Prepared for submission to JHEP Properties of 125 GeV Higgs boson in non-decoupling MSSM scenarios 2 1 0 2 l Kaoru Hagiwara,a Jae Sik Lee,b Junya Nakamuraa u J aKEK Theory Center and Sokendai, Tsukuba, Ibaraki 305-0801, JAPAN 9 bDepartment of Physics, National Tsing Hua University, Hsinchu, Taiwan 300 2 E-mail: [email protected], [email protected], ] h [email protected] p - p Abstract: Tantalizing hints of the Higgs boson of mass around 125 GeV have been e reported at the LHC. We explore the MSSM parameter space in which the 125 GeV state h [ is identified as the heavier of the CP even Higgs bosons, and study two scenarios where 2 the two photon production rate can be significantly larger than the standard model (SM). v ∗ In one scenario, Γ(H γγ) is enhanced by a light stau contribution, while the WW 2 → 0 (ZZ∗) rate stays around the SM rate. In the other scenario, Γ(H b¯b) is suppressed → 8 ∗ ∗ and not only the γγ but also the WW (ZZ ) rates should be enhanced. The ττ¯ rate 0 . can be significantly larger or smaller than the SM rate in both scenarios. Other common 7 0 features of the scenarios include top quark decays into charged Higgs boson, single and 2 pair production of all Higgs bosons in e+e− collisions at √s. 300 GeV. 1 : v i Keywords: Higgs boson, MSSM X r a Contents 1 Introduction 1 2 Higgs sector in MSSM 2 3 Scenarios giving large two photon rate 5 3.1 Fermion and sfermion contributions to r and r 7 gg γγ 3.2 Light stau scenario 9 3.2.1 R 10 γγ 3.2.2 R 10 VV 3.2.3 Rττ¯ 10 3.3 Small Γ(H b¯b) scenario 13 → 3.3.1 R and R 14 γγ VV 3.3.2 Rττ¯ 14 4 Constraints on the other Higgs bosons 15 5 Conclusion 16 1 Introduction LatestresultsfromtheHiggsbosonsearchbytheATLAS[1]andtheCMS[2]collaborations show an excess of events around the mass region of 125 GeV. The main search channel is the two photons decay mode of the Higgs boson, for which both experiments reported the ∗ rate higher than the standard model (SM) prediction. There are hints of the ZZ decay mode with less significance, while no hints have been reported for the ττ¯ mode. We expect that the data from the current 8 TeV run will make clear the properties of the Higgs boson candidate. The Higgs sector in the minimal supersymmetric standard model (MSSM) has five physical mass eigenstates, two CP even and one CP odd neutral scalar bosons, if CP is conserved in the Higgs sector, and one pair of charged scalar bosons [3]. The observed γγ resonance at 125 GeV can be one of the three neutral Higgs bosons. Among them, the CP odd state (A) cannot give the γγ rate greater than that of the SM Higgs bosons, mainly because it lacks the W boson loop contribution to the γγ decay [4]. Among the two CP even Higgs bosons, both the light (h) and heavy (H) mass eigenstates can be 125 GeV and can have enhanced γγ rate. MSSM scenarios where the lighter of the CP even Higgs boson is identified as the 125 GeV state are discussed in refs.[5–21], and the possibility of the 125 GeV state as the heavier of the CP even Higgs bosons is discussed in ref.