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Register a new userHadronic decay width from finite-volume energy spectrum in lattice QCD
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The standard approach to determine the parameters of a resonance is based on the study of the volume dependence of the energy spectrum. In this work we study a non-linear sigma model coupled to a scalar field in which a resonance emerges. Using an analysis method introduced recently, based on the concept of probability distribution, it is possible to determine the mass and the width of the resonance.
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We present results for the spectrum of excited mesons obtained from temporal correlations of spatially-extended single-hadron and multi-hadron operators computed in lattice QCD. The stochastic LapH algorithm is implemented on anisotropic, dynamical lattices for isovectors for pions of mass $390$ MeV. A large correlation matrix with single-particle and two-particle probe operators is diagonalized to identify resonances. The masses of excited states in the $I=1, S=0, T_{1u}^+$ channel as well as the mixing of single and multi-particle probe operators are presented.
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.,cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the Delta-resonance a clear resonance structure emerges in such an analysis. Consequently, measuring the volume-dependence of the energy levels in lattice QCD will allow to determine the mass and the width of the Delta with reasonable accuracy.
We perform a lattice QCD study of the $rho$ meson decay from the $N_f=2+1$ full QCD configurations generated with a renormalization group improved gauge action and a non-perturbatively $O(a)$-improved Wilson fermion action. The resonance parameters, the effective $rhotopipi$ coupling constant and the resonance mass, are estimated from the $P$-wave scattering phase shift for the isospin I=1 two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, $m_pi=410,{rm MeV}$ ($m_pi/m_rho=0.46$) and $m_pi=300,{rm MeV}$ ($m_pi/m_rho=0.35$), on a $32^3times 64$ ($La=2.9,{rm fm}$) lattice at the lattice spacing $a=0.091,{rm fm}$. We compare our results at these two quark masses with those given in the previous works using $N_f=2$ full QCD configurations and the experiment.
We study the finite-volume correction on the hadronic vacuum polarization contribution to the muon g-2 ($a_mu^{rm hvp}$) in lattice QCD at (near) physical pion mass using two different volumes: $(5.4~{rm fm})^4$ and $(8.1~{rm fm})^4$. We use an optimized AMA technique for noise reduction on $N_f=2+1$ PACS gauge configurations with stout-smeared clover-Wilson fermion action and Iwasaki gauge action at a single lattice cut-off $a^{-1}=2.33$ GeV. The calculation is performed for the quark-connected light-quark contribution in the isospin symmetric limit. We take into account the effects of backward state propagation by extending a temporal boundary condition. In addition we study a quark-mass correction to tune to the exactly same physical pion mass on different volume and compare those correction with chiral perturbation. We find $10(26)times10^{-10}$ difference for light quark $a_mu^{rm hvp}$ between $(5.4~{rm fm})^4$ and $(8.1~{rm fm})^4$ lattice in 146 MeV pion.
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