Light Higgses at the Tevatron and at the LHC and Observable Dark Matter in SUGRA and D Branes

Sparticle landscapes in mSUGRA, in SUGRA models with nonuniversalities (NUSUGRA), and in D brane models are analyzed. The analysis exhibits the existence of Higgs Mass Patterns (HPs) (for $\mu>0$) where the CP odd Higgs could be the next heavier particle beyond the LSP and sometimes even lighter than the LSP. It is shown that the Higgs production cross sections from the HPs are typically the largest enhancing the prospects for their detection at the LHC. Indeed it is seen that the recent Higgs production limits from CDF/D\O\ are beginning to put constraints on the HPs. It is also seen that the $B_s\to \mu^+\mu^-$ limits constrain the HPs more stringently. Predictions of the Higgs production cross sections for these patterns at the LHC are made. We compute the neutralino-proton cross sections $\sigma (\chi p)$ for dark matter experiments and show that the largest $\sigma (\chi p)$ also arise from the HPs and further that the HPs and some of the other patterns are beginning to be constrained by the most recent data from CDMS and from Xenon10 experiments. Finally, it is shown that the prospects are bright for the discovery of dark matter with $\sigma(\chi p)$ in the range $10^{-44\pm .5}$cm$^2$ due to a"Wall"consisting of a copious number of parameter points in the Chargino Patterns (CPs) where the chargino is the NLSP. The Wall, which appears in all models considered (mSUGRA, NUSUGRA and D branes) and runs up to about a TeV in LSP mass, significantly enhances the chances for the observation of dark matter by SuperCDMS, ZEPLIN-MAX, or LUX experiments which are expected to achieve a sensitivity of $10^{-45}$ cm$^2$ or more.

the parameter space. In our analysis we have carried out an exhaustive search under naturalness assumptions in exploring the sparticle landscape and the residual parameter space which satisfies the radiative electroweak symmetry breaking (REWSB), the dark matter relic density constraints and the collider constraints from flavor changing neutral currents and sparticle mass limits. The analysis exhibits a much larger set of patterns than previously seen.
In the analysis presented here we consider a larger class of models than discussed in [1].
Specifically we consider mSUGRA models (for recent works on mSUGRA see, e.g., [5]) with both signs of µ as well as SUGRA models with nonuniversalities (NUSUGRA), and D-brane models. The focus of our work will be Higgs Patterns which we collectively call HPs. It will be shown that typically the HPs lead to the largest production cross sections for the CP even and CP odd Higgs at the Tevatron and at the LHC. Further, they also lead to an LSP which has a very substantial Higgsino component. It is also shown that the HPs lead to the largest branching ratio for B s → µ + µ − . Finally, we show that the largest spin independent neutralinoproton cross section in dark matter experiments also arises from the HPs and the most recent results from the dark matter experiment are beginning to constrain the HPs, and more generally the dark matter experiments can also serve as a discriminator amongst sparticle mass patterns in the landscape.
We begin by discussing the details of the analysis. For the relic density of the neutralino LSP we impose the WMAP3 constraints [6], 0.0855 < Ω e χ 0 1 h 2 < 0.1189 (2σ). As is well known the experimental limits on the FCNC process b → sγ impose severe constraints and we use here the constraints from the Heavy Flavor Averaging Group (HFAG) [7] along with the BABAR, Belle and CLEO experimental results: Br(b → sγ) = (355 ± 24 +9 −10 ± 3) × 10 −6 . A new estimate of Br(B → X s γ) at O(α 2 s ) gives [8] Br(b → sγ) = (3.15 ± 0.23) × 10 −4 which moves the previous SM mean value of 3.6 × 10 −4 a bit lower. In the analysis we use a 3.5σ error corridor around the HFAG value. The total Br(B → X s γ) including the sum of SM and SUSY contributions (for the update on SUSY contributions see [9]) are constrained by this corridor. The process B s → µ + µ − can become significant for large tan β since the decay has a tan 6 β dependence and thus large tan β could be constrained by the current limit which is Br(B s → µ + µ − ) < 1.5 × 10 −7 (90% CL), 2.0 × 10 −7 (95% CL) [33]. We note that more recently the CDF and DØ have given limits which are about a factor of 10 more sensitive. We have included these preliminary [10] results in this analysis. Additionally, we also impose the current lower limits on the lightest CP even Higgs boson. For the Standard Model like Higgs boson this limit is ≈ 114.4 GeV [11], while a limit of 108.2 GeV at 95% CL is set on the production of an invisibly decaying Standard Model like Higgs by OPAL [11]. For the MSSM we take the constraint to be m h > 100 GeV. We take the other sparticle mass constraints to be m e χ ± 1 > 104.5 GeV [12] for the lighter chargino, m e t 1 > 101.5 GeV, m e τ 1 > 98.8 GeV for the lighter stop and the stau [5]. The mSUGRA analysis is based on a large Monte Carlo scan of the parameter space with the soft parameters in the range 0 < m 0 < 4000 GeV, 0 < m 1/2 < 2000 GeV, |A 0 /m 0 | < 10, 1 < tan β < 60 and both signs of µ are analyzed. In our analysis we use MicrOMEGAs version 2.0.7 [13] which includes the SuSpect 2.34 package [14] for the analysis of sparticle masses, with m MS b (m b ) = 4.23 GeV, m t (pole) = 170.9 GeV, requiring REWSB at the SUSY scale. We have cross checked with other codes [15,16,17,18,19,20,21] and find agreement up to ∼ O(10%).
