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Physics Letters B

www.elsevier.com/locate/physletb

Beyond the Higgs boson at the Tevatron: Detecting gluinos from Yukawa-unified SUSY

Howard Baera *, Sabine Kramlb, Andre Lessaa, Sezen Sekmenc, Heaya Summya

a Dept. of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA

b Laboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1, CNRS/IN2P3, ¡NPG, 53 Avenue des Martyrs, F-38026 Grenoble, France c Dept. of Physics, Florida State University, Tallahassee, FL 32306, USA

ARTICLE INFO

ABSTRACT

Article history:

Received 20 October 2009

Received in revised form 12 January 2010

Accepted 18 January 2010

Available online 21 January 2010

Editor: G.F. Giudice

Simple SUSY GUT models based on the gauge group S0(10) require t-b-T Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places strong constraints on the expected superparticle mass spectrum, with scalar masses ~ 10 TeV while gluino masses are much lighter: in the 300-500 GeV range. The very heavy squarks suppress negative interference in the qq ^ gg cross section, leading to a large enhancement in production rates. The gluinos decay almost always via three-body modes into a pair of b-quarks, so we expect at least four b-jets per signal event. We investigate the capability of Fermilab Tevatron collider experiments to detect gluino pair production in Yukawa-unified SUSY. By requiring events with large missing ET and ^ 2 or 3 tagged b-jets, we find a 5a reach in excess of mg ~ 400 GeV for 5 fb-1 of data. This range in mg is much further than the conventional Tevatron SUSY reach, and should cut a significant swath through the most favored region of parameter space for Yukawa-unified SUSY models.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

There is now an ongoing huge effort at the Fermilab Tevatron pp collider to extract a Standard Model Higgs boson signal from a daunting set of SM background processes. While such an effort is to be lauded—and if successful would complete the picture provided by the Standard Model (SM)—we note here that an even bigger prize may await in the form of the gluino of supersymmet-ric (SUSY) models [1]. Current searches from CDF and D0 Collaborations have explored values of mg up to ~ 300 GeV within the context of the minimal supergravity (mSUGRA or CMSSM) model [2,3]. Here, we show that Tevatron experiments should—with current data sets—be able to expand their gluino search much further: into the 400 GeV regime, in Yukawa-unified SUSY, which is a model with arguably much higher motivation than mSUGRA [4]. Since Yukawa-unified SUSY favors a light gluino in the mass range 300-500 GeV, with the lower portion of this range giving the most impressive Yukawa coupling unification [5-9], such a search would explore a huge swath of the expected model parameter space.

Supersymmetric grand unified theories (SUSY GUTs) based upon the gauge group S0(10) are extremely compelling [10]. For one,

they explain the ad-hoc anomaly cancellation within the SM and SU(5) theories. Further, they unify all matter of a single generation into the 16-dimensional spinor representation j/(16), provided one adds to the set of supermultiplets a SM gauge singlet superfield NC (i = 1-3 is a generation index) containing a right-handed neutrino.1 Upon breaking of S0(10), a superpotential term f 3 2MNiNCNC is induced which allows for a Majorana neutrino mass MNi which is necessary for implementing the see-saw mechanism for neutrino masses [11]. In addition, in the simplest S0(10) theories where the MSSM Higgs doublets reside in a 10 of S0(10), one expects t-b-T Yukawa coupling unification in addition to gauge coupling unification at scale Q = MGUT [12,13]. In models with Yukawa coupling textures and family symmetries, one only expects Yukawa coupling unification for the third generation [14].

In spite of these impressive successes, GUTs and also SUSY GUTs have been beset with a variety of problems, most of them arising from implementing GUT gauge symmetry breaking via large, unwieldy Higgs representations. Happily, in recent years physicists have learned that GUT theories—as formulated in spacetime dimensions greater than four—can use extra-dimension compact-ification to break the GUT symmetry instead [15]. This is much in the spirit of string theory, where anyway one must pass from

* Corresponding author.

