Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFermionic correlation functions from the staggered Schrodinger functional
134
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the Schrodinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are proposed, corresponding to the coarse lattice having size $(L/2a)^3 times (T/2a)$, with $T = T pm a$. The continuum limit is then defined at fixed $T/L$. Both cases have previously been investigated in the pure gauge theory. Here we define fermionic correlation functions and study their approach to the continuum limit at tree-level of perturbation theory.
rate research
Read More
Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the divergences induced by these surface interactions can be absorbed by a renormalization of their coefficients.
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.
We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral formulation with a finite but arbitrary Trotter number allows to derive a set of discrete functional equations with respect to the spectral parameters. We show that these equations yield a unique characterization of the density operator. Our functional equations are a discrete version of the reduced q-Knizhnik-Zamolodchikov equations which played a central role in the study of the zero temperature case. As a natural result, and independent of the arguments given by Jimbo, Miwa, and Smirnov (2009) we prove that the inhomogeneous finite temperature correlation functions have the same remarkable structure as for zero temperature: they are a sum of products of nearest-neighbor correlators.
The chirally rotated Schrodinger functional ($chi$SF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schrodinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O($a$) improvement to be operational in the $chi$SF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the $chi$SF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O($a$) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the $chi$SF framework and prepares the ground for non-perturbative applications.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
