GUT-Inspired Supersymmetric Model for h → γγ and Muon g − 2 M. Adeel Ajaiba,1, Ilia Gogoladzeb,2, and Qaisar Shafib,3 aDepartment of Physics and Astronomy, Ursinus College, Collegeville, PA 19426 bBartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA 5 1 0 2 Abstract n a J We study a GUT-inspired supersymmetric model with non-universal gaugino 6 masses that can explain the observed muon g − 2 anomaly while simultaneously 1 accommodating an enhancement or suppression in the h → γγ decay channel. In ] h order to accommodate these observations and m (cid:39) 125 − 126 GeV, the model h p requires a spectrum consisting of relatively light sleptons whereas the colored spar- - p ticles are heavy. The predicted stau mass range corresponding to R ≥ 1.1 is γγ e 100 GeV (cid:46) m (cid:46) 200 GeV. The constraint on the slepton masses, particularly on h τ˜ [ the smuons, arising from considerations of muon g−2 is somewhat milder. The slep- 1 tonmassesinthiscasearepredictedtolieinthefewhundredGeVrange. Thecolored v sparticles turn out to be considerably heavier with m (cid:38) 4.5 TeV and m (cid:38) 3.5 TeV, 5 g˜ t˜1 2 which makes it challenging for these to be observed at the 14 TeV LHC. 1 4 0 . 1 0 5 1 : v i X r a 1 E-mail: [email protected] 2E-mail: [email protected] On leave of absence from: Andronikashvili Institute of Physics, 0177 Tbilisi, Georgia. 3 E-mail: shafi@bartol.udel.edu 1 1 Introduction The ATLAS and CMS experiments at the LHC have independently reported the discovery [1, 2] of a Standard Model (SM)–like Higgs boson of mass m (cid:39) 125−126 h GeV using the combined 7 TeV and 8 TeV data. This discovery is compatible with low (TeV) scale supersymmetry [3]. At the same time, after the first LHC run we have the following lower bounds on the gluino and squark masses [4, 5] m (cid:38) 1.4 TeV (for m ∼ m ) and m (cid:38) 0.9 TeV (for m (cid:28) m ). (1) g˜ g˜ q˜ g˜ g˜ q˜ In some well motivated SUSY models the gluino is the NLSP in which case m (cid:38) 400 g˜ GeV [6]. These bounds combined with the bound of 125 GeV on the lightest CP even Higgs boson mass place stringent constraints on the slepton and gaugino (bino or wino) mass spectrum in several well studied scenarios such as constrained MSSM (cMSSM) [7], NUHM1 [8] and NUHM2 [9]. In particular, as we shall show later, in the above mentioned models, the first two generation sleptons are predicted to be more than 1 TeV in order to accommodate the light CP even Higgs with 125 GeV mass. The stau leptons can still be relatively light due to a relatively large trilinear soft supersymmetry breaking (SSB) A-term. There are several motivations to study models that allow for the sleptons be as light as ∼ 100 GeV. For instance, the SM prediction for the anomalous magnetic moment of the muon, a = (g −2) /2 (muon g −2) [10], shows a discrepancy with µ µ the experimental results [11]: ∆a ≡ a (exp)−a (SM) = (28.6±8.0)×10−10. (2) µ µ µ If supersymmetry is to offer a solution to this discrepancy, the smuon and gaugino (bino or wino) SSB masses should be O(100) GeV or so [12]. Thus, it is hard to simultaneously explain the observed Higgs boson mass and resolve the muon g − 2 anomaly if we consider CMSSM, NUHM1 or NUHM2, since in all these cases, the slepton masses are larger than 1 TeV. Recently, there have been several attempts to reconcile this apparent tension between muon g − 2 and the Higgs boson mass within the MSSM framework by assuming non-universal SSB mass terms for the gauginos [13, 14] or the sfermions [15, 16] at the GUT scale. Indeed, a simultaneous explanation of m and muon g−2 h is possible [17] in the presence of t − b − τ Yukawa coupling unification condition [18]. It has been shown [19] that constraints from FCNC processes are very mild and easily satisfied for the case in which the third generation sfermion masses are split from those of the first two generations. However, if the muon g−2 anomaly and the Higgs boson mass are simultaneously explained with non-universal gaugino and/or sfermionmasses, thecorrectrelicabundanceofneutralinodarkmatteristypicallynot obtained [16]. Consistency with the observed dark matter abundance would further constrain the SUSY parameter space. 