E-mail addresses: baer@nhn.ou.edu (H. Baer), sabine.kraml@lpsc.in2p3.fr (S. Kraml), lessa@nhn.ou.edu (A. Lessa), sezen.sekmen@cern.ch (S. Sekmen), -

heaya@nhn.ou.edu (H. Summy). 1 Here, we adopt the superfield "hat" notation as presented in Ref. [1].

0370-2693/$ - see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2010.01.035

a 10- or 11-dimensional theory to a 4-d theory via some sort of compactification.

Regarding Yukawa coupling unification in S0(10), our calculation begins with stipulating the b and t running masses at scale Q = MZ (for two-loop running, we adopt the DR regulariza-tion scheme) and the t-quark running mass at scale Q = mt. The Yukawa couplings are evolved to scale Q = MSUSY, where threshold corrections are implemented [16], as we pass from the SM effective theory to the Minimal Supersymmetric Standard Model (MSSM) effective theory. From MSUSY on to MGUT, Yukawa coupling evolution is performed using two-loop MSSM (or MSSM + RHN) RGEs. Thus, Yukawa coupling unification ends up depending on the complete SUSY mass spectrum via the t, b and t self-energy corrections.

In this work, we adopt the ISAJET 7.79 program for calculation of the SUSY mass spectrum and mixings [17]. ISAJET uses full two-loop RG running for all gauge and Yukawa couplings and soft SUSY breaking (SSB) terms. In running from MGUT down to Mweak, the RG-improved 1-loop effective potential is minimized at an optimized scale choice Q = ^m~tm~tR, which accounts for leading two-loop terms. Once a tree-level SUSY/Higgs spectrum is calculated, the complete 1-loop corrections are calculated for all SUSY/Higgs particle masses. Since the SUSY spectrum is not known at the beginning of the calculation, an iterative approach must be implemented, which stops when an appropriate convergence criterion is satisfied.

Yukawa coupling unification has been examined in a number of previous papers [12,5-9,13,18-20]. The parameter space to be considered is given by

mi6, mio, MD, mi/2, Ao, tanp, sign(^)

along with the top quark mass, which we take to be mt = 172.6 GeV [21]. Here, m16 is the common mass of all matter scalars at MGUT, m10 is the common Higgs soft mass at MGUT and M2d parameterizes either D-term splitting (DT) [19,5,9] or "just-so" Higgs-only soft mass splitting (HS) [20,5,6]. The latter is given by m2H = m20 ^ 2M2D. As in the minimal supergravity (mSUGRA) model, mi/2 is a common GUT scale gaugino mass, A0 is a common GUT scale trilinear soft term, and the bilinear SSB term B has been traded for the weak scale value of tan fi via the EWSB minimization conditions. The latter also determine the magnitude (but not the sign) of the superpotential Higgs mass term ¡.

What has been learned is that t-b-T Yukawa coupling unification does occur in the MSSM for ¡i > 0 (as preferred by the (g — 2)i anomaly), but only if certain conditions are satisfied.

• tan fi ~ 50.

• The gaugino mass parameter m1/2 should be as small as possible.

• The scalar mass parameter mig should be very heavy: in the range 8-20 TeV.

• The SSB terms should be related as A0 = 2m2w = 4m^6, with A0 < 0 (we use SLHA [22] conventions). This combination was found to yield a radiatively induced inverted scalar mass hierarchy (IMH) by Bagger et al. [23] for MSSM + right-hand neutrino (RHN) models with Yukawa coupling unification.

• EWSB can be reconciled with Yukawa unification only if the Higgs SSB masses are split at MGUT such that m2Hu < m2Hi .2 The HS prescription ends up working better than DT splitting [20,19].

In the case where the above conditions are satisfied, Yukawa coupling unification to within a few percent can be achieved.

The resulting sparticle mass spectrum has some notable features.

• First and second generation matter scalars have masses of order m16 ~ 8-20 TeV.

• Third generation scalars, mA and ¡i are suppressed relative to m16 by the IMH mechanism: they have masses on the 1-2 TeV scale. This reduces the amount of fine-tuning one might otherwise expect in such models.

• Gaugino masses are quite light, with mg ~ 300-500 GeV,

mxo ~ 50-80 GeV and m

100-160 GeV.

An exception is the case of highly split trilinears [24].

