International Journal of Modern Physics A

Some thoughts of a former particle physicist.

With the LHC (Large Hadron Collider) data arriving soon, carrying discoveries, we discuss a strategy for synthesizing a set of early measurements illuminating the dark matter of the universe.

In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.¹ Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.

The chiral effective Lagrangian for pseudoscalar meson nonet including eight Goldstone bosons and a SU(3) singlet η₀ is constructed with the breaking effect of chiral symmetry in both quark condensate and quark mass differences taken into account. The mixing is discussed. By solving the mass equations of pseudoscalar mesons, the quark mass ratios are obtained and the quark condensate ratios are constrained in ranges. The mass split of π⁰-π^± is discussed.

From several points of view, it is strongly suggested that the current universe is unstable and will ultimately decay to one that is exactly supersymmetric (SUSY). The possibility that atoms and molecules form in this future universe requires that the degenerate electron/selectron mass is non-zero and hence that electroweak symmetry breaking (EWSB) survives the phase transition to exact SUSY. However, the Minimal Supersymmetric Standard Model (MSSM) and several of its extensions have no EWSB in the SUSY limit. Among the extended Higgs models that have been discussed, one stands out in this regard. The Higgs sector that is revealed at the Large Hadron Collider (LHC) will therefore have implications for the future universe. We also address the question as to whether the transition to the exact SUSY phase with EWSB is exothermic.

In the Standard Model, the top quark decay width Γ_t is computed from the exclusive t → bW decay. We argue in favor of using the three body decays to compute Γ_t as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Γ_t = Γ(t → bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of Γ_t are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher-order radiative corrections.

We study six-dimensional (6D) SU(6) supersymmetric models where the doublet–triplet splitting, quark–lepton mass relations and gaugino-mediated supersymmetry breaking are taken into account. We find that effective 4D gauge coupling constants have highly nontrivial behavior between two compactification scales. It is shown that realistic patterns of Yukawa coupling constants are obtained for valid values of parameters and that hierarchical numbers are generated via suppression by extra-dimensional effects.

In this paper, we give a direct method for calculating the partition function, and hence the equation of state (EOS) of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper, the pressure density is the sum of two terms: the first term (the pressure density at μ = 0) is a μ-independent constant; the second term, which is totally determined by G[μ](p) (the dressed quark propagator at finite μ), contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson–Schwinger approach obtained in our previous study, Phys. Rev. C71, 015205 (2005), G[μ](p) is calculated from the model quark propagator proposed in Phys. Rev. D20, 2947 (1979). From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars. In the final part of this paper, our method is generalized to the case of finite temperature and the EOS of QCD at finite μ and T is derived. A comparison is made between the EOS derived in this paper and the EOS obtained in previous literatures by directly generalizing the CJT effective action at μ = 0 and T = 0 to finite μ and finite T.

Direct look at the celebrated "chaotic" Mandelbrot Set (in Fig. 1) immediately reveals that it is a collection of almost ideal circles and cardioids, unified in a specific forest structure. In the paper arXiv:hep-th/0501235, a systematic algebro-geometric approach was developed to the study of generic Mandelbrot sets, but emergency of nearly ideal circles in the special case of the family x² + c was not fully explained. In the present, paper, the shape of the elementary constituents of Mandelbrot Set is explicitly calculated, and difference between the shapes of root and descendant domains (cardioids and circles respectively) is explained. Such qualitative difference persists for all other Mandelbrot sets: descendant domains always have one less cusp than the root ones. Details of the phase transition between different Mandelbrot sets are explicitly demonstrated, including overlaps between elementary domains and dynamics of attraction/repulsion regions. Explicit examples of three-dimensional sections of Universal Mandelbrot Set are given. Also a systematic small-size approximation is developed for evaluation of various Feigenbaum indices.

We capture the off-shell as well as the on-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian densities of the four (3+1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four space–time coordinates x^μ (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and . One of the key results of our present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry invariance.

Recently a new time-evolution picture of the Dirac quantum mechanics was defined in charts with spatially flat Robertson–Walker metrics, under the name of Schrödinger picture (I. I. Cotăescu, Mod. Phys. Lett. A22, 2965 (2007)). In the present paper, new Dirac quantum modes are found in moving charts of the de Sitter space–time using the technical advantages offered by this picture. The principal result is a new set of energy eigenspinors which behave as polarized plane waves and form a complete system of orthonormalized solutions of the free Dirac equation.

Motivated by realizing open/closed string duality in the work by Gopakumar [Phys. Rev. D70, 025009 (2004)], we study two- and three-point correlation functions of R-current vector fields in super-Yang–Mills theory. These correlation functions in free field limit can be derived from the worldline formalism and are written as heat kernel integrals in the position space. We show that reparametrizing these integrals converts them to the expected AdS supergravity results which are known in terms of bulk to boundary propagators. We expect that this reparametrization corresponds to transforming open string moduli parametrization to the closed string ones.

The interaction of a fermion with the dense axion medium is investigated for the purpose of finding an axion medium effect on the fermion dispersion. It is shown that axion medium influence on the fermion dispersion under astrophysical conditions is negligible small if the correct Lagrangian of the axion–fermion interaction is used.