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Physics Letters B

www.elsevier.com/locate/physletb

A heavier gluino from t-b-T Yukawa-unified SUSY

Howard Baera *, Shabbar Razab1, Qaisar Shafib

a Dep't of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA

b Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

ARTICLE INFO

Article history: Received 13 February 2012 Accepted 30 April 2012 Available online 4 May 2012 Editor: G.F. Giudice

ABSTRACT

Supersymmetric models with t-b-t Yukawa coupling unification and unified gaugino masses at the GUT scale—with // > 0—show a mild preference for light gluino masses mg < 500 GeV. This range of mg is now essentially ruled out by LHC searches. We show that a heavier gluino with mg ~ 0.5-3 TeV can also be compatible with excellent t-b-t Yukawa coupling unification in supersymmetric models with nonuniversal Higgs masses (NUHM2). The gluino in such models is the lightest colored sparticle, while the squark sector displays an inverted mass hierarchy with mq ~ 5-20 TeV. We present some LHC testable benchmark points for which the lightest Higgs boson mass mh — 125 GeV. We also discuss LHC signatures of Yukawa-unified models with heavier gluinos. We expect gluino pair production followed by decay to final states containing four b-jets plus four W-bosons plus missing ET to occur at possibly observable rates at LHC.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Unification at MGUT (~ 2 x 1016 GeV) of t-b-T Yukawa couplings [1,2] is largely inspired by the simplest supersymmetric (SUSY) S0(10) or SU(4)c x SU(2)l x SU(2)r models [3]. It has become clear in recent years [4-11] that imposing t-b-T Yukawa coupling unification has important consequences for the sparticle and higgs mass spectrum of the minimal supersymmetric standard model (MSSM). The successful launch of the Large Hadron Collider (LHC) has provided important new impetus for these studies [1214]. For analogous discussion of b-T unification, see Ref. [15].

The parameter space of S0(10) SUSY GUT models for this investigation is given by

m16, mHu, mHd, mV2, A0, tan p, signQx), (1)

where m16 is the unified matter scalar mass, m2Hu and m2H are the GUT scale Higgs soft masses, m1/2 is the unified gaugino mass, A0 is the coefficient of the soft supersymmetry breaking (SSB) tri-linear term, and tan p is the ratio of Higgs field vevs. In order to allow for an appropriate radiative breaking of electroweak symmetry, the two GUT scale Higgs doublet masses must be split [16] according to mHu < m2Hi. This splitting might arise due to S0(10) D-terms (D-term splitting) or via GUT-scale threshold corrections

* Corresponding author.

E-mail addresses: baer@nhn.ou.edu (H. Baer), shabbar@udel.edu (S. Raza), shah@bartol.udel.edu (Q. Shafi). 1 On study leave from: Department of Physics, FUUAST, Islamabad, Pakistan.

0370-2693/$ - see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016Zj.physletb.2012.04.075

[7] (the Higgs splitting, or HS model). With the MSSM superpotential parameter \x> 0, this scenario predicts an inverted scalar mass hierarchy (IMH) [17] in the squark sector, wherein third generation squarks have masses in the few TeV range, while the first two generations of squarks have mass in the 5-30 TeV range [6]. The IMH allows one to reconcile a decoupling solution to the SUSY flavor and CP problems with relatively low fine-tuning in the EWSB sector. A successful implementation of the IMH scheme requires GUT-scale SSB terms to be related as A0 — 2m^0 — 4m^6, with unified third generation Yukawa couplings and the unified gaugino mass m1/2 on the low side: typically sub-TeV.

One particularly important prediction concerns the gluino which turns out to be the lightest colored SUSY particle.2 Since m1/2 is favored to be small in comparison to m16, there is some tendency in t-b-T unified models for mg < 500 GeV, which should be within range of SUSY searches at LHC operating with .Js = 7 TeV (LHC7) [20]. In this case, due to the large b-quark Yukawa coupling and the inverted squark mass spectrum, gluinos are expected to dominantly decay by 3-body modes such as g ^ bbXXi0, leading to final states at LHC consisting of multiple b-jets + MET [12,13].

