scholarly journals EVOLUTION OF TRANSVERSE-DISTANCE DEPENDENT PARTON DENSITIES AT LARGE-XB AND GEOMETRY OF THE LOOP SPACE

2014 ◽  
Vol 25 ◽  
pp. 1460006 ◽  
Author(s):  
IGOR O. CHEREDNIKOV ◽  
TOM MERTENS ◽  
PIETER TAELS ◽  
FREDERIK F. VAN DER VEKEN
Keyword(s):  
Loop Space ◽  
Wilson Loop ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Renormalization Group Equation ◽  
Distribution Functions ◽  
Group Equation ◽  
Parton Distribution Functions ◽  
Factorization Scheme ◽  
Transverse Distance

We discuss possible applications of the equations of motion in the generalized Wilson loop space to the phenomenology of the three-dimensional parton distribution functions in the large-xB approximation. This regime is relevant for future experimental programs to be launched at the (approved) Jefferson Lab 12 GeV upgrade and the (planned) Electron-Ion Collider. We show that the geometrical evolution of the Wilson loops corresponds to the combined rapidity and renormalization-group equation of the transverse-distance dependent parton densities in the large-xB factorization scheme.

scholarly journals One-loop matching for spin-dependent quasi-TMDs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Stella T. Schindler ◽  
Iain W. Stewart ◽  
Yong Zhao
Keyword(s):  
Spin Structure ◽  
Wilson Line ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Longitudinal Momentum ◽  
Loop Order ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Unique Probe ◽  
Transverse Position

Abstract Transverse momentum dependent parton distribution functions (TMDPDFs) provide a unique probe of the three-dimensional spin structure of hadrons. We construct spin-dependent quasi-TMDPDFs that are amenable to lattice QCD calculations and that can be used to determine spin-dependent TMDPDFs. We calculate the short-distance coefficients connecting spin-dependent TMDPDFs and quasi-TMDPDFs at one-loop order. We find that the helicity and transversity distributions have the same coefficient as the unpolarized TMDPDF. We also argue that the same is true for pretzelosity and that this spin universality of the matching will hold to all orders in αs. Thus, it is possible to calculate ratios of these distributions as a function of longitudinal momentum and transverse position utilizing simpler Wilson line paths than have previously been considered.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

The renormalization group equation for the Wilson loop

1981 ◽  
Vol 103 (4-5) ◽  
pp. 365-368 ◽  
Author(s):  
Alan J. McKane ◽  
Michael Stone
Keyword(s):  
Renormalization Group ◽  
Wilson Loop ◽  
Renormalization Group Equation ◽  
Group Equation

scholarly journals Spin Structure Functions of the Nucleon and Twist-3 Operators in QCD

1997 ◽  
Vol 50 (1) ◽  
pp. 79 ◽  
Author(s):  
Kazuhiro Tanaka
Keyword(s):  
Spin Structure ◽  
Unique Feature ◽  
Anomalous Dimension ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
View Point ◽  
Loop Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
The One

We investigate the twist-3 spin-dependent parton distribution functions hL(x; Q2) and gT (x; Q2). We discuss the physical relevance of the parton distributions from the view point of the factorization theorem in QCD. A unique feature of the ‘measurable’ higher-twist distributions hL and gT is emphasized. We investigate the Q2 -evolution of hL and gT in the framework of the renormalization group and standard QCD perturbation theory. We calculate the anomalous dimension matrix for the twist-3 operators for hL and gT in the one-loop order. The operator mixing among the relevant twist-3 operators, including the operators proportional to the QCD equations of motion, is treated properly in a consistent scheme. Implications for future experiments are also discussed.

scholarly journals Can $$ \overline{\mathrm{MS}} $$ parton distributions be negative?

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alessandro Candido ◽  
Stefano Forte ◽  
Felix Hekhorn
Keyword(s):  
Strong Coupling ◽  
Cross Sections ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Factorization Scheme ◽  
Perturbative Regime

Abstract It is common lore that Parton Distribution Functions (PDFs) in the $$ \overline{\mathrm{MS}} $$ MS ¯ factorization scheme can become negative beyond leading order due to the collinear subtraction which is needed in order to define partonic cross sections. We show that this is in fact not the case and next-to-leading order (NLO) $$ \overline{\mathrm{MS}} $$ MS ¯ PDFs are actually positive in the perturbative regime. In order to prove this, we modify the subtraction prescription, and perform the collinear subtraction in such a way that partonic cross sections remain positive. This defines a factorization scheme in which PDFs are positive. We then show that positivity of the PDFs is preserved when transforming from this scheme to $$ \overline{\mathrm{MS}} $$ MS ¯ , provided only the strong coupling is in the perturbative regime, such that the NLO scheme change is smaller than the LO term.

scholarly journals Generalized Loop Space and Evolution of the Light-Like Wilson Loops

2015 ◽  
Vol 37 ◽  
pp. 1560028
Author(s):  
Igor O. Cherednikov ◽  
Tom Mertens
Keyword(s):  
Loop Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Wilson Loops ◽  
Conformal Invariant ◽  
Gauge Invariant ◽  
Geometrical Properties ◽  
Group Behaviour ◽  
Non Local ◽  
Invariant Quantum

Equations of motion for the light-like QCD Wilson loops are studied in the generalized loop space (GLS) setting. To this end, the classically conformal-invariant non-local variations of the cusped Wilson exponentials lying (partially) on the light-cone are formulated in terms of the Fréchet derivative. The rapidity and renormalization-group behaviour of the gauge-invariant quantum correlation functions (in particular, the three-dimensional parton densities) are demonstrated to be connected to certain geometrical properties of the Wilson loops defined in the GLS.

DIMENSIONAL REDUCTION AND THE NON-TRIVIALITY OF λϕ4 IN FOUR DIMENSIONS AT HIGH TEMPERATURE

1993 ◽  
Vol 08 (19) ◽  
pp. 1779-1793 ◽  
Author(s):  
DENJOE O’CONNOR ◽  
C.R. STEPHENS ◽  
F. FREIRE
Keyword(s):  
High Temperature ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Infinite Temperature ◽  
Second Order Phase Transition

λϕ4 theory in four dimensions is shown perturbatively to have a non-trivial fixed point at finite temperature, the relevant anomalous dimensions at the second order phase transition being the three-dimensional ones. We emphasize the importance of having renormalization schemes and a renormalization group equation that can explicitly take into account the fact that the degrees of freedom of a theory may be qualitatively different at different scales. By applying such considerations to finite temperature λϕ4 where the low temperature degrees of freedom are effectively four-dimensional and the high temperature ones three-dimensional we are able to follow perturbatively the theory from zero to infinite temperature.

scholarly journals LOOP SPACE AND EVOLUTION OF THE LIGHT-LIKE WILSON POLYGONS

2012 ◽  
Vol 20 ◽  
pp. 109-117 ◽  
Author(s):  
I. O. CHEREDNIKOV ◽  
T. MERTENS ◽  
F. F. VAN DER VEKEN
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Loop Space ◽  
Degrees Of Freedom ◽  
Distribution Functions ◽  
Energy Evolution ◽  
Parton Distribution Functions ◽  
Gauge Invariant ◽  
Transverse Momentum Dependent ◽  
Quantum Dynamical

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.

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