[16]. The former scenario contains the so-called decoupling region where all the other Higgs bosons (H, A, – 1 – ± H ) are significantly heavier than the lighter CP even state h, whose properties resembles the SM Higgs boson. On the other hand, in the latter scenario where the heavier of the CP even state H has the mass 125 GeV, not only the mass of the lighter CP even state h ± but also those of the CP odd state A and the charged Higgs boson H are bounded from above. In this study, we study carefully the consequences of this non-decoupling scenario of MSSM where the 125 GeV state is the heavier of the CP even Higgs bosons, H. In particular, we study two sub-scenarios where the two photon production rate can be larger than the SM. In one scenario, the H γγ amplitude is enhanced by a light stau loop → ∗ ∗ which interferes constructively with the main W boson loop, while the WW (ZZ ) rate is around the SM prediction. In another scenario, the γγ rate is enhanced by suppressing the dominant partial decay width Γ(H b¯b), and not only γγ but also WW∗ (ZZ∗) → production rate can be large. In both scenarios, the ττ¯ rate can be significantly larger or smaller than in the SM. Prediction for the mass spectra of the other Higgs bosons is also examined. The enhancement of the two photon production rate due to a light stau in the de- coupling region has been studied in refs.[12, 20]. We show in this report that the same mechanism works in the non-decoupling region as well. The suppression of Γ(H b¯b) → in the non-decoupling region has been studied in ref.[16]. We study not only the γγ and ∗ ∗ WW (ZZ ) rates but also the ττ¯ rate in detail. 2 Higgs sector in MSSM In this section, we briefly review the mass spectrum of the Higgs bosons in MSSM. In our scenarios where the two photon production rate of the heavier CP even state H is higher than that of the SM, relatively large Higgs couplings to the weak bosons are necessary, since the main contribution to the H γγ amplitude comes from the W boson loop [4]. → Hence, H must be a SM-like Higgs boson. TheMSSMHiggs sector consists of two SU(2) doublets, φ andφ which give masses L u d to up type fermions and down type fermions, respectively [3]. When the electroweak symmetry is spontaneously broken, MSSM gives five physical mass eigenstates, two CP even scalar bosons h and H, one CP odd scalar boson A, and one pair of charged scalar ± bosons H . The two CP even scalar bosons are mixed states of the real components of the two Higgs doublets, h cosα sinα H0 = − u , (2.1) H sinα cosα H0 ! ! d! where we define h and H as the lighter and the heavier of the two CP even scalar bosons, respectively, whereas the current basis states H0 and H0 are defined as in u d v +H0 v +H0 Re(φ0)= u u, Re(φ0)= d d. (2.2) u √2 d √2 – 2 – Upon the convention that the above vacuum expectation values are written as v = vsinβ u and v = vcosβ with v ( 245) GeV being the vacuum expectation value of the SM Higgs d ≃ doublet, we can introduce another base H0 sinβ cosβ H u = − SM , (2.3) Hd0! cosβ sinβ ! H⊥ ! where H is a state whose couplings to the weak bosons are the same as those of the SM SM Higgs boson, and H⊥ is its orthogonal state which has no coupling to the weak bosons. From eqs.