2 These predictions are obtained under the assumption that the lightest neu-tralino is the lightest MSSM particle (LMP). This class of Yukawa-unified models tends to predict a thermal neutralino relic abundance QLMPh2 > 1 so that the neu-tralino LMP in this scenario is not a viable dark matter candidate. To overcome this drawback, one proposal [18,19] is to invoke axion physics and arrange for the lightest neutralino to decay before nucleosynthesis into an axino, which now plays the role of lightest SUSY particle (LSP). A combination of axions and axinos could then make up the dark matter content of the universe.

In fact, recent searches by the ATLAS experiment with less than 1 fb-1 of data already exclude mg < 500 GeV by searching for multijet plus missing ET (MET) plus one or more tagged b-jets [14]. Also, direct searches for gluinos and squarks under the assumption of unified gaugino masses by Atlas and CMS (again with ~ 1 fb-1 of data) typically exclude m~g < 550-750 GeV (depending on search techniques) [21,22]. Based on this critical input from experiment, the question arises: Are t-b-T unified models now excluded by LHC searches, or can Yukawa-unified solution be found with heavier gluinos with mass beyond current LHC reach? And if such solutions are found, what is the nature of the SUSY signal which is expected in near future runs of LHC7?

Our main goal in this Letter is to determine whether Yukawa-unified solutions with a heavier gluino can exist. In fact, we find numerous solutions, some of which are presented as a new set of benchmark points with mg in the range 0.5-3 TeV. In these solutions, the gluino retains its position as the lightest colored SUSY particle, while squarks remain in the multi-TeV range. Thus, we expect in this class of models that LHC searches should focus on gluino pair production. However, for these heavier gluino solutions, the g is expected to decay via g ^ tbjg± or ttx,°. After t ^ bW and x± ^ X® W decays, we expect gluino pair production final states to contain typically four b-jets, four W bosons plus MET. These are in rather sharp contrast with models containing mg < 500 GeV, where multi-b-jets + MET final states are expected, but without the numerous on-shell W bosons.

Note that due to potential threshold corrections which could arise from a variety of sources including a more complicated Higgs sector, higher order interaction terms, etc., we do not insist on exact (or perfect) unification of the three Yukawa couplings. Instead, in this Letter Yukawa unification realized at the 10% level (or better) is considered to yield an acceptable scenario. In practice, we find solutions with heavy (~ 2-3 TeV) gluino masses that are associated with Yukawa unification at a few percent level. Somewhat lighter gluino masses (~ 1-1.5 TeV) are accompanied by essentially perfect Yukawa unification! As expected, the squark masses display an inverted mass hierarchy, with the lightest (third family) squark masses ranging between 1 to 10 TeV. The first two family squarks turn out to be considerably heavier, of order 828 TeV. In the benchmark points that we highlight in this Letter, the mass of the SM-like Higgs boson is of order 124-126 GeV, a value which is consistent with results from recent ATLAS and CMS Higgs searches [23].

2. Phenomenological constraints and scanning procedure

We employ the ISAJET 7.80 [24] package Isasugra [25] to perform random scans over the fundamental parameter space. In this package, the weak scale values of gauge and third generation Yukawa couplings are evolved to MG via the MSSM renormaliza-tion group equations (RGEs) in the DR regularization scheme. We do not strictly enforce the unification condition g3 = g\ = g2 at MG, since a few percent deviation from unification can be assigned to unknown GUT-scale threshold corrections [26]. The deviation between gi = g2 and g3 at MG is no worse than 3-4%. For simplicity we do not include the Dirac neutrino Yukawa coupling in the RGEs, whose contribution is usually small [27].

