Minimal Supersymmetric Extension Of The Standard Model Research Articles

Supersymmetric radiative corrections at large tan β

In the minimal supersymmetric extension of the Standard Model (MSSM), fermion masses and Yukawa couplings receive radiative corrections at one loop from diagrams involving the supersymmetric particles. The corrections to the relation between down-type fermion masses and Yukawa couplings are enhanced by tan β, which makes them potentially very significant at large than β. These corrections affect a wide range of processes in the MSSM, including neutral and charged Higgs phenomenology, rare B meson decays, and renormalization of the CKM matrix. We give a pedagogical review of the sources and phenomenological effects of these corrections.

Low-energy supersymmetry and its phenomenology

The structure of low-energy supersymmetric models of fundamental particles and interactions is reviewed, with an emphasis on the minimal supersymmetric extension of the Standard Model (MSSM) and some of its variants. Various approaches to the supersymmetry-breaking mechanism are considered. The implications for the phenomenology of Higgs bosons and supersymmetric particles at future colliders are discussed.

Pair production of neutral Higgs bosons at the CERN Large Hadron Collider

We study the hadroproduction of two neutral Higgs bosons in the minimal supersymmetric extension of the standard model (MSSM), which provides a handle on the trilinear Higgs couplings. We include the contributions from quark-antiquark annihilation at the tree level and those from gluon-gluon fusion, which proceeds via quark and squark loops. We list compact results for the tree-level partonic cross sections and the squark loop amplitudes, and we confirm previous results for the quark loop amplitudes. We quantitatively analyze the hadronic cross sections at the CERN Large Hadron Collider assuming a favorable supergravity-inspired MSSM scenario.

Supersymmetric CP-violating currents and electroweak baryogenesis

In this work we compute the CP-violating currents of the right-handed stops and higgsinos, induced by the presence of non-trivial vacuum expectation values of the Higgs fields within the context of the minimal supersymmetric extension of the Standard Model (MSSM) with explicit CP-violating phases. Using the Keldysh formalism, we perform the computation of the currents at finite temperature, in an expansion of derivatives of the Higgs fields. Contrary to previous works, we implement a resummation of the Higgs mass insertion effects to all orders in perturbation theory. While the components of the right-handed stop current jμt̃R become proportional to the difference H2∂μH1−H1∂μH2 (suppressed by Δβ), the higgsino currents, jμH̃i, present contributions proportional to both H2∂μH1±H1∂μH2. For large values of the charged Higgs mass and moderate values of tanβ the contribution to the source proportional to H2∂μH1+H1∂μH2 in the diffusion equations become sizeable, although it is suppressed by the higgsino number violating interaction rate Γμ−1/2. For small values of the wall velocity, 0.04≲vω≲0.1, the total contribution leads to acceptable values of the baryon asymmetry for values of the CP-violating phases ϕCP in the range 0.04≲|sinϕCP|≲1. Finally, we comment on the relevance of the latest results of Higgs searches at LEP2 for the mechanism of electroweak baryogenesis within the MSSM.

Exploration of elastic scattering rates for supersymmetric dark matter

We explore the possible cross sections for the elastic scattering of neutralinos $\ensuremath{\chi}$ on nucleons $p,n$ in the minimal supersymmetric extension of the standard model (MSSM). Universality of the soft supersymmetry-breaking scalar masses for the Higgs multiplets is not assumed, but the MSSM parameters are nevertheless required to lead consistently to an electroweak vacuum. We explore systematically the region of MSSM parameter space where CERN LEP and other accelerator constraints are respected, and the relic neutralino density lies in the range $0.1<~{\ensuremath{\Omega}}_{\ensuremath{\chi}}{h}^{2}<~0.3$ preferred by cosmology. We also discuss models with ${\ensuremath{\Omega}}_{\ensuremath{\chi}}{h}^{2}<0.1,$ in which case we scale the density of supersymmetric dark matter in our galactic halo by ${\ensuremath{\Omega}}_{\ensuremath{\chi}}{h}^{2}/0.1,$ allowing for the possible existence of some complementary form of cold dark matter. We restrict our attention to $\mathrm{tan}\ensuremath{\beta}<~10,$ for which reliable relic-density calculations are available. Within this range of $\mathrm{tan}\ensuremath{\beta},$ we find values of the cross sections that are considerably lower than the present experimental sensitivities. At low neutralino masses, ${m}_{\ensuremath{\chi}}\ensuremath{\lesssim}100$ GeV, the cross sections may be somewhat higher than in the constrained MSSM with universal soft Higgs boson masses, though they are generally lower. In the case of large ${m}_{\ensuremath{\chi}},$ the cross sections we find may be considerably larger than in the constrained model, but still well below the present experimental sensitivity.

