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Stefano Capitani

Publications and source records attributed to Stefano Capitani.

At least 37 records · Page 2Linked to original sources
arXiv2010

Renormalization of minimally doubled fermions

We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Borici-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Borici-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

hep-lat↗
arXiv2009

Minimally doubled fermions at one-loop level

Single fermionic degrees of freedom together with standard chiral symmetry at finite lattice spacing, correct continuum limit and local interactions only are precluded by the Nielsen-Ninomiya no-go theorem. The class of minimally doubled fermion actions exhibits exactly two chiral modes. Recent interest in these actions has been sparked by the investigation of fermionic actions defined on "hyperdiamond" lattices. Due to the necessity of breaking hypercubic symmetry explicitly, radiative corrections generate operator mixings with relevant and marginal operators that should vanish in continuum QCD. These cannot be avoided and must be taken into account in particular by a peculiar wave-function renormalisation and additive momentum renormalisation. Renormalisation properties at one-loop level of the self-energy, local bilinears and conserved vector and axial-vector currents are presented for Borici-Creutz and Karsten-Wilczek actions. Distinct differences and similarities between both actions are elucidated.

hep-lat↗
arXiv2009

Minimally doubled fermions at one loop

Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which contains a linearly divergent piece. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.

hep-lat↗
arXiv2007

Moments of meson distribution functions with dynamical twisted mass fermions

We present our preliminary results on the lowest moment of quark distribution functions of the pion using two flavor dynamical simulations with Wilson twisted mass fermions at maximal twist. The calculation is done in a range of pion masses from 300 to 500 MeV. A stochastic source method is used to reduce inversions in calculating propagators. Finite volume effects at the lowest quark mass are examined by using two different lattice volumes. Our results show that we achieve statistical errors of only a few percent. We plan to compute renormalization constants non-perturbatively and extend the calculation to two more lattice spacings and to the nucleons.

hep-lat↗
arXiv2007

Rationale for UV-filtered clover fermions

We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1, to the fermion self-energy in Wilson's formulation of lattice QCD with UV-filtering in the fermion action. We derive results for m_{crit} and the renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation theory for several filtering recipes (APE, HYP, EXP, HEX), both with and without a clover term. The perturbative series is much better behaved with filtering, in particular tadpole resummation proves irrelevant. Our non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination of filtering and clover improvement efficiently reduces the amount of chiral symmetry breaking -- we find residual masses am_{res}=O(10^{-2}).

hep-lat↗
arXiv2007

Chiral violations from one-loop domain wall fermions

We present results from lattice perturbation theory for the residual mass and other matrix elements measuring the breaking of chiral symmetry in domain-wall fermions. We have used the exact propagators corresponding to a finite number of points in the fifth dimensions, and results were obtained for several choices of the domain-wall parameters.

hep-lat↗
arXiv2006

Perturbative chiral violations for domain-wall QCD with improved gauge actions

We investigate, in the framework of perturbation theory at finite $N_s$, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained.

hep-lat↗
arXiv2006

Testing UV-filtered ("fat-link") clover fermions

We investigate filtered clover fermions, built from fat gauge links, both in one-loop perturbation theory and in numerical simulations. We use a variety of filtering recipes (APE, HYP, EXP, HEX), some of which are suitable for a HMC with dynamical fermions. A generic filtering together with a (fat-link) clover term yields fermions with much reduced chiral symmetry breaking.

hep-lat↗
arXiv2006

Chiral violations in domain-wall QCD from one-loop perturbation theory at finite $N_s$

We present perturbative calculations made with domain-wall fermions which possess a finite number of points $N_s$ in the extra fifth dimension. We have derived the required propagator functions, investigated the one-loop properties of quark amplitudes at finite $N_s$ and evaluated three quantities that can provide insights on chirality-breaking effects from the perturbative side. First we have computed the residual mass for various choices of $N_s$ and of the domain-wall height $M$. We have found that this radiatively induced mass approaches zero reasonably fast with the extent of the fifth dimension, depending on $M$ and on a lesser extent on the coupling $g_0$. We have also computed the differences of the renormalization constants of the vector and axial-vector currents and of the scalar and pseudoscalar densities. Finally we have calculated the chirally-forbidden mixing (which at finite $N_s$ is suppressed only partially) of an operator which describes the lowest moment of the $g_2$ structure function. In general we see that at $M=1.8$, where simulations are usually performed, values of $N_s=20$ or larger would be desirable in order for chiral violations to be negligible. The quantities that we have studied turn out to lose gauge invariance when $N_s$ is not infinite. We have also found that anomalous dimensions of operators at finite $N_s$ generally depend on $N_s$ and $M$. In particular, the vector and axial-vector currents have in general a nonzero anomalous dimension at finite $N_s$.