In the analysis a scan of 2 × 10 6 models with Monte Carlo simulation was used for mSUGRA with µ > 0 and a scan of 1 × 10 6 models for µ < 0. Twenty two 4-sparticle patterns labeled mSP1-mSP22 survive the constraints from the radiative electroweak symmetry breaking, from the relic density constraint, and other collider constraints. mSP1-mSP16 which appear for µ > 0 are defined in [1]. For µ < 0 all of the patterns in µ > 0 case appear except for the cases mSP10, mSP14-mSP16. However, new patterns mSP17-mSP22 appear for µ < 0 and are given below A majority of the patterns discussed in [1] and this analysis do not appear in the Snowmass Benchmarks [22], and in the PostWMAP Benchmarks [23]. Since the HPs are a focus of this analysis, we exhibit these below where A, H indicates that the two Higgses A and H may sometimes exchange positions in the sparticle mass spectra 4 . The cases (i)-(iii) in Eq.(2) arise for µ > 0 and not for µ < 0, and   the HPs for mSUGRA case arise only for µ > 0, but also because of the recent results from the g µ − 2 experiment. As is well known the supersymmetric electroweak corrections to g µ − 2 can be as large or even larger than the Standard Model correction [24]. Further, for large tan β the sign of the supersymmetric correction to g µ − 2 is correlated with the sign of µ. The current data [25,26] on g µ − 2 favors µ > 0 and thus it is of relevance to discuss the possible physics that emerges if indeed one of these patterns is the one that may be realized in nature. Some benchmarks for the HPs are given in Table (1).
Higgs cross sections at the Tevatron and at the LHC: The lightness of A (and also of H and H ± ) in the Higgs Patterns implies that the Higgs production cross sections can be large (for some of the previous analyses where light Higgses appear see [28,29,30]). Quite interestingly the recent Tevatron data is beginning to constrain the HPs. This is exhibited in the left panel of Fig.(1) where the leading order (LO) cross section for the sum of neutral Higgs processes where sum over the neutral Φ fields is implied) vs the CP odd Higgs mass is plotted for CM energy of √ s = 1.96 TeV at the Tevatron. One finds that the predictions of σ Φτ τ (pp) from the HPs are the largest and lie in a narrow band followed by those from the Chargino Pattern mSP2. The recent data from the Tevatron is also shown [27].
A comparison of the theory prediction with data shows that the HPs are being constrained by experiment. Exhibited in the right panel of Fig.( arising from the HPs (and also from other patterns which make a comparable contribution) vs the CP odd Higgs mass with the analysis done at CM energy of √ s = 14 TeV at the LHC. Again it is seen that the predictions of σ Φτ τ (pp) arising from the HPs are the largest and lie in a very narrow band and the next largest predictions for σ Φτ τ (pp) are typically from the Chargino Patterns (CPs). The larger cross sections for the HPs enhance the prospects of their detection.
Further, the analysis shows that the Higgs production cross section when combined with the parameter space inputs and other signatures can be used to discriminate amongst mass patterns.
Since the largest Higgs production cross sections at the LHC arise from the Higgs Patterns and the Chargino Patterns we exhibit the mass of the light Higgs as a function of m 0 for these two patterns in the left panel of Fig.(2). We note that many of the Chargino Pattern points in this figure appear to have large m 0 indicating that they originate from the Hyperbolic Branch/Focus Point (HB/FP) region [46].
