Radiative Electroweak Symmetry Breaking Research Articles

B0-B-bar0 mixing and the epsilon K parameter in the minimal supergravity model.

\bb mixing and a CP violation parameter in \kk mixing $\epsilon_K$ are studied in the minimal supergravity model. We solve the one-loop renormalization group equations for the minimal supersymmetric standard model (MSSM) parameters numerically in order to determine the masses and mixings of the supersymmetric particles, while all off-diagonal (generation mixing) elements and phases of Yukawa coupling matrices and those of squark mass matrices are taken into account. Applying the radiative electroweak symmetry breaking condition and phenomenological constraints including the recent measurement of the \bsg inclusive branching ratio, we obtain the allowed parameter region. We have found that the present constraints still allow a parameter region where both \bb mass splitting $\Delta M_B$ and $\epsilon_K$ are $\sim 20$\% larger than the standard model values. By explicit numerical calculations, we have also found that the complex phase of \bb mixing matrix element in this model is almost the same as the standard model value in a good accuracy in the whole allowed parameter region. It is shown that $\Delta M_B$ and $\epsilon_K$ can put useful constraints on the supersymmetry's parameter space when the Cabibbo-Kobayashi-Maskawa matrix elements are determined through the measurements of CP violations in $B$ decay with future $B$-factories.

Radiative electroweak symmetry breaking in the minimal supersymmetric standard model and low energy thresholds.

We study Radiative Electroweak Symmetry Breaking in the Minimal Supersymmetric Standard Model (MSSM). We employ the 2-loop Renormalization Group equations for running masses and couplings taking into account sparticle threshold effects. The decoupling of each particle below its threshold is realized by a step function in all one-loop Renormalization Group equations (RGE). This program requires the calculation of all wavefunction, vertex and mass renormalizations for all particles involved. Adapting our numerical routines to take care of the succesive decoupling of each particle below its threshold, we compute the mass spectrum of sparticles and Higgses consistent with the existing experimental constraints. The effect of the threshold corrections is in general of the same order of magnitude as the two-loop contributions with the exception of the heavy Higgses and those neutralino and chargino states that are nearly

THE MINIMAL SUPERSYMMETRIC STANDARD MODEL

The structure of the MSSM is reviewed. We first motivate the particle content of the theory by examining the quantum numbers of the known standard model particles and by the requirement of anomaly cancellation. Once the particle content is fixed we can write down the most general renormalizable superpotential. However such a superpotential will contain terms breaking lepton and baryon number which leads us to the concept of R-parity conservation. The question of supersymmetry breaking is discussed next. We list the possible soft breaking terms. However the Lagrangian involving the most general soft breaking terms is phenomenologically intractable because of the appearance of many new parameters. It also leads to some unacceptable predictions. To reduce the number of parameters we restrict ourselves to the case with universal soft breaking terms at the GUT scale. We motivate the need for universal soft breaking terms by the apparent unification of gauge couplings in the MSSM and by the absence of flavor changing neutral currents. Then we discuss radiative electroweak symmetry breaking. Radiative breaking arises because the one-loop corrections involving the large top Yukawa coupling change the sign of the soft breaking mass parameter of the up-type Higgs doublet, this way introducing a nontrivial minimum in the Higgs potential. Finally we give an overview of the possible mixings in the MSSM and enumerate the physical (mass eigenstate) fields together with the mass matrices.

Minimal four-family supergravity model.

We investigate the phenomenology of minimal four-family MSSM supergravity theories containing an additional generation of heavy fermions along with their superpartners. We demand: gauge coupling constant unification at high energy scales; perturbative values for all Yukawa couplings for energy scales $\leq \mgut$; radiative electroweak symmetry breaking via renormalization group evolution; and a neutral LSP. The perturbative constraints imply a light fourth-family quark and lepton spectrum, and $\tanb\lsim 3$. The lightest CP-even Higgs mass is increased. Fourth-family Yukawa coupling contributions to the evolution of scalar masses lead to unexpected mass hierarchies; \eg\ the $\staupone$ is generally the lightest slepton and the lightest squark is the $\wt\bpr_1$. A significant lower bound is placed on the gluino mass by the requirement that the $\staupone$ not be the LSP. Sleptons of the first two families are much more massive compared to the LSP and other neutralinos and charginos than in the three-family models, and could easily lie beyond the reach of a $\sqrt s=500\gev$ $\epem$ collider. Relations between slepton masses and gaugino masses are shown to be very sensitive to the presence of a fourth generation. The most important near-future experimental probes of the four-family models are reviewed. A scenario with $\mt\sim\mw$ and $t\rta {\wt t_1}\cnone$ is shown to be inconsistent with universal soft-SUSY-breaking boundary conditions. Full four-family evolution of $\alpha_s$ is shown to lead to a significant enhancement in inclusive jet and di-jet spectra at Tevatron energies when all sparticle masses are near their lower bounds.