Since the lightest neutralino of S0(10) SUSY GUTs is nearly a pure bino state, it turns out that its relic density 0h2 would be

extremely high, of order 102-104 (unless it annihilates resonantly through the light Higgs [6], which is the case only in a very narrow strip of the parameter space). Such high values conflict with the WMAP observation [25], which gives

&CDMh2 = Pcdm/Pc = 0.1099 ± 0.0124 (2a), (2)

where h = 0.74± 0.03 is the scaled Hubble constant. Several solutions to the S0(10) SUSY GUT dark matter problem have been proposed in Refs. [26,6,8]. The arguably most attractive one is that the dark matter particle is in fact not the neutralino, but instead a mixture of axions a and thermally and non-thermally produced axinos a. Mixed axion/axino dark matter occurs in models where the MSSM is extended via the Peccei-Quinn (PQ) solution to the strong CP problem [27]. The PQ solution introduces a spin-0 ax-ion field into the model; if the model is supersymmetric, then a spin-1 axino is also required. The S0(10) SUSY GUT models with mixed axion/axino DM can [8]: 1. yield the correct abundance of CDM in the universe (where a dominant axion abundance is most favorable), 2. avoid the gravitino/BBN problem via m(gravitino) ~ m16 ~ 10 TeV and 3. have a compelling mechanism for generating the matter-antimatter asymmetry of the universe via non-thermal leptogenesis [28]. A consequence of the mixed ax-ion/axino CDM scenario with an axino as LSP is that WIMP search experiments will find null results, while a possible positive result might be found at relic axion search experiments [29].

A more direct consequence of the Yukawa-unified SUSY models is that the color-octet gluino particles are quite light, and possibly accessible to Fermilab Tevatron searches. Under the assumption of gaugino mass unification, the LEP2 chargino mass limit that mx± > 103.5 GeV normally implies that mg > 430 GeV, quite beyond the Tevatron reach. However, in Yukawa-unified SUSY, the trilinear soft breaking term is large: A0 ~ 10-20 TeV. Such a large trilin-ear term actually causes a large effect on gaugino mass evolution through two-loop RGE terms, as illustrated in Fig. 1. Here the left frame shows the gaugino mass evolution for the mSUGRA model point with (m0, m1/2, A0, tan fi, ¡) = (500 GeV, 157 GeV, 0, 10, +), which has m^± = 103.5 GeV, with mg = 426.1 GeV. In the right frame, we show the gaugino mass evolution for Point B of Table 2 of Ref. [8], but with a slightly lower m1/2 value. This point has the following GUT scale input parameters: m16 = 10 000 GeV, m10 = 12053.5 GeV, MD = 3287.12 GeV, m1/2 = 34 GeV, A0 = — 19 947.3 GeV, tanfi = 50.398 and ¡1 > 0. (tan fi is input as a weak scale value.) In this case, the gaugino mass evolution is strongly affected by the large two-loop terms, resulting in a much smaller splitting between gaugino masses M2 and M3. Here, we find (after computing physical masses including one-loop sparticle mass corrections) that while mx± = 108.2 GeV, the gluino mass is only mg = 322.8 GeV. This value of m~g may well be within range of Tevatron discovery, even while respecting chargino mass bounds from LEP2.

mSUGRA

102 104 106 108 1 010101210141016 Q (GeV)

102 104 106 108 1 010101210141016 Q (GeV)

Fig. 1. Evolution of soft SUSY breaking gaugino mass parameters using two-loop RG evolution in the case of mSUGRA and in the case of the HS model with parameters as listed in the text.

400 rn. (GeV)

In Yukawa-unified models, the b and t Yukawa couplings are large, while the top and bottom squark masses are much lighter than their first/second generation counterparts. As a consequence, gluino decays to third generation particles—in particular decays to b quarks—are enhanced. In addition, gluino pair production via qq fusion is normally suppressed by t- and s-channel interferences in the production cross section. For mq ~ 10 TeV, the negative interference is suppressed, leading to greatly enhanced gluino pair cross sections. Use may be made of the large gluino pair production cross section, and the fact that each gg production event is expected to have four or more identifiable b-jets, along with large Emlss, to reject SM backgrounds.

