scholarly journals Solution of the NLO BFKL Equation and γ*γ* Cross-Section at NLO

2015 ◽  
Vol 37 ◽  
pp. 1560055
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Cross Section ◽  
Operator Product Expansion ◽  
Scattering Amplitude ◽  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Bfkl Equation ◽  
Operator Product ◽  
Scattering Process

The analytic NLO cross section of the γ*γ* scattering process at high-energy is calculated. The result is obtained factorizing the scattering amplitude in rapidity space using the high-energy Operator Product Expansion in terms of composite Wilson line operators. The next-to-leading logarithmic resummation is included employing the solution of the NLO BFKL equation which obtained from the linearization of the evolution in rapidity space of the composite Wilson line operators.

scholarly journals High-energy operator product expansion at sub-eikonal level

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Operator Product Expansion ◽  
Evolution Equations ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Impact Factors ◽  
Operator Product ◽  
The Impact ◽  
New Distribution

Abstract The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

scholarly journals HIGH-ENERGY QCD FACTORIZATION FROM DIS TO pA COLLISIONS

2012 ◽  
Vol 20 ◽  
pp. 200-207 ◽  
Author(s):  
GIOVANNI ANTONIO CHIRILLI
Keyword(s):  
Gluon Distribution ◽  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Distribution Functions ◽  
Operator Product ◽  
Parton Distribution Functions ◽  
Qcd Factorization ◽  
Fragmentation Functions ◽  
Line Operator

The high-energy QCD factorization for Deep Inelastic Scattering and for proton-nucleus collisions using Wilson line formalism and factorization in rapidity is discussed. We show that in DIS the factorization in rapidity reduces to the k T -factorization when the 2-gluon approximation is applied, provided that the composite Wilson line operator is used in the high-energy Operator Product Expansion. We then show that the inclusive forward cross-section in proton-nucleus collisions factorizes in parton distribution functions, fragmentation functions and dipole gluon distribution function at one-loop level.

THE FORWARD PEAK OF ELASTIC HARDON-HADRON SCATTERING AND UNITARITY BOUNDS FOR THE DIFFERENTIAL CROSS-SECTION

1992 ◽  
Vol 07 (21) ◽  
pp. 1905-1913 ◽  
Author(s):  
M. KAWASAKI ◽  
T. MAEHARA ◽  
M. YONEZAWA
Keyword(s):  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Forward Peak ◽  
Forward Scattering Amplitude ◽  
Interaction Radius ◽  
Interaction Range ◽  
Small Momentum

Unitarity bounds for the differential cross-section of high-energy elastic hadron-hadron scattering are obtained under the constraints of fixed total cross-section σt, elasticity x, real part to imaginary part ratio ρ of the forward scattering amplitude, and forward slope b by assuming a finite interaction range. The obtained upper bound has an observed curvature structure at small momentum transfers and is nearly saturated by the experimental data of pp and [Formula: see text] scattering at −t=0−0.3 (GeV/c)2 in the energy region [Formula: see text] , if we take the interaction radius scaled as [Formula: see text].

NLO EVOLUTION OF STRUCTURE FUNCTIONS AT SMALL x

2011 ◽  
Vol 04 ◽  
pp. 46-55
Author(s):  
GIOVANNI ANTONIO CHIRILLI
Keyword(s):  
Impact Factor ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Coordinate Space ◽  
Operator Product ◽  
Leading Order ◽  
Small X ◽  
Evolution Of Structure ◽  
First Time

Using the high-energy Operator Product Expansion of the T-product of two electromagnetic currents, we calculate the Photon Impact Factor for Deep Inelastic Scattering at small value of the Bjorken variable x B at the next-to-leading order (NLO) accuracy in αs. We provide for the first time an analytic expression in coordinate space and in Mellin space of the NLO impact factor for the forward unpolarized structure functions.