2 Figure 1: Plots in the m vs. m plane for CMSSM (left panel) and NUHM2 (right h ˜l panel). Gray points are consistent with REWSB and neutralino LSP. Green points form a subset of the gray points and satisfy the sparticle and Higgs mass bounds, as well as all other constraints described in Section 2. The Higgs decay channel h → γγ in recent times attracted a fair amount of attention [20] because of the apparent deviation compared to the SM prediction. Currently, the deviation from the SM prediction has significantly reduced but has not completely disappeared. For example, the ATLAS collaboration reported µ = γγ 1.17±0.27 [21], where µ = σ(pp→h→γγ) . The CMS collaboration reported a best- γγ σ(pp→h→γγ)SM fit signal strength in their main analysis µ = 1.14+0.26 [22]. On the other hand, γγ −0.23 a cut-based analysis by CMS produced µ = 1.29+0.29, which is a slightly different γγ −0.26 value. This enhancement or suppression in the h → γγ channel with respect to the SM may provide a clue for physics beyond the SM if it is confirmed in the second LHC run. It is known that in order to accommodate an enhancement or suppression in the h → γγ decay channel in the framework of MSSM, the stau is the one of the best candidates, and its mass has to be around 200 GeV or so. It is problematic to accommodate an enhancement or suppression in the h → γγ decay channel in the framework of CMSSM, NUHM1 or NUHM2 models. In this paper we present a GUT inspired model which explains the observed g−2 anomaly while simultaneously accommodating an enhancement or suppression in the h → γγ channel. The paper is organized as follows: In Section 2 we describe the phenomenological constraints and the scanning procedure we implement in our analysis. In Section 3 we provide motivations for the model used in this paper by briefly reviewing the status of the muon g−2 anomaly and h → γγ in CMSSM and NUHM2. Our results for the h → γγ channel in the proposed model are presented in Section 4 and for the muon g −2 anomaly in Section 5. Our conclusions are outlined in Section 6. 3 2 Phenomenological Constraints and Scanning Pro- cedure We employ Isajet 7.84 [23] interfaced with Micromegas 2.4 [24] and FeynHiggs 2.10.0 [25] to perform random scans over the parameter space. In Isajet, the weak scale values of gauge and third generation Yukawa couplings are evolved to M via the GUT MSSM renormalization group equations (RGEs) in the DR regularization scheme. We do not strictly enforce the unification condition g = g = g at M , since 3 1 2 GUT a few percent deviation from unification can be assigned to unknown GUT-scale threshold corrections [26]. With the boundary conditions given at M , the SSB GUT parameters, along with the gauge and third family Yukawa couplings, are evolved back to the weak scale M . Z In evaluating the Yukawa couplings the SUSY threshold corrections [27] are taken √ into account at a common scale M = m m . The entire parameter set is itera- S t˜L t˜R tively run between M and M using the full 2-loop RGEs until a stable solution Z GUT is obtained. To better account for the leading-log corrections, one-loop step-beta functions are adopted for the gauge and Yukawa couplings, and the SSB scalar mass parameters m are extracted from RGEs at appropriate scales m = m (m ).The i i i i RGE-improved 1-loop effective potential is minimized at an optimized scale M , S which effectively accounts for the leading 2-loop corrections. Full 1-loop radiative corrections are incorporated for all sparticle masses. We implement the following random scanning procedure: A uniform and logarith- micdistributionofrandompointsisfirstgeneratedinthegivenparameterspace. The