Xerxes Tata

Honolulu University, Honolulu, Hawaii, United States

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Publications (226)875.43 Total impact

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    Howard Baer · Vernon Barger · Andre Lessa · Xerxes Tata
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    ABSTRACT: After completion of the LHC8 run in 2012, the plan is to upgrade the LHC for operation close to its design energy sqrt{s}=14 TeV, with a goal of collecting hundreds of fb^{-1} of integrated luminosity. The time is propitious to begin thinking of what is gained by even further LHC upgrades. In this report, we compute an LHC14 reach for SUSY in the mSUGRA/CMSSM model with an anticipated high luminosity upgrade. We find that LHC14 with 300 (3000) fb^{-1} has a reach for SUSY via gluino/squark searches of m(gluino)\sim3.2 TeV (3.6 TeV) for m(squark)\sim m)gluino), and a reach of m(gluino)\sim1.8 TeV (2.3 TeV) for m(squark)>> m(gluino). In the case where m(squark)>> m(gluino), then the LHC14 reach for chargino-neutralino production with decay into the Wh+MET final state reaches to m(gluino)\sim2.6 TeV for 3000 fb^{-1}.
    Preview · Article · Jul 2012 · Physical review D: Particles and fields
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    Howard Baer · Vernon Barger · Peisi Huang · Xerxes Tata
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    ABSTRACT: Particle physics models with Natural Supersymmetry are characterized by a superpotential parameter \mu \sim m_h \sim125$ GeV, while third generation squarks have mass <0.5-1.5 TeV. Gluinos should be lighter than several TeV so as not to destabilize the lighter squarks. First and second generation sfermions can be at the tens-of-TeV level which yields a decoupling solution to the SUSY flavor and CP problems. Adopting a top-down approach, we delineate the range of GUT scale SUSY model parameters which leads to a Natural SUSY mass spectrum. We find natural SUSY models to be tightly constrained by the b-> s\gamma branching fraction measurement while it is also difficult but not impossible to accommodate a light Higgs scalar of mass ~125 GeV. We present several benchmark points which are expandable to slopes and planes. Natural SUSY is difficult to see at LHC unless some third generation squarks are very light. The top- and bottom- squarks cascade decay mainly to higgsino-like charginos and neutralinos via numerous possibilities, leading to a rather complex set of signatures. Meanwhile, a linear e^+e^- collider operating at \sqrt{s}\sim 0.25-0.5 TeV would be a higgsino factory and is essentially guaranteed a SUSY discovery of the low-lying charged and neutral higgsino states. Since thermal neutralino cold dark matter is underproduced, we conjecture that the incorporation of a Peccei-Quinn sector or light moduli into the theory will augment higgsino dark matter production, possibly together with an admixture of axions. We present rates for direct and indirect higgsino dark matter detection for the case where light higgsinos dominate the dark matter abundance.
    Preview · Article · Mar 2012 · Journal of High Energy Physics
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    Howard Baer · Vernon Barger · Andre Lessa · Xerxes Tata
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    ABSTRACT: We extend our earlier results delineating the supersymmetry reach of the CERN Large Hadron Collider operating at a center-of-mass energy √s=7 TeV to integrated luminosities in the range 5–30 fb-1. Our results are presented within the paradigm minimal supergravity model or constrained minimal supersymmetric standard model. Using a six-dimensional grid of cuts for the optimization of signal to background ratio—including missing ET—we find for mg˜∼mq˜ an LHC 5σ supersymmetry discovery reach of mg˜∼1.3, 1.4, 1.5, and 1.6 TeV for 5, 10, 20, and 30 fb-1, respectively. For mq˜≫mg˜, the corresponding reach is instead mg˜∼0.8, 0.9, 1.0, and 1.05 TeV, for the same integrated luminosities.
    Preview · Article · Mar 2012 · Physical review D: Particles and fields
  • Howard Baer · Xerxes Tata
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    ABSTRACT: Preface; 1. The Standard Model; 2. What lies beyond the Standard Model; 3. The Wess-Zumino model; 4. The supersymmetry algebra; 5. Superfield formalism; 6. Supersymmetric gauge theories; 7. Supersymmetry breaking; 8. The Minimal Supersymmetric Standard Model; 9. Implications of the MSSM; 10. Local supersymmetry; 11. Realistic supersymmetric models; 12. Sparticle production at colliders; 13. Sparticle decays; 14. Supersymmetric event generation; 15. The search for supersymmetry at colliders; 16. R parity violation; 17. Epilogue; Appendices.
