Testing Yukawa-unified SUSY during year 1 of LHC: the role of multiple b-jets, dileptons and missing E_T

We examine the prospects for testing SO(10) Yukawa-unified supersymmetric models during the first year of LHC running at \sqrt{s}= 7 TeV, assuming integrated luminosity values of 0.1 to 1 fb^-1. We consider two cases: the Higgs splitting (HS) and the D-term splitting (DR3) models. Each generically predicts light gluinos and heavy squarks, with an inverted scalar mass hierarchy. We hence expect large rates for gluino pair production followed by decays to final states with large b-jet multiplicity. For 0.2 fb^-1 of integrated luminosity, we find a 5 sigma discovery reach of m(gluino) ~ 400 GeV even if missing transverse energy, E_T^miss, is not a viable cut variable, by examining the multi-b-jet final state. A corroborating signal should stand out in the opposite-sign (OS) dimuon channel in the case of the HS model; the DR3 model will require higher integrated luminosity to yield a signal in the OS dimuon channel. This region may also be probed by the Tevatron with 5-10 fb^-1 of data, if a corresponding search in the multi-b+ E_T^miss channel is performed. With higher integrated luminosities of ~1 fb^-1, using E_T^miss plus a large multiplicity of b-jets, LHC should be able to discover Yukawa-unified SUSY with m(gluino) up to about 630 GeV. Thus, the year 1 LHC reach for Yukawa-unified SUSY should be enough to either claim a discovery of the gluino, or to very nearly rule out this class of models, since higher values of m(gluino) lead to rather poor Yukawa unification.