We discuss now briefly the Higgs to bb decay at the Tevatron. From the parameter space of mSUGRA that enters in Fig.(1) we can compute the quantity Experimentally, however, this quantity is difficult to measure because there is a large background to the production from qq, gg → bb. For this reason one focuses on the production [(pp → Φb)BR(Φ → bb)] [47]. For the parameter space of B s → µ + µ − and the Higgs Patterns: The process B s → µ + µ − is dominated by the neutral Higgs exchange [31] and is enhanced by a factor of tan 6 β. It is thus reasonable to expect that the HPs will be constrained more severely than other patterns by the B s → µ + µ − experiment, since HP points usually arise from the high tan β region (we note, however, that the nonuniversalities in the Higgs sector (NUH) can also give rise to HPs for moderate values of tan β (see Table(1))).
This is supported by a detailed analysis which is given in Fig.(3) where the branching ratio case correspond to tan β in the range of 50 -55. A similar limit on tan β is also observed for the nonuniversal models. We remark, however, that the HPs are not restricted to large tan β in particular for the case of the NUH model, where two such benchmarks are given in Table(1) for quite moderate values of tan β. Here the HP model points in mSP14 for the NUH case in Table(1) have Br(B s → µ + µ − ) ∼ (3.1, 3.8) × 10 −9 which are significantly lower than what is predicted by the very large tan β case in models with universality and thus these cases are much less constrained by the Br(B s → µ + µ − ) limits.

Dark Matter-Direct Detection:
We discuss now the direct detection of dark matter. In Fig.(4) we give an analysis of the scalar neutralino-proton cross section σ(χ 0 1 p) as a function of the LSP mass (complete analytic formulae for the computation of dark matter cross sections can be found in [34] and for a sample of Post-WMAP3 analysis of dark matter see [35,36]). The upper left panel of Fig.(4) gives the scalar σ(χ 0 1 p) for the mSUGRA parameter space for µ > 0. We note that the Higgs patterns typically give the largest dark matter cross sections (see the upper left and lower left panels of Fig.(4)) and are the first ones to be constrained by experiment. The  [32,33], and the bottom two horizontal lines are preliminary limits from the CDF and DØ data [10]. For convenience we draw the limits extending past the observable mass of the CP odd Higgs at the Tevatron.
currently underway and improved experiments in the future [37,38,39,40,41,42]. Indeed the analysis of Fig.(4) shows that some of the parameter space of the Higgs Patterns is beginning to be constrained by the CDMS and the Xenon10 data [41].    [43], ZEPLIN-MAX [44] or LUX [42] in this region.
What is very interesting is the fact that for the case µ > 0 the B s → µ + µ − limits, the Tevatron limits on the CP odd Higgs boson production, and the CDMS and Xenon10 limits converge on constraining the Higgs Patterns and specifically the pattern mSP14 and as well as some other patterns. Thus the CDMS and Xenon10 constraints on the mSPs are strikingly similar to the constraints of B s → µ + µ − from the Tevatron. We also observe that although the case µ < 0 is not currently accessible to the B s → µ + µ − constraint (and may also be beyond the ATLAS/CMS sensitivity for B s → µ + µ − ), it would, however, still be accessible at least partially to dark matter experiment. Finally we remark that the proton-neutralino cross sections act as a discriminator of the SUGRA patterns as it creates a significant dispersion among some of the patterns (see upper left and the two lower panels in Fig.(4)).

Nonuniversalities of soft breaking:
Since the nature of physics at the Planck scale is largely unknown it is useful to consider other soft breaking scenarios beyond mSUGRA. One such possibility is to consider nonuniveralities in the Kähler potential, which can give rise to nonuniversal soft breaking consistent with flavor changing neutral current constraints. We consider three possibilities which are nonuniversalities in (i) the Higgs sector (NUH), (ii) the third generation squark sector (NUq3), and (iii) the gaugino sector (NUG) (for a sample of previous work on dark matter analyses with nonuniversalities see [45]). We parametrize these at the GUT scale as follows: (i) NUH: M u3,d3 = m 0 (1 + δ tbR ), and, (iii) NUG: with −0.9 δ 1. In each case we carry out a Monte Carlo scan of 1 × 10 6 models. The above covers a very wide array of models. The analysis here shows that the patterns that appear in mSUGRA (i.e., mSPs) also appear here. However, in addition to the mSPs, new patterns appear which are labeled NUSP1-NUSP15 (see Table(2)), and we note the appearance of gluino patterns, and patterns where both the Higgses and gluinos are among the lightest sparticles.