In this Letter, we examine gluino pair production at the Fer-milab Tevatron collider. While negative searches for gluino pair production have been made, and currently require (under an analysis with ~ 2 fb-1 of integrated luminosity) mg > 308 GeV [2,3] in mSUGRA-like models, use has not yet been made of the large gluino pair production cross section and high b-jet multiplicity expected from Yukawa-unified models.3 Here, we point out the importance of exploiting the b-jet multiplicity to maximize the reach. By requiring Tevatron events with > 4 jets plus large ETlss, along with > 2 or 3 tagged b-jets, QCD and electroweak backgrounds can be substantially reduced relative to expected signal rates. We find that the CDF and DO experiments should be sensitive to mg ~ 400-440 GeV with 5-10 fb-1 of integrated luminosity. Thus, Tevatron experiments are sensitive to much higher values of gluino mass than otherwise expected from conventional searches. With 5-10 fb-1 of data, Tevatron experiments can indeed begin to explore a large swath of Yukawa-unified SUSY model parameter space.

In Section 2, we review gluino pair production total cross sections and expected branching fractions, and introduce a special Yukawa-unified SUSY model line. In Section 3, we provide details of our event simulation program, and show how the requirement of events with > 4 jets plus large ETlss, along with > 2 or 3 identified b-jets, rejects much SM background, at little cost to signal. We provide our reach results versus mg. In Section 4, we present a summary and conclusions.

2. Production and decay of gluinos at the Tevatron

21. Gluino pair production

Recent studies of squark and gluino pair production at the Fer-milab Tevatron collider, using data corresponding to 2 fb-1 of in-

Fig. 2. Production cross section a (pp ^ ggX) in fb at the V? = 1.96 TeV Fermilab Tevatron collider versus mg, for mq = 10 TeV.

tegrated luminosity and a beam energy of «fs = 1.96 TeV, have produced limits at the 95% CL that mg > 280 GeV (in the case of CDF [2]), and mg > 308 GeV (in the case of D0 [3]). These studies— in the parts focused on gluino pair production—essentially asked for the presence of events with > 4 hard jets, plus large E flss and large HT, where HT is the scalar sum of the ET s of all identified jets in the event, beyond an expected SM background level. These studies do not use some of the unique characteristics common to gluino pair production in Yukawa-unified SUSY, so we expect Teva-tron experiments to be able to do much better in this case.

First, we present the expected total cross section rates for gluino pair production in Fig. 2, displaying leading order (LO) and next-to-leading order (NLO) cross sections as given by Prospino [31]. We adopt a common first/second generation squark mass of mq = 10 TeV, and take the Tevatron energy as V? = 1.96 TeV. We see from the figure that for mg = 300 GeV, the cross section is about 900 fb, dropping to about 65 fb for mg ~ 400 GeV. Moreover, it remains at the level of several fb even for mg as high as 500 GeV.

These cross sections are well in excess of those which enter the CDF and D0 search for gluino pair production. To understand why, we first note that gluino pair production for mg ~ 300-500 GeV is dominated by valence quark annihilation via qq fusion at the Teva-tron. The gg fusion subprocess is dominant at much lower gluino masses, where the gluon PDFs have their peak magnitude at small parton fractional momentum x. The qq ^ gg subprocess cross section receives contributions from s-channel gluon exchange, along with t- and u-channel squark exchange diagrams [32]. The st-and su-channel interference terms contribute negatively to the total production cross section, thereby leading to an actual suppression of a(pp ^ ggX) for mq ~ mg. For mq ^ mg on the other hand, the t-channel, u-channel and interference terms are all highly suppressed, leaving the s-channel gluon exchange contribution un-suppressed and dominant. The situation is illustrated in Fig. 3, where we plot the LO and NLO gluino pair production cross section for mg = 300, 400 and 500 GeV versus mq (since the gluino mass ranges between 300 and 500 GeV in Yukawa-unified SUSY, as noted in Section 1). We see that as mq grows, the total production cross section increases, and by a large factor: for mg = 400 GeV, as mq varies from 400 GeV to 10 TeV, we see a factor of ~ 10 increase in total rate!