Introduction
Grand unified theories (GUTs) find a welcome inclusion of supersymmetry (SUSY) into their structure in that SUSY tames the gauge hierarchy problem via the well-known cancellation of quadratic divergences [1]. In particular, the GUT group SO(10) is highly motivated in that it allows for-in addition to gauge unification-the unification of all the matter superfields of each generation into the 16-dimensional spinor representation [2]. The matter unification only works if the 15 matter superfields of the Minimal Supersymmetric Standard Model (MSSM) are augmented by a SM gauge singlet superfieldN c i which contains a right-hand neutrino (RHN) field. The presence of RHN fields is essential to describe data from the past decade on neutrino mass and flavor oscillations; in particular a Majorana mass term near the GUT scale, needed to implement see-saw neutrino masses [3], should be generated by the breakdown of SO(10) gauge symmetry. In addition to gauge and matter unification, in the simplest SO(10) SUSY GUT models-wherein both MSSM Higgs doublets reside in a 10 of SO(10)-one expects Yukawa coupling unification in the third generation: Recently, a variety of studies have examined the MSSM(+RHN) to check whether the measured values of gauge couplings and third generation fermion masses do indeed allow for t − b − τ Yukawa coupling unification [4][5][6][7][8][9][10][11][12][13][14][15]. Essential to the calculation is the inclusion of 2-loop renormalization group equations [16] (RGEs) and inclusion of weak scale threshold corrections [17] which occur due to the MSSM → SM transition in effective field theories. These threshold corrections imply that Yukawa coupling unification depends on the entire spectrum of SUSY particles, since the SUSY particles enter the various t, b and τ self-energy diagrams [17].
Assuming universal boundary conditions at the GUT scale, the parameter space of SO(10)-motivated SUSY consists of m 1/2 , m 16 , m 10 , M 2 D , A 0 , tan β, sign(µ), (1.1) where m 1/2 is the common gaugino mass at M GUT , m 16 is the common GUT mass of all matter scalars, m 10 is that of the Higgs soft terms, and M 2 D parametrizes potential splittings in the GUT scale Higgs (and possibly matter scalar) soft terms. Such splittings are expected to arise from the breaking of the SO (10). It has been found that t − b − τ Yukawa coupling unification can occur in the MSSM within this setup, but only for very restricted forms of the soft SUSY breaking (SSB) parameters at M GUT . These include, for the case of µ > 0: • A 2 0 = 2m 2 10 = 4m 2 16 , • m 16 ∼ 5 − 15 TeV, • m 1/2 ≪ m 16 , • tan β ∼ 50.
These boundary conditions were found in Ref. [18] to give rise to an inverted scalar mass hierarchy (IMH), wherein first/second generation scalars end up with masses ∼ 10 TeV, while third generation scalars, Higgs scalars A, H and H ± and µ are of order ∼ 1 − 2 TeV. A problem with the IMH scheme is that it is inconsistent with radiative electroweak symmetry breaking (REWSB), unless the Higgs soft terms are split at M GUT [19]: m 2 Hu < m 2 H d , thus giving m 2 Hu a head start over m 2 H d in its running towards the weak scale. 1 Such splitting naturally occurs due to D-term (DT) contributions to all scalar masses arising from the breakdown of SO (10). However, applying the splitting to only the Higgs sector ("just-so" Higgs splitting, HS) (HS model) (1.2) results in better accuracy of Yukawa unification as compared to full DT splitting. Recently, it has been shown that DT splitting, combined with the running effect of the neutrino Yukawa coupling f ντ and a small mass splitting between first/second versus third generation scalars (the DR3 model) can allow for Yukawa coupling unification to a few percent [15]. Both the HS and DR3 schemes lead to sparticle mass spectra characterized by • mq ,l (1, 2) ∼ 10 TeV, • mq ,l (3) and µ ∼ 1 − 3 TeV, • mg ∼ 300 − 500 GeV, • m e Z 1 ∼ 50 − 90 GeV. Figure 1 shows the location of a large number of Yukawa-unified models in the R vs. mg plane, for the HS model (red dots) and the DR3 model (blue dots) obtained through a Markov Chain Monte Carlo (MCMC) scan of the parameter space (for details, see [15]).
Here, the degree of Yukawa unification is quantified as where f t , f b and f τ are the top, bottom and tau Yukawa couplings, respectively, evaluated at Q = M GUT . In the DR3 case, if we require R < 1.05, then mg 450 GeV. In the HS model, while mg ∼ 300 − 500 GeV is favored for low R < 1.05 solutions, it is possible (but not likely) to have occassional models with mg as large as ∼ 700 GeV.
In models with the above listed superpartner spectrum and a bino-like Z 1 state, the neutralino relic density is computed to be ∼ 10 2 −10 4 times the measured abundance [9,11], and the models are seemingly excluded. However, if one invokes the Peccei-Quinn solution to the strong CP problem [20][21][22][23][24], then an axion/axino supermultiplet is expected in the theory [25]. With an axino of mass mã ∼ 1 MeV the neutralinos will decay via Z 1 →ãγ, which greatly reduces the dark matter density by a large factor: mã/m e Z 1 . Cold dark matter (CDM) solutions can be found consisting of mainly cold axions and thermally produced axinos, with a small component of warm axinos arising from Z 1 → γã decay, which occurs on time scales of order 1 sec. Since m 16 ∼ 10 TeV, and we expect m 16 ∼ mG, the axion/axino CDM scenario allows for a solution to the gravitino BBN problem, and can generate re-heat temperatures T R ∼ 10 6 − 10 9 GeV, which can allow for baryogenesis mechanisms such as non-thermal [26] or Affleck-Dine [27] leptogenesis to occur [28].
Since the value of mg is so low in Yukawa-unified SUSY models, we expect the whole scenario to soon be tested at the CERN LHC. 2 LHC has already turned on in Fall, 2009. As time progresses, the centre-of-mass energy √ s will be increased into the ∼ 7 TeV regime.
An integrated luminosity of 0.1 − 1 fb −1 is expected to be collected. 3 Earlier work on Yukawa-unified SUSY at LHC with √ s = 14 TeV showed the model to be easily testable at LHC [30]. The LHC SUSY events should be characterized by gluino pair production followed by three-body decays to states including a high multiplicity of b-jets. In addition, opposite-sign dileptons with mass between 40 − 80 GeV (i.e. between the γ and Z peaks) may be evident. In the intervening past year, while LHC recovered from an unfortunate incident involving faulty circuits and quenched magnets, the experiments have been measuring millions of cosmic muon events. This cosmic data has allowed them to fine-tune their detector response to muons, and to make great strides in alignment of detector elements. We expect thus that isolated muons, jets and b-jets should be readily measurable very early on during LHC running, while reliable electron identification (e ID) and even more so reliable E miss T measurement, may require additional time to establish.
2 Indeed experiments at the Fermilab Tevatron collider may also probe up to mg ∼ 400 − 430 GeV [29]. 3 The quoted physics data to be collected at 7 TeV as of November 2009 is 0.2 fb −1 .  In this paper, we expand upon the analysis presented in Ref. [30], and address several new issues: • We focus on the LHC potential to discover or rule out Yukawa-unified SUSY during year 1 of running. 4 To this end, we calculate signal and background production rates for the LHC turn-on energy of √ s = 7 TeV rather than the maximal collider energy of √ s = 14 TeV used earlier. Part of the effect of LHC turn-on at lower than expected energies can be gleaned from Fig. 2, where we plot σ(pp →ggX) vs. collider energy √ s, for mg = 300, 400 and 500 GeV, while taking mq = 10 TeV. We show both LO and NLO QCD results as derived from Prospino [34]. For mg = 400 GeV, LHC operating at √ s = 7 TeV yields a cross section of σ ∼ 10 4 fb. It is expected that, after about 0.1 fb −1 of integrated luminosity, the LHC will move up in energy to the √ s ∼ 10 TeV regime, where σ ∼ 3 × 10 4 fb. Ultimately, the LHC should move up to its design energy of √ s = 14 TeV, where the cross section increases to ∼ 10 5 fb. Various background rates will also change accordingly. In this paper, we take a conservative approach, and evaluate all signal and background cross sections at √ s = 7 TeV. Increasing the beam energy beyond 7 TeV should only increase the SUSY reach projections which we calculate here.
• We include as well many more background subprocesses than before, including the effect of many 2 → 3 and 2 → 4 body subprocesses.
• We particularly hone in on what LHC can accomplish with very low integrated luminosity. After turn-on, some time will be required to examine detector response to well-known SM processes like W , Z and tt production. To be able to use the classic SUSY signature of jets + E miss T production, the measurement of E miss T -which depends on a knowledge of the entire detector response-will be required. However, in Ref. [32,33], it is pointed out that LHC experiments can examine multi-jet + isolated multi-muon events in lieu of jets + E miss T events as a gain for signal over background. We find that for very low integrated luminosity, using either large isolated muon multiplicity, or large b-jet multiplicity, allows mg values of up to 400 GeV to be probed with just 0.2 fb −1 of integrated luminosity. (Note that we expect a similar reach for the Tevatron in the ≥ 2 − 3 b-jets + E miss T channel with 5 − 10 fb −1 [29].) • We also discuss the case when E miss T measurements and e ID are established. Here we find that LHC can explore mg values as high as ∼ 630 GeV with 1 fb −1 of integrated luminosity. Thus, during year 1 the LHC may well be able to either discover or very nearly rule out Yukawa-unified SUSY.
The paper is organized as follows. We first establish in Sec. 2 two Yukawa-unified model lines: one in the HS model and one in the DR3 model. We also examine general features in sparticle production and decay for these model lines. In Sec. 3, we present some technical details of our signal and background calculations. In Sec. 4, we present expectations for early SUSY searches in the multi b-jets channel 5 without using E miss T cuts. We also examine rates for early multi-muon production plus jets without using E miss T . We find that the HS and DR3 models may be distinguishable by measuring the ratio of OS dilepton events to multi b-jet events, since both models produce multi-b-jets at a similar rate. However, while OS dimuons from Z 2 decay are abundant in the HS model, they are relatively scarce in the DR3 model. In Sec. 5.4, we move beyond the 0.1 fb −1 level, and calculate the LHC reach for the two model lines using as well E miss T and e ID for 1 fb −1 of integrated luminosity. In this case, the 5σ LHC reach should extend to mg ∼ 630 GeV, enough to cover the bulk of parameter space of these simple Yukawa-unified models. In Sec. 7, we present our conclusions.

