New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

CP violation in the inclusive b -> s g decay in the framework of multi Higgs doublet models

We study the decay width and CP asymmetry of the inclusive process b--> s g (g denotes gluon) in the multi Higgs doublet models with complex Yukawa couplings, including next to leading QCD corrections. We analyse the dependencies of the decay width and CP asymmetry on the scale \mu and CP violating parameter \theta. We observe that there exist an enhancement in the decay width and CP asymmetry is at the order of 10^{-2}.Comment: 11 pages, 8 Figure

Decay constants, semi-leptonic and non-leptonic decays in a Bethe-Salpeter Model

We evaluate the decay constants for the B and $D$ mesons and the form factors for the semileptonic decays of the B meson to $D$ and $D^*$ mesons in a Bethe-Salpeter model. From data we extract $V_{cb}=0.039 \pm 0.002$ from ${\bar B} \to D^* l {\bar{\nu}}$ and $V_{cb}=0.037 \pm 0.004$ from ${\bar B} \to D l {\bar{\nu}}$ decays. The form factors are then used to obtain non-leptonic decay partial widths for $B\to D \pi (K)$ and $B \to D D (D_s)$ in the factorization approximation.Comment: 15 Pages, 3 Postscript figures (available also from [email protected]

B-Decay CP Asymmetries, Discrete Ambiguities and New Physics

The first measurements of CP violation in the $B$ system will likely probe $\sin 2\alpha$, $\sin 2\beta$ and $\cos 2\gamma$. Assuming that the CP angles $\alpha$, $\beta$ and $\gamma$ are the interior angles of the unitarity triangle, these measurements determine the angle set $(\alpha,\beta,\gamma)$ except for a twofold discrete ambiguity. If one allows for the possibility of new physics, the presence of this discrete ambiguity can make its discovery difficult: if only one of the two candidate solutions is consistent with constraints from other measurements in the $B$ and $K$ systems, one is not sure whether new physics is present or not. We review the methods used to resolve the discrete ambiguity and show that, even in the presence of new physics, they can usually be used to uncover this new physics. There are some exceptions, which we describe in detail. We systematically scan the parameter space and present examples of values of $(\alpha,\beta,\gamma)$ and the new-physics parameters which correspond to all possibilities. Finally, we show that if one relaxes the assumption that the bag parameters \BBd and \BK are positive, one can no longer definitively establish the presence of new physics.Comment: 29 pages, LaTeX, 1 figures, presentation substantially reworked, physics conclusions unchanged. This version will be published in Phys. Rev.

An analysis of two-body non-leptonic B decays involving light mesons in the standard model

We report a theoretical analysis of the exclusive non-leptonic decays of B mesons into two light mesons,some of which have been measured recently by the CLEO collaboration. Our analysis is carried out in the context of an effective Hamiltonian based on the Standard Model using next-to-leading order perturbative QCD calculations. Using a factorization ansatz for the hadronic matrix elements, we show that existing data are accounted for in this approach. Thus, theoretical scenarios with a substantially enhanced Wilson coefficient of the chromomagnetic dipole operator (as compared to the SM) and/or those with a substantial color-singlet $c\bar{c}$ component in the wave function of $\eta^\prime$ are not required by these data. Implications of some of these measurements for the parameters of the CKM matrix are presented.Comment: 42 pages including 21 postscript figures; uses epsfig, some ref. added; improved mixing scheme for (eta,eta') system implemented; error corrected in (3.61) as explained below eq. (3.64) in the present version. Figs. 17-20 update

Measurements of Charmless Hadronic b->s Penguin Decays in the pi+pi-K+pi- Final State and First Observation of B0 -> rho0K+pi-

We report measurements of charmless hadronic B^0 decays into the pi+pi-K+pi+ final state. The analysis uses a sample of 657x10^6 BBbar pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider at the Y(4S) resonance. The decay B^0 -> rho0 Kpi is observed for the first time; the significance is 5.0sigma and the corresponding partial branching fraction for M_Kpi in (0.75,1.20) GeV/c^2 is [2.8 +- 0.5(stat) +-0.5(syst)] x 10^{-6}. We also obtain the first evidence for B^0 -> f0Kpi with 3.5sigma significance and for B^0 -> pi+pi-K*0 with 4.5sigma significance. For the two-body decays B^0 -> rho0K*0 and B^0 -> f0K*0, the significances are 2.7sigma and 2.5sigma, respectively, and the upper limits on the branching fractions are 3.4x10^{-6} and 2.2x10^{-6} at 90% confidence level.Comment: 6 pages, 3 figures. accepted by PRD(RC