The various HS model boundary conditions are imposed at MG and all the SSB parameters, along with the gauge and Yukawa couplings, are evolved back to the weak scale MZ. In the evaluation of Yukawa couplings, the SUSY threshold corrections [28] are taken into account at the common scale MSUSY = ^mg~mg~. The entire parameter set is iteratively run between MZ and MG 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 adopted for gauge and Yukawa couplings, and the SSB parameters mj are extracted from RGEs at multiple scales mj = mj(mj). The RGE-improved 1-loop effective potential is minimized at MSUSY, which effectively accounts for the leading 2-loop corrections. Full 1-loop radiative corrections are incorporated for all sparticle masses.

The requirement of radiative electroweak symmetry breaking (REWSB) imposes an important theoretical constraint on the parameter space. In order to reconcile REWSB with Yukawa unification, the MSSM Higgs soft supersymmetry breaking (SSB) masses should be split in such way that m2Hd/m2Hu > 1.2 at MG [29]. As mentioned above, the MSSM doublets reside in the 10 dimensional representation of S0(10) GUT for Yukawa unification condition to hold. In the gravity mediated supersymmetry breaking scenario [30], the required splitting in the Higgs sector can be generated by involving additional Higgs fields [10], or via D-term contributions [31]. In our Yukawa-unified SUSY spectrum calculations, the lightest neutralino is always turns out to be the LMP.

We have performed Markov-chain Monte Carlo (MCMC) scans for the following parameter range:

0 < m16 < 30 TeV, 0 < mHu < 35 TeV, 0 < mHi < 35 TeV, 0 < m1/2 < 5 TeV,

30 < tan fi < 60, -3 < Ao/mo < 3

with ¡i > 0 and mt = 173.3 GeV [32]. Note that our results are not too sensitive to one or two sigma variation in the value of mt [10]. We use mDR(mZ) = 2.83 GeV which is hard-coded into ISAJET.

In scanning the parameter space, we employ the Metropolis-Hastings algorithm as described in [33]. The data points collected all satisfy the requirement of REWSB, with the neutralino in each case being the LMP. After collecting the data, we impose the mass bounds on all the particles [34] and use the IsaTools package [35, 36] and Ref. [37] to implement the various phenomenological constraints. We successively apply the following experimental constraints on the data that we acquire from Isasugra:

mh (lightest Higgs mass) > 114.4 GeV

BR(Bs ^ i+i-) < 1.1 x 10

2.85 x 10-4 < BR(b ^ sy) < 4.24 x 10-4(2ct) [40]

0.15 < BRiBu„^rTri)MSSM < 2.41 (3ct)

^ BR(Bu ^TVT)SM

As far as the muon anomalous magnetic moment a| is concerned, we require that the benchmark points are at least as consistent with the data as the Standard Model is. For a presentation of (g - 2)x values in NUHM2 models, see [42].

3. A heavier gluino from Yukawa-unified SUSY

In order to quantify Yukawa coupling unification, we define the quantity RtbT as

Rtbr =

max(yt, yb, yr) min(yt, yb, yr).

In Fig. 1 we plot RtbT versus the various S0(10) model input parameters. Gray points are consistent with REWSB and neutralino LSP. Orange points satisfy the mass bounds (including mh

Fig. 1. Plots in mi6 — RtbT, mi/2 — RtbT, tanp — RtbT, A0/m16 — RtbT, and mg — RtbT planes. Gray points are consistent with REWSB and neutralino LSP. Orange points satisfy mass bounds (including mh in the range 115-131 GeV and mg ^ 0.5 TeV), constraints from BR(Bs ^ BR(Bu ^ tvt) and BR(b ^ sy). Blue point solutions belong to

a subset of orange points and represent mh in the range 123-127 GeV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

in the range 115-131 GeV and mg > 0.5 TeV), constraints from BR(Bs ^ BR(Bu ^ tvt) and BR(b ^ sy). Blue point so-

lutions belong to a subset of orange points and represent mh in the range 123-127 GeV. In Fig. 1a), we see, as is well known, that m16 > 10 TeV for solutions with RtbT < 1.1, as required by the inverted scalar mass hierarchy. In Fig. 1b), we also see that low values of mi/2 are favored. While previous works favored mi/2 < 0.1-0.2 TeV, here our dedicated MCMC scans show t-b-T unified solutions can also occur for mi/2 values in the 0.3-1 TeV range. Fig. 1c) shows that tan/) ~ 50-60 is required, while Fig. 1d) shows that A0 ~ -2m16 is required for the IMH. Our key result here occurs in Fig. 1e), where we plot the value of mg vs. RtbT. Here, we

find that while many solutions occur with mg < 0.5 TeV, there also exist solutions with near perfect Yukawa unification with substantially heavier gluino masses ranging up to mg ~ 1.4 TeV. And if we only require RtbT < 1.1, then some solutions can occur with mg as large as 3 TeV!

