scholarly journals Fragmentation function of g → $$ Q\overline{Q} $$(3$$ {S}_1^{\left[8\right]} $$) in soft gluon factorization and threshold resummation

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
An-Ping Chen ◽  
Xiao-Bo Jin ◽  
Yan-Qing Ma ◽  
Ce Meng
Keyword(s):  
Fragmentation Function ◽  
Short Distance ◽  
Phenomenological Study ◽  
Renormalization Group Equation ◽  
Soft Gluon ◽  
Group Equation ◽  
Hard Part ◽  
Threshold Resummation ◽  
Color Octet ◽  
Gluon Fragmentation

Abstract We study the fragmentation function of the gluon to color-octet 3S1 heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet 3S1 soft gluon distribution (SGD). The short distance hard part is calculated to the next-to-leading order in αs and all orders in velocity expansion. By deriving and solving the renormalization group equation of the SGD, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.

scholarly journals NEXT-TO-LEADING ORDER CALCULATION OF THE COLOR-OCTET 3S1 GLUON FRAGMENTATION FUNCTION FOR HEAVY QUARKONIUM

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 229-231
Author(s):  
JUNGIL LEE
Keyword(s):  
Fragmentation Function ◽  
Short Distance ◽  
Feynman Diagrams ◽  
Heavy Quarkonium ◽  
Leading Order ◽  
Light Cone Gauge ◽  
Color Octet ◽  
Feynman Gauge ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

Next-to-leading order corrections to fragmentation functions in a light-cone gauge are discussed. This gauge simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. As an application, the short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are re-calculated to order [Formula: see text]. We show that the ill-defined spurious poles cancel and the appropriate prescriptions for the remaining spurious poles can be determined by calculating a subset of the diagrams in the Feynman gauge. Our answer agrees with the recent calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation.

scholarly journals Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

2009 ◽  
Vol 324 (2) ◽  
pp. 414-469 ◽  
Author(s):  
Alessandro Codello ◽  
Roberto Percacci ◽  
Christoph Rahmede
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals The framed Standard Model (II) — A first test against experiment

2015 ◽  
Vol 30 (30) ◽  
pp. 1530060
Author(s):  
Hong-Mo Chan ◽  
Sheung Tsun Tsou
Keyword(s):  
Standard Model ◽  
Renormalization Group Equation ◽  
Fermion Mass ◽  
Group Equation ◽  
Unknown Parameters ◽  
Mass Matrices ◽  
The Standard Model ◽  
Experimental Values ◽  
The Masses ◽  
Independent Parameters

Apart from the qualitative features described in Paper I (Ref. 1), the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] all of which are known, except for [Formula: see text]. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses [Formula: see text], [Formula: see text], [Formula: see text], the CKM elements [Formula: see text], [Formula: see text], and the neutrino oscillation angle [Formula: see text], one can then calculate and compare with experiment the following 12 other quantities [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

scholarly journals EFFECTIVE AVERAGE ACTION IN STATISTICAL PHYSICS AND QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1951-1982 ◽  
Author(s):  
CHRISTOF WETTERICH
Keyword(s):  
Field Theory ◽  
Statistical Physics ◽  
Thermal Fluctuations ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Four Dimensions ◽  
Average Action ◽  
Exact Renormalization Group ◽  
Unified Description

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

scholarly journals NLO QCD corrections to gluon fragmentation function into η and η based on the Suzuki's model

2020 ◽  
Vol 956 ◽  
pp. 115036 ◽  
Author(s):  
S. Mohammad Moosavi Nejad ◽  
Maryam Roknabady ◽  
Mahdi Delpasand
Keyword(s):  
Fragmentation Function ◽  
Gluon Fragmentation
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