Light Higgsinos, Heavy Gluino and b-τ Quasi-Yukawa Unification: Will the LHC find the Gluino?
LLight Higgsinos, Heavy Gluino and b − τ Quasi-Yukawa Unification:Will the LHC find the Gluino?Aditya Hebbar a, , Qaisar Shafi a, and Cem Salih ¨U n b, a Bartol Research Institute, Department of Physics and Astronomy,University of Delaware, Newark, DE 19716, USA b Department of Physics, Uluda˜g University, TR16059 Bursa, Turkey
Abstract
A wide variety of unified models predict asymptotic relations at M GUT between theb quark and τ lepton Yukawa couplings. Within the framework of supersymmet-ric SU(4) × SU(2) L × SU(2) R , we explore regions of the parameter space that arecompatible with b- τ quasi-Yukawa unification and the higgsinos being the lightestsupersymmetric particles ( (cid:46) E-mail: [email protected] E-mail: shafi@bartol.udel.edu E-mail: [email protected] a r X i v : . [ h e p - ph ] F e b Introduction
Low scale supersymmetry (SUSY) remains an attractive extension of the Standard Modeldespite the apparent absence thus far of any direct experimental signature for its existence,or any new physics for that matter, at the LHC [1]. A supersymmetric scenario consistingof relatively light ( (cid:46) µ parameter and related parameters associated with radiative electroweaksymmetry breaking (REWSB) are restricted to be comparable in magnitude to the Z-bosonmass.Our motivation in this paper is to realize a supersymmetric scenario with light higgsinoswithin the framework of unified models that also displays approximate third family Yukawacoupling unification (YU). Well-known examples include approximate t-b- τ Yukawa uni-fication [4, 5] in SO(10)[6] and SU(4) × SU(2) L × SU(2) R (4-2-2)[7], and b- τ Yukawaunification which can occur in SO(10), 4-2-2 and SU(5) models. t-b- τ YU requires thatthe two MSSM Higgs doublets (H d and H u ) reside in the 10 - plet of SO(10). However, toincorporate fermion masses and mixings, it is necessary to extend the Higgs sector by intro-ducing additional Higgs fields in the (15,1,3) and/or the (15,1,1) representations of 4-2-2.This breaks exact Yukawa unification, but the deviation from Yukawa unification can berestricted to within 20%, and such a modified scheme is often referred to as Quasi-YukawaUnification (QYU)[8, 9]. If Higgs fields from the above two (and possibly other) represen-tations are present, then the top quark Yukawa coupling, in particular, may receive largecorrections and therefore no longer unify with the b- τ Yukawa couplings. This particularscenario, called b- τ QYU, will be the focus of our study in this work. Note that TeV scalesupersymmetry plays a critical role via radiative corrections [10] in implementing approxi-mate Yukawa unification at M
GUT . This may be considered additional evidence in supportof supersymmetric Grand Unified Theories (GUTs) versus their non-supersymmetric coun-terparts which do not possess such threshold corrections.The supersymmetric 4-2-2 with left-right symmetry naturally allows for non-universalityin the MSSM gaugino sector. Thus, we can write M = 35 M + 25 M (1)which is implied by LR symmetry and hypercharge composition: M R = M L ≡ M , Y = (cid:114) I R + (cid:114)
25 ( B − L ) , (2)where M , M and M are the asymptotic soft supersymmetric breaking (SSB) gauginomasses for U (1) Y , SU (2) L and SU (3) C . For the scalar sector we work with the so-calledNon-Universal Higgs Model 2 (NUMH 2) structure in which the soft scalar masses asso-ciated with the sfermions and the two MSSM Higgs doublets are treated as independentparameters.In order to explore the parameter space compatible with quasi b- τ QYU and lighthiggsino, we employ the the fine-tuning parameter ∆ EW defined in [3]1 EW ≡ max i (C i ) / (M / , (3)where C H u = | − m H u tan β/ (tan β − | , C H d = | m H d / (tan β − | and C µ = | − µ | ,along with analogous definitions for C Σ uu ( k ) and C Σ dd ( k ) . We further constrain the parameterspace by requiring that ∆ EW (cid:46) µ (cid:46) EW we have considered here will result in mostly higgsino-like LSP. For smallervalues of ∆ EW , say of order 25-50, a second dark matter component, such as an axion,is needed to satisfy the dark matter abundance reported by WMAP [11]. Values close tothe upper limit (where µ ∼ y t : y b : y τ = | C t | : | − C bτ | : | C bτ | , (4)where C t measures deviation in y t , while C bτ measures the deviation of y b and y τ . Thefactor of 3 in Eq.