Renormalization-group-improved effective potential for the MSSM Higgs sector with explicit CP violation

Abstract We perform a systematic study of the one-loop renormalization-group-improved effective potential of the minimal supersymmetric extension of the Standard Model (MSSM), including CP violation induced radiatively by soft trilinear interactions related to squarks of the third generation. We calculate the charged and neutral Higgs-boson masses and couplings, including the two-loop logarithmic corrections that arise from QCD effects, as well as those associated with the top- and bottom-quark Yukawa couplings. We also include the potentially large two-loop non-logarithmic corrections induced by one-loop threshold effects on the top- and bottom-quark Yukawa couplings, due to the decoupling of the third-generation squarks. Within this minimal CP-violating framework, the charged and neutral Higgs sectors become intimately related to one another and therefore require a unified treatment. In the limit of a large charged Higgs-boson mass, M H ± ≫M Z , the lightest neutral Higgs boson resembles that in the Standard Model (SM), and CP violation occurs only in the heavy Higgs sector. Our analysis shows that sizeable radiative effects of CP violation in the Higgs sector of the MSSM may lead to significant modifications of previous studies for Higgs-boson searches at LEP 2, the Tevatron and the LHC. In particular, CP violation could enable a relatively light Higgs boson to escape detection at LEP 2.

Reconciling the two-loop diagrammatic and effective field theory computations of the mass of the lightest -even Higgs boson in the MSSM

The mass of the lightest CP-even Higgs boson of the minimal supersymmetric extension of the Standard Model (MSSM) has previously been computed including O(alpha alpha_s) two-loop contributions by an on-shell diagrammatic method, while approximate analytic results have also been obtained via renormalization-group-improved effective potential and effective field theory techniques. Initial comparisons of the corresponding two-loop results revealed an apparent discrepancy between terms that depend logarithmically on the supersymmetry-breaking scale, and different dependences of the non-logarithmic terms on the squark mixing parameter, X_t. In this paper, we determine the origin of these differences as a consequence of different renormalization schemes in which both calculations are performed. By re-expressing the on-shell result in terms of MS-bar parameters, the logarithmic two-loop contributions obtained by the different approaches are shown to coincide. The remaining difference, arising from genuine non-logarithmic two-loop contributions, is identified, and its effect on the maximal value of the lightest CP-even Higgs boson mass is discussed. Finally, we show that in a simple analytic approximation to the Higgs mass, the leading two-loop radiative corrections can be absorbed to a large extent into an effective one-loop expression by evaluating the running top quark mass at appropriately chosen energy scales.

Variations of the neutralino elastic cross-section with CP-violating phases

We analyze the neutralino–nucleus elastic cross-section in the minimal supersymmetric extension of the standard model (MSSM), including contributions from CP-violating phases, using the four-fermi neutralino–quark interaction. Over a wide range of the MSSM parameter space, we show the variations in the cross-sections due to these phases. We further concentrate on the regions which are consistent with constraints from the electric dipole moment of the electron, neutron and mercury atom. In the regions we examine in detail, we find suppressions by up to a factor of two, while enhancements in the cross-sections are no greater than ∼10%.

Virtual sfermion effects on vector-boson pair production at e +e − colliders

We study the quantum effects on vector-boson pair production in e +e − annihilation induced by the sleptons and squarks of the minimal supersymmetric extension of the standard model (MSSM) in the one-loop approximation. We list full analytic results, and quantitatively analyze the resulting deviation from the standard-model prediction of e +e −→ W + W − for the supergravity-inspired MSSM. The latter can be rendered small throughout the whole parameter space by an appropriate choice of renormalization scheme.

Search for neutral Higgs bosons in ${\mathrm{e}}^+ {\mathrm{e}}^-$ collisions at $\sqrt s \approx$ 189 GeV