    No preview · Article · Mar 2012
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    ABSTRACT: LHC searches for supersymmetry currently focus on strongly produced sparticles, which are copiously produced if gluinos and squarks have masses of a few hundred GeV. However, in supersymmetric models with heavy scalars, as favored by the decoupling solution to the SUSY flavor and CP problems, and m_{\tg}> 500 GeV as indicated by recent LHC results, chargino--neutralino (\tw_1^\pm\tz_2) production is the dominant cross section for m_{\tw_1} \sim m_{\tz_2} < m_{\tg}/3 at LHC with \sqrt{s}=7 TeV (LHC7). Furthermore, if m_{\tz_1}+m_Z \lesssim m_{\tz_2}\lesssim m_{\tz_1}+m_h, then \tz_2 dominantly decays via \tz_2\to\tz_1 Z, while \tw_1 decays via \tw_1\to \tz_1 W. We investigate the LHC7 reach in the WZ + MET channel (for both leptonic and hadronic decays of the W boson) in models with and without the assumption of gaugino mass universality. In the case of the mSUGRA/CMSSM model with heavy squark masses, the LHC7 discovery reach in the WZ+MET channel becomes competetive with the reach in the canonical MET + jets channel for integrated luminosities \sim 30 fb^-1. We also present the LHC7 reach for a simplified model with arbitrary m_{\tz_1} and m_{\tw_1} \sim m_{\tz_2}. Here, we find a reach of up to m_{\tw_1}\sim 200 (250) GeV for 10 (30) fb^-1.
    Preview · Article · Jan 2012 · Journal of High Energy Physics
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    ABSTRACT: A summary is given of the results obtained by the Superstring working group. New physics phenomena arising from superstring models that might be detected at the SSC as well as their possible backgrounds were investigated. Topics examined were models with extra Z bosons and right handed W bosons, detection of Winos, Zinos and gluinos and production of heavy squarkonium.
    No preview · Article · Jan 2012 · International Journal of Modern Physics A
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    ABSTRACT: We give explicit formulas for the decays of the Higgs bosons of the minimal supersymmetric model to neutralinos and charginos. The important features of these decays are illustrated and their phenomenological implications discussed. When phase space allowed, this class of two-body decays is at least as important as, and often dominates, other types of Higgs decay modes, such as WW or ZZ and heavy fermion anti-fermion channels.
    No preview · Article · Jan 2012 · International Journal of Modern Physics A
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    ABSTRACT: We give explicit formulas for the decays of the neutralinos and charginos of the minimal model of supersymmetry into other neutralinos and charginos plus a W, Z, or Higgs boson. The important features of these decays are illustrated and their phenomenological implications discussed. In general, this class of two-body decays is dominant for the heaviest charginos and neutralinos.
    No preview · Article · Jan 2012 · International Journal of Modern Physics A
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    ABSTRACT: In SUSY models with heavy squarks and gaugino mass unification, the gaugino pair production reaction pp-> \tw_1^\pm\tz_2 dominates gluino pair production for m_{\tg}\agt 1 TeV at LHC with \sqrt{s}=14 TeV (LHC14). For this mass range, the two-body decays \tw_1\to W\tz_1 and \tz_2\to h\tz_1 are expected to dominate the chargino and neutralino branching fractions. By searching for \ell b\bar{b}+MET events from \tw_1^\pm\tz_2 production, we show that LHC14 with 100 fb^{-1} of integrated luminosity becomes sensitive to chargino masses in the range m_{\tw_1}\sim 450-550 GeV corresponding to m_{\tg}\sim 1.5-2 TeV in models with gaugino mass unification. For 10^3 fb^{-1}, LHC14 is sensitive to the Wh channel for m_{\tw_1}\sim 300-800 GeV, corresponding to m_{\tg}\sim 1-2.8 TeV, which is comparable to the reach for gluino pair production followed by cascade decays. The Wh+MET search channel opens up a new complementary avenue for SUSY searches at LHC, and serves to point to SUSY as the origin of any new physics discovered via multijet and multilepton + MET channels.
