Implications of precision electroweak experiments for mt, rho 0, sin2 theta W, and grand unification

E6 GUT and Baryon Asymmetry Generation in the E6CHM

Grand unified theories (GUTs) may result in the E6-inspired composite Higgs model (E6CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the E6-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E6CHM is confined on the brane where E6 is broken down to its SU(6) subgroup. Near the scale of f≳5TeV, this approximate SU(6) symmetry is expected to be further broken down to its SU(5) subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E6CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E6CHM in which the baryon number and CP invariance are violated.

A Review of the Exceptional Supersymmetric Standard Model

Local supersymmetry (SUSY) provides an attractive framework for the incorporation of gravity and unification of gauge interactions within Grand Unified Theories (GUTs). Its breakdown can lead to a variety of models with softly broken SUSY at low energies. In this review article, we focus on the SUSY extension of the Standard Model (SM) with an extra U ( 1 ) N gauge symmetry originating from a string-inspired E 6 GUTs. Only in this U ( 1 ) extension of the minimal supersymmetric standard model (MSSM) can the right-handed neutrinos be superheavy, providing a mechanism for the baryon asymmetry generation. The particle content of this exceptional supersymmetric standard model (E 6 SSM) includes three 27 representations of the E 6 group, to ensure anomaly cancellation. In addition it also contains a pair of S U ( 2 ) W doublets as required for the unification of gauge couplings. Thus, E 6 SSM involves exotic matter beyond the MSSM. We consider symmetries that permit suppressing flavor changing processes and rapid proton decay, as well as gauge coupling unification, the gauge symmetry breaking and the spectrum of Higgs bosons in this model. The possible Large Hadron Collider (LHC) signatures caused by the presence of exotic states are also discussed.

Searching for supersymmetry and its avatars

Why continue looking for supersymmetry? Over and above the aesthetic and theoretical motivations from string theory, there are several longstanding pheno- menological motivations for TeV-scale super- symmetry, such as the electroweak scale, and the lightest supersymmetric particle as cold dark matter. Run 1 of the Large Hadron Collider (LHC) has actually provided three extra motivations, namely the stabilization of the electroweak vacuum, and successful predictions for the Higgs mass and couplings. How to look for it? There are several examples of emergent supersymmetry, the most recent being on the surfaces of topological insulators, and some sort of effective supersymmetry could be useful for boosting the power of laser arrays. At the LHC, attention is moving towards signatures that had previously been neglected, such as long-lived charged particles-which might be an opportunity for the MoEDAL experiment. This article is part of a discussion meeting issue 'Topological avatars of new physics'.

Stop coannihilation in the CMSSM and SubGUT models

Stop coannihilation may bring the relic density of heavy supersymmetric dark matter particles into the range allowed by cosmology. The efficiency of this process is enhanced by stop-antistop annihilations into the longitudinal (Goldstone) modes of the W and Z bosons, as well as by Sommerfeld enhancement of stop annihilations and the effects of bound states. Since the couplings of the stops to the Goldstone modes are proportional to the trilinear soft supersymmetry-breaking A-terms, these annihilations are enhanced when the A-terms are large. However, the Higgs mass may be reduced below the measured value if the A-terms are too large. Unfortunately, the interpretation of this constraint on the stop coannihilation strip is clouded by differences between the available Higgs mass calculators. For our study, we use as our default calculator FeynHiggs 2.13.0, the most recent publicly available version of this code. Exploring the CMSSM parameter space, we find that along the stop coannihilation strip the masses of the stops are severely split by the large A-terms. This suppresses the Higgs mass drastically for μ andA 0 > 0 , whilst the extent of the stop coannihilation strip is limited forA 0 < 0 and either sign of μ . However, in sub-GUT models, reduced renormalization-group running mitigates the effect of the large A-terms, allowing larger LSP masses to be consistent with the Higgs mass calculation. We give examples where the dark matter particle mass may reach ≳ 8  TeV.

Collider Interplay for Supersymmetry, Higgs and Dark Matter

We discuss the potential impacts on the CMSSM of future LHC runs and possible [Formula: see text] and higher-energy proton-proton colliders, considering searches for supersymmetry via  [Formula: see text] events, precision electroweak physics, Higgs measurements and dark matter searches. We validate and present estimates of the physics reach for exclusion or discovery of supersymmetry via [Formula: see text] searches at the LHC, which should cover the low-mass regions of the CMSSM parameter space favoured in a recent global analysis. As we illustrate with a low-mass benchmark point, a discovery would make possible accurate LHC measurements of sparticle masses using the MT2 variable, which could be combined with cross-section and other measurements to constrain the gluino, squark and stop masses and hence the soft supersymmetry-breaking parameters [Formula: see text] and [Formula: see text] of the CMSSM. Slepton measurements at CLIC would enable [Formula: see text] and [Formula: see text] to be determined with high precision. If supersymmetry is indeed discovered in the low-mass region, precision electroweak and Higgs measurements with a future circular [Formula: see text] collider (FCC-ee, also known as TLEP) combined with LHC measurements would provide tests of the CMSSM at the loop level. If supersymmetry is not discovered at the LHC, it is likely to lie somewhere along a focus-point, stop-coannihilation strip or direct-channel A / H resonance funnel. We discuss the prospects for discovering supersymmetry along these strips at a future circular proton-proton collider such as FCC-hh. Illustrative benchmark points on these strips indicate that also in this case FCC-ee could provide tests of the CMSSM at the loop level.