(2.1, 2.3), we have h = sin(α β)HSM cos(α β)H⊥, (2.4a) − − − − H = cos(α β)HSM sin(α β)H⊥. (2.4b) − − − The masses and the eigenstates of the CP even Higgs bosons in the MSSM are determined by diagonalizing the symmetric mass-squared matrix in the space of (H0,H0)T, u d M2 M2 uu ud , (2.5) M2 M2 ud dd! whose elements can be approximated as [22] 3 M2 3v2 M2 A¯2 3v2 M2 M2 1 Y2ln susy + Y4 ln susy +A¯2 1 t Y4µ¯4, uu ∼ Z − 8π2 t M2 8π2 t M2 t − 12 − 96π2 b t ! " t (cid:18) (cid:19)# (2.6a) v2 v2 M2 M2 Y4µ¯2A¯2 Y4µ¯2A¯2, (2.6b) dd ∼ A− 32π2 t t − 32π2 b b v2 v2 M2 cosβ M2 +M2 + Y4µ¯2(A¯2 3)+ Y4µ¯2(A¯2 3) ud ∼ − A Z 16π2 t t − 16π2 b b − (cid:20) (cid:21) v2 v2 + Y4µ¯A¯ A¯2 6 + Y4µ¯3A¯ , (2.6c) 32π2 t t t − 32π2 b b (cid:0) (cid:1) where only the leading terms for large tanβ (tanβ 1) are kept, since large value of tanβ ≫ isnecessarytohaveaSM-likeHiggs bosonasheavyas125GeV.Y andY are, respectively, t b the top and bottom Yukawa couplings in the MSSM. The soft SUSY breaking A terms f and the Higgsino mass µ are made dimensionless as A¯ = A /M , A¯ = A /M , t t susy b b susy µ¯ = µ/M with t susy M2 +M2 M2 = t˜1 t˜2, (2.7) susy 2 where Mt˜1 and Mt˜2 are masses of the stop mass eigenstates. Full analytic formulae of the mass matrix elements can be found in ref.[22]. By diagonalizing the matrix eq.(2.5), we obtain the masses of the two CP even Higgs bosons, 2 2 2 2 2 2 M = M cos α+M sin α M sin2α, (2.8a) h uu dd ud − 2 2 2 2 2 2 M = M sin α+M cos α+M sin2α, (2.8b) H uu dd ud – 3 – with M2 sinα = ud , (2.9a) (M2 M2 )2+(M2 )2 H − uu ud q M2 M2 cosα = H − uu , (2.9b) (M2 M2 )2+(M2 )2 H − uu ud q where we can choose the mixing angle α in the region π < α < π, since M2 M2 > 0 −2 2 H − uu (cosα> 0) is always satisfied. The region of α can further be separated depending on the sign of sinα, π 2 1. sinα < 0 (M < 0), < α <0, (2.10a) ud −2 π 2 2. sinα > 0 (M > 0), 0< α < . (2.10b) ud 2 Here the region 2 (sinα > 0) takes place if the loop contribution dominates over the negative definite tree-level contribution in eq.(2.6c), which can happen, for example when both µ¯A¯ > 0 and A¯2 > 6 are satisfied for tiny cosβ (large tanβ). t t In the limit that the state H has the SM-like couplings to the weak bosons, we have cos(α β) 1 (2.11) | − | ≃ in eq.(2.4b). At large tanβ (β π/2), this condition eq.(2.11) selects two distinct regions, ≃ α β 0 (α π/2) or α β π (α π/2). In both cases, we have cosα 1, and − ≃ ≃ − ≃ − ≃ − ≪ the mass eigenstates in eq.(2.8) are approximated by 2 2 2 2 M M 2M cosα+O(cos α), (2.12a) h ≃ dd− ud 2 2 2 2 M M +2M cosα+O(cos α). (2.12b) H uu ud ≃ By neglecting small terms proportional to cosα, the condition that the SM-like state H is heavier than the other state approximately implies 2 2 M M & 0, (2.13) uu dd − or from eq.(2.6) 3 M2 2 2 susy 2 2 2 M + Y ln (v Y M ) Z 8π2 t M2 t − Z t 3 A¯2 µ¯2 1 + v2Y4A¯2 1 t − + v2Y4µ¯2(A¯2 µ¯2) & M2. (2.14) 8π2 t t − 12 32π2 b b − A (cid:18) (cid:19) Hence M is bounded from above by the loop contribution to the Higgs potential. A Itshouldalsobenoted fromeqs.(2.6a, 2.12b)that, inordertomake H aSM-like Higgs boson and as heavy as 125 GeV, large M and A¯2 6 are necessary, and we explore the susy t ∼ MSSM parameter region which satisfies these conditions in the following sections. – 4 – 3 Scenarios giving large two photon rate In our analysis, we consider the following Higgs production processes at the LHC, Gluon fusion gg φ+X, (3.1a) → Weak boson fusion qq qqφ+X, (3.1b) → Bottom quark annihilation b¯b φ+X, (3.1c) → where φ can be h,H or A. The SM Higgs production cross sections for the processes in eq.