    Preview · Article · Jan 2012 · Physical review D: Particles and fields
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    Vernon Barger · Yu Gao · Andre Lessa · Xerxes Tata
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    ABSTRACT: We propose a new way to determine the squark mass based on the shape of di-jet invariant mass distribution of supersymmetry (SUSY) di-jet events at the Large Hadron Collider (LHC). Our algorithm, which is based on event kinematics, requires that the branching ratio $B(\tilde{q} \rightarrow q \tilde{z}_1)$ is substantial for at least some types of squarks, and that $m_{\tilde{z}_1}^2/m_{\tilde{q}}^2 \ll 1$. We select di-jet events with no isolated leptons, and impose cuts on the total jet transverse energy, $E_T^{tot}=E_T(j_1)+E_T(j_2)$, on $\alpha = E_T(j_2)/m_{jj}$, and on the azimuthal angle between the two jets to reduce SM backgrounds. The shape of the resulting di-jet mass distribution depends sensitively on the squark mass, especially if the integrated luminosity is sufficient to allow a hard enough cut on $E_T^{tot}$ and yet leave a large enough signal to obtain the $m_{jj}$ distribution. We simulate the signal and Standard Model (SM) backgrounds for 100 fb$^{-1}$ integrated luminosity at 14 TeV requiring $E_T^{tot}> 700$ GeV. We show that it should be possible to extract $m_{\tilde{q}}$ to within about 3% at 95% CL --- similar to the precision obtained using $m_{T2}$ --- from the di-jet mass distribution if $m_{\tilde{q}} \sim 650$ GeV, or to within $\sim 5$% if $m_{\tilde{q}}\sim 1$ TeV.
    Preview · Article · Feb 2011 · Physical review D: Particles and fields
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    ABSTRACT: We investigate the phenomenology of Effective Supersymmetry (ESUSY) models wherein electroweak gauginos and third generation scalars have masses up to about 1 TeV while first and second generation scalars lie in the multi-TeV range. Such models ameliorate the SUSY flavor and CP problems via a decoupling solution, while at the same time maintaining naturalness. In our analysis, we assume independent GUT scale mass parameters for third and first/second generation scalars and for the Higgs scalars, in addition to m 1/2, tan β and A 0, and require radiative electroweak symmetry breaking as usual. We analyse the parameter space which is consistent with current constraints, by means of a Markov Chain Monte Carlo scan. The lightest MSSM particle (LMP) is mostly, but not always the lightest neutralino, and moreover, the thermal relic density of the neutralino LMP is frequently very large. These models may phenomenologically be perfectly viable if the LMP before nucleosynthesis decays into the axino plus SM particles. Dark matter is then an axion/axino mixture. At the LHC, the most important production mechanisms are gluino production (for m 1/2 ≲ 700 GeV) and third generation squark production, while SUSY events rich in b-jets are the hallmark of the ESUSY scenario. We present a set of ESUSY benchmark points with characteristic features and discuss their LHC phenomenology.
    Preview · Article · Jul 2010 · Journal of High Energy Physics
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    Howard Baer · Vernon Barger · Andre Lessa · Xerxes Tata
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    ABSTRACT: We examine the capability of the CERN Large Hadron Collider to discovery supersymmetry (SUSY) with energy sqrt {s} = 7{text{TeV}} and integrated luminosity of about 1 fb-1. Our results are presented within the paradigm minimal supergravity model (mSUGRA or CMSSM). Using a 6-dimensional grid of cuts for optimization of signal to background --- including missing E T --- we find for {m_{tilde{g}}} ˜ {m_{tilde{q}}} an LHC reach of {m_{tilde{g}}} 800, 950, 1100 and 1200 GeV for 0.1, 0.3, 1 and 2 fb-1, respectively. For {m_{tilde{g}}} &Lt; {m_{tilde{q}}} , the reach is instead near {m_{tilde{g}}} 480, 540, 620 and 700 GeV, for the same integrated luminosities. We also examine the LHC reach in the case of very low integrated luminosity where missing E T may not be viable. We focus on the multi-muon, multi-lepton (including electrons) and dijet signals. Although the LHC reach without E T miss is considerably lower in these cases, it is still substantial: for 0.3 fb-1, the dijet reach in terms of gluino mass is up to 600 GeV for very low m 0, while the dilepton reach is to gluino masses of ˜500 GeV over a range of m 0 values.