function RNORMX [28] is then employed to generate a Gaussian distribution around each point in the parameter space. The data points collected all satisfy the require- ment of radiative electroweak symmetry breaking (REWSB), with the neutralino in each case being the LSP. We use Micromegas to calculate the relic density and BR(b → sγ). The diphoton ratio R is calculated using FeynHiggs. After collecting the data, we impose the γγ mass bounds on all the particles [29] and use the IsaTools package [30] to imple- ment the various phenomenological constraints. We successively apply the following experimental constraints on the data that we acquire from ISAJET 7.84: 123 GeV ≤ m ≤ 127 GeV [1, 2] h 0.8×10−9 ≤ BR(B → µ+µ−) ≤ 6.2×10−9 (2σ) [31] s 2.99×10−4 ≤ BR(b → sγ) ≤ 3.87×10−4 (2σ) [32] 0.15 ≤ BR(Bu→τντ)MSSM ≤ 2.41 (3σ). [32] BR(Bu→τντ)SM 4 3 Slepton Masses in CMSSM and NUHM2 Before discussing the scenarios where we address the muon g − 2 anomaly and the decay rate h → γγ, we first present the relationship between the light CP even Higgs boson and slepton masses in two well studied models, namely CMSSM and NUHM2. While it is true that radiative corrections to the light CP even Higgs boson mass from the first two family sleptons are negligible, in the following section we show that relations among SSB mass terms from GUT scale boundary conditions in CMSSM and NUHM2 models yield a strong correlation between them. We do not consider the NUHM1 model since it is an intermediate step between CMSSM and NUHM2 in terms of the independent SSB parameters. Therefore, the light CP even Higgs boson mass dependence on slepton masses in NUHM1 can be inferred, more or less, from the CMSSM and NUHM2 models. We have performed random scans in the fundamental parameter space of CMSSM and NUHM2 with ranges of the parameters given as follows: 0 ≤ m ≤ 5TeV 16 0 ≤ M ≤ 3TeV 1/2 −3 ≤ A /m ≤ 3 0 3 35 ≤ tanβ ≤ 55; For CMSSM : m = M = M 16 Hu Hd For NUMH2 : 0 ≤ M (cid:54)= M ≤ 5TeV (3) Hu Hd Here m is the universal SSB mass parameter for sfermions, and M denotes the 16 1/2 universal SSB gaugino masses. A is the SSB trilinear scalar interaction coupling, 0 tanβ is the ratio of the MSSM Higgs vacuum expectation values (VEVs), and M , Hu M standfortheSSBmasstermsfortheMSSMupanddownHiggsdoublets. Since H d the masses of the light CP even Higgs boson and sleptons do not change significantly for tanβ < 35, we used data from our former analysis for 35 ≤ tanβ ≤ 55 to generate Figure 1. In Figure 1 we display our results in the m −m plane for CMSSM (left panel) h ˜l and NUHM2 (right panel). Here m stands for the left handed slepton masses for ˜l the first two families. We observe that in the CMSSM and NUHM2 models there is a fairly strong correlation between the Higgs boson mass (m ) and the first two h generation slepton masses (m ). Note that the bounds for the right handed slepton ˜l massesareverysimilarandarethereforenotdisplayed. Thegraypointsareconsistent with REWSB and neutralino LSP, and the green points form a subset of the gray pointsandsatisfythesparticleandHiggsmassbounds, aswellasallotherconstraints described in Section 2. We see from Figure 1 that for both the CMSSM and NUHM2 models, compatibil- itywiththemeasurement123GeV ≤ m ≤ 127GeV requiresthatthesleptonmasses h 5 lie above 1 TeV. The salient features of the results in Figure 1 can be understood by noting that in order for the stop quark mass to be more than 1 TeV [33] (which is necessary to achieve m ≈ 125 GeV), with universal SSB parameters M and m , h 1/2 0 the first and second generation squark masses acquire masses in the multi-TeV range, and the corresponding smuon masses lie around the TeV scale. On the other hand, as mentioned above, in order to have an enhancement in muon g−2 and in the decay rate of h → γγ, the sleptons need to be much lighter than 1 TeV. Overall, we learn from Figure 1 that in the CMSSM, NUHM1 and NUHM2 scenarios, it is not possible to have enhancement in muon g − 2 and the decay rate of h → γγ relative to the Standard Model. This conclusion motivates us to explore alternative scenarios which can simultaneously accommodate an enhancement or suppresion of h → γγ and an enhancement in muon g −2. 