Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Fermi matrix element with isospin breaking

Prompted by the level of accuracy now being achieved in tests of the unitarity of the CKM matrix, we consider the possible modification of the Fermi matrix element for the β  -decay of a neutron, including possible in-medium and isospin violating corrections. While the nuclear modifications lead to very small corrections once the Behrends–Sirlin–Ademollo–Gatto theorem is respected, the effect of the u−d$u-d$ mass difference on the conclusion concerning V_ud$V_{ud}$ is no longer insignificant. Indeed, we suggest that the correction to the value of |V_ud|²+|V_us|²+|V_ub|²${|V_{ud}|}^2+{|V_{us}|}^2+{|V_{ub}|}^2$ is at the level of ¹⁰⁻⁴${10}^{-4}$.     

Dark Supersymmetry

We propose a model of Dark Supersymmetry, where a supersymmetric dark sector is coupled to the classically scale invariant non-supersymmetric Standard Model through the Higgs portal. The dark sector contains a mass scale that is protected against radiative corrections by supersymmetry, and the portal coupling mediates this scale to the Standard Model, resulting in a vacuum expectation value for the Higgs field and the usual electroweak symmetry breaking mechanism. The supersymmetric dark sector contains dark matter candidates, and we show that the observed dark matter abundance is generated for a natural choice of parameters, while avoiding the current experimental bounds on direct detection. Future experiments can probe this scenario if the dark sector mass scale is not too high.     

Spin Chains with Dynamical Lattice Supersymmetry

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the $\mathcal{N}=(2,2)$ superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension possess a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured.     

Supersymmetry breaking

We review the various mechanisms of supersymmetry breaking and its transmission to the observable sector. We argue that hybrid models where gauge dominates over gravity mediation, but gravity provides the main contributions to the Higgs sector masses and the neutralino mass, are able to combine the advantages and reduce the disadvantages of the two transmission mechanisms.      

Leptons with high weak isospin and compositeness

Heavy leptons with high weak isospin, predicted in a subcomponent model of quarks and leptons with SU(2)_L × U(1) symmetry, are examined phenomenologically in connection with recently reported anomalous events and super high energy physics. In constructing the effective lagrangian based on the subcomponent structure, I_W = 1 heavy leptons play a special role in the effective interaction.     

Supersymmetry and Combinatorics

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli’s exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting subspace. Some of our results can be rephrased in terms of generalizations of the well-known Witten index.     

Supersymmetry and instantons

We show that the eigenvalue equations for the fluctuation of scalars, fermions and gluon around any classical self-dual solution of the Yang-Mills theory have the same spectrum of non-zero eigenvalues. In the case of a supersymmetric Yang- Mills theory this implies that the one loop correction around any self-dual instanton is just given by a counting of the zero modes of the gluon, fermion and ghost.     

Supersymmetry Without Hermiticity

The PT symmetry requirement of a potential defines an inhomogeneous system of first-order differential equations for the real/imaginary and even/odd components of the relevant superpotential. By identifying the general solutions of this system we search for non-trivial supersymmetric partner potentials and analyze whether they both possess PT symmetry. As an illustrative example we present the case of the Rosen-Morse I potential.     

Supersymmetry and localization

We study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a (super)manifold. We also show that in many cases these conditions guarantee exactness of the stationary phase approximation of such integrals. Research is partially supported by NSF grant No. DMS-9500704.     

Supersymmetry and LHC

Motivations for introducing supersymmetry in high-energy physics are discussed along with the possibility of discovering supersymmetry at the Large Hadron Collider (LHC). Various regions of the space of parameters of the minimal supersymmetric standard model are analyzed, and phenomenological manifestations of supersymmetry inherent in these regions are discussed. The discovery potential of LHC at the planned luminosity is indicated for various channels.     

Supersymmetry versus replica

It is shown that already in the simplest case of the averaged one-point Green function of the gaussian unitary ensemble (Wigner model) the replica and the supersymmetric approaches provide different results. In particular, replica is likely to suppress oscillatory behaviour in the 1/N expansion.