Model lines
Using the parameter space in Eq. 1.1, Ref. [28] found a large number of SUSY spectral solutions with good Yukawa coupling unification in the HS model. We adopt Point B with R = 1.02 of this paper as a Yukawa-unified benchmark point, and label it as HSb. The HSb input parameters and mass spectra are listed in Table 1.
To construct a HS model line, we keep most of the above parameters fixed, but allow m 1/2 to vary. This keeps the Yukawa-unification generally low, but allows us to vary mg ∼ 3.5m e Z 2 ∼ 7m e Z 1 continuously. We plot the value of R versus mg in Fig. 3. We see that at low mg (∼ 325 GeV), R < 1.03, while as mg increases, Yukawa unification gets worse until mg ∼ 700 GeV, where we find R ∼ 1.13.  Table 1: Masses in GeV units and parameters for Yukawa-unified benchmark points HSb [28] and DR3b [15]. For the DR3 model, we use M N3 = 10 13 GeV.
We also adopt from Ref. [15] a DR3 model line, labelled as DR3b, with parameters in Table 1. where m 16 (1,2,3), is the scalar mass for the 1st, 2nd and 3th generations and M N 3 , f ντ , A ντ and mṽ R3 are the right-handed neutrino mass, Yukawa coupling, A-term and the scalar mass for the sneutrino. We construct a DR3 model line by again keeping most parameters fixed, but letting m 1/2 to vary. In the DR3 model line, we find R ∼ 1.03 for mg ∼ 325 GeV, while R increases to ∼ 1.15 for mg ∼ 700 GeV. 6 Due to the heavy scalar masses in the HS and DR3 model lines, the scalars essentially decouple at LHC energies. What results is a low energy effective theory where onlyg, Z 1,2 and W ± 1 are the new physics matter states. In the next two sections we discuss the production cross-sections and decay rates for these states.

HS and DR3 production cross sections
We plot in Fig. 4 the leading ordergg, W 1 Z 2 and W + 1 W − 1 production cross sections as a function of mg for collider energy √ s = 7 TeV. From the figure, we see that gluino pair production is dominant up to mg ∼ 520 GeV (at NLO, it dominates up to mg ∼ 560 GeV), with cross sections typically greater than 10 3 fb, and in excess of 10 4 fb in the lower gluino mass range. Thus, even with integrated luminosities as low as 0. of gluino pair events in the upcoming LHC year 1 physics data sample for the HS and DR3 models. Gluino pair production cross sections at the Fermilab Tevatron collider show a large increase in rate as mq increases [29]. This is due to suppression of negative interference terms in the qq →gg subprocess cross section. At the LHC, gluino pair production for mg ∼ 300−500 GeV is dominated instead by the gg →gg subprocess, which is independent of mq. Thus,gg cross sections show only a slight (∼10-20%) increase with increasing mq at the LHC.