Prospects for supersymmetry at CERN LEP 2.

Working within the framework of the mininal supergravity (SUGRA) model with gauge coupling unification and radiative electroweak symmetry breaking we map out regions of parameter space explorable by experiments at CERN LEP 2, for center-of-mass energy options of \ensuremath{\surd}s =150, 175, 190, and 205 GeV. We compute signals from all accessible 2\ensuremath{\rightarrow}2 supersymmetry (SUSY) pair production processes using the isaget simulation program, and devise cuts that enhance the signal relative to standard model backgrounds, and which also serve to differentiate various supersymmetric processes from one another. We delineate regions of SUGRA parameter space where production of neutralino pairs, chargino pairs, slepton pairs, and the production of the light Higgs scalar of SUSY is detectable above standard model backgrounds and distinguishable from other SUSY processes. In addition, we find small regions of SUGRA parameter space where e\ifmmode \tilde{}\else \~{}\fi{} e\ifmmode \tilde{}\else \~{}\fi{}, Z${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{2}$Z${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{2}$, and \ensuremath{\nu}${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{L}}$\ensuremath{\nu}${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{L}}$ production yields spectacular events with up to four isolated leptons. The combined regions of parameter space explorable by LEP 2 are compared with the reach of Fermilab Tevatron Main Injector era experiments. Finally, we comment on how the reach via the neutralino pair channel is altered when the radiative electroweak symmetry breaking constraint is relaxed.

Signals for minimal supergravity at the CERN Large Hadron Collider: Multijet plus missing energy channel.

We use ISAJET to perform a detailed study of the missing transverse energy $\eslt$ plus multi-jet signal expected from superparticle production at the CERN LHC. Our analysis is performed within the framework of the minimal supergravity model with gauge coupling unification and radiative electroweak symmetry breaking. We delineate the region of parameter space where the $\eslt$ supersymmetry signal should be observable at the LHC and compare it to the regions explorable via searches for sleptons and for chargino/neutralino production. We confirm that, given a data sample of 10~$\fb^{-1}$, $m_{\tg}\sim 1300$ GeV can be explored if $m_{\tq}\gg m_{\tg}$, while $m_{\tg}\sim 2000$ GeV can be probed if $m_{\tq}\simeq m_{\tg}$. We further examine what information can be gleaned from scrutinizing this event sample. For instance, the multi-jet multiplicity yields information on whether squark production makes a significant contribution to the observed $\eslt$ sample. Furthermore, reconstructing hemispheric masses may yield a measure of $m_{\tg}$ to $\sim 15-25\%$. Finally, for favourable ranges of parameters, by reconstructing masses of tagged $b\bar{b}$ jet pairs, it may be possible to detect Higgs bosons produced via sparticle cascade decay chains.

Supersymmetry reach of an upgraded Fermilab Tevatron collider.