(4) has its origin in the Clebsch-Gordon coefficient associated with the15-dimensional SU(4) C representation [8, 12]. Note that C t does not have to be related to C bτ . For definiteness, we restrict C bτ ≤ C t ≤ We employ the ISAJET 7.84 package [13] to perform random scans over the parameterspace given below. In this package, the weak scale values of gauge and third generationYukawa couplings are evolved to M GUT via the MSSM renormalization group equations(RGEs) in the DR regularization scheme. We do not strictly enforce the unification condi-tion g = g = g at M GUT , since a few percent deviation from unification can be assignedto unknown GUT-scale threshold corrections [14]. With the boundary conditions given at M GUT , all the SSB parameters, along with the gauge and Yukawa couplings, are evolvedback to the weak scale M Z .In evaluating Yukawa couplings, the SUSY threshold corrections [15] are taken intoaccount at the common scale M SUSY = √ m ˜ t L m ˜ t R . The entire parameter set is iterativelyrun between M Z and M GUT using the full 2-loop RGEs until a stable solution is obtained.To better account for leading-log corrections, one-loop step-beta functions are adoptedfor gauge and Yukawa couplings, and the SSB parameters m i are extracted from RGEs atappropriate scales m i = m i ( m i ). The RGE-improved 1-loop effective potential is minimizedat an optimized scale M SUSY , which effectively accounts for the leading 2-loop corrections.Full 1-loop radiative corrections are incorporated for all sparticle masses.2he requirement of radiative electroweak symmetry breaking (REWSB) [16] puts animportant theoretical constraint on the parameter space. Another important constraintcomes from limits on the cosmological abundance of stable charged particles [17]. Thisexcludes regions in the parameter space where charged SUSY particles, such as ˜ τ or ˜ t ,become the LSP.We have performed random scans for the following parameter space:0 ≤ m ≤
20 TeV0 ≤ M ≤ ≤ M ≤ − ≤ A /m ≤ ≤ tan β ≤ ≤ m H u ≤
20 TeV0 ≤ m H d ≤
20 TeV , with µ > m t = 173 . m t [10]. We use m DRb ( M Z ) = 2 .
83 GeV which ishard-coded into ISAJET.In scanning the parameter space, we employ the Metropolis-Hastings algorithm as de-scribed in [19]. The data points collected all satisfy the requirement of REWSB, withthe neutralino being the LSP in each case. After collecting the data, we impose the massbounds on all the particles [17] and use the IsaTools package to implement the followingphenomenological constraints [20, 21, 22]: m h = 123 −
127 GeV (6) m ˜ g ≥ . . × − ≤ BR( B s → µ + µ − ) ≤ . × − (2 σ ) (8)2 . × − ≤ BR( b → sγ ) ≤ . × − (2 σ ) (9)0 . ≤ BR( B u → τ ν τ ) MSSM
BR( B u → τ ν τ ) SM ≤ .
41 (3 σ ) (10)0 . ≤ Ω CDM h (WMAP9) ≤ . σ ) [11] . (11)We emphasize the mass bounds on the Higgs boson [23, 24], and the gluino [25], since theexperiments at the Large Hadron Collider (LHC) have had a strong impact on the boundson these particles. The rare B − meson decays have a strong impact on the parameter space,since the SM predictions are already in good agreement with the experimental results. Wehave applied the constraints from BR( B s → µ + µ − ) [26] and BR( b → sγ ) [27] within2 σ uncertainty, while the MSSM predictions on BR( B u → τ ν τ ) are limited to within 3 σ uncertainty [28].Another strict constraint comes from the DM observables. Since the LSP is proposed asa candidate for DM, the regions in the fundamental parameter space which yield chargedsparticles as LSP are excluded. Thus, we accept only those solutions for which one of theneutralinos is the lightest supersymmetric particle (LSP) without necessarily saturating3he 5 σ dark matter relic abundance bound observed by WMAP9. This is due to the factthat we are primarily motivated by ‘natural’ SUSY which we interpret to mean MSSM µ parameter (cid:46) a µ is concerned, we requirethat the solutions must be at least as consistent with the data as the Standard Model(0 ≤ ∆ a µ ≤ . × − [29]). Figure 1: Plots in the C bτ − m , C bτ − M , C bτ − M and C bτ − tan β planes. All pointsare compatible with REWSB and neutralino LSP. Green points satisfy the experimentalconstraints. Blue points form a subset which is compatible with b − τ QYU, µ (cid:46) EW < b − τ QYU and discussits impact on the low scale. Figure 1 displays C bτ vs. the fundamental parameters withplots in C bτ − m , C bτ − M , C bτ − M and C bτ − tan β planes. All points are compatiblewith REWSB and neutralino LSP. Green points satisfy all experimental constraints. Bluepoints form a subset which is compatible with µ (cid:46) EW < C bτ ≤ .
