Saturation of counterterms by resonances in K→πe+e−K \to \pi e^{+} e^{-} decays

The decays $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$, $K_{S} \rightarrow \pi^{0} e^{+} e^{-}$ and $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the large $N_{c}$ limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on the $H_{1}$ coupling, defined in the effective chiral Lagrangian of the ${\it O} (p^{4})$ order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodete $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$ decay rate within the factorization approach. The CP violating $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ decay rate is discussed.Comment: 24 pages, LaTe

Phenomenology of flavor-mediated supersymmetry breaking

The phenomenology of a new economical SUSY model that utilizes dynamical SUSY breaking and gauge-mediation (GM) for the generation of the sparticle spectrum and the hierarchy of fermion masses is discussed. Similarities between the communication of SUSY breaking through a messenger sector, and the generation of flavor using the Froggatt-Nielsen (FN) mechanism are exploited, leading to the identification of vector-like messenger fields with FN fields, and the messenger U(1) as a flavor symmetry. An immediate consequence is that the first and second generation scalars acquire flavor-dependent masses, but do not violate FCNC bounds since their mass scale, consistent with effective SUSY, is of order 10 TeV. We define and advocate a minimal flavor-mediated model (MFMM), recently introduced in the literature, that successfully accommodates the small flavor-breaking parameters of the standard model using order one couplings and ratios of flavon field vevs. The mediation of SUSY breaking occurs via two-loop log-enhanced GM contributions, as well as several one-loop and two-loop Yukawa-mediated contributions for which we provide analytical expressions. The MFMM is parameterized by a small set of masses and couplings, with values restricted by several model constraints and experimental data. The next-to-lightest sparticle (NLSP) always has a decay length that is larger than the scale of a detector, and is either the lightest stau or the lightest neutralino. Similar to ordinary GM models, the best collider search strategies are, respectively, inclusive production of at least one highly ionizing track, or events with many taus plus missing energy. In addition, D^0 - \bar{D}^0 mixing is also a generic low energy signal. Finally, the dynamical generation of the neutrino masses is briefly discussed.Comment: 54 pages, LaTeX, 8 figure

Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas

Recently, a new perspective of gravitational-thermodynamic duality as an entropic force arising from alterations in the information connected to the positions of material bodies is found. In this paper, we generalize some aspects of this model in the presence of noncommutative Schwarzschild black hole by applying the method of coordinate coherent states describing smeared structures. We implement two different distributions: (a) Gaussian and (b) Lorentzian. Both mass distributions prepare the similar quantitative aspects for the entropic force. Our study shows, the entropic force on the smallest fundamental unit of a holographic screen with radius $r_0$ vanishes. As a result, black hole remnants are unconditionally inert even gravitational interactions do not exist therein. So, a distinction between gravitational and inertial mass in the size of black hole remnant is observed, i.e. the failure of the principle of equivalence. In addition, if one considers the screen radius to be less than the radius of the smallest holographic surface at the Planckian regime, then one encounters some unusual dynamical features leading to gravitational repulsive force and negative energy. On the other hand, the significant distinction between the two distributions is conceived to occur around $r_0$, and that is worth of mentioning: at this regime either our analysis is not the proper one, or non-extensive statistics should be employed.Comment: 15 pages, 2 figures, new references added, minor revision, Title changed, to appear in EPJ Plu