The neutral Higgs production cross section for the NUSUGRA case is given in the right panel of Fig.(2). The analysis shows that the Higgs Patterns produce the largest cross sections followed by the Chargino Patterns as in mSUGRA case. The constraints of Br(B s → µ + µ − ) on the NUSUGRA Higgs patterns are exhibited in the lower right hand panel of Fig.(3). Again one finds that the Br(B s → µ + µ − ) data constrains the parameter space of the HPs in the NUSUGRA case. One feature which is now different is that the Higgs Patterns survive significantly beyond the CP odd Higgs mass of 600 GeV within our assumed naturalness assumptions.

Light Higgses and Dark Matter in D-brane Models:
The advent of D-branes has led to a new wave of model building [50], and several Standard Model like extensions have been constructed using intersecting D-branes [51]. The effective action and soft breaking in such models have been discussed [52] and there is some progress also on pursuing the phenomenology of intersecting D-brane models [53,54,55]. Here we discuss briefly the Higgses and dark matter in the context of D-branes. In our analysis we use the scenario of toroidal orbifold compactification based on where T 6 is taken to be a product of 3 T 2 tori. This model has a moduli sector consisting of volume moduli t m , shape moduli u m (m = 1, 2, 3) and the axion-dilaton field s.
is given in the lower right panel of Fig.(5). Here also one finds that the Higgs Patterns typically give the largest scalar cross sections followed by the Chargino Patterns (mSP1-mSP3) and then by the Stau Patterns. Further, one finds that the Wall of Chargino Patterns persists in this case as well.  mSP2  mSP3  mSP5  mSP6  mSP7  mSP8  mSP10  mSP11  mSP12  mSP13  mSP14  mSP15  mSP18  mSP19  NUSP3  NUSP5  NUSP6  DBSP1  DBSP2  DBSP3  DBSP4  DBSP5  DBSP6 200 400 600 800 1000 10  mSP2  mSP3  mSP5  mSP6  mSP7  mSP8  mSP10  mSP11  mSP12  mSP13  mSP14  mSP15  mSP18  mSP19  NUSP3  NUSP5  NUSP6  DBSP1  DBSP2  DBSP3  DBSP4  DBSP5  DBSP6  D∅ + CDF  We comment briefly on the signals from the chargino patterns. The chargino patterns correspond typically to low values of m 1/2 and arise dominantly from the hyperbolic branch/focus point region of radiative breaking of the electroweak symmetry. The above situation then gives rise to light charginos and neutralinos which can produce a copious number of leptonic signatures. We note that in the recent analysis of Ref. [1], the chargino pattern was studied in detail and the signatures at the LHC investigated. In particular it is found that the chargino patterns can give rise to substantial di-lepton and tri-leptonic signatures. Thus suppose we consider a 085. An analysis of leptonic signatures at the LHC with 10 fb −1 in this case gives the number of di-lepton and tri-lepton SUSY events (N ) with the cuts im-posed as in Ref. [1], so that (N 2L , N 3L ) jet≥2 ∼ (350, 40), (where (L = e, µ)). Both signatures are significantly above the 5σ discovery limits at the LHC (see Ref. [1]).
Conclusions: It is seen that Higgs Patterns (HPs) arise in a wide range of models: in mSUGRA, in NUSUGRA and in D-brane models. The HPs are typically seen to lead to large Higgs production cross sections at the Tevatron and at the LHC, and to the largest B s → µ + µ − branching ratios, and thus are the first to be constrained by the B s → µ + µ − experiment. It is also seen that the HPs lead typically to the largest neutralino-proton cross sections and would either be the first to be observed or the first to be constrained by dark matter experiment. The analysis presented here shows the existence of a Chargino Wall consisting of a copious number of parameter points in the Chargino Patterns where the NLSP is a chargino which give a σ(χ 0 1 p) at the level of 10 −44±.5 cm 2 in all models considered for the LSP mass extending up to 900 GeV in many cases. These results heighten the possibility for the observation of dark matter in improved dark matter experiments such as SuperCDMS [43], ZEPLIN-MAX [44], and LUX [42] which are expected to reach a sensitivity of 10 −45 cm 2 or more. Finally, we note that several of the patterns are well separated in the σ(χ 0 1 p)-LSP mass plots, providing important signatures along with the signatures from colliders for mapping out the sparticle parameter space.