Sparticle branching fractions in the HS and DR3 model lines
Since mg ≪ mq in the HS or DR3 model lines, we will get dominant gluino decays into three-body modes. The gluino branching ratios will be largely model dependent, but sincẽ t i andb i are always the lightest squarks, and tan β is large [36], the decays will mostly be restricted to the following channels: The general feature mg ≪ mq is common to both the HS and DR3 models, since it relies mostly on the fact that m 1/2 ≪ m 16 . However, the inclusion of the D-term splitting  Table 1 but with m 1/2 varying from 30 to 180 GeV. for all matter scalars in the DR3 model pushes mb R to lower values, when compared to the HS model, where mb L ∼ mb R . 7 As a result we have: Now, since Z 2 is wino-like in both models, it just couples to left-squarks, what suppresses theg → Z 2 + bb decay in the DR3 model and favors it in the HS case. This behavior is shown in Fig. 5, where the main gluino branching ratios for both models are plotted as a function of the gluino mass. From Fig. 5 it can also be seen that-in the HS model- c. channel starts to dominate, since mt 1 < mb 1 (for mg > 500 GeV). We can also see thatg → Z 1 tt becomes relevant for heavy gluinos (mg > 600 GeV) and it is enhanced in the DR3 model, wheret 1 is usually lighter than in the HS model. From Fig. 5 we see that, for the HSb benchmark case: On the other hand, the DR3b point has:  Figure 5: Gluino branching ratios for the HS and DR3 model-lines as a function of the gluino mass. The model parameters are the same as in Table 1, but with m 1/2 varying from 30 to 180 GeV.   Figure 6: Z 2 branching ratios for the HS and DR3 model-lines as a function of the gluino mass. The model parameters are the same as in Table 1, but with m 1/2 varying from 30 to 180 GeV.
• BR(g → Z 2 + bb) = 11% The Z 2 and W 1 are expected to decay via three body modes: where the decays are dominated by the intermediate virtual W * and Z * diagrams. If mg 500 GeV, then the two-body modes W 1 → Z 1 W and Z 2 → Z 1 Z will turn on.

Event Simulation
In order to study the discovery potential of the LHC at √ s = 7 TeV we used AlpGen [37] and MadGraph [38] to generate the background hard scattering events and Pythia [39] for the subsequent showering and hadronization. Table 2 lists the 2 → n subprocesses included in this study where jets = u, d, s, c and g. For all the processes involving multiple jets, the MLM matching algorithm [37] was used to avoid double counting. All the above processes were generated at LO, but a relatively low renormalization and factorization scale (Q = √ŝ /6) was used to bring the total cross-sections closer to their NLO values (for more details see Ref. [33]). The signal events were generated using Isajet 7.79 [40].
• Leptons are considered isolated if they have p T (l) > 5 GeV with visible activity within a cone of ∆R < 0.2 of ΣE cells T < 5 GeV.
Jets are tagged as b-jets if they contain a B hadron with E T (B) > 15 GeV, η(B) < 3 and ∆R(B, jet) < 0.5. We assume a tagging efficiency of 60% and light quark and gluon jets can be mis-tagged as a b-jet with a probability 1/150 for E T ≤ 100 GeV, 1/50 for E T ≥ 250 GeV, with a linear interpolation for 100 GeV ≤ E T ≤ 250 GeV (see R. Kadala et al. in Ref. [35]).

Early searches without E miss
T or electron ID During the early stages of data taking at the LHC with integrated luminosity of order ∼ 0.1 fb −1 , it is possible that E miss T and electron identification will not be reliable observables (see Refs. [32,33]). Therefore we separate our analysis into two stages: • early searches, where no E miss T cuts are applied and only muons are considered for the leptonic channels, and • full analysis, using a minimum E miss T cut and including both e's and µ's.
In both cases we assume that the b-jets can be reliably tagged due to their displaced vertices as reconstructed in the micro-vertex detector or via a non-isolated muon tag. For initial searches we apply the following set of minimal cuts, labelled C0: C0 cuts: • Jet cuts: n(jets) ≥ 4 with E T (j) ≥ 50 GeV, η(j) ≤ 3 and for the hardest jet E T (j1) ≥ 100 GeV, • Lepton cuts: E T (ℓ) ≥ 10 GeV and η(ℓ) ≤ 2, where S T is the transverse sphericity and for now ℓ = µ only.

