four models are pairwise the same, σ (Model X) = σ (Model I) , and σ (Model Y) = σ (Model II) , (5.1)but the decay rates would be different if lepton modes were considered. Because of thedependence on the H and A (or H , H ) masses, there is some uncertainty associated withthe cross sections. The main features are: The cross sections fall off at high masses, mainly due to falling pdf’s and phase spacereduction, and • The Model I cross section falls with tan β approximately as 1 / tan β , whereas the Model IIcross section has a minimum around tan β = O ( (cid:112) m t /m b ) due to the competition amongthe two terms in the coupling (2.4). Table 3.
Theoretical cross sections [10] for √ s = 14 TeV and a range of mass val-ues M H ± = 500 − M , M ) = (500 , − and 10 − are extracted where indicated.500 GeV 600 GeV 700 GeV 800 GeV 900 GeV 1000 GeVtan β = 1 1 . / .
27 0 . / .
64 0 . / .
37 0 . / .
22 0 . / .
14 0 . / . β = 3 [10 − ] 1 . / .
81 0 . / .
72 0 . / .
41 0 . / .
25 0 . / .
16 0 . / . β = 30 [10 − ] 0 . / .
24 0 . / .
95 0 . / .
31 0 . / .
30 0 . / .
61 0 . / . τ ν channel Search results from the τ ν channel are given in Table 4. For comparison, we quote the theoreticalexpectation for tan β = 1, for both Model I and Model II. It is seen that the expectation, attan β = 1 is lower by factors ranging from 200 to 600. For higher values of tan β , the discrepancywould be even larger. Thus, searches in the τ ν channel are not yet constraining the 2HDM inthis mass range. Table 4.
Experimental limits on σ · BR( H + → τ + ν ) [pb] together with the theo-retical expectation for tan β = 1, in the format “Model I/Model II”, approximatingBR( H + → τ ν ) (cid:39) ( m τ /m t ) (cid:39) − . Overall factors 10 − and 10 − are extracted whereindicated. 500 GeV 600 GeV 700 GeV 800 GeV 900 GeV 1000 GeVATLAS [17] [10 − ], 8 TeV 2 .
46 1 .
11 0 . − ], 13 TeV 9 .
25 5 .
15 3 .
35 2 .
36 2 .
10 1 . β = 1 [10 − ], 14 TeV 1 . / .
27 0 . / .
64 0 . / .
37 0 . / .
22 0 . / .
14 0 . / . t ¯ b channel While the H + → t ¯ b channel suffers from large QCD backgrounds, the constraints obtainedare more interesting. Experimental exclusion limits are given in Table 5, and can be directlycompared with the theoretical expectations quoted in Table 3, approximating BR( H + → t ¯ b ) = 1.It is seen that in the range M H ± = 500 −
600 GeV low values of tan β , namely tan β = O (1) areon the verge of being excluded for both Model I and Model II. Since no leptonic couplings areinvolved, this conclusion applies equally to Models X and Y. able 5. Experimental limits on σ · BR( H + → t ¯ b ) [pb].500 GeV 600 GeV 700 GeV 800 GeV 900 GeV 1000 GeVATLAS [25], 8 TeV 0.68 0.24ATLAS [25], 8 TeV 2.89 1.42 0.70 0.37 0.24 0.15CMS [18], 8 TeV 0.20 0.13ATLAS [24], 13 TeV 1.32 1.01 0.53 0.34 0.31 0.18
6. Summary
Within the 2HDM, the search for charged Higgs bosons has mainly proceeded in two channels, H + → τ + ν and H + → t ¯ b . In the τ ν channel, the searches have already excluded low values oftan β for Yukawa Models I and X and low masses, M H ± < m t . At higher masses, this channelis not yet competitive.In the intermediate-mass region, m t < M H ± <
480 GeV, searches in the t ¯ b channel excludethe 2HDM at low values of tan β , tan β < ∼ O (3). In the high-mass region, 480 GeV < M H ± ,tan β values of order unity are also on the verge of being excluded up to about 600 GeV.The bosonic decay modes, H + → W + A , H + → W + H and H + → W + h should also be keptin mind, though the former suffer from limited phase space, and the latter from the vanishingof the coupling in the alignment limit. References [1] Aad G et al. [ATLAS Collaboration], 2012 Observation of a new particle in the search for the StandardModel Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B et al. [CMS Collaboration], 2012 Observation of a new boson at a mass of 125 GeV with theCMS experiment at the LHC, Phys. Lett. B
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