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Title: An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization

Abstract

A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.

Authors:
 [1];  [1];  [2];  [2];  [1];  [3]
  1. Physics Department, Brown University, Providence, RI 02912 (United States)
  2. Université de Nice Sophia-Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS, 06560 Valbonne (France)
  3. (France)
Publication Date:
OSTI Identifier:
22451192
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 359; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGE RENORMALIZATION; CLUSTER EXPANSION; CORRELATION FUNCTIONS; GAUGE INVARIANCE; QUANTUM CHROMODYNAMICS; QUARKS; SELF-ENERGY

Citation Formats

Fried, H.M., E-mail: fried@het.brown.edu, Tsang, P.H., E-mail: Peter_Tsang@brown.edu, Gabellini, Y., E-mail: yves.gabellini@inln.cnrs.fr, Grandou, T., E-mail: thierry.grandou@inln.cnrs.fr, Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu, and Université de Nice Sophia-Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS, 06560 Valbonne. An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.03.024.
Fried, H.M., E-mail: fried@het.brown.edu, Tsang, P.H., E-mail: Peter_Tsang@brown.edu, Gabellini, Y., E-mail: yves.gabellini@inln.cnrs.fr, Grandou, T., E-mail: thierry.grandou@inln.cnrs.fr, Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu, & Université de Nice Sophia-Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS, 06560 Valbonne. An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization. United States. doi:10.1016/J.AOP.2015.03.024.
Fried, H.M., E-mail: fried@het.brown.edu, Tsang, P.H., E-mail: Peter_Tsang@brown.edu, Gabellini, Y., E-mail: yves.gabellini@inln.cnrs.fr, Grandou, T., E-mail: thierry.grandou@inln.cnrs.fr, Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu, and Université de Nice Sophia-Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS, 06560 Valbonne. Sat . "An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization". United States. doi:10.1016/J.AOP.2015.03.024.
@article{osti_22451192,
title = {An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization},
author = {Fried, H.M., E-mail: fried@het.brown.edu and Tsang, P.H., E-mail: Peter_Tsang@brown.edu and Gabellini, Y., E-mail: yves.gabellini@inln.cnrs.fr and Grandou, T., E-mail: thierry.grandou@inln.cnrs.fr and Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu and Université de Nice Sophia-Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS, 06560 Valbonne},
abstractNote = {A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.},
doi = {10.1016/J.AOP.2015.03.024},
journal = {Annals of Physics},
number = ,
volume = 359,
place = {United States},
year = {Sat Aug 15 00:00:00 EDT 2015},
month = {Sat Aug 15 00:00:00 EDT 2015}
}
  • Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional 'idealistic' description of QCD and a more 'realistic' description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green's functional G{sub c}(x,y|A) and the vacuum functional L[A]. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect ofmore » this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called 'Effective Locality', in which the interactions between quarks by the exchange of a 'gluon bundle'-which 'bundle' contains an infinite number of gluons, including cubic and quartic gluon interactions-display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that 'non-perturbative' here refers to the effective summation of all gluons between a pair of quark lines-which may be the same quark line, as in a self-energy graph-but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the 'Bundle Diagram'. As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon-nucleon binding potential to form a model deuteron, will appear separately. - Highlights: Black-Right-Pointing-Pointer An analytic, non-perturbative and gauge-invariant formulation for QCD processes. Black-Right-Pointing-Pointer A new property called Effective Locality appears in the QCD fermionic amplitudes. Black-Right-Pointing-Pointer An effective quark-antiquark and 3-quark binding potential is obtained. Black-Right-Pointing-Pointer A single 'gluon bundle' replaces the sum of an infinite number of Feynman graphs.« less
  • This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into 'Gluon Bundles' (GBs),more » as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by {sup B}undle Graphs{sup .} In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. 'Transverse Imprecision' is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk-top computer. A fantastic simplification{exclamation_point} With the aid of the above techniques, this presentation will describe each of the above paragraphs, with explicit descriptions of gauge-invariance, of the summation of all relevant Feynman graphs, of quark-binding into hadrons, and of nucleon-nucleon binding to form a deuteron. To our knowledge, the latter calculation is the first analytic example of Nuclear Physics obtained directly from basic QCD.« less
  • The Ward--Slavnov identities satisfied by the Green's functions with one insertion of a gauge-invariant operator are studied in the background-field gauge. As a consequence, the counterterms for a given gauge-invariant operator must satisfy a system of equations, whose general solution is found in the simplest cases of operators of low dimension (d < or = 6) or low twist (tau < or = 3) and conjectured in the general case. It then follows that the renormalized Green's functions satisfy the same Ward identities as the bare, regularized ones. We deduce a definite prescription for the practical calculation of the anomalousmore » dimensions of gauge-invariant operators which do not vanish in the classical limit: this prescription is formulated in the background gauge or in the usual Fermi-type gauge.« less
  • The problem of renormalization scheme and gauge dependence of perturbative QCD predictions in the momentum subtraction schemes is considered. A renormalization-group-improved expression for the QCD contribution to the /sigma//sub /ital T//(e/sup +/e/sup /minus///r arrow/hadrons)//sigma/ (/ital e//sup +/e/sup /minus///r arrow//mu//sup +//mu//sup /minus//) ratio is discussed in detail in the next-to-next-to-leading order. A rather strong gauge dependence is found because a nontrivial gauge dependence of the running coupling constant is not compensated by the gauge dependence of the expansion coefficients. The three-loop expression is found to have a stronger gauge dependence than the two-loop expression. Thus an important problem arises: How shouldmore » the results of perturbative calculations in the momentum subtraction schemes be compared with the experimental data« less
  • We calculate one-loop renormalization factors of generic {delta}S=2 four-quark operators for domain-wall QCD with the plaquette gauge action and the Iwasaki gauge action. The renormalization factors are presented in the modified minimal subtraction (MS) scheme with the naive dimensional regularization. As an important application we show how to construct the renormalization factors for the operators contributing to K{sup 0}-K{sup 0} mixing in the supersymmetric models with the use of our results.