2, but instead indicate thisbound with a horizontal line. As seen from the C bτ − m , C bτ − M and C bτ − M plots,most of the solutions are below the horizontal line at C bτ = 0.2 and hence, b − τ QYUis not a strong constraint on these parameters. The plots show that while m cannot belower than about 2 TeV or heavier than 10 TeV, M and M can be as low as about 800GeV. However, we note that all the solutions with C bτ < . M > M < C bτ − tan β plot shows that the fine-tuning condition requires tan β (cid:38) M − µ , M − µ planes, which represent the low scale values of theseparameters. Color coding is the same as in Figure 1 except that the blue points now satisfy C bτ ≤ . µ (cid:46) EW < M = µ (left) and M = µ (right)We continue discussing the fundamental parameters in Figure 2 with plots in M − µ , M − µ planes, which represent the low scale values of these parameters. The color codingis the same as Figure 1, except that the blue points now satisfy C bτ < . µ (cid:46) EW < M and M are the SSB mass terms for bino and wino respectively,while µ determines masses of the higgsinos. Except for a few points near the line in thetwo plots which indicate a higgsino-bino or higgsino-wino mixture dark matter, we see thatfor much of the parameter space, the dark matter is composed mainly of higgsinos.Figure 3: Plots in the C bτ − ∆ EW and the Ω h − ∆ EW plane. Color coding is the same asFigure 2. 5e next discuss fine-tuning through the C bτ − ∆ EW and the Ω h − ∆ EW plots in Figure3. The color coding is the same as Figure 2. If dark matter is to be solely composed ofHiggsinos, then the WMAP bound imposes a lower bound of ∼
100 on ∆ EW , as seen fromthe C bτ − ∆ EW plot. However, if we allow for multi-component dark matter, then solutionswith ∆ EW as low as about 10 can also be found. Figure 4: Plots in the m ˜ t − m ˜ χ , m ˜ g − m ˜ χ , m ˜ τ − m ˜ χ and m ˜ χ ± − m ˜ χ . Color coding isthe same as in Figure 2. The lines depict the regions where the sparticle and the LSP arenearly mass degenerate. 6n this section, we discuss the mass spectrum compatible with the b − τ QYU. Figure4 displays plots in the m ˜ t − m ˜ χ , m ˜ g − m ˜ χ , m ˜ τ − m ˜ χ and m A − m ˜ χ planes. The colorcoding is the same as in Figure 2. The lines depict the regions where the sparticle and theLSP are nearly degenerate in mass. We see that the mass of the stop squarks is (cid:38) . . (cid:38) m ˜ τ vs m ˜ χ , from whichwe note that there exist solutions with NNLSP stau of mass as low as 200-250 GeV.Figure 5: Plots in the m ˜ g − ∆ EW and m ˜ t − ∆ EW planes. The color coding is the same asFigure 2. The LHC lower bound on the gluino mass m ˜ g ≥ . EW . The color coding is the same as inFigure 2. We note that it is possible to have a gluino with mass ∼ EW aslow as 30 or so [31]. We further observe that the stop mass can be as low as 1.5 TeV forthe entire range of ∆ EW that we consider. In order to be consistent with the measuredmass of the Higgs boson at the LHC, we require either a heavy stop, or large SSB trilinearscalar coupling or a suitable combination of the two. Large SSB trilinear scalar coupling,however, leads to higher fine-tuning [32]. This section discusses the DM implications of b − τ QYU in the light of current and expectedfuture results from the direct detection experiments. Figure 6 shows the results with plotsin the σ SI − m ˜ χ and σ SD − m ˜ χ planes. The color coding is the same as in Figure 2. Inthe σ SI − m ˜ χ plane, the dashed (solid) black line represents the current (future) resultsfrom the SuperCDMS experiment [33], and dashed (solid) red line(s) shows the current(future) results from the Xenon experiment [34]. The brown solid line is the latest resultfrom the LUX experiment [35]. In the σ SD − m ˜ χ plane, the current upper bounds are setby Super-K [36] (red dashed line) and the IceCube DeepCore indicated by black dashed(solid) line for its current(future) results. In addition, the purple dashed line