4 h → γγ Decay and Particle Spectra One of the most promising Higgs boson decay channels is the γγ final state which, at leading order, proceeds through a loop containing charged particles, including the charged Higgs, sfermions and charginos. In the SM, the leading contribution to h → γγ decay comes from the W boson loop, the top loop being the next dominant one. The decay width is given by (see [34, 35] and references therein) Γ(h → γγ) = GFα√2m3h (cid:12)(cid:12)N Q2g Ah (τ )+g Ah(τ )+Aγγ (cid:12)(cid:12)2, (4) 128 2π c t htt 1/2 t hWW 1 W SUSY where g is the coupling of h to the W boson. The supersymmetric contribution hWW Aγγ is given by SUSY m2 (cid:88) m2 Aγγ = g W Ah(τ )+ N Q2 g Z Ah(τ )+ SUSY hH+H− m2 0 H± c f hf˜f˜ m2 0 f˜ H± f f˜ (cid:88) m g W Ah(τ ), (5) i hχ+i χ−i mχi 12 χi where g is the coupling of h to the particle X (= H±,f˜,χ±). hXX i The stop and sbottom loop factors have similar contributions as the gluon fusion case. In this case, however, the stau can also contribute to enhance the decay width without changing the gluon fusion cross section. The chargino contribution to the decay width is known to be less than 10% for m (cid:38) 100 GeV. The charged Higgs χ± i contributionisevensmallersinceitscouplingtotheCP-evenHiggsisnotproportional to its mass and also due to the loop suppression m2 /m2 . W H± In the MSSM framework it was shown [20] that only a light stau can give signifi- cant enhancement/suppresion in the process gg → h → γγ, while keeping the lightest CP-even Higgs boson mass in the interval 123 GeV ≤ m ≤ 127 GeV. h 6 Figure 2: Plots in theR −M /M , R −M /M , R −M /M , R −M , R −M γγ 1 2 γγ 1 3 γγ 2 3 γγ 1 γγ 2 and R −M planes. Gray points are consistent with REWSB and neutralino LSP. γγ 3 Green points form a subset of the gray points and satisfy the sparticle and Higgs mass bounds, as well as all other constraints described in Section 2. Brown points belong to a subset of green points and satisfy the following bound on the LSP neutralino relic abundance, 0.001 ≤ Ωh2 ≤ 1. 7 In this paper we discuss the scenario with non-universal and opposite sign gaugino masses at M , while the sfermion masses at M assumed to be universal. This GUT GUT is a follow up of the work presented in ref. [13], where it was shown that the muon g−2 anomaly can be explained in this model, but the decay rate for h → γγ was not analyzed. Itwasshownin ref. [13] thatthe sleptons canbe aslightas 100GeVin this model. This observation motivated us to investigate the decay rate for h → γγ and study the parameter space which yields enhancement or suppression for this process. We perform random scans for following ranges of the parameters: 0 ≤ m ≤ 3TeV 16 0 ≤ M ≤ 5TeV 1 0 ≤ M ≤ 5TeV 2 −5 ≤ M ≤ 0TeV 3 −3 ≤ A /m ≤ 3 0 16 2 ≤ tanβ ≤ 60 0 ≤ m ≤ 5TeV 10 µ > 0. (6) Here M , M , and M denote the SSB gaugino masses for U(1) , SU(2) and SU(3) 1 2 3 Y L c respectively. We choose different sign for gauginos which was again motivated from the work presented in ref [13], where it was shown that an opposite sign non-universal gaugino mass case is more preferable from the muon g − 2 point of view than the same sign non-universal gaugino case. The main message of Section 3 is that with universal SSB mass terms for the gaugino and sfermion sectors, it is impossible to have significant SUSY contributions to the decay h → γγ and muon g − 2. On the other hand, as shown in ref. [13], non-universal gaugino masses allow for sufficiently light sleptons while keeping the colored sparticles in the multi TeV region. Because of this observation, we investigate the extent to which non-universality is allowed in the