We examine the capability of a $\sqrt{s}=2$ TeV Tevatron $p\bar p$ collider to discover supersymmetry, given a luminosity upgrade to amass $25\ fb^{-1}$ of data. We compare with the corresponding reach of the Tevatron Main Injector ($1\ fb^{-1}$ of data). Working within the framework of minimal supergravity with gauge coupling unification and radiative electroweak symmetry breaking, we first calculate the regions of parameter space accessible via the clean trilepton signal from $\tw_1\tz_2\to 3\ell +\eslt$ production, with detailed event generation of both signal and major physics backgrounds. The trilepton signal can allow equivalent gluino masses of up to $m_{\tg}\sim 600-700$ GeV to be probed if $m_0$ is small. If $m_0$ is large, then $m_{\tg}\sim 500$ GeV can be probed for $\mu <0$; however, for $\mu >0$ and large values of $m_0$, the rate for $\tz_2\to\tz_1\ell\bar{\ell}$ is suppressed by interference effects, and there is {\it no} reach in this channel. We also examine regions where the signal from $\tw_1\overline{\tw_1}\to \ell\bar{\ell}+\eslt$ is detectable. Although this signal is background limited, it is observable in some regions where the clean trilepton signal is too small. Finally, the signal $\tw_1\tz_2\to jets+\ell\bar{\ell} +\eslt$ can confirm the clean trilepton signal in a substantial subset of the parameter space where the trilepton signal can be seen. We note that although the clean trilepton signal may allow Tevatron experiments to identify signals in regions of parameter space beyond the reach of LEP II, the dilepton channels generally probe much the same region as LEP II.

Flavor mixing in the gluino coupling and nucleon decay.

Flavor mixing in the quark-squark-gluino coupling is studied for the minimal SU(5) SUGRA-GUT model and applied to evaluation of the nucleon lifetime. All off-diagonal (generation mixing) elements of Yukawa coupling matrices and of squark/slepton mass matrices are included in solving numerically one-loop renormalization group equations for MSSM parameters, and the parameter region consistent with the radiative electroweak symmetry breaking condition is searched. It is shown that the flavor mixing in the gluino coupling for a large $\tan\beta$ is of the same order of magnitude as the corresponding Kobayashi-Maskawa matrix element in both up-type and down-type sector. There exist parameter regions where the nucleon decay amplitudes for charged lepton modes are dominated by the gluino dressing process, while for all the examined regions the neutrino mode amplitudes are dominated by the wino dressing over the gluino dressing.

String and string-inspired phenomenology

Abstract In these lectures I review the progress made over the last few years in the subject of string and string-inspired phenomenology. I take a practical approach, thereby concentrating more on explicit examples rather than on formal developments. Topics covered include: introduction to string theory, the free-fermionic formulation and its general features, generic conformal field theory properties, SU(5) × U(1) GUT and string model-building, supersymmetry breaking, the bottom-up approach to string-inspired models, radiative electroweak symmetry breaking, the determination of the allowed parameter space of supergravity models and the experimental constraints on this class of models, and prospects for direct and indirect tests of string-inspired models.

Low-energy effective Lagrangian in unified theories with nonuniversal supersymmetry-breaking terms.

Supersymmetric grand unified theories with non-universal soft supersymmetry breaking terms are studied. By integrating out the superheavy fields at an unification scale, we compute their low-energy effective Lagrangian. We find new contributions to the scalar potential specific to the non-universal supersymmetry breaking. $D$-term contribution to the scalar masses is one example. The gauge hierarchy achieved by a fine-tuning in the superpotential would be violated in general due to the non-universal SUSY breaking terms. We show, however, it is preserved for a certain class of the soft terms derived from a {\em hidden} ansatz. We also discuss some phenomenological implications of the non-universal supersymmetry breaking, including predictions of the radiative electroweak symmetry breaking scenario and of no-scale type models.

Implications of a heavy top in supersymmetric theories

In the context of the radiative electroweak symmetry breaking scenario, we investigate the implications of a heavy top quark mass, close to its infrared fixed point, on the low energy parameters of the minimal supersymmetric standard model. We use analytic expressions to calculate the Higgs masses as well as the supersymmetric masses of the third generation. We further assume bottom-tau unification at the GUT scale and examine the constraints put by this condition on the parameter space (tan β, α 3), using the renormalization group procedure at the two-loop level. For supersymmetry breaking scale varying in the range (250–1000) GeV we find only a small fraction of the parameter space where the above conditions can be satisfied, namely 1 ≤ tan β ≤ 2, while 0.114 ≤ α 3( M Z ) ≤ 0.125. We further analyse in brief the case where all three Yukawa couplings reach the perturbative limit just after the unification scale. In this case, due to the large corrections on the bottom mass from sparticle loops, the top-mass and tan β predictions are significantly lower than those estimated when such corrections were ignored.

