Continuum limit improved lattice action for pure Yang-Mills theory (II)

Wilson loops are calculated to one-loop order using lattice actions including 6-link loops. The static potential is extracted and its small-a expansion performed using coefficients determined at tree level. The Λ-parameter for Symanzik's improved action is thereby obtained and constraints placed on the coefficients appearing in the action at order g².     

Renormalisation of composite operators in lattice perturbation theory with clover fermions: non-forward matrix elements

We consider the renormalisation of lattice QCD operators with one and two covariant derivatives related to the first and second moments of generalised parton distributions and meson distribution amplitudes. Employing the clover fermion action we calculate their non-forward quark matrix elements in one-loop lattice perturbation theory. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators and compute the matrices of the renormalisation factors in one-loop approximation. We describe how tadpole improvement is applied to the results. PACS 11.15.Ha; 12.38.Bx; 12.38.Gc An erratum to this article can be found at     

Computation of the action for on-shell improved lattice gauge theories at weak coupling

The coefficient in Symanzik's improved lattice action for (pure) SU(2) and SU(3) gauge theories are determined to one-loop order by requiring the absence of leading scaling violations in a set of on-shell quantities, which arise in a world where two dimensions are compactified in a twisted manner.     

The sigma-model with Wilson lattice fermions

The σ-model with Wilson fermions is considered in one-loop lattice perturbation theory and in the hopping-parameter expansion at large bare couplings. Chiral-symmetry restoration in the large cut-off limit of perturbation theory is only possible if asymmetric counterterms are added to the lattice action. In the hopping-parameter expansion at infinitely large bare Yukawa coupling, dynamical parity doubling of the fermion occurs.     

O(N)模型破缺相的红外重正化群计算

利用一个与质量有关的重正化方案,研究了O(N)模型破缺相的红外重正化群性质.得到了与质量有关的一圈重正化群系数以及在红外极限下的二圈重正化群系数.利用标准的微扰场论计算方法,发现特殊的抵消效应,该效应使得二圈的重正化群系数与一圈重正化群系数在红外极限下相同.     

Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions

We describe an algebraic algorithm which allows us to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.     

Renormalization group improved lattice action and Monte Carlo calculations for the non-linear O(3) sigma model

Monte Carlo calculations for the two-dimensional O(3) nonlinear sigma model are performed with a renormalization group improved lattice action proposed previously. The relation between the correlation function on the renormalized trajectory and that on a canonical curve is discussed from the viewpoint of the renormalization group and is investigated numerically. The scaling behavior of the correlation length and the magnetic susceptibility is also examined. A comment on a large discrepancy between the Symanzik one-loop improved model and other models is given.     

Supersymmetric correction to top quark pair production near threshold

We studied the leading supersymmetric contribution to top–antitop threshold production using the NRQCD framework. The one-loop matching to the potential and the Wilson coefficient of the leading ³S₁ production current were considered. We point out that the leading correction to the potential is zero due to SU(3)_c gauge invariance. This is true in general for any new physics that enters above the electroweak scale. The shape of the top quark pair production cross section is therefore almost unaffected near threshold, allowing a precise determination of the top quark mass based on the Standard Model calculations. The supersymmetric correction to the Wilson coefficient c₁ of the production current decouples for heavy super particles. Its contribution is smaller than the Standard Model next-to-next-leading-log results.     

A convergent series for the QED effective action

The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one-loop effective action of QED.     

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.     

Infrared regularization of superstring theory and the one-loop calculation of coupling constants

Infrared regularized versions of 4-D N = 1 superstring ground states are constructed by curving the spacetime. A similar regularization can be performed in field theory. For the IR regularized string ground states we derive the exact one-loop effective action for non-zero U(1) or chromomagnetic fields as well as gravitational and axionic-dilatonic fields. This effective action is IR and UV finite. Thus, the one-loop corrections to all couplings (gravitational, gauge and Yukawas) are unambiguously computed. These corrections are necessary for quantitative string superunification predictions at low energies. The one-loop corrections to the couplings are also found to satisfy Infrared Flow Equations.     

Path integrals and the indefiniteness of the gravitational action

The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies.     

Restoration of Lorentz invariance in the lattice O(3) model with improved actions

Symanzik one-loop and block-spin renormalization group improved actions are studied by Monte Carlo simulation. Scaling sets in at small correlation length for the considered actions. The approach to the continuum relativistic energy-momentum dispersion is best for Symanzik one-loop improved action.     

Four-dimensional heterotic strings and conformal field theory

The techniques of (super) conformal field theory are applied to 4-dimensional heterotic string theories. We discuss certain aspects of 4-dimensional strings in the framework of the bosonic lattice approach such as the realization of superconformal symmetry, character valued partition functions, construction of vertex operators and ghost picture changing. As an application we compute all possible 3- and 4-point tree amplitudes of the massless fields and derive from them the low energy effective action of the massless modes. Some effects for the massless spectrum due to one-loop string effects are also mentioned.     

Detecting the long-distance structure of the X(3872)

Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein–Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein–Hawking form, is not modified.     

Flavor symmetry breaking and scaling for improved staggered actions in quenched QCD

We present a study of the flavor symmetry breaking in the pion spectrum for the p4-improved fermion action. Three different variants of the p4 action – p4fat3, p4fat7, and p4fat7tad – are compared to the Asqtad and naive staggered actions. To study the pattern of symmetry breaking, we measure all 15 pion masses in the four-flavor staggered theory. The measurements are done on a quenched gauge background, generated using a one-loop improved Symanzik action with β=10/g²=7.40, 7.75, and 8.00, corresponding to lattice spacings of approximately a= 0.31 fm, 0.21 fm, and 0.14 fm. PACS 11.15.Ha; 11.30.Rd; 12.38.Aw; 12.38.-t; 12.38.Gc     

Regularization using the generalized zeta function in the proper-time method

We propose regularization with the generalized zeta function in order to calculate one-loop corrections to the original action in quantum field theory. The Schwinger proper-time formalism is used to define the zeta function. The method is illustrated by calculation of the one-loop corrections to the Maxwell Lagrangian in QED with anomalous moments.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 78–83, November, 1987.     

Proton Spin Sum Rule from Large Momentum Effective Field Theory

In high energy scattering experiments, the proton spin is understood as the sum of the spin and orbital angular momentum of the quarks and gluons in Feynman’s parton picture. The Jaffe–Manohar form of the proton spin sum rule is justified as physical, and it is shown that the individual terms can be related to the proton matrix elements of certain quasi-obervables through a large momentum effective field theory. The relation is expressed as a factorization formula where the leading contribution to the quasi-observable is factorized into the parton observables and perturbative matching coefficients, and we present the results for the latter at one-loop order in perturbation theory. This will provide us with the basis to extract the proton spin content from the lattice QCD calculations of the quasi-observables.