Multi b-jet signal
As discussed in Sec. 2 the points HSb and DR3b are expected to be rich in b-jets and possibly isolated leptons. In Fig. 7 we plot the b-jet multiplicity for the signal and backgrounds (BG) after applying the C0 set of cuts. As expected, the BG distribution falls much faster than the signal. Signal exceeds BG for n(b) ≥ 4, where the BG is dominated by multi b production (bb and bbbb). We also note that the DR3b case has larger rates for 1 ≤ n(b) ≤ 4 when compared with the HSb point, due to a lighter gluino. However, the HSb benchmark gives a larger signal for n(b) ≥ 5, since in this case Z 2 → Z 1 bb also contributes, and Z 2 are produced at large rates from gluino cascade decay. We note here that a signal rate above an expected SM BG level may not be sufficient to claim a discovery, due to both theoretical and experimental uncertainties in the multi-b background rate. However, the overall shape of the n(b) distribution should be to some extent self-normalizing, as one can fix the BG levels in the n(b) = 0, 1, 2 channels, and look for a harder n(b) distribution in the signal case. Thus, some of the uncertainty is   Results after C0-based selection  removed when one looks for an excess in ratios such as σ(n(b) = 3)/σ(n(b) = 1). Table 3 shows the n(b) ≥ 3 and 4 cross-sections for both points and the background. The signal in the n(b) ≥ 4 channel is at the 200 fb level and is well above SM background levels. Such a signal may be visible with very low integrated luminosity values ∼ 0.05 fb −1 ! As mentioned above, a mere excess in one or more of the multi b-jet channels may not be sufficient to claim discovery, due to large uncertainties in the normalization of the high jet multiplicities BGs, such as bb, tt and Z + 2 jets. With this in mind, we present some signal distributions with distinct shapes from the BG ones, which could help corroborate a discovery and provide some information on the sparticle masses. As discussed in Sec. 2, events with n(b) ≥ 4 usually come fromg → Z i bb decays. Therefore the invariant mass of the bb pair is expected to have edges at mg − m e Z i . This is shown in Figs. 8 and 9, where max[m b 1b1 , m b 2b2 ] is plotted 8 at the parton level (dashed black line). As expected, in the DR3b case the mg − m e Z 1 mass edge is much more evident than the mg − m e Z 2 edge, due to the largeg → Z 1 + bb branching fraction, while the opposite happens for the HSb point. At the detector level, the main difficulty in obtaining max[m b 1b1 , m b 2b2 ] comes from combining the correct b-jets into pairs coming from the same gluino. As pointed out in Ref. [30], usually the two hardest b-jets come from different gluinos. Furthermore, in most cases the pair coming from the sameg has smaller separation angles. Using these two facts, we select b 1 and b 2 as the hardest and second hardest jets andb 2 as the remaining jet that minimizes ∆φ(b 2 ,b 2 ). Also, to avoid event topologies with no small angular separation, we apply the cut ∆R(b 2 ,b 2 ) < 1, where R = ∆φ(b 2 ,b 2 ) 2 + ∆η(b 2 ,b 2 ) 2 . Using this procedure and adding the C0 set of cuts we obtain the solid curves shown in Figs. 8 and 9, where the BG contribution was added to the signal. We also show the statistical error bars for 1 fb −1 of integrated luminosity. As can be seen, the invariant-mass distributions have the expected shape, although the mass edges seem to require higher integrated luminosity to become statistically relevant.

Dimuon channels
In Fig. 10 we show the muon multiplicity for the HSb and DR3b signal points and the BG. For n(µ) = 0, 1, the BG is well above the signal, but for n(µ) ≥ 2, signal starts to dominate over the BG. As expected from the discussion in Sec. 2, the DR3b has much smaller rates to multileptons. Separating the n(µ) = 2 channel into opposite sign (OS) and same sign (SS) muons, we see that almost all the signal comes from the OS dimuon case. Due to the smallg → W − 1 tb + c.c. branching fraction, the SS signal is almost 2 orders of magnitude below the OS one, which makes it irrelevant for luminosities 1 fb −1 . As seen in Table 3, the OS cross-section for the HSb point is around 100 fb and has a discovery potential similar to the multi b-jet channel, while the DR3b benchmark will require more    Figure 10: Muon distribution after C0 cuts at the LHC, with √ s = 7 TeV. We show the signal levels for the HSb (red) and DR3b (green) points along with various SM backgrounds. In the n(µ) = 2 bin, the left (pluses) and right (crosses) columns show the background (black) and signal components for OS (with invariant mass cuts) and SS dimuons. integrated luminosity to be seen in the OS dimuon channel.
As is well known, the invariant mass of OS muons has a mass edge at m e Z 2 − m e Z 1 , since most OS muons come from Z 2 → Z 1 µ + µ − decays. In Fig. 11, we show the m(µ + µ − ) distribution for the HSb and DR3b points. As discussed in Sec. 2, the DR3b point has small leptonic rates but may still be visible above background. In both cases, the mass edges are visible and give the correct m e Z 2 − m e Z 1 values. We also show the statistical error bars for the combined signal plus background for 1 fb −1 of integrated luminosity. From Fig. 11, we can see that the HSb point gives a statistically significant edge while the DR3b case may require higher integrated luminosities.
Finally, we point out that in both the n(b) ≥ 4 and OS dimuon channels the invariant mass distributions shown in Figs. 8, 9 and 11 have distinct features from the BG, which should corroborate a discovery claim.

Early SUSY search: reach results
To estimate the LHC reach in the multi-b and multi-µ channels, we plot in Fig. 12 the signal cross section for the HS and DR3 model lines versus mg using cuts C0 plus a). n(b) ≥ 3 and b). n(b) ≥ 4, along with the expected BG rate. We also plot the 5σ discovery lines for integrated luminosity values 0.1 and 0.2 fb −1 . The significance in σs 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 [41]. For both the HS and DR3 model lines, the approximate 5σ LHC reach extends to mg ∼ 360 GeV for 0.1 fb −1 , and ∼ 400 GeV for 0.2 fb −1 . We remind the reader that this is comparable to what Tevatron experiments can achieve using E miss T cuts and > 5 fb −1 of integrated luminosity [29]. The reach using cuts C0 and requiring an OS dimuon pair is shown in Fig. 13. In this case, the reach in the HS model is similar to the multi-b reach: LHC should explore to mg ∼ 360 GeV with 0.1 fb −1 , and mg ∼ 400 GeV with 0.2 fb −1 . In the DR3 model line, however, there is no reach in the OS dimuon channel at these low values of integrated luminosity. In fact, the rate of multi-b-jet events compared to the rate for OS dimuon events would be one way to distinguish early-on whether one might be seeing SUSY in the HS or the DR3 model case.
We also point out that despite giving the maximum reach for both models, the n(b) ≥ 3 channel has a small signal/BG ratio, what makes it more dependent on the knowledge of the background.