First Measurement of Inclusive B -> X_s eta Decays

We report a first measurement of inclusive B -> X_s eta decays, where X_s is a charmless state with unit strangeness. The measurement is based on a pseudo-inclusive reconstruction technique and uses a sample of 657 x 10^6 BB-bar pairs accumulated with the Belle detector at the KEKB e^+e^- collider. For M_{X_s} < 2.6 GeV/c^2, we measure a branching fraction of (26.1 +/- 3.0 (stat) +1.9 -2.1 (syst) +4.0 -7.1 (model)) x 10^-5 and a direct CP asymmetry of A_{CP} = -0.13 +/- 0.04 +0.02 -0.03. Over half of the signal occurs in the range M_{X_s} > 1.8 GeV/c^2.Comment: 6 pages, 1 figure, 1 table, submitted to Physical Review Letter

Evidence for a new resonance and search for the Y(4140) in γγ→ϕJ/ψ\gamma \gamma \to \phi J/\psi

The process \gamma \gamma \to \phi \jpsi is measured for \phi \jpsi masses between threshold and 5 GeV/${\it c}^2$, using a data sample of 825 fb$^{-1}$ collected with the Belle detector. A narrow peak of $8.8^{+4.2}_{-3.2}$ events, with a significance of 3.2 standard deviations including systematic uncertainty, is observed. The mass and natural width of the structure (named X(4350)) are measured to be $(4350.6^{+4.6}_{-5.1}(\rm{stat})\pm 0.7(\rm{syst})) \hbox{MeV}/{\it c}^2$ and $(13^{+18}_{-9}(\rm{stat})\pm 4(\rm{syst})) \hbox{MeV}$, respectively. The product of its two-photon decay width and branching fraction to \phi\jpsi is $(6.7^{+3.2}_{-2.4}(\rm{stat}) \pm 1.1(\rm{syst})) \hbox{eV}$ for $J^P=0^+$, or $(1.5^{+0.7}_{-0.6}(\rm{stat}) \pm 0.3(\rm{syst})) \hbox{eV}$ for $J^P=2^+$. No signal for the Y(4140)\to \phi \jpsi structure reported by the CDF Collaboration in B\to K^+ \phi \jpsi decays is observed, and limits of \Gamma_{\gamma \gamma}(Y(4140)) \BR(Y(4140)\to\phi \jpsi)<41 \hbox{eV} for $J^P=0^+$ or $<6.0 \hbox{eV}$ for $J^P=2^+$ are determined at the 90% C.L. This disfavors the scenario in which the Y(4140) is a $D_{s}^{\ast+} {D}_{s}^{\ast-}$ molecule.Comment: 9 pages, 3 figures, publication in Phys. Rev. Lett. 104, 112004, 201

Bounds on the width, mass difference and other properties of X(3872) --> pi+pi-J/psi decays

We present results from a study of X(3872) --> pi+pi- J/psi decays produced via exclusive B--> K X(3872) decays. We determine the mass to be M_X(3872)= (3871.84\pm 0.27 (stat)\pm 0.19 (syst)) MeV, a 90% CL upper limit on the natural width of Gamma_X(3872) K+X(3872))xBf(X(3872)-->pi+pi-J/psi)=(8.61 \pm 0.82(stat) \pm 0.52 (syst)) x10^{-6}, and a ratio of branching fractions Bf(B0--> K0 X(3872))/BF(B+--> K+ X(3872))=0.50\pm 0.14(stat)\pm0.04(syst). The difference in mass between the X(3872)-->pi+pi-J/psi signals in B+ and B0 decays is Delta M_{X(3872)= (-0.69 \pm 0.97 (stat)} \pm 0.19 (syst)) MeV. A search for a charged partner of the X(3872) in the decays Bbar0-->K- X+ or B+-->K0X+, X+-->pi+pi0 J/psi resulted in upper limits on the product branching fractions for these processes that are well below expectations for the case that the X(3872) is the neutral member of an isospin triplet. In addition, we examine possible J^{PC} quantum number assignments for the X(3872) based on comparisons of angular correlations between final state particles in X(3872)-->pi+pi-J/psi decays with simulated data for J^{PC} values of 1^{++} and 2^{-+}. We examine the influence of rho-omega interference in the M(pi+pi-) spectrum. The analysis is based on a 711fb^{-1} data sample that contains 772 million BBbar meson pairs collected at the Upsilon(4S) resonance in the Belle detector at the KEKB e+e- collider.Comment: 15 pages, 10 figures and 6 tables. Submitted to Physical Review