gaugino sector to enhance or suppress the decay channel h → γγ. The color coding in Figure 2 is given as follows, Gray points are consistent with REWSB and neutralino LSP. Green points form a subset of the gray points and satisfy the sparticle and Higgs mass bounds, as well as all other constraints described in Section 2. Brown points belong to a subset of green points and satisfy the constraint 0.001 ≤ Ωh2 ≤ 1 on the LSP neutralino relic abundance. We have chosen to display our results for a wider range of Ωh2, keeping in mind that one can always find points compatible with the current WMAP range for relic abundance with dedicated scans within the brown regions. The results from the R −M /M , R −M /M and R −M /M planes show γγ 1 2 γγ 1 3 γγ 2 3 that a significant deviation from universality of gaugino masses in order to have sizable SUSY contribution to h → γγ decay is necessary. For instance, the ratio 8 Figure 3: Plots in the R −m , R −µ, R −m and R −tanβ planes. Color γγ 16 γγ γγ 10 γγ coding same as in Figure 2. 9 M /M needs to be more than 5, while M /M > 3 and M /M > 2. Not only do 1 3 2 3 1 2 we observe a strict prediction of gaugino mass ratios, but also a precise prediction of their values. In particular, from the R − M panel we can see that it is difficult γγ 1 to have an enhancement of h → γγ if M (cid:38) 300 GeV. At the same time, the upper 1 bound on M is less stringent and enhancement of h → γγ occurs even with M 2 2 around 1 TeV. We observe from the R − M panel that the parameter M (cid:38) 2.5 TeV. The γγ 3 3 reason for such a large value of M is the following. Since we assume universality 3 in sfermion masses and seek solutions with sleptons not heavier than a few hundred GeV, m is required to be around a few hundred GeV. Moreover, with a tau slepton 16 mass of around a hundred GeV, in order to avoid breaking the charge symmetry, A needs to be around a hundred GeV. This places a constraint on A because we τ t assumea universal trilinearSSBA term. Consequently, a relatively smallvalueofA 0 t is obtained at low scale. On the other hand, it was shown in [33] that the stop mass needs to be more than 3 TeV if A is not the dominant contributor to the radiative t corrections of the light CP-even Higgs boson mass. In order to obtain such a heavy stop quark, when m is of order hundred GeV, a fairly large M is required. This 16 3 tendency can be observed from the following semi-analytic expressions for stop quark masses [36] m2 ≈ 5.41M2 +0.392M2 +0.64m2 +0.115M A −0.072M M +..., Qt 3 2 16 3 t0 3 2 m2 ≈ 4.52M2 −0.188M2 +0.273m2 −0.066A2 −0.145M M +.... (7) Ut 3 2 16 t0 3 2 It is clear from Eq. (7) that if m , M and A are of the order of hundred GeV or so, 16 2 t the way to obtain several TeV stop quark masses is to also have M around several 3 TeV. InFigure3wedisplayourresultsforthefundamentalparametersintheR −m , γγ 16 R −µ, R −m and R −tanβ planes. We can see that an enhancement in the γγ γγ 10 γγ h → γγ channelconstrainstheparametersinthismodel. Thefundamentalparameter m is restricted to a narrow range, 200 GeV (cid:46) m (cid:46) 600 GeV, for R ≥ 1.1. 16 16 γγ Similarly, the range for the other parameters for a corresponding enhancement in the h → γγ channel are: 2.5 TeV (cid:46) µ (cid:46) 5.5 TeV, m (cid:46) 2 TeV, 10 (cid:46) tanβ (cid:46) 20. 10 Figure 4 shows our results for the sparticle masses in the R −m , R −m , γγ τ˜ γγ χ˜0 1 R −m and R −m planes. For R ≥ 1.1, the stau and the neutralino are both γγ g˜ γγ t˜1 γγ relatively light with mass ranges 100 GeV (cid:46) m (cid:46) 200 GeV and 50 GeV (cid:46) m (cid:46) τ˜ χ˜0 1 200 GeV. From the lower panels of Figure 4 we can see that the colored sparticles corresponding to R ≥ 1.1 are heavy with m (cid:38) 4.5 TeV and m (cid:38) 3.5 TeV. The γγ g˜ t˜1 reason for such heavy stop and gluino masses has been discussed above. Testing squarks and gluinos with this mass would be challenging at 14 TeV LHC. 10