T cut and electron ID
As the experiments accumulate data, knowledge of the detectors and their response to SM background will improve. Also, at some point in time, the LHC center-of-mass energy will increase beyond 7 TeV into the 10 TeV range. To be conservative, we will continue our analysis assuming √ s = 7 TeV. Moving to higher values of √ s should only increase the possibility of discovering new, high mass matter states. As detector response becomes better understood, it will be possible to utilize both E miss T and electrons in the analysis. The E miss T variable is well known to be a powerful discriminator between SUSY and SM events, and is considered to be the "classic" signature for SUSY. In Fig. 14 we show the E miss T distributions for the BG as well as the HSb and DR3b points after applying the C0 cuts. As expected, the DR3b signal has a harder E miss T spectrum than HSb, due to its largeg → Z 1 bb branching ratio.
In order to reduce most of the background and still keep considerably large crosssections for the signal, we henceforth: • include the E miss T > 100 GeV cut and • include e's into the C0 leptonic cuts into our analysis. The cuts C0 augmented with the E miss T cut and inclusion of e's, but with no n(b) requirement, will be called C1 cuts: C1 cuts: • Jet cuts: n(jets) ≥ 4 with E T (j) ≥ 50 GeV, η(j) ≤ 3 and for the hardest jet E T (j1) ≥ 100 GeV, • Lepton cuts: E T (ℓ) ≥ 10 GeV and η(ℓ) ≤ 2, where ℓ = µ, e.

Multi
The main effect of adding an E miss T cut to our previous analysis is the drastic reduction of background in the multi b-jet channel. However, the signal will also be significantly reduced, and so will be the statistics in the invariant mass distributions.
The n(b) distribution after C1 cuts is shown in Fig. 15. Now the signal's peak at n(b) =1, 2 is visible above the BG, and the hard distribution in n(b) should be a striking signature for both the DR3b and HSb models, since the combined signal plus BG distribution becomes approximately flat for 0 ≤ n(b) ≤ 2. The E miss T cut reduces most of the bb and bbbb backgrounds, leaving tt as the dominant one for n(b) ≥ 1. This results in a considerable reduction of the BG in the n(b) = 1, 2 and 3 bins, where now the signal/background ratio is larger than one. The cross-sections for n(b) ≥ 3, 4 are shown in Table 4. Due to the large signal cross-section in these bins, the signal could be visible with less than 0.05 fb −1 of integrated luminosity (in the happy case where an E miss T measurement is immediately viable)!
The invariant mass distributions from Figs. 8 and 9 are now re-plotted in Figs. 16 and 17 after the E miss T cut is included. Now, due to the drastic reduction in the background, the m bb distribution is nearly free of BG events. However, the decrease in the signal statistics   Figure 15: b-jet distribution after C1 cuts at the LHC, with √ s = 7 TeV. We show the signal levels for the HSb (red) and DR3b (green) points along with various SM backgrounds.
Results after C1-based selection  Table 4: Cross-sections for the n(b) ≥ 3, 4 and OS channels after the C1 cuts for the points HSb, DR3b and the background.
makes it impossible to obtain any information on the sparticle masses from the shape of A quantity that may still reveal some information on the gluino mass scale is the effective mass, M eff = p T (jets) + E miss T , plotted in Fig. 18 for the HSb and DRb points, as well as for two points on the HS and DR3 model lines with heavier gluinos (mg = 576 GeV and mg = 581 GeV, respectively).

Multi-lepton channels
In Fig. 19, we show the isolated lepton multiplicity distribution after cuts C1. In the n(ℓ) = 0 channel, the DR3b signal exceeds BG, while in the n(ℓ) = 2 channel, the HSb signal exceeds BG. In the n(ℓ) = 1 channel, BG from tt production is larger than both signal cases. One can pull out a better signal rate in the 1ℓ channel by imposing in addition a M T (ℓ, E miss T ) > 100 GeV cut, as is well known [42]. We divide the n(ℓ) = 2 channel into opposite-sign/same-flavor (OS/SF) events (e + e − or µ + µ − ), and same-sign events. For the OS/SF channel, we see the E miss T cut has little effect on the signal-to-BG ratio, since the background, mainly tt production, also has large  . Again, we expect the entire distribution to be self normalizing, since tt is the dominant BG, and one can fix the total tt cross section by normalizing to the 1ℓ channel. Then the n(ℓ) distribution should be harder than expected from just SM physics if a SUSY signal is present.
In Fig. 20, we show the OS/SF dilepton invariant mass distribution after cuts C1. Now, despite the negligible background, the reduction in the signal makes the mass edges less visible. In particular, the dilepton invariant mass still shows the m e Z 2 − m e Z 1 edge, but with a smaller statistical significance as evident from the error bars. Performing a

BG HSb
DR3b bbbb bbtt tttt bb QCD tt bb + W(lν) bb + Z tt + Z W + jets Z + jets Figure 19: Lepton multiplicity distribution after C1 cuts at the LHC, with √ s = 7 TeV. We show the signal levels for the HSb (red) and DR3b (green) points along with various SM backgrounds. In the n(ℓ) = 2 bin, the left (pluses) and right (crosses) columns show the background (black) and signal components for OS/SF and SS dileptons. different-flavor subtraction may reduce the already negligible BG even further.

