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Register a new userAnalyticity of $etapi$ isospin-violating form factors and the $tautoetapi u$ second-class decay
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We consider the evaluation of the $etapi$ isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the $eta$ meson in QCD. Unitarity relates the vector form factor to the $etapi to pipi$ amplitude: we exploit progress in formulating and solving the Khuri-Treiman equations for $etato 3pi$ and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the $rho$-meson peak. Observing this peak in the energy distribution of the $tauto eta pi u$ decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the $etapi$ elastic scattering $S$-wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the $a_0(980)$ scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the $tautopipi u$ decay.
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A model for S-wave $etapi$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $Kbar{K}$ channel. The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $etapitoetapi$, $etapito Kbar{K}$ amplitudes and approximately for $Kbar{K}to Kbar{K}$. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omn`es problem, thus allowing to compute the $etapi$ and $Kbar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $a_0(980)$, $a_0(1450)$ resonances, as well as the chiral results of the $etapi$ and $Kbar{K}$ scalar radii which are predicted to be remarkably small at $O(p^4)$. This $T$-matrix model could be used for a unified treatment of the $etapi$ final-state interaction problem in processes such as $etato eta pipi$, $phitoetapigamma$, or the $etapi$ initial-state interaction in $etato3pi$.
I discuss recent applications of QCD light-cone sum rules to various form factors of pseudoscalar mesons. In this approach both soft and hard contributions to the form factors are taken into account. Combining QCD calculation with the analyticity of the form factors, one enlarges the region of accessible momentum transfers.
Isospin breaking in the Kl4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the Kpm -> pi^+ pi^- e^pm nu_e channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S- and P-wave pi-pi phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only pi-pi rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a_0^0 and a_0^2 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K^pm -> pi^+ pi^- e^pm nu_e form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a_0^0 and a_0^2, as well as for low-energy constants and order parameters of two-flavour ChPT.
We report recent progress in calculating semileptonic form factors for the $bar{B} to D^ast ell bar{ u}$ and $bar{B} to D ell bar{ u}$ decays using the Oktay-Kronfeld (OK) action for bottom and charm quarks. We use the second order in heavy quark effective power counting $mathcal{O}(lambda^2)$ improved currents in this work. The HISQ action is used for the light spectator quarks. We analyzed four $2+1+1$-flavor MILC HISQ ensembles with $aapprox 0.09,mathrm{fm}$, $0.12,mathrm{fm}$ and $M_pi approx 220,mathrm{MeV}$, $310,mathrm{MeV}$: $a09m220$, $a09m310$, $a12m220$, $a12m310$. Preliminary results for $Bto D^astell u$ decays form factor $h_{A_1}(w)$ at zero recoil ($w=1$) are reported. Preliminary results for $B to D,ell u$ decays form factors $h_pm(w)$ over a kinematic range $1<w<1.3$ are reported as well.
In the two body hadronic tau decays, such as tau->to K pi (eta)nu, vector mesons play important role. Belle and Babar measured hadronic invariant mass spectrum of tau -> K pi nu decay. To compare the spectrum with theoretical prediction, we develop the chiral Lagrangian with vector mesons in Kimura:2012nx. We compute the form factors of the hadronic tau decay taking account of the quantum corrections of Nambu Goldstone bosons. We also show how to renormalizethe divergence of the Feynman diagrams with arbitrary number of loops and determine the counterterms within one loop using background field method.In this report, we discuss the renormalization of Kimura:2012nx by considering the one loop Feynman diagrams.
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