Showing papers on "Dimensional regularization published in 1992"
TL;DR: In this article, the effects of next-to-leading corrections on the Wilson coefficients of current-current and QCD penguin operators are analyzed. But the results are restricted to the case of γ5 and γ4.
290 citations
TL;DR: In this paper, a new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale, and the Fourier transform is then defined by formal integration by parts.
285 citations
01 Jan 1992
TL;DR: In this article, the prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated and the three-loop anomalous dimension of the singlet axial current is calculated.
Abstract: The prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
257 citations
TL;DR: It is shown that in the non-Abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions.
Abstract: Perturbative renormalization of a non-Abelian Chern-Simons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure Chern-Simons theory, the $\ensuremath{\beta}$ function for the coefficient of the Chern-Simons term vanishes to three-loop order. Both dimensional regularization and regularization by introducing a conventional Yang-Mills term in the action are used. It is shown that dimensional regularization is not gauge invariant at two loops. A variant of this procedure, similar to regularization by dimensional reduction used in supersymmetric field theories, is shown to obey the Slavnov-Taylor identity to two loops and gives no renormalization of the Chern-Simons term. Regularization with the Yang-Mills term yields a finite integer-valued renormalization of the coefficient of the Chern-Simons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of Chern-Simons theory coupled to matter. We show that in the non-Abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the $\ensuremath{\beta}$ function for the gauge coupling constant is zero to two-loop order, consistent with the topological quantization condition for this constant.
154 citations
TL;DR: In this paper, a new simple γ5 regularization scheme was proposed for radiative correction, which can be formulated in terms of simple projection operations and can be used in the standard radiative corrections.
Abstract: We present a new simpleγ5 regularization scheme. We discuss its use in the standard radiative correction calculations including the anomaly contributions. The new scheme features an anticommutingγ5 which leads to great simplifications in practical calculations. We carefully discuss the underlying mathematics of ourγ5-scheme which is formulated in terms of simple projection operations.
129 citations
TL;DR: In this paper, the authors presented the general formalism and results of the two-loop effective action in Einstein quantum gravity on the background MN × Tk, where MN is Minkowski space and Tk is a k-dimensional torus.
Abstract: For the first time we present the general formalism and results of calculation of the two-loop effective action in Einstein quantum gravity on the background MN × Tk, where MN is Minkowski space and Tk is a k-dimensional torus We discuss the case of a zero cosmological constant as well as of a nonzero one The method of calculating variations of the action on a metric tensor and the technique of calculating momentum integrals in dimensional regularization are presented Some applications to spontaneous compactification are discussed, as well as some prospects
122 citations
TL;DR: In this article, general expressions for scalar one-loop massive Feynman diagrams with any number of external lines and with arbitrary momenta of these lines, with arbitrary values of masses and powers of denominators of internal lines, the space-time dimension n also being arbitrary.
Abstract: General expressions are obtained for scalar one‐loop massive Feynman diagrams with any number of external lines and with arbitrary momenta of these lines, with arbitrary values of masses and powers of denominators of internal lines, the space‐time dimension n also being arbitrary. Special cases are considered when two (or more) masses are equal to 0. The results are represented in terms of hypergeometric functions.
106 citations
TL;DR: In this article, a class of once subtracted dispersion relations for the vacuum-polarization functions of massive fermions is proposed, in which the subtraction constants are determined explicitly from Ward identities.
81 citations
TL;DR: In this paper, the authors study quantum Chern-Simons theory as the large-mass limit of the limit D --> 3 of dimensionally regularized topologically massive Yang-Mills theory.
75 citations
TL;DR: In this article, the QCD correction to the one-loop electroweak radiative correction of the partial Z-decay width into b-quarks is calculated analytically in the limit of large top mass.
65 citations
TL;DR: In this article, an explicit example of a one-loop triangle graph where dimensional regularization fails to regulate the infra-red singularities that emerge at intermediate steps of studying large-Q 2 Sudakov factorization is presented.
TL;DR: In this article, the authors present a program written in FORM for the analytic calculation of propagator-type one-and two-loop Feynman graphs with external lines corresponding to massive as well as massless particles on-shell.
