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Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {it a priori} information about the $Q^2$ dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various $Q^2$, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
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We present a model-independent calculation of hadron matrix elements for all dimension-six operators associated with baryon number violating processes using lattice QCD. The calculation is performed with the Wilson quark action in the quenched approximation at $beta=6/g^2=6.0$ on a $28^2times 48times 80$ lattice. Our results cover all the matrix elements required to estimate the partial lifetimes of (proton,neutron)$to$($pi,K,eta$) +(${bar u},e^+,mu^+$) decay modes. We point out the necessity of disentangling two form factors that contribute to the matrix element; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which could give strong constraints on several GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of chiral lagrangian.
Results on semileptonic decay matrix elements of heavy-light mesons and charmonium spectrum and decay constant using a fine quenched lattice are presented.
We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Luscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating $K to 3pi$ weak decay, the isospin-breaking $eta to 3pi$ QCD transition, and the electromagnetic $gamma^*to 3pi$ amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic $g-2$.
We present a fast and simple algorithm that allows the extraction of multiple exponential signals from the temporal dependence of correlation functions evaluated on the lattice including the statistical fluctuations of each signal and treating properly backward signals. The basic steps of the method are the inversion of appropriate matrices and the determination of the roots of an appropriate polynomial, constructed using discretized derivatives of the correlation function. The method is tested strictly using fake data generated assuming a fixed number of exponential signals included in the correlation function with a controlled numerical precision and within given statistical fluctuations. All the exponential signals together with their statistical uncertainties are determined exactly by the algorithm. The only limiting factor is the numerical rounding off. In the case of correlation functions evaluated by large-scale QCD simulations on the lattice various sources of noise, other than the numerical rounding, can affect the correlation function and they represent the crucial factor limiting the number of exponential signals, related to the hadronic spectral decomposition of the correlation function, that can be properly extracted. The algorithm can be applied to a large variety of correlation functions typically encountered in QCD or QCD+QED simulations on the lattice, including the case of exponential signals corresponding to poles with arbitrary multiplicity and/or the case of oscillating signals. The method is able to to detect the specific structure of the multiple exponential signals without any a priori assumption and it determines accurately the ground-state signal without the need that the lattice temporal extension is large enough to allow the ground-state signal to be isolated.
We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of Charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited state contributions without assuming quark-hadron duality.
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