The NUHM2 after LHC Run 1

We make a frequentist analysis of the parameter space of the NUHM2, in which the soft supersymmetry (SUSY)-breaking contributions to the masses of the two Higgs multiplets, [Formula: see text], vary independently from the universal soft SUSY-breaking contributions [Formula: see text] to the masses of squarks and sleptons. Our analysis uses the MultiNest sampling algorithm with over [Formula: see text] points to sample the NUHM2 parameter space. It includes the ATLAS and CMS Higgs mass measurements as well as the ATLAS search for supersymmetric jets + [Formula: see text] signals using the full LHC Run 1 data, the measurements of [Formula: see text] by LHCb and CMS together with other B-physics observables, electroweak precision observables and the XENON100 and LUX searches for spin-independent dark-matter scattering. We find that the preferred regions of the NUHM2 parameter space have negative SUSY-breaking scalar masses squared at the GUT scale for squarks and sleptons, [Formula: see text], as well as [Formula: see text]. The tension present in the CMSSM and NUHM1 between the supersymmetric interpretation of [Formula: see text] and the absence to date of SUSY at the LHC is not significantly alleviated in the NUHM2. We find that the minimum [Formula: see text] with 21 degrees of freedom (dof) in the NUHM2, to be compared with [Formula: see text] in the CMSSM, and [Formula: see text] in the NUHM1. We find that the one-dimensional likelihood functions for sparticle masses and other observables are similar to those found previously in the CMSSM and NUHM1.

Natural Higgs-flavor-democracy solution of the μ problem of supersymmetry and the QCD axion

We show that the hierarchically small μ term in supersymmetric theories is a consequence of two identical pairs of Higgs doublets taking a democratic form for their mass matrix. We briefly discuss the discrete symmetry S(2)×S(2) toward the democratic mass matrix. Then, we show that there results an approximate Peccei-Quinn symmetry and hence the value μ is related to the axion decay constant.

Gauge coupling unification in F-theory grand unified theories

We investigate gauge coupling unification for F-theory type IIB orientifold constructions of SU(5) grand unified theories (GUT) with gauge symmetry breaking via nontrivial hypercharge flux. This flux has the nontrivial effect that it splits the values of the three minimal supersymmetric standard model gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way.

Supersymmetry facing experiment: much ado (already) about nothing (yet)

This report emphasizes the comparison between supersymmetric models and experiments. A minimal theoretical introduction is included as a guide to the interpretation of results. The existing constraints from low energy measurements, accelerator searches (LEP, Tevatron and HERA) and non-accelerator searches for neutralinos are presented. Prospects for upgrades of these facilities and for the LHC and linear collider are summarized. Most discussions are made in the framework of the minimal supersymmetric standard model inspired by supergravity (MSUGRA). But alternatives such as gauge mediated supersymmetry breaking (GMSB), anomaly mediated supersymmetry breaking (AMSB), models with R-parity violation and even alternatives to supersymmetry are also briefly considered.

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting theta(sol)+theta(C)=pi/4, where theta(C) is the Cabibbo angle, theta(atm)+theta(CKM)(23)=pi/4 and theta(MNS)(13) approximately theta(CKM)(13) approximately O(lambda(3)), in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.

Dark matter and dark energy: summary and future directions

This paper reviews the progress reported at the Discussion Meeting and advertises some possible future directions in our drive to understand dark matter and dark energy. Additionally, a first attempt is made to place in context the exciting new results from the Wilkinson Microwave Anisotropy Probe satellite, which were published shortly after this meeting. In the first part of this paper, pieces of observational evidence shown here that bear on the amounts of dark matter and dark energy are reviewed. Subsequently, particle candidates for dark matter are mentioned, and detection strategies are discussed. Finally, ideas are presented for calculating the amounts of dark matter and dark energy, and possibly relating them to laboratory data.

Two-loop renormalization group equations in the standard model

Two-loop renormalization group equations in the standard model are recalculated. A new coefficient is found in the beta function of the quartic coupling and a class of gauge invariants is found to be absent in the beta functions of hadronic Yukawa couplings. The two-loop beta function of the Higgs mass parameter is presented in complete form.

Limit on the detectability of the energy scale of inflation

We show that the polarization of the cosmic microwave background can be used to detect gravity waves from inflation if the energy scale of inflation is above 2x10(15) GeV. These gravity waves generate polarization patterns with a curl, whereas (to first order in perturbation theory) density perturbations do not. The limiting "noise" arises from the second-order generation of curl from density perturbations, or rather residuals from its subtraction. We calculate optimal sky coverage and detectability limits as a function of detector sensitivity and observing time.

Predictions for Higgs and supersymmetry spectra from SO(10) Yukawa unification with mu > 0

We use t, b, tau Yukawa unification to constrain supersymmetry parameter space. We find a narrow region survives for mu>0 (suggested by b-->sgamma and the anomalous magnetic moment of the muon) with A0 approximately -1.9m(16), m(10) approximately 1.4m(16), m(16) approximately 1200-3000 GeV and muM(1/2) approximately 100-500 GeV. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses.

Natural quintessence with gauge coupling unification

We show that a positive accelerating universe can be obtained simply by the dynamics of a non-Abelian gauge group. The condensates of the chiral fields obtain a negative power potential below the condensation scale Lambda(c) and allow for a quintessence interpretation of these fields. The only free parameters are N(c), N(f), and the number of dynamically gauge singlet bilinear fields straight phi generated below Lambda(c). We show that it is possible to have unification of all coupling constants, while having an acceptable phenomenology of straight phi as quintessance, without any fine-tuning of the initial conditions. The coincidence problem is not solved but it is put at the same level as that of the particle content of the standard model.