Searches for the neutral Higgs bosons predicted by the Standard Model (SM) and the Minimal Supersymmetric extension of the Standard Model (MSSM) have been performed with the OPAL detector at LEP. Approximately 170 pb\(^{-1}\) of \(\mathrm{e}^+ \mathrm{e}^-\) collision data collected at \(\sqrt{s} \approx 189\) GeV were used to search for Higgs boson production in the SM process \({\mathrm{e}}^+{\mathrm{e}}^- \rightarrow \mathrm{H}^{0}\mathrm{Z}^{0}\) and the MSSM processes \({\mathrm{e}}^+{\mathrm{e}}^- \rightarrow \mathrm{h}^{0} \mathrm{Z}^{0}\) and \({\mathrm{e}}^+ {\mathrm{e}}^- \rightarrow \mathrm{A}^{0} \mathrm{h}^{0}\). The searches are sensitive to the \(\mathrm{b}\bar{\mathrm{b}}\) and \(\tau^+\tau^-\) decay modes of the Higgs bosons, and also to the MSSM decay mode \(\mathrm{h}^{0} \rightarrow \mathrm{A}^{0} \mathrm{A}^{0}\). OPAL search results at lower centre-of-mass energies have been incorporated in the limits, which are valid at the 95% confidence level. For the SM Higgs boson, a lower mass bound of 91.0 GeV is obtained. In the MSSM, the limits are \(m_{\mathrm{H}} >74.8\) GeV and \(m_{\mathrm{A}} >76.5\) GeV, assuming \(\tan\beta > 1\), that the mixing of the scalar top quarks is either zero or maximal, and that the soft SUSY-breaking masses are 1 TeV. For the case of zero scalar top mixing, the values of \(\tan\beta\) between 0.72 and 2.19 are excluded.

Cosmic Antiprotons as a Probe for Supersymmetric Dark Matter?

The flux of cosmic ray antiprotons from neutralino annihilations in the galactic halo is computed for a large sample of models in the MSSM (the Minimal Supersymmetric extension of the Standard Model). We also revisit the problem of estimating the background of low-energy cosmic ray induced secondary antiprotons, taking into account their subsequent interactions (and energy loss) and the presence of nuclei in the interstellar matter. We consider a two-zone diffusion model, with and without a galactic wind. We find that, given the uncertainties in the background predictions, there is no need for a primary (exotic) component to explain present data. However, allowing for a signal by playing with the uncertainties in the background estimate, we discuss the characteristic features of the supersymmetric models which give a satisfactory description of the data. We point out that in some cases the optimal kinetic energy to search for a signal from supersymmetric dark matter is above several GeV, rather than the traditional sub-GeV region. The large astrophysical uncertainties involved do not, one the other hand, allow the exclusion of any of the MSSM models we consider, on the basis of data. We present besides numerical results also convenient parameterizations of the antiproton yields of all `basic' two-body final states. We also give examples of the yield and differential energy spectrum for a set of supersymmetric models with high rates. We also remark that it is difficult to put a limit on the antiproton lifetime from present measurements, since the injection of antiprotons from neutralino annihilation can compensate the loss from decay.

Neutrino masses, mixing angles and the unification of couplings in the MSSM

In the light of the gathering evidence for $\nu_{\mu}-\nu_{\tau}$ neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of $\tan\beta$ on the characteristics of the high-energy quark and lepton mass matrices. In particular, we find that, in the presence of large lepton mixing, Yukawa unification can be achieved for intermediate values of $\tan\beta$ that were previously disfavoured. The renormalization-group sensitivity to the structures of different mass matrices may enable Yukawa unification to serve as a useful probe of GUT models.

Higgs boson mass bounds in three and four generation scenarios

In light of recent experimental results, we present updated bounds on the lightest Higgs boson mass in the Standard Model (SM) and in the Minimal Supersymmetric extension of the Standard Model (MSSM). The vacuum stability lower bound on the pure SM Higgs boson mass when the SM is taken to be valid up to the Planck scale lies above the MSSM lightest Higgs boson mass upper bound for a large amount of SUSY parameter space. If the lightest Higgs boson is detected with a mass M_{H} < 134 GeV (150 GeV) for a top quark mass M_{top} = 172 GeV (179 GeV), it may indicate the existence of a fourth generation of fermions. The region of inconsistency is removed and the MSSM is salvagable for such values of M_{H} if one postulates the existence of a fourth generation of leptons and quarks with isodoublet degenerate masses M_{L} and M_{Q} such that 60 GeV < M_{L} < 110 GeV and M_{Q} > 170 GeV.

Neutralino-stau coannihilation and the cosmological upper limit on the mass of the lightest supersymmetric particle

We consider the effects of neutralino-stau ( χ− τ ̃ ) coannihilations on the cosmological relic density of the lightest supersymmetric particle (LSP) χ ̃ in the minimal supersymmetric extension of the Standard Model (MSSM), particularly in the constrained MSSM in which universal supergravity inputs at the GUT scale are assumed. For much of the parameter space in these models, χ ̃ is approximately a U(1) gaugino B ̃ , and constraints on the cosmological relic density Ω B ̃ h 2 yield an upper bound on m B ̃ . We show that in regions of parameter space for which the cosmological bound is nearly saturated, coannihilations of the B ̃ with the τ ̃ , the next lightest sparticle, are important and may reduce significantly the B ̃ relic density. Including also B ̃ coannihilations with the e ̃ and μ ̃ , we find that the upper limit on m χ ̃ is increased from about 200 GeV to about 600 GeV in the constrained MSSM, with a similar new upper limit expected in the MSSM.