Electroweak symmetry breaking with non-universal scalar soft terms and large tan β solutions

We discuss radiative electroweak symmetry breaking with non-universal scalar masses at the GUT scale. Large tan β solutions are investigated in detail and it is shown that qualitatively new (as compared to the universal case) solutions exist, with much less correlation between soft terms. We identify two classes of non-universalities which give solutions with A o ⋍ B o ⋍ M 1 2 ⋍ O(M z) and with μ ⪢ M Z or μ ⋍ O(M Z) , respectively. In each case, after imposing gauge and Yukawa coupling unification, we discuss the predictions for m t , m b and the spectrum of supersymmetric particles. One striking consequence is the possibility of light charginos and neutralinos which in the second option can be higgsino-like. Cosmological constraint on the relic abundance of the lightest neutralino is also included.

Supercollider signatures of supergravity models with Yukawa unification.

We study the predictions of the simplest SU(5) grand unified model within the framework of minimal supergravity, including constraints from the radiative breaking of electroweak symmetry. As a consequence of the unification of the $b$-quark and $\tau$-lepton Yukawa couplings, the top quark mass is predicted to be close to its fixed point value. We delineate the regions of the supergravity parameter space allowed by constraints from the non-observation of proton decay and from the requirement that the LSP does not overclose the universe. These constraints lead to a definite pattern of sparticle masses: the feature unique to Yukawa unified models is that some of the third generation squarks are much lighter than those of the first two generations. Despite the fact that all sparticle masses and mixings are determined by just four SUSY parameters at the GUT scale (in addition to $m_t$), we find that the signals for sparticle production can vary substantially over the allowed parameter space. We identify six representative scenarios and study the signals from sparticle production at the LHC. We find that by studying the signal in various channels, these scenarios may be distinguished from one another, and also from usually studied ``minimal models'' where squarks and sleptons are taken to be degenerate. In particular, our studies allow us to infer that some third generation squarks are lighter than other squarks---a feature that could provide the first direct evidence of supergravity grand unification.

Radiative electroweak symmetry breaking and the infrared fixed point of the top quark mass

The infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model explains in a natural way large values of the top quark mass and appears as a prediction in many interesting theoretical schemes. Moreover, as has been recently pointed out, for moderate values of tan β, in order to achieve gauge and bottom-tau Yukawa coupling unification, the top quark mass must be within 10% of its fixed point value. In this work we show that the convergence of the top quark mass to its fixed point value has relevant consequences for the (assumed) universal soft supersymmetry breaking parameters at the grand unification scale. In particular, we show that the low-energy parameters do not depend on A 0 and B 0 but on the combination δ = B 0 − A 0/2. Hence, there is a reduction in the number of independent parameters. Most interesting, the radiative SU(2) L × U(1) Y breaking condition implies strong correlations between the supersymmetric mass parameter μ and the supersymmetry breaking parameters δ and M 1 2 or m 0. These correlations, which become stronger for tan β<2, may have some fundamental origin, which would imply the need of a reformulation of the naive fine-tuning criteria. We analyse the implications of these correlations for the supersymmetric and Higgs particle spectrum of the theory.

Accurate neutralino relic density computations in supergravity models.

We investigate the question of the proper thermal averaging of neutralino annihilation amplitudes which possess poles and thresholds, as they impact on the calculated neutralino relic density and therefore on the cosmological viability of supersymmetric models. We focus on two typical resonances, namely the $Z$ boson and the lightest Higgs boson ($h$). In the context of supergravity models with radiative electroweak symmetry breaking, an exploration of the whole parameter space of the model is possible and the overall relevance of these sophisticated analyses can be ascertained. As an example we chose the minimal $SU(5)$ supergravity model since the presence of such poles is essential to obtain a cosmologically acceptable model. We find that the proper thermal averaging is important for individual points in parameter space and that the fraction of cosmologically acceptable points is increased somewhat by the accurate procedure. However, qualitatively the new set of points is very similar to that obtained previously using the usual series approximations to the thermal average. We conclude that all phenomenological analyses based on the previously determined cosmologically allowed set remain valid.