At the present time—Fall 2009—CDF and D0 have amassed over 5 fb-1 of integrated luminosity.4 Thus, if mg ~ 400 GeV, there

3 The utility of b-jet tagging for extracting SUSY signals at the LHC has been ex-

amined in Ref. [30].

4 It is expected that CDF and D0 will reach the - 10 fb-1 level during 2010.

= _______

: ^^^^^^^ nig = 300 GeV

- ^^ m~ = 400 GeV

- ^^^ nr^ = 500 GeV

rrv(GeV)

Fig. 3. Cross section of gluino pair production (in fb) at the Fermilab Tevatron collider as a function of mq, for mg = 300, 400 and 500 GeV. Dashed line is LO QCD, while solid line is NLO, as given by Prospino.

could be ~ 300 gluino pair events in each group's data. Such a large event sample may well be visible if appropriate background rejection cuts can be found. The exact collider signatures depend on the dominant gluino decay modes, which we discuss in the next section.

2.2. Gluino decays in Yukawa-unified SUSY

To examine the gluino decay modes in Yukawa-unified SUSY, we will adopt a model line which allows us to generate typical Yukawa-unified models over the entire range of m g which is expected. First, we note in passing that Yukawa unification is not possible in the mSUGRA model, since the large t-b-T Yukawa couplings tend to drive the m2Hi soft SUSY breaking term more negative than m2H , in contradiction to what is needed for an appropriate breakdown of electroweak symmetry. Yukawa-unified models can be found if one instead moves to models with non-universal Higgs masses, where m2H^ < mH already at the GUT scale [33,18]. In this case, mH gets a head start in its running towards negative values. Detailed scans over the parameter space in Ref. [6] using the parameter space in (1) found a variety of solutions in the Higgs splitting (HS) model. We will adopt Point B of Table 2 of Ref. [8] as a template model. This point has the following GUT scale input parameters: m16 = 10000 GeV, m10 = 12053.5 GeV, MD = 3287.12 GeV, m1/2 = 43.9442 GeV, A0 = -19947.3 GeV, tan /) = 50.398 and > 0 (where tan /) is again at the weak scale). The Yukawa couplings at MGUT are found to be ft = 0.557, fb = 0.557 and fT = 0.571, so unification is good at the 2% level. The gluino mass which is generated is m g = 351 GeV.

If we now allow m\/2 to vary, we still maintain valid Yukawa-unified solutions over the range of mi/2: 35-100 GeV, corresponding to a variation in m g : 325-508 GeV. (The Yukawa unification gets worse as m\/2 increases, and at m\/2 = 100 GeV diminishes to 7.3%.) The value of the chargino mass at mi/2 = 35 GeV is mx± = 108 GeV, i.e. slightly above the LEP2 limit. We will label Point B with variable m1/2 as the Higgs splitting, or HS, model line. The value of the light Higgs boson is mh — 127 GeV all along the HS model line.

Armed with a Yukawa-unified SUSY model line, we can now examine how the gluino decays as a function of gluino mass. The gluino decay branching fractions as calculated by ISAJET are shown in Fig. 4. Here, we see that at low m g ~ 325 GeV, the mode g ^ bboccurs at over 60%, and dominates the g ^ bbx0

Fig. 4. Dominant gluino branching fractions versus mg for the Yukawa-unified SUSY HS model line.

branching fraction, which occurs at typically 10-20% [34]. As mg increases, the decay modes g ^ tbx- + c.c. grows from the kine-matically suppressed value of below 10% at mg ~ 325 GeV, to ~ 40% at mg ~ 500 GeV. All these dominant decay modes lead to two bs per gluino in the final state, so that for gluino pair production at the Tevatron, we expect collider events containing almost always > 4 jets + ETlss, with > 4 b-jets. Even more b-jets can come from x2 decays, since x2 ^ bbx0 at around 20% all across the HS model line. Only a very small fraction of gluino decays, less than 1 0%, lead to first/second generation quarks in the final state.