hep-lat↗
arXiv2006

A lattice calculation of the pion form factor with Ginsparg-Wilson-type fermions

Results for Monte Carlo calculations of the electromagnetic vector and scalar form factors of the pion in a quenched simulation are presented. We work with two different lattice volumes up to a spatial size of 2.4 fm at a lattice spacing of 0.148 fm. The pion form factors in the space-like region are determined for pion masses down to 340 MeV.

hep-lat↗
arXiv2006

Perturbative renormalization of the first moment of structure functions for domain-wall QCD

Using the domain-wall formulation of lattice fermions, we have computed the one-loop renormalization factors of one-link operators which measure the first nontrivial moment of the unpolarized, polarized and transversity structure functions, in the flavor nonsinglet sector. The knowledge of these factors is necessary in order to extract physical numbers from domain-wall Monte Carlo simulations of parton distributions. We have automated the perturbative calculations by developing suitable FORM codes. The results show that in many instances the total renormalization factors are almost equal to one, and that hence the corresponding operators are, for the appropriate values of the Dirac mass $M$ and the coupling $g_0$, practically unrenormalized.

hep-lat↗
arXiv2005

Pion form factor with chirally improved fermions

We present results for Monte Carlo calculations of the electromagnetic vector and scalar form factors of the pion in a quenched simulation. We work at a lattice spacing of 0.15 fm and use two lattice volumes up to a spatial size of 2.4 fm. The pion form factors in the space-like region are determined for pion masses down to 340 MeV.

hep-lat↗
arXiv2002

Lattice Perturbation Theory

The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of computations on the lattice, especially for investigating the behavior of lattice theories near the continuum limit. Particularly important is its role in connecting the outcome of Monte Carlo simulations to continuum physical results. For these matchings the calculation of the renormalization factors of lattice matrix elements is required. In this review we explain the main methods and techniques of lattice perturbation theory, focusing on the cases of Wilson and Ginsparg-Wilson fermions. We will illustrate, among other topics, the peculiarities of perturbative techniques on the lattice, the use of computer codes for the analytic calculations and the computation of lattice integrals. Discussed are also methods for the computation of 1-loop integrals with very high precision. The review presents in a pedagogical fashion also some of the recent developments in this kind of calculations. The coordinate method of Lüscher and Weisz is explained in detail. Also discussed are the novelties that Ginsparg-Wilson fermions have brought from the point of view of perturbation theory. Particular emphasis is given throughout the paper to the role of chiral symmetry on the lattice and to the mixing of lattice operators under renormalization. The construction of chiral gauge theories regularized on the lattice, made possible by the recent advances in the understanding of chiral symmetry, is also discussed. Finally, a few detailed examples of lattice perturbative calculations are presented.

hep-lat↗
arXiv2002

Status of lattice structure function calculations

Lattice QCD allows computations of moments of structure functions from first principles. An overview of the present status of the calculations is given. Recent results and future perspectives are discussed.

hep-ph↗
arXiv2001

Perturbative renormalization for overlap fermions

Using lattice overlap fermions, we have computed the 1-loop renormalization factors of several operators that measure DIS structure functions and weak amplitudes. Computer codes written in the algebraic manipulation language FORM have been used. The improvement of the operators is also discussed.

hep-lat↗
arXiv2000

Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions

Using overlap as well as Wilson fermions, we have computed the one-loop renormalization factors of ten non-singlet operators which measure the third moment of quark momentum and helicity distributions (the lowest two having been computed in a previous paper), as well as the lowest three moments of the $g_2$ structure function and the lowest two non-trivial moments of the $h_1$ transversity structure function (plus the tensor charge). These factors are needed to extract physical observables from Monte Carlo simulations of the corresponding matrix elements. An exact chiral symmetry is maintained in our calculations with overlap fermions, and its most important consequence here is that the operators measuring $g_2$ do not show any of the power-divergent mixings with operators of lower dimension which are present in the Wilson case. Many of our results for Wilson fermions are also new; for the remaining ones, we agree with the literature except in one case. The computations have been carried out using the symbolic language FORM, in a general covariant gauge, which turns out also to be useful in checking the gauge-invariance of the final results.

hep-lat↗
arXiv2000

Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions. These factors are necessary to extract physical numbers from Monte Carlo simulations made with overlap fermions. An exact chiral symmetry is maintained in all our results, and the renormalization constants of corresponding unpolarized and polarized operators which differ by a $γ_5$ matrix have the same value. We have considered two lattice representations for each continuum operator. The computations have been carried out using the symbolic language FORM, in a general covariant gauge. In some simple cases they have also been checked by hand.

hep-lat↗