is the limitset by the CMS analyses [37], while the brown dashed line represents the latest result fromthe LUX experiment[38].As can be seen from the σ SI − m ˜ χ plane, the DM scattering rate on nuclei yieldsrelatively large cross-sections ( ∼ − pb). These solutions involve higgsino-like DM, and7igure 6: Plots in the σ SI − m ˜ χ and σ SD − m ˜ χ planes. Color coding is the same asin Figure 1. In the σ SI − m ˜ χ plane, the dashed (solid) black line represents the current(future) results from the SuperCDMS experiment [33], and dashed (solid) red line(s) showsthe current (future) results from the Xenon experiment [34]. The brown solid line showsthe latest result from the LUX experiment [35]. In the σ SD − m ˜ χ plane, the current upperbounds are set by the Super-K [36], indicated by the red dashed line, and the IceCubeDeepCore by the black dashed (solid) line for its current and expected future results. Inaddition, the purple dashed line is the limit set by the CMS analysis [37], while the browndashed line represents the latest results from the LUX experiment[38].the large cross-section comes from the Yukawa interactions between the higgsinos andquarks in nuclei. Although some of these solutions are excluded by the current resultsfrom the LUX experiment, they will be further tested by the SuperCDMS experiment. Thepenultimate solid red line represents the future results from Xenon 1T, which accordingto present plans, will be reached in 2017. The last solid red line is the projected resultfrom the Xenon experiment over the next 20 years. The spin-dependent scattering resultsare shown in the σ SD − m ˜ χ plane, and all solutions are allowed by the current and futurereaches of the experiments.Finally, we present a table of six benchmark points, which exemplify our findings. Thepoints chosen are consistent with the experimental constraints in 2. The lowest value of∆ EW that we found was 9.6 , with a LSP mass of 207 GeV, displayed in Point 1. Notethat since the relic LSP density is about 10 % of the desired DM abundance, we positthat an additional DM component such as axion is also present. Points 2, 3 and 4 haveprogressively heavier LSPs which form a larger component of DM, but they require higherfine-tuning as measured by ∆ EW . Point 4 with an LSP mass of 688 GeV is the lightesthiggsino DM compatible with the WMAP bound and we do not need any other dark mattercomponent in this case. This point also corresponds to the lowest value of ∆ EW ≈ h = 0.113).8 oint 1 Point 2 Point 3 Point 4 Point 5 m M M M M H d
615 725 800 609 752 M H u β A /m -0.57 -0.62 -0.66 -0.72 -0.65 µ ∆ EW m h m H m A m H ± m ˜ χ , , , , , , m ˜ χ , m ˜ χ ± , , 4845 , 4120 , 3720 , 4189 , 3728 m ˜ g m ˜ u L,R m ˜ t , m ˜ d L,R m ˜ b , m ˜ ν e,µ m ˜ ν τ m ˜ e L,R m ˜ τ , σ SI (pb) 0 . × − . × − . × − . × − . × − σ SD (pb) 0 . × − . × − . × − . × − . × − Ω h y t,b,τ ( M GUT ) 0.55, 0.30, 0.41 0.54, 0.30, 0.39 0.54, 0.28, 0.36 0.55, 0.32, 0.42 0.54, 0.30, 0.39 C Table 1: Benchmark points consistent with the experimental constraints mentioned inSection 2. All masses are given in GeV. All points involve essentially 100% higgsino darkmatter.
We have explored how light ( (cid:46) C × SU(2) L × SU(2) R models which exhibit quasi b- τ Yukawa unification. We also requirethat the electroweak fine tuning measure ∆ EW (cid:46) cknowledgments This work is supported in part by the DOE Grant DE-SC0013880(A.H. and Q.S.), and the Scientific and Technological Research Council of Turkey (TUBITAK)Grant no. MFAG-114F461 (C.S. ¨U.). This work used the Extreme Science and EngineeringDiscovery Environment (XSEDE), which is supported by the National Science Founda-tion grant number OCI-1053575. Part of the numerical calculations reported in this paperwere performed at the National Academic Network and Information Center (ULAKBIM)of TUBITAK, High Performance and Grid Computing Center (TRUBA Resources).
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