    Preview · Article · Apr 2010 · Journal of High Energy Physics
  • Xerxes Tata · Xerxes
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    ABSTRACT: The conceptually simplest scenario for dark matter (DM) is that it is a stable thermal relic from standard Big Bang cosmology, in many SUSY models the lightest neutralino. The relic density determination selects special regions in SUSY model parameter space with concomitant implications for collider physics, dark matter searches and low energy measurements. By studying various one-parameter extensions of the much-studied mSUGRA model (where we relax the untested universality assumptions) constructed to be in accord with the measured relic density, we show that these implications are in general model-dependent, so that LHC and DM measurements will provide clues to how sparticles acquire their masses. We point out some relatively robust implications for LHC and DM searches and conclude with an outlook for the future.
    No preview · Article · Feb 2010
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    ABSTRACT: The Large Hadron Collider presents an unprecedented opportunity to probe the realm of new physics in the TeV region and shed light on some of the core unresolved issues of particle physics. These include the nature of electroweak symmetry breaking, the origin of mass, the possible constituent of cold dark matter, new sources of CP violation needed to explain the baryon excess in the universe, the possible existence of extra gauge groups and extra matter, and importantly the path Nature chooses to resolve the hierarchy problem – is it supersymmetry or extra dimensions. Many models of new physics beyond the standard model contain a hidden sector which can be probed at the LHC. Additionally, the LHC will be a top factory and accurate measurements of the properties of the top and its rare decays will provide a window to new physics. Further, the LHC could shed light on the origin of neutralino masses if the new physics associated with their generation lies in the TeV region. Finally, the LHC is also a laboratory to test the hypothesis of TeV scale strings and D brane models. An overview of these possibilities is presented in the spirit that it will serve as a companion to the Technical Design Reports (TDRs) by the particle detector groups ATLAS and CMS to facilitate the test of the new theoretical ideas at the LHC. Which of these ideas stands the test of the LHC data will govern the course of particle physics in the subsequent decades.
    Full-text · Article · Jan 2010 · Nuclear Physics B - Proceedings Supplements
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    Howard Baer · Vernon Barger · Andre Lessa · Xerxes Tata
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    ABSTRACT: We examine the supersymmetry (SUSY) reach of the CERN LHC operating at s1/2 = 10 and 14 TeV within the framework of the minimal supergravity model (mSUGRA). We improve upon previous reach projections by incorporating updated background calculations including a variety of 2 --> n Standard Model (SM) processes. We show that SUSY discovery is possible even before the detectors are understood well enough to utilize either ETmiss or electrons in the signal. We evaluate the early SUSY reach of the LHC at s1/2 = 10 TeV by examining multi-muon plus >= 4 jets, and also lepton-free, acollinear dijet events with no missing ET cuts, and show that the greatest reach in terms of m1/2 occurs in the dijet channel, where it may be possible to probe mbar q ~ mbar g lesssim 1 TeV with just 1 fb-1 of integrated luminosity. The reach in multi-muons is slightly smaller in m1/2, but extends to higher values of m0. We find that an observable multi-muon signal will first appear in the opposite-sign dimuon channel, but as the integrated luminosity increases the relatively background-free but rate-limited same-sign dimuon, and ultimately the trimuon channel yield the highest reach. The optimized reach in these channels extends to mbar g lesssim 600 (800) GeV for an integrated luminosity of 100 pb-1 (1 fb-1). We show characteristic distributions in these channels that serve to distinguish the signal from the SM background, and also help to corroborate its SUSY origin. We then evaluate the LHC reach in various no-lepton and multi-lepton plus jets channels including missing ET cuts for s1/2 = 10 and 14 TeV, and plot the reach for integrated luminosities ranging up to 3000 fb-1 at the SLHC. For s1/2 = 10 TeV, the LHC reach extends to mbar g = 1.9, 2.3, 2.8 and 2.9 TeV for mbar q ~ mbar g and integrated luminosities of 10, 100, 1000 and 3000 fb-1, respectively. For s1/2 = 14 TeV, the LHC reach for the same integrated luminosities is to mbar g = 2.4, 3.1, 3.7 and 4.0 TeV, respectively. The reach estimates for ab-1 luminosities may be over-optimistic due to low statistics of background with very hard cuts.
