Renormalization of N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by N = 1 mass term

N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by mass terms are considered. It is proved that for N = 4 there are no ultraviolet divergences in the mass renormalization constants to all orders of perturbation theory. For N = 2 our two-loop calculations show that the charge and mass renormalization constants contain only one-loop divergences and are the same in this order. It is shown by direct calculation that mass terms can acquire finite quantum corrections starting from the two-loop approximation. The renormalization scheme dependence of N = 4 renormalization group functions is investigated. We have found that unlike renormalization schemes with minimal subtractions of divergences other renormalization schemes give a nonzero β-function. At nonzero masses the β-function in MOM schemes is not zero even at the one-loop level. In the massless case β≠0 beginning from the two-loop approximation.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Relating mHiggs to mSUSY by a loop factor

We assume that the scale of the soft supersymmetry breaking masses, m_S, sliding at tree level, is fixed by the minimization of the potential, but without a significant contribution of the cosmological term. Under these assumptions the electroweak breaking scale gets related to m_S by a loop factor. Applied to specific models of supersymmetry breaking, this mechanism naturally gives sparticles slightly above all present accelerator bounds.     

On messengers and metastability in gauge mediation

One notoriously difficult problem in perturbative gauge mediation of supersymmetry breaking via messenger fields is the generic presence of a phenomenologically unacceptable vacuum with messenger vevs, with a lower energy than the desired (“MSSM”) vacuum. We investigate the possibility that quantum corrections promote the latter to the ground state of the theory, and find that this is indeed feasible. For this to happen, the couplings of the messengers to the goldstino superfield must be small, and this implies an additional suppression of the MSSM soft terms with respect to the supersymmetry breaking scale. This in turn sets a lower limit on the masses of the messengers and of the supersymmetry breaking fields, which makes both sectors inaccessible at colliders. Contrary to other scenarios like direct gauge mediation, gaugino masses are unsuppressed with respect to scalar masses.     

πN scattering and electromagnetic corrections in the perturbative chiral quark model

We apply the perturbative chiral quark model to give predictions for the electromagnetic O(p²) low-energy couplings of the ChPT effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e²) radiative corrections to the πN scattering amplitude. We estimate the leading isospin-breaking correction to the strong energy shift of the π⁻p atom in the 1s state, which is relevant for the experiment “Pionic Hydrogen” at PSI.     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.     

Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description

The problem of consistent Hamiltonian structure for O(N) nonlinear sigma model in the presence of five different types of boundary conditions is considered in detail. For the case of Neumann, Dirichlet and the mixture of these two types of boundaries, the consistent Poisson brackets are constructed explicitly, which may be used, e.g., for the construction of current algebras in the presence of boundary. While for the mixed boundary conditions and the mixture of mixed and Dirichlet boundary conditions, we prove that there is no consistent Poisson brackets, showing that the mixed boundary conditions are incompatible with all nontrivial subgroups of O(N).     

Vector multiplets coupled to N=2 supergravity: Super-Higgs effect, flat potentials and geometric structure

We obtain general properties of N=2 gauged extended supergravity coupled to vector multiplets, which can gauge an arbitrary group. General formulas for masses and curvatures are derived. Particular attention is devoted to the scalar potential of the theory which determines the classical vacuum structure. Explicit examples are given in which the potential is identically zero, but supersymmetry is broken. It is found that these theories are symmetric under generalized duality transformations.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

Soft supersymmetry breaking, scalar top-charm mixing and Higgs signatures

The squark mass-matrix from the soft supersymmetry (SUSY) breaking sector contains a rich flavor-mixing structure that allows O(1) mixings among top- and charm-squarks while being consistent with all the existing theoretical and experimental bounds. We formulate a minimal flavor-changing-neutral current scheme in which the squark mixings arise from the non-diagonal scalar trilinear interactions. This feature can be realized in a class of new models with a horizontal U(1)_H symmetry which generates realistic quark-mass matrices and provides a solution to the SUSY μ-problem. Finally, without using the mass-insertion approximation, we analyze SUSY radiative corrections to the H^±bc and h⁰tc couplings, and show that these couplings can reveal exciting new discovery channels for the Higgs boson signals at the Tevatron and the LHC.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

Specific scalar mass relations in SU(3) × SU(2) × U(1) orbifold model

We study flat directions and soft scalar masses using a Z₃ orbifold model with SU(3) × SU(2) × U(1) gauge group and extra gauge symmetries including an anomalous U(1) symmetry. Soft scalar masses contain D-term contributions and particle mixing effects after symmetry breaking and they are parametrized by a few parameters. Some specific relations among scalar masses are obtained.     

Gribov horizon in the presence of dynamical mass generation in Euclidean Yang–Mills theories in the Landau gauge

We find the Goldstino action descending from the N=1 Goldstone–Maxwell superfield action associated with the spontaneous partial supersymmetry breaking, N=2 to N=1, in superspace. The new Goldstino action has higher (second-order) spacetime derivatives, while it can be most compactly described as a solution to the simple recursive relation. Our action seems to be related to the standard (having only the first-order derivatives) Akulov–Volkov action for Goldstino via a field redefinition.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Supermembranes

An example is given of the spontaneous breaking of D = 4, N = 2 global supersymmetry down to N = 1. The example is a four-dimensional membrane in a six-dimensional supersymmetric gauge theory. The effective low-energy action for the membrane is a generalization of the Green—Schwarz covariant action.     

Algebraic derivation of N = 2 supergravity constraints

A purely algebraic derivation is given of the superspace constraints of N = 2 extended supergravity. The derivation proceeds through an analysis of the integrability conditions needed to preserve the irreducible representations of rigid N = 2 supersymmetry, taking account of the local complex dilation and SU(2) invariances of the constraints.     

Virtual corrections to the decay b → s + γ

We calculate the O(_s) virtual corrections to the matrix element for b → sγ, taking into account the contributions of the four-Fermi operator O₂ and the electromagnetic and color dipole-type operators. The results are combined with existing O(_s) Bremsstrahlung corrections in order to obtain the relevant inclusive rate. The new result drastically reduces the large scale dependence of the leading logarithmic approximation. It implies that a very accurate prediction for the branching ratio for B → X_sγ will become possible once also the corrections to the Wilson coefficients are available.     

Fixed-t partial wave analysis of πN scattering

The last full Karlsruhe PW analysis of πN scattering was finished ca. 20 years ago. After that a huge pile of new accurate πN scattering data has emerged, with which the old analysis is not completely compatible. We are making a highly modernized version of the old analysis to all (recent and old) data, aiming to pay particular attention to the discrepancies between different data sets and to the handling of the experimental errors as well as to the electromagnetic corrections and the effects of isospin breaking.     

Renormalization group invariant matrix elements of ΔS=2 and ΔI=3/2 four-fermion operators without quark masses

We introduce a new parameterization of four-fermion operator matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties. In order to simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of renormalization group invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of ΔI=3/2 and SUSY ΔS=2 operators have been computed. The calculations have been performed using the tree-level improved Clover lattice action at two different values of the strong coupling constant (β=6/g²=6.0 and 6.2), in the quenched approximation. Renormalization constants and mixing coefficients of lattice operators have been obtained non-perturbatively. Using lowest order χPT, we also obtain ππ|O₇|K^NDR_I=2=(0.11±0.02) GeV⁴ and ππ|O₈|K^NDR_I=2=(0.51±0.05) GeV⁴ at μ=2 GeV.