3. Reach of the Fermilab Tevatron for gluinos in Yukawa-unified SUSY

Next, we examine whether experiments at the Fermilab Teva-tron can detect gluino pair production in the HS model line assuming 5- 1 0 fb- 1 of integrated luminosity. We generate signal and background events using ISAJET 7.79, with a toy detector simulation containing hadronic calorimetry ranging out to \n\ < 4, with cell size An x Afi = 0.1 x 0.262. We adopt hadronic smearing of AE = 0.7/\/~E and EM smearing of AE = 0.15/VÊ. We adopt the ISAJET GETJET jet finding algorithm, requiring jets in a cone size of AR = 0.5 with E^ > 15 GeV. Jets are ordered from highest Et (j1) to lowest ET. Leptons within \nl\ < 2.5 (I = e, ¡) are classified as isolated if pT(I) > 10 GeV and a cone of AR = 0.4 about the lep-ton direction contains ET < 2 GeV. Finally, if a jet with \nj\ < 2 has a B-hadron with ET > 15 GeV within AR < 0.5, it is tagged as a b-jet with an efficiency of 50%. Ordinary QCD jets are mis-tagged as b-jets at a 0.4% rate [35].

We also generate SM background (BG) event samples from W + jets production, Z + bb production, tt production, vector boson pair production,hadronic bb production, bb bb production, ttbb production and Zbbbb (followed by Z ^ vv) production.5 The W + jets sample uses QCD matrix elements for the primary parton emission, while subsequent emissions (including g ^ bb splitting) are generated from the parton shower. For Z + bb, we use the exact 2 ^ 3 matrix element, which is pre-programmed into ISAJET using Madgraph [36]. We use AlpGen [37] plus Pythia [38] for bb bb and ttbb production, and Madgraph plus Pythia for Zbbbb production [36].

5 We do not take into account the QCD dijet backgrounds which turn out to be negligible after the cuts described below.

w 2 s 10

50 100 150 200 250 300 350 400 Efss (GeV)

Fig. 5. Distribution in missing Et from gluino pair production in Yukawa-unified SUSY Pt. B, along with summed SM backgrounds (gray histogram), with minimal cuts listed in text.

Table 1

Sets of cuts from Refs. [39,2,3] used in this analysis. In addition we require throughout ^ 4 jets, no isolated leptons, at least one jet with \m \ < 0.8 and A4>(j1, j2) < 160°.

Cuts Emiss Ht Et (j1) Et (j2) Et (j3) Et (j4)

BMPT ^ 75 GeV - 15 15 15 15

CDF ^ 90 GeV 280 95 55 55 25

D0 ^ 100 GeV 400 35 35 35 20

01234567 01234567 01234567 n.

Fig. 6. Distribution in tagged b-jet multiplicity for gluino pair production in Yukawa-unified SUSY Pt. B, along with summed SM backgrounds (brown histogram), after cut sets BMPT, CDF, and D0 given in Table 1. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)

tal BG rates. Then, as one moves towards large b-jet multiplicity nb > 2 or 3, there should be much higher rates than expected from SM BG.

Table 2 shows a listing of expected contamination from each BG source after the different sets of cuts. The hard Em'ss and HT cuts largely eliminate the bb BG. The isolated lepton veto combined with large Eflss requirement cuts much of W + jets. The remaining large BGs come from tt production and Z + bb production, where Z ^ vv. Requiring > 4 jets along with large HT for the CDF and D0 cuts largely reduces Zbb to small levels, leaving tt as the dominant BG.

In light of these results, we proceed by requiring BMPT, CDF or D0 cuts, along with

For our first results, we exhibit the distribution in ETlss in Fig. 5 as generated for the HS model line Pt. B (with mg = 350 GeV) as the blue histogram, along with the summed SM backgrounds (gray histogram). (For interpretation of the colors in this figure, the reader is referred to the web version of this article.) While the signal histogram is harder than the BG histogram, the BG level is so high that signal doesn't exceed BG until Emiss > 300 GeV. Of course, this Pt. B gluino mass is well beyond the current Tevatron gluino mass limits, so this is easy to understand.

To do better, we must adopt a set of cuts that selects out canonical gluino pair production events. Here, we will follow the recent papers BMPT [39], CDF [2] and D0 [3], and require the cuts listed in Table 1.