    Preview · Article · Sep 2009 · Journal of High Energy Physics
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    R. S. Hundi · Sandip Pakvasa · Xerxes Tata
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    ABSTRACT: We present a locally supersymmetric extension of the minimal supersymmetric standard model (MSSM) based on the gauge group SU(3)C×SU(2)L×U(1)Y×U(1)' where, except for the supersymmetry-breaking scale which is fixed to be ˜1011GeV, we require that all non-standard-model parameters allowed by the local spacetime and gauge symmetries assume their natural values. The U(1)' symmetry, which is spontaneously broken at the intermediate scale, serves to (i) explain the weak scale magnitudes of mu and bmu terms, (ii) ensure that dimension-3 and dimension-4 baryon-number-violating superpotential operators (and, in a class of models, all DeltaB=1 operators) are forbidden, solving the proton-lifetime problem, and (iii) predict bilinear lepton-number violation in the superpotential at just the right level to accommodate the observed mass and mixing pattern of active neutrinos (leading to a novel connection between the SUSY-breaking scale and neutrino masses), while corresponding trilinear operators are strongly suppressed. The phenomenology is like that of the MSSM with bilinear R-parity violation, where the would-be lightest supersymmetric particle decays leptonically with a lifetime of ˜10-12-10-8s. Theoretical consistency of our model requires the existence of multi-TeV, stable, color-triplet, weak-isosinglet scalars or fermions, with either conventional or exotic electric charge which should be readily detectable if they are within the kinematic reach of a hadron collider. Null results of searches for heavy exotic isotopes imply that the reheating temperature of our Universe must have been below their mass scale which, in turn, suggests that sphalerons play a key role for baryogenesis. Finally, the dark matter cannot be the weakly interacting neutralino.
    Full-text · Article · May 2009 · Physical review D: Particles and fields
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    Howard Baer · Eun-Kyung Park · Xerxes Tata
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    ABSTRACT: We present an overview of supersymmetry searches, both at collider experiments and via searches for dark matter (DM). We focus on three DM possibilities in the SUSY context: the thermally produced neutralino, a mixture of axion and axino, and the gravitino, and compare and contrast signals that may be expected at colliders, in direct detection (DD) experiments searching of DM relics left over from the Big Bang, and indirect detection (ID) experiments designed to detect the products of DM annihilations within the solar interior or galactic halo. Detection of DM particles using multiple strategies provides complementary information that may shed light on the new physics associated with the dark matter sector. In contrast to the mSUGRA model where the measured cold DM relic density restricts us to special regions mostly on the edge of the m_0-m_{1/2} plane, the entire parameter plane becomes allowed if the universality assumption is relaxed in models with just one additional parameter. Then, thermally produced neutralinos with a well-tempered mix of wino, bino and higgsino components, or with a mass adjusted so that their annihilation in the early universe is Higgs-resonance-enhanced, can be the DM. Well-tempered neutralinos typically yield heightened rates for DD and ID experiments compared to generic predictions from minimal supergravity. If instead DM consists of axinos (possibly together with axions) or gravitinos, then there exists the possibility of detection of quasi-stable next-to-lightest SUSY particles at colliding beam experiments, with especially striking consequences if the NLSP is charged, but no DD or ID detection. The exception for mixed axion/axino DM is that DD of axions may be possible. Comment: 28 pages, 11 eps figures; invited contribution to NJP Focus Issue on "Dark Matter and Particle Physics"
    Preview · Article · Mar 2009 · New Journal of Physics
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    Andrew D. Box · Xerxes Tata
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    ABSTRACT: We re-examine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric Standard Model with broken supersymmetry, allowing for arbitrary flavour structure of the soft SUSY breaking (SSB) parameters. We include threshold effects by evaluating the $\beta$-functions in a sequence of (non-supersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high scale SSB parameters that obtains if we assume that the supersymmetry breaking mechanism does not introduce new inter-generational couplings. This form, possibly amended to allow additional sources of flavour-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY GUT with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by ${\cal O}$(10%). As another illustration, we show that in mSUGRA, the rate for the flavour-violating $\tilde{t}_1\to c\tilde{Z}_1$ decay obtained using the complete RGE solution is smaller than that obtained using the commonly-used "single-step" integration of the RGEs by a factor 10-25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix B of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavour-effects necessary for two-loop accuracy.