EVOLUTION OF CONFORMAL COLOR DIPOLES AND HIGH-ENERGY AMPLITUDES IN $\mathcal{N} = 4$ SYM

2011 ◽  
Vol 04 ◽  
pp. 9-19
Author(s):  
IAN BALITSKY
Keyword(s):  
Perturbation Theory ◽  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Conformal Structure ◽  
Coefficient Function ◽  
Large N ◽  
Energy Behavior ◽  
Regge Limit ◽  
Point Amplitude

The high-energy behavior of the [Formula: see text] SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large Nc, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. [1]. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four Z2 currents in the first two orders in perturbation theory.

AN OPERATOR PRODUCT EXPANSION ANALYSIS OF e+e-ANNIHILATION DATA

2013 ◽  
Vol 28 (25) ◽  
pp. 1360009 ◽  
Author(s):  
HUBERT SPIESBERGER
Keyword(s):  
Quantum Chromodynamics ◽  
Cross Section ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Perturbative Quantum Chromodynamics ◽  
Power Corrections ◽  
Perturbative Quantum ◽  
Vacuum Condensates

Perturbative Quantum Chromodynamics combined with the operator product expansion is expected to provide a framework for the description of phenomena in hadron interactions including contributions of nonperturbative origin. Applied to the correlator of two electromagnetic currents, this framework can be confronted with e+e-annihilation into hadrons. Data from the total hadronic e+e-cross-section have become much more precise in recent years and the power corrections in the operator product expansion, i.e. the vacuum condensates are expected to be determined with higher precision than previously. We present an analysis of the condensates of dimensions d = 2, 4 and 6 and find reasonably stable results, though still within rather large errors. Our results are in agreement with values obtained from τ-decay. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors.

ASYMPTOTIC BEHAVIOR OF PHYSICAL AMPLITUDES IN A FINITE FIELD THEORY

1990 ◽  
Vol 05 (10) ◽  
pp. 1861-1880
Author(s):  
J.A. HELAYËL-NETO ◽  
S. RAJPOOT ◽  
A. WILLIAM SMITH
Keyword(s):  
Cross Section ◽  
Scattering Amplitude ◽  
High Energy ◽  
Energy Limit ◽  
Heavy Particles ◽  
Yang Mills ◽  
Physical Amplitude ◽  
Mass Terms ◽  
Scalar Scattering ◽  
The One

Using the N=4 super Yang-Mills theory softly broken by supersymmetric N=1 mass terms for the matter superfields, we compute the one-loop chiral+chiral→antichiral+antichiral scattering amplitude directly in superspace. By suitable choices of the mass parameters, one can endow the model with a hierarchy of light and heavy particles, and the decoupling of the heavy sector from the light-light physical amplitude is studied. We also analyze the high energy limit of the cross section for a two physical scalar scattering and find a (logs) behavior, which then respects the Froissart bound.

HIGH-ENERGY AMPLITUDES IN ${\cal N}\, = \,4$ SYM IN THE NEXT-TO-LEADING ORDER

2010 ◽  
Vol 25 (02n03) ◽  
pp. 401-410 ◽  
Author(s):  
IAN BALITSKY
Keyword(s):  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Conformal Structure ◽  
Coefficient Function ◽  
Leading Order ◽  
Large N ◽  
Energy Behavior ◽  
Regge Limit ◽  
Point Amplitude

The high-energy behavior of the of [Formula: see text] SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large Nc, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in first two orders in coupling constant : LO BFKL intercept and NLO BFKL calculated in Ref. [1]. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four Z2 currents in the leading and next-to-leading order.

scholarly journals OPE of Green functions of chiral currents

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Operator Product Expansion ◽  
Chiral Limit ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
High Energy Behavior ◽  
Energy Behavior

Abstract In this paper, we investigate the high-energy behavior of two-point and three-point Green functions of the QCD chiral currents and densities using the framework of the operator product expansion in the chiral limit. In detail, we study the contributions of the quark, gluon, quark-gluon and four-quark condensates to all the relevant non-vanishing three-point correlators.

scholarly journals Contribution of QCD condensates to the OPE of Green functions of chiral currents

2019 ◽  
Vol 199 ◽  
pp. 05025
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Perturbation Theory ◽  
Operator Product Expansion ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
Chiral Perturbation ◽  
Unknown Parameters ◽  
Energy Behaviour ◽  
Intrinsic Parity ◽  
Effective Theories

A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.

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