(3.1) are calculated by using the programs HIGLU [23], HAWK [24] and BBH@NNLO [25],respectively. TheMSSMHiggscrosssectionsareobtainedbyscalingthecorresponding SM Higgs cross sections with the ratio of the corresponding MSSM decay width over the SM one. The decay widths, couplings and mass spectra of the Higgs bosons and SUSY particles are calculated with an updated version of CPsuperH2.0 [26] which includes the stau contribution to the Higgs boson masses. Although the SM cross section of the bottom quark annihilation process is quite small compared to the dominant gluon fusion process, it can be significant in some MSSM scenarios. We consider the following constraints from the collider experiments. For the stau and stop masses, we adopt the lower mass bounds [27] Stau Mτ˜ >81.9 GeV, (3.2a) Stop Mt˜>92.6 GeV. (3.2b) Upper bounds on the e+e− annihilation cross sections σ e+e− Zh( Zb¯b and Zττ¯) , (3.2c) → → σ e+e−(cid:0) Ah( b¯bb¯b, b¯bττ¯ and ττ¯ττ¯)(cid:1) (3.2d) → → (cid:0) (cid:1) are taken from ref.[28], and those on the cross sections at the LHC σ pp h,A,H( ττ¯) (3.2e) → → (cid:0) (cid:1) are taken from ref.[29]. Upper bound on the branching fraction + B t bH ( bτ¯ν ) (3.2f) τ → → (cid:0) (cid:1) is taken from ref.[30]. Since all the physical Higgs bosons are relatively light in our non- decoupling scenario when M < M 125 GeV, all the above constraints in eqs.(3.2) are h H ≈ required to be satisfied in all the results presented below. In particular, significant portion of very large tanβ regions is excluded by the h,A,H ττ¯ and t bH+( τ¯ν ) search τ → → → limits (eqs.(3.2e, 3.2f)). We define the ratio of a production rate at the LHC as σ(pp H)B(H AB) R = → → , (3.3) AB σ(pp H)SMB(H AB)SM → → – 5 – which gives the H AB production rate normalized to the SM prediction. Although we → calculate the Higgs boson cross section σ(pp H +X) at √s = 7 TeV in this study, the → ratio R should not change significantly even for √s = 8 TeV, since the dominance of AB the gluon fusion process remains to be valid. Hence, our results can also be applied for future results of √s = 8 TeV. Since the gluon fusion process dominates over the other production processes and the total decay width is dominated by Γ(H b¯b) for the heavy → CP even state H with mass around 125 GeV, R may be approximately written by using AB the partial decay widths, Γ(H gg) Γ(H b¯b) −1 Γ(H AB) R → → → . (3.4) AB ≃ Γ(H gg)SM · Γ(H b¯b)SM · Γ(H AB)SM (cid:18) → (cid:19) (cid:18) → (cid:19) (cid:18) → (cid:19) By introducing a short hand notation Γ(H ab) r = → , (3.5) ab Γ(H ab)SM → for a partial width normalized to the corresponding SM value, the production rate R of AB eq.