TL;DR: In this paper, two classes of renormalizable 1/N expandable two-dimensional models are analyzed to O(1/N) and the asymptotic behavior of the renormalized two-point functions is nonperturbatively evaluated.
Abstract: Two classes of renormalizable 1/N expandable two-dimensional models are analyzed to O(1/N) and the asymptotic behavior of the renormalized two-point functions is nonperturbatively evaluated. These results are taken as a benchmark to study the applicability of dimensional regularization and perturbative minimal subtraction renormalization to the context of the 1/N expansion. Perturbation theory is applied to O(1/N) diagrams to all orders in the weak coupling constant and, after resummation, the same finite renormalization group invariant asymptotic amplitudes are obtained. As a byproduct, the O(1/N) contributions to renormalization group Z functions in the minimal subtraction scheme are extracted and the critical index η is evaluated and compared to previous nonperturbative results, finding complete agreement. The appendix is devoted to the extension of these results to a supersymmetric version of the models.
TL;DR: In this article, an explicit operator representation corresponding to the Dirac matrix γ5 is given, and the decay width of the pion is investigated both in the sharp cutoff and in the dimensional regularization.
TL;DR: Using dimensional regularization for both infrared and ultraviolet divergences, it was shown in this paper that the QCD corrections to the decay width of a large quark mass are equal to those to the corresponding decay width in the limit of a single quark.
Abstract: Using dimensional regularization for both infrared and ultraviolet divergences, we confirm that the QCD corrections to the decay width $\Gamma(t\to H^+b)$ are equal to those to $\Gamma(t\to W^+b)$ in the limit of a large $t$ quark mass.
TL;DR: In this paper, the authors extend the recently invented method of calculating massive Feynman integrals, namely the differential equations method, to vertex-type diagrams, and show that for calculations of one-and two-loop diagrams this method is a simple procedure for evaluating the result without calculating D-space integrals (for dimensional regularization).
Abstract: We extend the recently invented method of calculating massive Feynman integrals, namely the differential equations method, to vertex-type diagrams. As an example, for calculations of one-and two-loop diagrams we show that by analogy with propagator-type diagrams this method is a simple procedure for evaluating the result without calculating D-space integrals (for dimensional regularization).
TL;DR: This work computing the renormalization group functions to lowest order in a model for a massive scalar in three dimensions with four- and six-point couplings shows that divergence arises only beyond one-loop order when {ital n} is odd.
Abstract: Dimensional regularization characterizes divergences using poles that occur in Feynman integrals when {ital n} (the number of dimensions in the regulated theory) equals {ital D} (the number of dimensions in the initial classical action). Since these poles are generated by gamma functions of the form {Gamma}({ital A}{minus}{ital n}/2), a divergence arises only if {ital A}{minus}{ital n}/2 is a negative integer; consequently the need for renormalization arises only beyond one-loop order when {ital n} is odd. We illustrate this by computing the renormalization group functions to lowest order in a model for a massive scalar in three dimensions with four- and six-point couplings.
TL;DR: In this article, the two-loop calculation of the renormalization constant Z 1 for the on-shell fermion-fermion-vector vertex function of a general gauge theory with one massive fermions and the other particles massless is presented.
TL;DR: In this paper, a numerical technique to regularize divergent loop diagrams in cavity QCD is discussed, which is closely related to dimensional regularization in free space, and the energy shift is expressed as the integral of a divergent spectral function.
TL;DR: In this article, a discussion of the renormalization of the singlet axial anomaly equation in a vector-like nonabelian gauge theory such as QCD regularized by ordinary dimensional regularization is given.
Abstract: A careful and complete discussion is given of the renormalization of the singlet axial anomaly equation in a vector-like nonabelian gauge theory such as QCD regularized by ordinary dimensional regularization. Pseudotensorial structures are treated with the 't Hooft-Veltman prescription. A general framework for calculations is developed, and subsequently verified by explicit computations through two loops. This is followed by a discussion of the matrix elements obtained.
Journal Article•
TL;DR: In this article, an extension of the Fierz transformation to a spinor space determined by dimensional regularization is discussed, based on the idea of dimension regularization, which is similar to the one proposed in this paper.
