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Register a new userNucleon Decay Matrix Elements for Domain-Wall Fermions
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We report on the nucleon decay matrix elements with domain-wall fermions in quenched approximation. Results from direct and indirect method are compared with a focus on the process of a proton decaying to a pion and a lepton. We discuss the renormalization necessary for the matching to the continuum theory. Preliminary results for the renormalized chiral lagrangian parameters are presented.
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Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with non-perturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements, as well as the indirect estimate of them from the nucleon to vacuum matrix elements, are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative value for the low energy constants from the nucleon to vacuum matrix elements are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable estimate of the physical low energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give smaller value of the form factors, compared to the indirect one, thus enhancing the proton life-time; indeed for the pi^0 final state the difference between the two methods is quite appreciable.
We report on our on-going project to calculate the nucleon decay matrix elements with domain-wall fermions. Operator mixing is discussed employing a non-perturbative renormalization. Bare matrix elements of all the possible decay modes induced by the dimension-six operators are calculated with the direct method, which are compared with the indirect calculation using chiral perturbation theory.
The nucleon decay matrix elements of three-quark operators are calculated with domain-wall fermions. Operators are renormalized non-perturbatively to match the MS bar (NDR) scheme at NLO. Quenched simulation studies involve both direct measurement of the matrix elements and the chiral Lagrangian parameters, alpha and beta. We also report on the dynamical quark effects on these parameters.
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.
We present a calculation of the $Ktopipi$ decay amplitudes from the $Ktopi$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $Delta I=1/2$ enhancement is only half of the experimental value, and $epsilon/epsilon$ is negative.
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