4. Heavier gluino benchmark points and implications for SUSY searches at LHC

In Table 1, we list four benchmark (BM) Yukawa-unified solutions from Isajet 7.80 with mg > 500 GeV. Each BM point also has

Table 1

Sparticle and Higgs masses (in GeV). AH of these benchmark points satisfy the various constraints mentioned in Section 2 and are compatible with Yukawa unification. Point 1 exhibits a solution near the current reach limit of LHC. Point 2 exhibits 'perfect' Yukawa unification. Point 3 displays an example of a relatively heavy gluino within reach of LHC14. Point 4 represents a solution with the heaviest gluino (— 3 TeV) we have in our scans; it is likely beyond reach of LHC. The uncertainty in the Higgs mass (mh) estimates is about ±2 GeV.

point 1 point 2 point 3 point 4

m16 21370 20 230 18 640 26130

m1/2 93.41 364 579 1021

^ü/m16 -2.43 -2.13 -2.09 -2.11

tan p 57.2 51 50 52

mHd 22 500.0 26 770 24430 34210

mHu 13 310.0 23 260 21 780 30 590

mh 126.7 125 124 124

mH 9389 3192 3145 4066

mA 9328 3171 3125 4040

mH± 9390 3193 3147 4067

mg 750 1375 1853 2991

mX 0 X1,2 122, 285 232, 491 323, 661 557, 1114

mX 0 X3,4 mX ± X1,2 19295, 19295 286, 19330 6048, 6048 493, 6021 4570, 4571 664, 4542 6315, 6315 1118, 6275

mUL,R mt1,2 21389, 21132 7389, 8175 20 230, 20115 3465, 5356 18 653, 18 574 3089, 5447 26187, 26079 4376, 7901

m dL,R mb b1,2 21389, 21513 7836, 8234 20 230, 20333 5417, 6047 18 653, 18 742 5534, 6584 26187, 26304 8038, 9652

m¡¡1 21 196 20128 18 565 26 037

m¡3 15 502 15 066 14 032 19441

mh,R mh,2 21193, 21717 7490, 15463 20123, 20416 8048, 15 079 18 559, 18 779 7796, 14 042 26027, 26319 9984, 19455

ncoMh2 12 642 190 972 1377

RtbT 1.06 1.00 1.05 1.07

BF(g ^ bbXi0) 0.33 0.13 0.07 0.06

BF(g ^ ttX0) 0.15 0.15 0.69 0.75

BF(g ^ tbX- + c.c.) 0.45 0.33 0.22 0.18

mh = 125 ± 2 GeV, so all are consistent with the Atlas/CMS hint of a Higgs signal around 125 GeV.

For point 1, with mi6 ~ 21 TeV, all the squarks and slep-tons are far beyond the reach of LHC. However, for this point, mg = 750 GeV, and so gluinos would be pair-produced at LHC7 with a cross section of ~ 60 fb [12]. In Ref. [12], LHC search strategies assumed a much lighter gluino of mass ~ 0.3-0.6 TeV, in which case gluino three body decays to bbXf are dominant, and the search strategy was to look for collider events containing multiple b-jets + MET. For point 1, at the bottom of the table we list the dominant gluino branching fractions. In this case, with mg ~ 750 GeV, the decay modes g ^ ttx0 and g ^ tbX- occur at substantial rates: in this case - 60%. Here, X- ^ X? W at 100% branching fraction, while t ^ bW also at 100%. Thus, gluino pair production for Yukawa-unified benchmarks and a heavier gluino lead to final states including four b-jets, four on-shell W -bosons + MET. Since the Ws decay into hard isolated leptons over 20% of the time, these gluino pair production events will contain high multiplicities of isolated leptons, including same sign (SS) and opposite-sign (OS) pairs, trileptons and four-leptons! There are few SM background (BG) processes that can lead to events containing for instance four b-jets plus four isolated leptons. The major BG process would likely be four top production: pp ^ ttttX.