Bottom-up approach to unified supergravity models

A new approach is proposed to the phenomenological study of a generic unified supergravity model, which reduces to the minimal supersymmetric standard model. The model is effectively parametrized in terms of five low energy observables. In consequence, it is easy to investigate systematically the parameter space of the model, allowed by the requirement of radiative electroweak symmetry breaking and by the present experimental limits. Radiative corrections due to large Yukawa couplings and particle-sparticle mass splitting are included into the analysis and found to have important effects, in particular on the degree of fine tuning in the model. In this framework there are presented the predictions of the model for various low energy physical observables, and their dependence on the values of the top quark mass and tan β is discussed. Results are also given for the large tan β scenario, tan β ≈ m t / m b . Our approach can be easily extended to non-minimal supergravity models, which do not assume the universality of the soft breaking parameters at the unification scale M X . Such an extension will be particularly useful once the masses of some sparticles are known, allowing for a model independent study of the parameter space at M X .

LEP and radiative electroweak breaking close to the light gluino window

Wer show that the LEP lower bound on the chargino mass, in conjunction with the well motivated theoretical requirement of radiative electroweak symmetry breaking, imply an upper bound on the lightest Higgs boson mass (mh ⪅ 62 GeV) in a supersymmetry breaking scenario where the gluino mass is a few GeV. Moreover, Higgs searches at LEP in the context of this model require mh ⪆ 61 GeV. The remaining experimentally allowed region in the five-dimensional parameter space of this light gluino model is severely fine-tuned (with tan β = 1.88−1.89 and mt = 114.0–114.3 GeV) and cosmologically troublesome (with a neutralino relic abundance over five-hundred time larger than allowed). Modest improvements in sensitivity in LEP Higgs searches and Tevatron top-quark searches should soon exclude this theoretically disfavored model completely.

Aspects of radiative electroweak breaking in supergravity models

We discuss several aspects of state-of-the-art calculations of radiative electroweak symmetry breaking in supergravity models. These models have a five-dimensional parameter space in contrast with the 21-dimensional one of the MSSM. We examine the Higgs one-loop effective potential V 1 = V 0 + ΔV, in particular how its renormalization-scale ( Q) independence is affected by the approximation used to calculate ΔV and by the presence of a Higgs-field-independent term which makes V 1(0) ≠ 0. We show that the latter must be subtracted out to achieve Q-independence. We also discuss our own approach to the exploration of the five-dimensional parameter space and the fine-tuning constraints within this approach. We apply our methods to the determination of the allowed region in parameter space of two models which we argue to be the prototypes for conventional (SSM) and string (SISM) unified models. To this end we impose the electroweak breaking constraint by minimizing the one-loop effective potential and study the shifts in μ and B relative to the values obtained using the tree-level potential. These shifts are most significant for small values of μ and B, and induce corresponding shifts on the lightest μ-and/or B-independent particle masses, i.e., those of the lightest stau, neutralino, chargino, and Higgs boson states. Finally, we discuss the predictions for the squark, slepton, and one-loop corrected Higgs boson masses.

Loop corrections to radiative breaking of electroweak symmetry in supersymmetry.

One-loop corrections to the radiative breaking of electroweak symmetry in supergravity unified models are analyzed. It is shown that in a physically interesting domain of parameter space there is a large cancellation among the contributions of the first two generations of squarks and the three generations of sleptons to the vacuum expectation value (VEV) equations. Partial cancellations in other sectors are also found. These cancellations reduce the effect of the one-loop contributions to the VEV equations.

A new string-inspired standard model (SISM)

The unification of gauge couplings in string models is predicted to occur at scales (∼10 16 GeV) which are in disagreement with those obtained, using presice LEP data, in supersymmetric models with minimal matter content (∼10 16 GeV). We present a string-inspired extension of the standard model with one pair of extra vector-like Q and D c representations which allows string unification for D c masses in the few TeV region or less, predicts a light (<1 TeV) sparticle spectrum which differs from that of the standard supersymmetric model, and allows for edequate radiative electroweak symmetry breaking. The proposed model is the unique minimal choice in this class of extra vector models, it can be embedded most economically in a flipped SU (5) structure, and may be derivable from string.