scholarly journals High-energy asymptotic behavior of the S matrix in the saturation region with the smallest dipole running coupling prescription

2020 ◽  
Vol 101 (7) ◽  
Author(s):  
Wenchang Xiang ◽  
Yanbing Cai ◽  
Mengliang Wang ◽  
Daicui Zhou
Keyword(s):  
Asymptotic Behavior ◽  
High Energy ◽  
Running Coupling ◽  
Saturation Region ◽  
S Matrix

scholarly journals Relative entropy in scattering and the S-matrix bootstrap

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Anjishnu Bose ◽  
Parthiv Haldar ◽  
Aninda Sinha ◽  
Pritish Sinha ◽  
Shaswat Tiwari
Keyword(s):  
Relative Entropy ◽  
Cross Sections ◽  
High Energy ◽  
Quantum Field Theories ◽  
Superstring Theory ◽  
Information Theoretic ◽  
Pion Scattering ◽  
S Matrix ◽  
Information Theoretic Measures ◽  
Scattering Lengths

We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include \phi^4ϕ4 theory, chiral perturbation theory (\chi PTχPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In \chi PTχPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the \rhoρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop \chi PTχPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin.

scholarly journals High-energy QCD asymptotic behavior of photon-photon collisions

JETP Letters ◽  
2002 ◽  
Vol 76 (5) ◽  
pp. 249-252 ◽  
Author(s):  
S. J. Brodsky ◽  
V. S. Fadin ◽  
V. T. Kim ◽  
L. N. Lipatov ◽  
G. B. Pivovarov
Keyword(s):  
Asymptotic Behavior ◽  
High Energy

scholarly journals On systematic effects in the numerical solutions of the JIMWLK equation

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Salvatore Calì ◽  
Krzysztof Cichy ◽  
Piotr Korcyl ◽  
Piotr Kotko ◽  
Krzysztof Kutak ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
High Energy ◽  
Gluon Density ◽  
Longitudinal Momentum ◽  
Coupling Constant ◽  
Longitudinal Momentum Fraction ◽  
Running Coupling ◽  
Systematic Effects ◽  
Gluon Distributions ◽  
Comprehensive Study

AbstractIn the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian–Marian–Iancu–McLerran–Weigert–Leonidov–Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: “square root” and “noise” prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases.

scholarly journals ANALYTIC INVARIANT CHARGE AND THE LATTICE STATIC QUARK–ANTIQUARK POTENTIAL

2004 ◽  
Vol 19 (21) ◽  
pp. 3471-3480 ◽  
Author(s):  
A. V. NESTERENKO
Keyword(s):  
Asymptotic Behavior ◽  
High Accuracy ◽  
Lattice Data ◽  
Lattice Simulation ◽  
Simulation Data ◽  
Running Coupling ◽  
The One ◽  
Static Quark ◽  
Analytic Invariant ◽  
Good Agreement

A recently developed model for the QCD analytic invariant charge is compared with quenched lattice simulation data on the static quark–antiquark potential. By employing this strong running coupling one is able to obtain the confining quark–antiquark potential in the framework of the one-gluon exchange model. To achieve this objective a technique for evaluating the integrals of a required form is developed. Special attention is paid here to removing the divergences encountered the calculations. All this enables one to examine the asymptotic behavior of the potential at both small and large distances with high accuracy. An explicit expression for the quark–antiquark potential, which interpolates between these asymptotics, and satisfies the concavity condition, is proposed. The derived potential coincides with the perturbative results at small distances, and it is in a good agreement with the lattice data in the nonperturbative physically-relevant region. An estimation of the parameter Λ QCD is obtained for the case of pure gluodynamics. It is found to be consistent with all the previous estimations of Λ QCD in the framework of approach in hand.

ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD I: THE SUPER-CRITICAL POMERON

1991 ◽  
Vol 06 (11) ◽  
pp. 1859-1959 ◽  
Author(s):  
ALAN R. WHITE
Keyword(s):  
Field Theory ◽  
Matrix Theory ◽  
Spectral Component ◽  
High Energy ◽  
Vector Particle ◽  
Regge Theory ◽  
Regge Behavior ◽  
Energy Behavior ◽  
S Matrix ◽  
Full Structure

The formalism of analytic multi-Regge theory is developed as a basis for the study of abstract critical and super-critical pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of field theory and S-matrix theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexagraphs. Further consequences are distinct Sommerfeld-Watson representations for each hexagraph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of “reggeon unitarity” the critical pomeron solution of the reggeon field theory gives the only known “non-trivial” unitary high-energy S-matrix. By exploiting the full structure of multi-Regge amplitudes as the pomeron becomes super-critical, one can study the simultaneous modification of hadrons and the pomeron. The result is a completely consistent description of the super-critical pomeron appearing in hadron scattering. Reggeon unitarity is satisfied in the super-critical phase by the appearance of a massive “gluon” (Reggeized vector particle) coupling pair-wise to the pomeron.

scholarly journals Running coupling corrections to high energy inclusive gluon production

2011 ◽  
Vol 849 (1) ◽  
pp. 72-97 ◽  
Author(s):  
W.A. Horowitz ◽  
Yuri V. Kovchegov
Keyword(s):  
High Energy ◽  
Running Coupling ◽  
Gluon Production
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