On a converse theorem for G2G_2 over finite fields

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, $GL_1$ and $GL_2$-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of $G_2(k)$

Perturbative renormalization factors for generic Δs=2\Delta s=2 four-quark operators in domain-wall QCD with improved gauge action

We calculate one-loop renormalization factors of generic DeltaS=2 four-quark operators for domain-wall QCD with the plaquette gauge action and the Iwasaki gauge action. The renormalization factors are presented in the modified minimal subtraction (MS-bar) scheme with the naive dimensional regularization. As an important application we show how to construct the renormalization factors for the operators contributing to K^0-K^0bar mixing in the supersymmetric models with the use of our results.Comment: 22 pages,uses revtex

Zappa-Sz\'ep products of Garside monoids

A monoid $K$ is the internal Zappa-Sz\'ep product of two submonoids, if every element of $K$ admits a unique factorisation as the product of one element of each of the submonoids in a given order. This definition yields actions of the submonoids on each other, which we show to be structure preserving. We prove that $K$ is a Garside monoid if and only if both of the submonoids are Garside monoids. In this case, these factors are parabolic submonoids of $K$ and the Garside structure of $K$ can be described in terms of the Garside structures of the factors. We give explicit isomorphisms between the lattice structures of $K$ and the product of the lattice structures on the factors that respect the Garside normal forms. In particular, we obtain explicit natural bijections between the normal form language of $K$ and the product of the normal form languages of its factors.Comment: Published versio

Analysis of the B→K2∗(→Kπ)l+l−B \to K^*_{2} (\to K \pi) l^+ l^- decay

In this paper we study the angular distribution of the rare B decay $B \to K^*_2 (\to K \pi) l^+ l^-$, which is expected to be observed soon. We use the standard effective Hamiltonian approach, and use the form factors that have already been estimated for the corresponding radiative decay $B \to K^*_2 \gamma$. The additional form factors that come into play for the dileptonic channel are estimated using the large energy effective theory (LEET), which enables one to relate the additional form factors to the form factors for the radiative mode. Our results provide, just like in the case of the $K^*(892)$ resonance, an opportunity for a straightforward comparison of the basic theory with experimental results which may be expected in the near future for this channel.Comment: 14 pages, 5 figures; as accepted for Phys. Rev.

Electroweak properties of the π\pi, KK and K∗(892)K^*(892) in the three forms of relativistic kinematics

The electromagnetic form factors, charge radii and decay constants of pion, K and K*(892) are calculated using the three forms of relativistic kinematics: instant form, point form and (light) front form. Simple representations of the mass operator together with single quark currents are employed with all the forms. Making use of previously fixed parameters, together with the constituent quark mass for the strange quark, a reasonable reproduction of the available data for form factors, charge radii and decay constants of pion, rho, K and K*(892) is obtained in front form. With instant form a similar description, but with a systematic underestimation of the vector meson decay constants is obtained using two different sets of parameters, one for pion and rho and another one for K and K*(892). Point form produces a poor description of the data.Comment: Accepted in Eur. Phys. Jour. A (2005

Analysis of DsDK∗D_s D K^* and DsD∗K∗D_s D^{*} K^* vertices and branching ratio of B+→K∗0π+B^+\to {K^*}^0 \pi^+

In this paper, the strong form factors and coupling constants of $D_sDK^*$ and $D_sD^*K^*$ vertices are investigated within the three-point QCD sum rules method with and without the $SU_{f}(3)$ symmetry. In this calculation, the contributions of the quark-quark, quark-gluon, and gluon-gluon condensate corrections are considered. As an example of specific application of these coupling constants, the branching ratio of the hadronic decay $B^+\to {K^*}^0 \pi^+$ is analyzed based on the one-particle-exchange which is one of the phenomenological models. In this model, $B$ decays into a $D_s D^*$ intermediate state, and then these two particles exchange a $D (D^*)$ producing the final $K^*$ and $\pi$ mesons. In order to compute the effect of these interactions, the $D_s D K^*$ and $D_s D^* K^*$ form factors are needed.Comment: 14 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1509.0171