(3.4) can be expressed as −1 RAB ≃ rgg ·(rb¯b) ·rAB. (3.6) In this study, we examine Rγγ, RVV (V = W, Z) and Rττ¯, −1 Rγγ ≃ rgg ·(rb¯b) ·rγγ, (3.7a) −1 RVV ≃ rgg ·(rb¯b) ·rVV, (3.7b) −1 Rττ¯ ≃ rgg ·(rb¯b) ·rττ¯, (3.7c) and identify two scenarios where the following two conditions are satisfied for the heavier CP even Higgs boson in the MSSM, 123 <M < 127 GeV, (3.8a) H 1 <R < 3. (3.8b) γγ Specifically, they are −1 Light stau scenario : rγγ > 1 and rgg ·(rb¯b) ∼ 1, (3.9a) Small Γ(H → b¯b) scenario : (rb¯b)−1 > 1 and rgg ·rγγ ∼ 1. (3.9b) Since the two scenarios, light stau scenario and small Γ(H b¯b) scenario, have distinct → predictionsforRVV andRττ¯,whichcanbetestedinthecurrentrunoftheLHC,weexplore their consequences carefully in the extended parameter space of the MSSM. For definiteness, we explore the following MSSM parameter region, 5 tanβ 40, 110 MH± 210, ≤ ≤ ≤ ≤ 500 GeV A 5000 GeV, 500 GeV µ 1500 GeV, t ≤ ≤ ≤ ≤ 300 GeV ≤ MQ˜ =MU˜ = MD˜ ≤ 1500 GeV, (3.10a) – 6 – where MH± is the charged Higgs boson mass, Mf˜ is the SUSY breaking sfermion mass parameter. The following parameters are set to fixed values, A = A = 1 TeV, b τ M3 = 800 GeV, M2 = 200 GeV, M1 = 100 GeV, (3.10b) where M are gaugino mass parameters, since they do not affect significantly the property i of the Higgs bosons. The slepton soft mass parameters are explored in the region 50 GeV ≤ ML˜ = ME˜ ≤ 500 GeV (3.10c) for the light stau scenario, while it is set to a fixed value ML˜ = ME˜ = 1 TeV (3.10d) for the small Γ(H b¯b) scenario. → 3.1 Fermion and sfermion contributions to r and r gg γγ In the SM, top quark loop contributes dominantly to the H gg amplitude. The SM → bottom quark loop interferes destructively with the top quark loop for M & 30 GeV, HSM and for M 125 GeV it counteracts the top quark loop contribution by roughly 10 %. HSM ∼ In the MSSM, the heavier CP even Higgs boson, H, couples up and down type fermions, respectively, with the couplings sinα √2m u g = , (3.11a) Huu sinβ v ! cosα √2m d g = . (3.11b) Hdd cosβ v ! Hence, when sinα > 0 in eq.(2.10b) and M & 30 GeV are satisfied, the bottom quark H loop interferes destructively with the top quark loop as in the SM. When sinα < 0 in eq.(2.10a) and M & 30 GeV are satisfied, on the other hand, the bottom quark loop H interferes constructively with the top quark loop, which can lead to r >1. gg Similar discussion is applied for r . In the SM, the W boson loop contributes domi- γγ nantly to the H γγ amplitude. The sub-dominant top quark loop interferes destruc- SM → tively with the W boson loop, whereas the bottom quark loop interferes constructively, for M & 30 GeV. In the MSSM, the H coupling to the weak bosons normalized to the HSM SM value is cos(α β). Hence, when H ( 125 GeV) has the SM-like coupling to the − ∼ weak bosons and tanβ 1, we have cos(α β) sinα and the top quark loop always ≫ − ≃ interferes destructively with the W boson loop, whereas the bottom quark loop interferes constructively when sinα> 0 as in the SM and destructively when sinα < 0. Sfermions in the third generation can have important contribution to the H gg and → the H γγ amplitudes due to their large Yukawa couplings. The mass eigenstates of the → – 7 – 2.0 2.0 HaLsinΑ<0 HbLsinΑ>0 1.5 1.5 r gg r ΓΓ 1.0 1.0 r r ΓΓ gg 0.5 0.5 r ×r r ×r gg ΓΓ gg ΓΓ 0.0 MŽ @GeVD 0.0 MŽ @GeVD 500 1000 1500 2000 t 1 500 1000 1500 2000 t 1 Figure 1. r (solid line), r (dashed line) and r r (dotted line) as functions of the lighter gg γγ gg γγ · stop mass for sinα < 0 (a) and sinα > 0 (b). MH = 125 GeV, At/MQ˜ = 2.6, MQ˜ = MU˜ = MD˜, tanβ =10, µ=1 TeV, sinα =sinβ and only the stops are considered among SUSY particles in | | the amplitudes. sfermions f˜1,2 (Mf˜1 < Mf˜2) are mixed states of the current eigenstates f˜L,R with a mixing angle θ , f f˜1 cosθf sinθf f˜L = − . (3.12) f˜2! sinθf cosθf ! f˜R! The mass matrix of the sfermions in the current basis is given by [31] ML2L ML2R = Mf2˜L +m2f +DLf mf(Af −µrf) , (3.13) ML2R MR2R! mf(Af −µrf) Mf2˜R +m2f +DRf! where m is the corresponding fermion mass and r = 1/r = tanβ for down and up type f d u fermions. The D terms are given in terms of the electric charge e , the weak isospin I3 f f and the weak mixing angle θ by w f 3 2 2 D = (I e sin θ )M cos2β, (3.14a) L f − f w Z f 2 2 D = e sin θ M cos2β. (3.14b) R f w Z The mass eigenvalues are M2 +M2 1 M2 = LL RR (M2 M2 )2+4(M2 )2, (3.15) f˜± 2 ± 2 LL − RR LR q where f˜− = f˜1 and f˜+ = f˜2 are the lighter and heavier mass eigenstates, respectively, and – 8 – the mixing angle θ (θ < π/2) is given by f f | | 2m (A µr ) f f f sin2θ = − , (3.16) f M2 M2 f˜2 − f˜1 M2 +Df M2 Df cos2θ = f˜R R− f˜L − L. (3.17) f M2 M2 f˜2 − f˜1 The heavier CP even Higgs boson, H, couples to up and down type sfermions in the mass eigenstate basis as follows [31] 2 sinα 2 2 3 2 2 g = m +M cos(α+β) I cos θ e cos2θ sin θ Hu˜±u˜± v fsinβ Z f f − f f w (cid:20) (cid:21) (cid:0)mf (cid:1) cosαµ sinαA sin2θ , (3.18a) f f ∓vsinβ − h i 2 cosα 2 2 3 2 2 g = m +M cos(α+β) I cos θ e cos2θ sin θ Hd˜±d˜± v fcosβ Z f f − f f w (cid:20) (cid:21) (cid:0)mf (cid:1) sinαµ cosαA sin2θ . (3.18b) f f ∓vcosβ − h i When H is a SM-like Higgs boson with tanβ 1 and when the mixing between f˜ and L ≫ f˜ is large, these couplings are approximated by R 2m2A2 g = u u sinα, (3.19a) Hu˜±u˜± ±vsinβ(M2 M2 ) u˜2 − u˜1 2m2µ2tanβ g = d sinα, (3.19b) Hd˜±d˜± ±vcosβ(M2 M2 ) ˜ ˜ d2 − d1 which are proportional to sinα, and the lighter of the mass eigenstates of the sfermions always interferes destructively with the top quark loop, while the heavier interferes con- structively with the top quark loop, independently of the sign of sinα. The lighter one generally contributes dominantly, and hence the squarks with large mixing always reduce r and increase r at the same time. Figure 1 shows r (solid line), r (dashed line) gg γγ gg γγ and r r (dotted line) as functions of the lighter stop mass for sinα < 0 (left) and gg γγ · sinα > 0 (right), where MH = 125 GeV, MQ˜ = MU˜ = MD˜, At = 2.6MQ˜, tanβ = 10, µ =1 TeV, sinα = sinβ and only the stops are considered among SUSY particles in the | | amplitudes. In both cases, the reduction of r due to stop contribution is always larger gg than the corresponding enhancement in r , and hence the light stop reduces the product γγ r r . When tanα = tanβ = 10, the bottom quark contributes constructively to gg γγ · − − the top quark loop, giving r > 1 in Figure 1 (a) for large stop masses. In contrast to gg squarks, stau can increase r without affecting r . γγ gg 3.2 Light stau scenario In this section, we examine Rγγ, RVV and Rττ¯ in the light stau scenario of eq.(3.9a) where the mass of the heavier CP even Higgs boson is 125 2 GeV and a large R is obtained γγ ± by increasing r . γγ – 9 –