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Register a new user$K pi$ scattering and the $K^*(892)$ resonance in 2+1 flavor QCD
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In this project, we will compute the form factors relevant for $B to K^*(to K pi)ell^+ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B to K pi$ matrix elements, the $K pi$ scattering amplitude needs to be determined using Luschers method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K pi$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.
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We calculate results for K to pi and K to 0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low energy constants of the chiral effective theory can be determined. The low energy constants of these matrix elements are necessary for an understanding of the Delta I=1/2 rule, and for calculations of epsilon/epsilon using current lattice QCD simulations.
We present results for form factors of semileptonic decays of $D$ and $B$ mesons in 2+1 flavor lattice QCD using the MILC gauge configurations. With an improved staggered action for light quarks, we successfully reduce the systematic error from the chiral extrapolation. The results for $D$ decays are in agreement with experimental ones. The results for B decays are preliminary. Combining our results with experimental branching ratios, we then obtain the CKM matrix elements $|V_{cd}|$, $|V_{cs}|$, $|V_{cb}|$ and $|V_{ub}|$. We also check CKM unitarity, for the first time, using only lattice QCD as the theoretical input.
In this paper we report on results for the s-wave scattering length of the $pi$-$K$ system in the $I=3/2$ channel from $N_f=2+1+1$ Lattice QCD. The calculation is based on gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450,text{MeV}$ at three values of the lattice spacing. Our main result reads $M_{pi},a_0^{3/2,text{phys}} = -0.059(2)$. Using chiral perturbation theory we are also able to estimate $M_{pi},a_0^{1/2,text{phys}} = 0.163(3)$. The error includes statistical and systematic uncertainties, and for the latter in particular errors from the chiral and continuum extrapolations.
We extend our study of the $Kpi$ system to moving frames and present an exploratory extraction of the masses and widths for the $K^*$ resonances by simulating $Kpi$ scattering in p-wave with $I=1/2$ on the lattice. Using $Kpi$ systems with non-vanishing total momenta allows the extraction of phase shifts at several values of $Kpi$ relative momenta. A Breit-Wigner fit of the phase renders a $K^*(892)$ resonance mass and $K^*to K pi $ coupling compatible with the experimental numbers. We also determine the $K^*(1410)$ mass assuming the experimental $K^*(1410)$ width. We contrast the resonant $I=1/2$ channel with the repulsive non-resonant $I=3/2$ channel, where the phase is found to be negative and small, in agreement with experiment.
We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $Kpi$ scattering amplitudes as a function of the center-of-mass energy using Luschers method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $sqrt{3}frac{2pi}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $kappa$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of $317.2(2.2)$ and $175.9(1.8)$ MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $kappa$-resonance pole positions are found to be $left[0.86(12) - 0.309(50),iright]:{rm GeV}$ at the heavier pion mass and $left[0.499(55)- 0.379(66),iright]:{rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $left[ 0.8951(64) - 0.00250(21),i right]:{rm GeV}$ at the heavier pion mass and $left[0.8718(82) - 0.0130(11),iright]:{rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* Kpi}=5.02(26)$ and $g_{K^* Kpi}=4.99(22)$, respectively.
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