Jets plus
We also show in Fig. 20 two additional HS and DR3 cases with mg ∼ 525 GeV. In this case, according to Fig. 6, the value of m e Z 2 is high enough that the two-body decay Z 2 → Z 1 Z is now dominant. We then expect a signature of multiple b-jets plus E miss T plus a dilepton pair which reconstructs to m(ℓ + ℓ − ) ≃ M Z [43]. While signal rates can be very high for this channel, SM background is low, coming from processes such as tt and Z + tt.

LHC reach for Yukawa-unified SUSY using E miss
T and e ID Next, we investigate the full LHC reach for Yukawa-unified SUSY along the HS and DR3 model lines. First, we require the cut set C1, which includes E miss T > 100 GeV, and then require n(b) ≥ 2 or n(b) ≥ 3. The SM background level and 5σ level for 0.2 and 1 fb −1 are shown in the plots of Fig. 21, along with expected signal rates from the HS and DR3 model lines. For the n(b) ≥ 2 case, we find an LHC reach for Yukawa-unifed SUSY out to mg = 500 (600) GeV for 0.2 (1) fb −1 . The reach is largely independent of whether one is in the HS or the DR3 model.
For n(b) ≥ 3, the SM background is greatly reduced. In this case, we find a reach to mg = 540 (630) GeV for 0.2 (1) fb −1 . Again, the reach in the multi-b-jet channel is largely independent of the model line, since both give large numbers of b-jets + E miss T in the final state. We have also calculated the reach in the n(b) ≥ 4 channel; here, the result is qualitatively similar to that obtained in the n(b) ≥ 2 case.
Next, in Fig. 22, we show the LHC reach for Yukawa-unified SUSY using the C1 cuts plus requiring a pair of OS/SF dileptons. In this case, the LHC reach is model dependent. For the HS model, where we obtain a high rate forg → bb Z 2 decays, we find a reach up to mg = 400 (500) GeV for 0.2 (1) fb −1 of integrated luminosity. For the DR3 model line, there is no reach for 0.2 fb −1 , since here theg → bb Z 1 decay is dominant. With 1 fb −1 , however, a signal with 5σ significance should be visible for mg ∼ 300 − 450 GeV.
For mg 450 GeV, the two body decay mode Z 2 → Z 1 Z opens up and we expect to reconstruct Z → e + e − and Z → µ + µ − within the class of signal events. Here, we will adopt cuts C1, but in addition require a OS/SF dilepton pair with 75 GeV< m(ℓ + ℓ − ) < 105 GeV (cuts C1 ′ ). For this topology-≥ 4 jets +E miss T + Z → ℓ + ℓ − -the dominant SM BG comes from tt production. The LHC reach is shown in Fig. 23. As can be seen, no significant excess is expected with 0.2 fb −1 of data. However, for 1 fb −1 , we find that this topology can produce a 5σ signal for mg ∼ 450 − 530 GeV for both the HS and DR3 model lines.

Differentiating the HS and DR3 models
Here we discuss the possibility of distinguishing the two models discussed so far using low luminosities and the channels investigated in the previous sections. As seen from last section results (Figs. 21 and 22) and the discussion in Sec. 2, for low to moderate mg masses we expect the HS and DR3 models to have rather distinct signatures. The first one is rich in multi-b jets (n(b) ≥ 4, 5) and OS/SF dileptons coming from theg → Z 2 + bb followed by Z 2 → Z/Z * + bb/ℓ + ℓ − decays, but has a softer E miss T spectrum due to the two step cascade decays. On the other hand, the DR3 model is mainly dominated byg → Z 1 + bb, with small cross-sections in the multi-lepton channels, a moderate number of b-jets (n(b) ≥ 3,4) and a harder E miss T spectrum. To explore these features and discuss how well we can distinguish both models with year one data, we plot in Fig. 24 the ratio of the OS and n(b) ≥ 3 channels. As expected from the above discussion, we see that the ratio is larger for the HS model and suppressed in the DR3 case for mg 600 GeV. As the gluino mass increases, the W 1 + bt and Z 1 + bb gluino decay channels become available (see Fig. 5), increasing the OS channel in both models. From Fig. 24 we see that the OS/3b ratio should be a good discriminator up to mg ∼ 450 GeV. For mg 450 GeV, higher luminosities are required in order to distinguish the models. But with high enough luminosities, we should be able to tell the models apart up to mg ∼ 600 GeV. For even higher mg values, the signal features are too similar and the simple OS/3b ratio is no longer useful.