In addition, X±X20 production can occur at large rates for the Yukawa-unified BM points [12]. For all cases listed, X± ^ X° W at ~ 100% branching fraction, and X2 ^ Xfh with typically a branch-

ing fraction > 90%. Recently, it has been pointed out [43] that the process pp ^ x±X20 ^ Whx0x0 should be visible at LHC with V = 14 TeV and ~ 100-1000 fb-1 of integrated luminosity. This latter gaugino pair production signal offers a second corroborative channel for claiming a SUSY discovery in models with lighter gaug-inos and decoupled squarks and sleptons. In addition, in the Wh channel, the pT (h) distribution may allow a chargino/neutralino mass extraction provided a very large data sample is acquired. Likewise, for mg — 500-800 GeV, then X20 ^ X?Z. In this case, X±X20 production will yield WZ + MET events, for which the WZ ^ 31 and possibly WZ ^ ¿+i- + jets signatures may be visible at LHC7 [44].

For point 2 in Table 1, we show a case with essentially perfect Yukawa unification, RtbT = 1.0, but with mg = 1375 GeV. In this case, the combined branching fraction for gluinos into top quark final states has increased to — 86%. With such a heavy gluino, this case would likely be beyond the reach of LHC7 [20]. However, it should be within reach of LHC with «Js = 14 TeV (LHC14), which should start operating around 2015. Benchmark point 3 in Table 1 shows a case with mg = 1853 GeV and decoupled scalars. This case, with such a heavy gluino mass, lies right around the ultimate reach of LHC14 with 100 fb-1, in a search for gluino pair production. However, the Wh search channel from X±X20 production may be competitive with gluino pair searches in this case assuming 100-1000 fb-1 of integrated luminosity.

The last point 4 in Table 1 corresponds to RtbT = 1.07, but with mg = 2991 GeV and decoupled scalars. This is the case with the largest gluino mass we were able to find while requiring RtbT < 1.1 and mh ~ 125 GeV. This case would likely lie beyond reach of LHC14 for any luminosity upgrade. Detection of a SUSY signal in this case would likely require a pp collider with V ~ 40-100 TeV.

5. Conclusion

Previous papers examining t-b-T Yukawa-unified models with gaugino mass unification and > 0 have focused on solutions with rather light gluinos: mg < 0.5 TeV. These models are now likely all excluded by recent or soon-to-be-released LHC SUSY searches. In light of these earlier results, we were motivated to examine if Yukawa-unified solutions with heavier gluinos could exist, while also requiring mh ~ 125 GeV, as is recently hinted at by Atlas and CMS. Using dedicated MCMC scans over S0(10) parameter space, we have found solutions with excellent Yukawa unification and mg ranging up to 1.4 TeV, well beyond current LHC search limits. Loosening the Yukawa-unification criteria to RtbT < 1.1, we even find solutions with mg nearly 3 TeV.

We have listed four S0(10) benchmark points with mg spanning the range 0.75-2.9 TeV. Regarding LHC SUSY searches, we note that these heavier gluino solutions will be characterized by gluino pair production at LHC, followed by decays to final states including four b-jets, four on-shell W-bosons + MET. The gluino pair events should be rich in multiple isolated leptons plus b-jets, and the dominant SM background will likely arise from four top production.

Acknowledgements

S.R. and Q.S. would like to thank Ilia Gogoladze for useful discussions. This work is supported in part by the DOE Grant No. DE-FG02-04ER41305 (HB) and DE-FG02-91ER40626 (SR and QS). This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation Grant No. 0CI-1053575.

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