The Higgs boson mass as a probe of the minimal supersymmetric standard model

Recently, the LEP collaborations have reported a lower bound on a Standard Model-like Higgs boson of order 89 GeV. We discuss the implications of this bound for the minimal supersymmetric extension of the Standard Model (MSSM). In particular, we show that the lower bound on tan β, which can be obtained from the presently allowed Higgs boson mass value, becomes stronger than the one set by the requirement of perturbative consistency of the theory up to scales of order M GUT (associated with the infrared fixed-point solution of the top quark Yukawa coupling) in a large fraction of the allowed parameter space. The potentiality of future LEP2 searches to further probe the MSSM parameter space is also discussed.

Searches for the neutral Higgs bosons of the MSSM in e +e − collisions at centre-of-mass energies of 181–184 GeV

The data collected by ALEPH at LEP at centre-of-mass energies ranging from 181 to 184 GeV, corresponding to an integrated luminosity of 57 pb −1, are analysed to search for pair-produced neutral Higgs bosons h and A, in the b b ̄ b b ̄ and τ + τ − b b ̄ final states. Two events are found in the data with 2.5 expected from standard model processes. When combined with the lower energy data collected by ALEPH and with earlier reported searches for associated hZ production, these analyses are interpreted in the context of the minimal supersymmetric extension of the standard model (MSSM). For standard choices of MSSM parameter sets, this combination results in 95% C.L. exclusion lower limits of 72.2 and 76.1 GeV/ c 2 for m h and m A, irrespective of tan β. A scan of the MSSM parameter space is performed in which the model parameters are varied over wide ranges. For low values of tan β, i.e., for 1< tanβ≲ 2 , the limit on m h of ∼88 GeV/ c 2 is shown to be robust, being satisfied in essentially all of the physically allowed domain.

The status of the minimal supersymmetric standard model and beyond

The minimal supersymmetric extension of the Standard Model (MSSM) is reviewed. In the most general framework with minimal field content and R-parity conservation, the MSSM is a 124-parameter model (henceforth called MSSM-124). An acceptable phenomenology occurs only at exceptional points (and small perturbations around these points) of MSSM-124 parameter space. Among the topics addressed in this review are: gauge coupling unification, precision electroweak data, phenomenology of the MSSM Higgs sector, and supersymmetry searches at present and future colliders. The implications of approaches beyond the MSSM are briefly addressed.

The fine-tuning price of LEP

We quantify the amount of fine tuning of input parameters of the Minimal Supersymmetric Extension of the Standard Model (MSSM) that is needed to respect the lower limits on sparticle and Higgs masses imposed by precision electroweak measurements at LEP, measurements of b→ X s γ, and searches at LEP 2. If universal input scalar masses are assumed in a gravity-mediated scenario, a factor of ≳180 is required at tan β∼1.65, decreasing to ∼20 at tan β∼10. The amount of fine tuning is not greatly reduced if non-universal input scalar Higgs masses are allowed, but may be significantly reduced if some theoretical relations between MSSM parameters are assumed.

Flavor-dependent and basis-independent measures ofRviolation

We construct lepton flavour-dependent and basis-independent measures of R-parity violation in the minimal supersymmetric extension of the Standard Model (MSSM). We work in the context of exact supersymmetry, neglecting the effects of Higgs vacuum expectation values and soft supersymmetry-breaking terms. We devote particular attention to appropriate choices of flavour eigenstates, and to the counting and enumeration of R-violating invariants in two- and three-generation models. We also make an indicative application of our results to derive possible basis-independent cosmological upper bounds on flavour-dependent violation of R parity.

Unification bounds on the possible N = 2 supersymmetry-breaking scale

In this letter, the possible appearance of N=2 supersymmetry at a low energy scale is investigated in the context of unified theories. Introducing mirror particles for all the gauge and matter multiplets of the Minimal Supersymmetric extension of the Standard Model (MSSM), the measured values of sin^2 \theta_W and \alpha_3(M_Z) indicate that the N=2 threshold scale M_{S_2} cannot be lower than \sim 10^{14}GeV. If the U(1) normalization coefficient k is treated as a free parameter, M_{S_2} can be as low as 10^9 GeV. On the other hand, if mirror quarks and leptons are absent and a non-standard value for k is used, N=2 supersymmetry breaking could in principle occur at the electroweak scale.