    Preview · Article · Oct 2008 · Physical review D: Particles and fields
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    Howard Baer · Xerxes Tata
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    ABSTRACT: An abundance of astrophysical evidence indicates that the bulk of matter in the universe is made up of massive, electrically neutral particles that form the dark matter (DM). While the density of DM has been precisely measured, the identity of the DM particle (or particles) is a complete mystery. In fact, within the laws of physics as we know them (the Standard Model, or SM), none of the particles have the right properties to make up DM. Remarkably, many new physics extensions of the SM -- designed to address theoretical issues with the electroweak symmetry breaking sector -- require the introduction of new particles, some of which are excellent DM candidates. As the LHC era begins, there are high hopes that DM particles, along with their associated new matter states, will be produced in pp collisions. We discuss how LHC experiments, along with other DM searches, may serve to determine the identity of DM particles and elucidate the associated physics. Most of our discussion centers around theories with weak-scale supersymmetry, and allows for several different DM candidate particles.
    Preview · Article · Jun 2008
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    ABSTRACT: We present brief synopses of supersymmetric models where either the neutralino composition or its mass is adjusted so that thermal relic neutralinos from the Big Bang saturate the measured abundance of cold dark matter in the universe. We first review minimal supergravity (mSUGRA), and then examine its various one-parameter extensions where we relax the assumed universality of the soft supersymmetry breaking parameters. Our goal is to correlate relic-density-allowed parameter choices with expected phenomena in direct, indirect and collider dark matter search experiments. For every non-universal model, we first provide plots to facilitate the selection of ``dark-matter allowed'' parameter space points, and then present salient features of each model with respect to searches at Tevatron, LHC and ILC and also direct and indirect dark matter searches. We present benchmark scenarios that allow one to compare and contrast the non-universal models with one another and with the paradigm mSUGRA framework. We show that many implications about sparticle properties and collider signals drawn from the analysis of the relic density constraint within mSUGRA do not carry over to simple one-parameter extensions of the mSUGRA framework. We find that in many relic-density-consistent models, there is one (or more) detectable edge in the invariant mass distribution of same-flavour, opposite sign dileptons in SUSY cascade decay events at the LHC. Finally, we scan the parameter space of these various models, requiring consistency with the LEP2 constraint on the chargino mass, and with the observed relic density, and examine prospects for direct and indirect dark matter detection. We find that in a large number of cases the mechanism that causes the early universe neutralino annihilation rate to be large (so as to produce the measured relic density) also enhances the direct detection rate, and often also the rates for indirect detection of neutralino dark matter.
    Preview · Article · Mar 2008 · Journal of High Energy Physics

Publication Stats

9k Citations
875.43 Total Impact Points

Institutions

  • 1990-2015
    • Honolulu University
      Honolulu, Hawaii, United States
  • 1985-2014
    • CERN
      • Physics Department (PH)
      Genève, Geneva, Switzerland
  • 1989-2013
    • University of Hawaiʻi at Mānoa
      • Department of Physics and Astronomy
      Honolulu, Hawaii, United States
    • High Energy Accelerator Research Organization
      Tsukuba, Ibaraki, Japan
  • 1987-2012
    • University of Wisconsin–Madison
      • Department of Physics
      Madison, Wisconsin, United States
  • 1994-2006
    • Florida State University
      • Department of Physics
      Tallahassee, Florida, United States
  • 2005
    • California Institute of Technology
      • Division of Physics, Mathematics, and Astronomy
      Pasadena, California, United States
  • 1997
    • Institute for Theoretical and Experimental Physics
      Moskva, Moscow, Russia
  • 1995-1997
    • University of Hawaiʻi at Hilo
      Hilo, Hawaii, United States
  • 1991
    • Oklahoma State University - Stillwater
      • Department of Physics
      SWO, Oklahoma, United States
  • 1988
    • University of Wisconsin - Stout
      Menominee, Wisconsin, United States
  • 1984-1986
    • University of Oregon
      • Institute of Theoretical Science
      Eugene, Oregon, United States
  • 1979-1985
    • University of Texas at Austin
      • Department of Physics
      Austin, Texas, United States