Comparison with CDF/CMS multijets + E miss
T channel Next we would like to compare our results for the multi-b-jets + E miss T signature with a multijets + E miss T analysis for SUSY searches proposed and used by CDF [44] and further developed in CMS [45]. We implement the following selection.
• n(jets) ≥ 3 (we take jet p T > 50 GeV), • Finally, we require the highest E T object in each signal event to be hadronic, rather than leptonic 9 .
The angular cuts are introduced in multijets + E miss T analyses where no lepton information is explicitly used in order to guarantee the discrimination of QCD backgrounds which may have large E miss T arising primarily due to jet mismeasurements. In such events, E miss T typically aligns with the 2nd hardest jet, as the hardest jet has a tendency to be mismeasured most and eventually becomes the 2nd hardest jet.
The reach results for CDF/CMS multijets + E miss T cuts with no n(b) requirement can be seen in Fig. 25. The 5σ reach for 0.2 (1) fb −1 of integrated luminosity is found to be mg ∼ 370 (430) GeV.
In Figure 26, we plot the n(b) signal and background distributions after CDF/CMS cuts, which share similar characteristics with the distributions after C1 cuts. The dominance of signal starting with n(b) = 1 illustrates the importance of considering b−jet tagging in the multijets + E miss T analyses. The original CMS analysis made use of the B−triggers to significantly enhance the signal/BG ratio, while here we directly cut on n(b). We show in Table 5 the cross sections found after implementing CDF/CMS cuts with no requirement on n(b) and with n(b) = 1, 2, 3. 9 This is an approximation for the leading track isolation step of the indirect lepton veto (ILV) technique included in the CDF/CMS selection. Normally in multijets E miss T analyses where lepton information is not explicitly used, W/Z/tt + n jets backgrounds with leptonic W, Z decays can be eliminated by vetoing the events whose leading track is isolated. We omit the second step of ILV featuring jet electromagnetic and charged fractions since it is designed to eliminate machine and cosmic backgrounds which we do not consider here.    Figure 26: b-jet distribution after CDF/CMS multijets + E miss T cuts at the LHC, with √ s = 7 TeV. We show the signal levels for the HSb (red) and DR3b (green) points along with various SM backgrounds.
As before, we can do much better by requiring a high multiplicity of b-jets. In Fig. 27, we adopt the same cuts as in Fig. 25, but in addition require n(b) ≥ 3. In this case, the BG drops by a factor of ∼ 150, while the signal drops merely by a factor of ∼ 7 for mg ∼ 300 GeV. The LHC reach increases to mg ∼ 400 (500) GeV for 0.2 (1) fb −1 of integrated luminosity.  Table 5: Cross-sections for the channels with no n(b) requirement, n(b) ≥ 1, 2 and 3 after the CDF/CMS multijets + E miss T cuts for the points HSb, DR3b and the background. CDF/CMS jets + E T miss cuts -n(b) ≥ 3 CDF/CMS jets + E T miss cuts -n(b) ≥ 3 CDF/CMS jets + E T miss cuts -n(b) ≥ 3

Conclusions
In t−b−τ Yukawa-unified SUSY, we expect a characteristic spectrum of superpartners with first/second generation squarks and sleptons around 10 TeV, third generation sparticles, heavy Higgs bosons and µ around the few TeV level, and very light gauginos, with mg ∼ 300− 500 GeV (although here we consider even higher values). Thus, at LHC, we expect to see gluino pair production at a high rate, followed by gluino decays to bb Z i or tb W − 1 + c.c.. SUSY searches should therefore exploit the high multiplicity of b-jets expected in this scenario.
We investigated two model lines-the HS and DR3 cases. The HS case leads to large rates for OS/SF dileptons in the final state, while DR3 case does not. We computed numerous 2 → 2, 2 → 3 and 2 → 4 background processes. We found that with just 0.1-0.2 fb −1 of integrated luminosity, the LHC discovery reach with √ s = 7 TeV extends out to mg ∼ 400 GeV, even without using E miss T cuts. Crucial use is made of the high multiplicity of b-jets in the final state. In the case of the HS model, a corroborating signal appears in the µ + µ − + jets+ ≥ 1 b-jet channel.  The LHC reach at very low luminosity and without E miss T is comparable to the Tevatron reach in the multi-b + E miss T channel with 5-10 fb −1 of data. This may lead to a tight competition for the discovery or exclusion of the simplest Yukawa-unified SUSY scenario! Moving beyond about 0.2 fb −1 , we expect reliable E miss T resolution and electron identification to become available. We find that the LHC reach, using √ s = 7 TeV and 1 fb −1 of integrated luminosity, will move into the mg ∼ 600 − 650 GeV range for both the HS and DR3 model lines, if we require E miss T ≥ 100 GeV along with n(b) ≥ 3. This reach is presumably sufficient to rule out Yukawa unification in the DR3 case. In the HS case, somewhat larger values of mg can be allowed, although they seem very improbable. The LHC reach for 1 fb −1 using the multi-jets + E miss T signature-but making no requirement on n(b)-turns out to be much lower. A summary of our various results is presented in a convenient form in Table 6.
At some point LHC energy will be increased to ∼ 10 TeV, and this will allow the reach to be extended past the values presented here. Thus, our main conclusion is that LHC stands an excellent chance to either discover Yukawa-unifed SUSY during year 1 of operation, or exclude almost all its model parameter space! Last but not least we note that, if the scenario discussed here is realized, a trilepton signal from Drell-Yang W 1 Z 2 production should appear when moving into the several fb −1 regime, giving direct access to the chargino/neutralino sector.
Note added: While finalizing this manuscript, we found an Atlas note [46] which also investigates using multiple b-jets to enhance the LHC reach for SUSY in the mSUGRA model. They examine integrated luminosity values of 0.1 and 1 fb −1 , but take √ s = 14 TeV. Their overall results seem quite consistent with the results given here.