We have yet to make use of the high b-jet multiplicity which is expected from Yukawa-unified SUSY. In Fig. 6, we plot the multiplicity of b-jets expected from SM background (brown histogram), and the summed BG plus signal from HS Pt. B. (The BG in the nb = 0 channel is very under-estimated, since we leave off QCD multi-jet production.) We see that the BG distribution has a sharp drop-off as nb increases. Especially, there is a very sharp dropoff in BG in going from the nb = 2 to the nb = 3 bin. When we add in the signal distribution, we see the histogram expanding out to large values of nb due to the presence of 4-6 b-jets per SUSY event. For the softer BMPT cuts, the signal hardly influences the nb = 0, 1 , 2 bins. However, in the nb = 3 bin, there is a huge jump in rate, reflecting the presence of a strong source of > 3 b-jet events. In the case of the CDF and D0 cuts, which are much harder, the total BG is much diminished. In this case, the summed signal plus BG distribution actually becomes rounded, and is again much harder than just BG alone. For the CDF (D0) cuts, signal exceeds BG in the nb = 2 bin by a factor of 2 (3). By the time we move to the nb = 3 bin, then for both CDF and D0 cuts, signal exceeds BG by over an order of magnitude. Using soft cuts and low b-jet multiplicity, one should gain a good normalization of to-

• nb > 2 or 3.

In Fig. 7 we plot the resultant SM background (blue dashed lines), along with expected signal rates for the HS model line (full lines) for the three sets of cuts with nb > 2 (upper row) as well as nb > 3 (lower row). (For interpretation of the colors in this figure, the reader is referred to the web version of this article.) The SM background comes almost entirely from ttt production. The third b-jet in tt production can come from additional g ^ bit radiation, or from QCD jet mis-tags. Since the dominant BG comes from tt production, and the a(pp ^ ttX) cross section is well known from standard top search channels, the background should be rather well understood.

We see from Fig. 7 that signal actually exceeds BG for a substantial range of mg for all cases except the BMPT cuts with nb > 2. We also compute the signal cross sections required for a 5a discovery for each selection assuming 5 and 10 fb-1 of integrated luminosity, shown as the dot-dashed and dotted lines, respectively. The significance in as is derived from the p-value corresponding to the number of S + B events in a Poisson distribution with a mean that equals to the number of background events. The best reach is achieved with the hard D0 cuts. In this case, requiring nb > 2, we find that signal exceeds the 5a level for 5 (10) fb-1 of integrated luminosity for mg < 395 (410) GeV. Requiring nb > 3, the 5a reach for 5 (10) fb-1 increases to mg = 405 (430) GeV. Thus, in the case of Yukawa-unified SUSY where an abundance of b-jets are expected to accompany gluino pair production, we expect Fermilab Tevatron experiments to be able to probe values ofmg to much higher values than have previously been found.

Since the value of mg is expected to lie in the range 300500 GeV for Yukawa-unified models, and in fact the Yukawa unification is best on the lower range of mg values, it appears to us that CDF and D0, using current data samples, stand a good chance of either discovering Yukawa-unified SUSY, or excluding a huge portion of the allowed parameter space.

Table 2

SM backgrounds in fb before and after cuts BMPT, CDF and DO for nb ^ 2 and ^ 3. The pT range for bb subprocess generation is 15-200 GeV. The pT range for tt subprocess generation is 10-300 GeV. The Vs range for Zbb subprocess generation is 100-400 GeV. In the above, V = W or Z.

BG a (fb) Events BMPT CDF D0

^ 2bs ^ 3bs ^ 2bs ^ 3bs ^ 2bs ^ 3bs

bb 3.8 x 108 106 - - - - - -

tt 5.9 x 103 106 51.9 1.3 8.6 0.3 3.9 0.14

bb + (Z ^ vv) 1.3 x 104 106 15.7 0.4 - - - -

W+jets 4.8 x 106 5 x 106 1.9 - - - - -

VV 9.7 x 103 106 0.6 0.01 - - - -

bbbb 6.3 x 104 9.7 x < 105 0.39 0.13 0.065 0.065 - -

tttbbt 11 4.1x < 105 0.39 0.13 0.066 0.019 0.037 0.013

bbbb + (Z ^ vv) 0.54 6.6 x 103 0.03 0.01 < 10-2 < 10-2 < 10-3 < 10-

Total 70.9 1.98 8.7 0.38 3.94 0.15

n 1 ............... .............