Abstract: We discuss an extension of the Fierz transformation to a spinor space determined by dimensional regularization
TL;DR: In this paper, an explicit example of a one-loop triangle graph where dimensional regularization fails to regulate the infra-red singularities that emerge at intermediate steps of studying large-Q^2$ Sudakov factorization is presented.
Abstract: An explicit example is presented (a one-loop triangle graph) where dimensional regularization fails to regulate the infra-red singularities that emerge at intermediate steps of studying large-$Q^2$ Sudakov factorization. The mathematical nature of the phenomenon is explained within the framework of the theory of the $As$-operation.
TL;DR: In this paper, a cavity regularization method, which is closely related to the dimensional regularization technique, is applied to the gluon self-energy in cavity QCD.
Posted Content•
TL;DR: In this paper, the authors investigate the renormalization of nonlocal interactions in effective field theory using dimensional regularization with minimal subtraction and present an integro-differential renormalisation group equation for every possible class of graph at one loop order.
Abstract: We investigate the renormalization of ``nonlocal'' interactions in an effective field theory using dimensional regularization with minimal subtraction In a scalar field theory, we write an integro-differential renormalization group equation for every possible class of graph at one loop order
TL;DR: In this paper, the authors study quantum Chern-Simons theory as the large mass limit of the limit of dimensionally regularized topologically massive Yang-Mills theory and show that there is no two-loop correction to the one-loop shift.
Abstract: We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.
TL;DR: In this article, the authors describe the program DTRACE, which is capable of calculating products of traces of γ-matrices in d dimensions and gives the result in a form suitable as input for algebraic manipulation programs.
TL;DR: In this paper, the β-functions of a non-linear σ-model coupled to two-dimensional gravity were studied in the light cone gauge and a simple diagrammatic derivation of the induced 2D gravitational action from the nonlinear model was presented.
TL;DR: In this article, a covariant perturbation theory for the interpolating fields and the S matrix was developed, where the coupling terms in the Larangian density involve arbitrary (first and higher) derivatives.
Abstract: The formalism of partial differential equations with respect to coupling constants is used to develop a covariant perturbation theory for the interpolating fields and theS matrix when the coupling terms in the Larangian density involve arbitrary (first and higher) derivatives. Through the notion of pure noncovariant contractions, the free-fieldT and the (covariant)T* products can be related to each other, allowing us to avoid the Hamiltonian density altogether when dealing with theS matrix. The important ingredients in our approach are (1) the adiabatic switching on and off of the interactions in the infinite past and future, respectively, and (2) the vanishing of four-dimensional delta functions and their derivatives at zero space-time points. The latter ingredient is a prerequisite that our formalism and the canonical formalism be consistent with each other, and on the other hand, it is supported by the dimensional regularization. Corresponding to any Lagrangian, the generalized interaction Hamiltonian density is defined from the covariantS matrix with the help of the pure noncovariant contractions. This interaction Hamiltonian density reduces to the usual one when the Lagrangian density depends on just first derivatives and when the usual canonical formalism can be applied.
TL;DR: In this paper, the authors considered the regulated propagator G'e(ξ, ξ) for points ξ and ξ' on the two-dimensional flat torus and with a regularization analogous to the proper-time method with cut-off e. In this regularization, the propagator has an expansion in eigenmodes which is a particular Jacobi-Riemann function with beautiful properties and which can be transformed to an integral representation by a Sommerfeld-Watson method.
Abstract: The regulated propagator G’e(ξ,ξ’) is considered for points ξ and ξ’ on the two‐dimensional flat torus and with a regularization analogous to the proper‐time method with cut‐off e. The inequivalent tori are labeled by a modular parameter τ. In this regularization, the propagator has an expansion in eigenmodes which is a particular Jacobi–Riemann function with beautiful properties and which can be transformed to an integral representation by a Sommerfeld–Watson method. This latter method allows one to derive exact analytic expressions in several domains of the parameters ‖ξ−ξ’‖, e, and of the parameter τ. For generic value of τI≡Im(τ) and small value of the cut‐off e we recover the known results relative to short‐distance phenomena. At large value of τI≂O(cst/4πe), the propagator diverges as τI and the coefficient is computed. A general formula for the Weyl variation of the propagator is derived; again the behavior of the Weyl variation at fixed τI is reproduced, while the behavior at large τI is novel. As...