320 360 400 440 320 360 400 440 320 360 400 440

m~ (GeV)

Fig. 7. Reach of the Fermilab Tevatron collider for gluino pair production in Yukawa-unified SUSY HS model line, versus mg. We show the reach for 5 and 10 fb-1 of integrated luminosity.

4. Conclusions

In this Letter, we explored the capability of the CDF and D0 experiments to search for gluinos with properties as predicted by supersymmetic models with t-b-T Yukawa coupling unification. While a vast effort is rightfully being placed by CDF and D0 to search for the SM Higgs boson, a potentially bigger prize—the gluinos from supersymmetric models—could be lurking in their data. The Yukawa-unified SUSY model is extremely compelling, in part because it combines four of the most profound ideas in physics beyond the SM: S0(10) grand unification (which unifies matter as well as gauge couplings), weak scale supersymmetry, see-saw neutrino masses and the Peccei-Quinn-Weinberg-Wilczek solution to the strong CP problem. While we do not present a specific model which incorporates all these ideas into a single framework, a wide array of low energy, collider and astrophysical data give some indirect and also direct support to each of these ideas. The requirement of Yukawa coupling unification forces upon us a very specific and compelling sparticle mass spectrum, including first/second generation scalars at the ~ 10 TeV scale, while gluinos are quite light: in the ~ 300-500 GeV range. We investigated here whether these light gluinos are accessible to Tevatron searches for supersymmetry.

Our main result is that the CDF and D0 experiments should be already sensitive to gluino masses far beyond currently published bounds (which lie around the 300 GeV scale). This is due to three main factors:

1. Two-loop RGE effects allow for gluinos as light as 320 GeV in the Yukawa-unified model with multi-TeV trilinear soft terms, even while respecting LEP2 limits on the chargino mass. In the case of generic SUSY models with TeV scale soft parameters, the LEP2 chargino mass limit usually implies mg > 425 GeV.

2. Gluino pair production cross sections with mg ~ 300-500 GeV are enhanced at the Tevatron due to the extremely high squark masses expected in Yukawa-unified SUSY. The huge value of mq acts to suppress negative interference effects in the qq ^ g g subprocess cross section, leading to elevated production rates.

3. Gluinos of Yukawa-unified SUSY decay through cascade decays to final states almost always containing four b-jets, and sometimes six or eight b-jets, depending if x0 ^ x0bb occurs. By searching for collider events with > 4 jets plus large Emlss, along with > 2 or 3 b-jets which are tagged through the micro-vertex detector, SM backgrounds can be reduced by large factors, at only a small cost to signal.

This may allow Tevatron experiments to search for gluinos with mass in excess of 400 GeV. Such gluino masses are far beyond currently published bounds, and would allow exploration of a huge swath of parameter space of Yukawa-unified SUSY models.

In addition, in the case of the HS model where g ^ bbx0 at a

large rate, followed by x0 ^ (typically at ~ 3% branching

ratio for each of £ = e or f), there may be a corroborating signal

at much lower rates in the multi-b-jet + E™lss + £+£— mode, where

m(£+£—) < mx0 — mx0.

We note finally that the results presented here in the context of Yukawa-unified models are more generally applicable to any model with very heavy scalars, and large enough tan /) such that gluinos dominantly decay via three-body modes into b-quarks. They are also applicable to models with hierarchical soft terms, where first/second generation scalars are extremely heavy, and third generation scalars are much lighter; some references for such models are located in [40].

Acknowledgements

We thank Phil Gutierrez for a discussion and Xerxes Tata for comments on the manuscript. We thank Harrison Prosper for discussion on statistics issues and sharing with us his p-value and significance code. This work is funded in part by the US Department of Energy, grant number DE-FG-97ER41022 and by the French ANR project ToolsDMColl, BLAN07-2-194882.

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