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Setting Limits on Supersymmetry Using Simplified Models
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Published on: November 15, 2013

Total nucleon-nucleon cross section at large N(c).

Thomas D Cohen1

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. cohen@physics.umd.edu

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

At high energies and large N(c) (number of colors), the total nucleon-nucleon cross section becomes constant. This finding relates to the Froissart-Martin bound in quantum chromodynamics (QCD).

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Area of Science:

  • High-energy particle physics
  • Quantum Chromodynamics (QCD)
  • Nuclear physics

Background:

  • The behavior of total nucleon-nucleon cross sections at high energies is a fundamental question in particle and nuclear physics.
  • Understanding these cross sections provides insights into the strong force and the structure of hadrons.
  • Previous studies have explored various models to describe high-energy scattering, but a definitive result in the large N(c) limit was lacking.

Purpose of the Study:

  • To investigate the behavior of the total nucleon-nucleon cross section in the limit of a large number of colors (N(c)).
  • To determine if the cross section becomes independent of incident momentum at high energies and large N(c).
  • To explore the connection between this large N(c) result and established theoretical bounds like the Froissart-Martin bound.

Main Methods:

  • Analysis within the framework of Quantum Chromodynamics (QCD) in the limit of large N(c).
  • Calculation of the total nucleon-nucleon cross section for incident momenta significantly larger than the QCD scale.
  • Asymptotic analysis of the cross section in the extreme large N(c) regime (log(N(c))>>1).

Main Results:

  • The total nucleon-nucleon cross section becomes independent of incident momentum at sufficiently large N(c) and high energies.
  • The constant cross section is given by the formula σ(total)=2πlog(2)(N(c))/(m(π)(2)).
  • Corrections to this result are of the order log(log(N(c)))/log(N(c)).

Conclusions:

  • The study demonstrates a significant simplification of the total nucleon-nucleon cross section in the large N(c) limit.
  • The derived constant cross section provides a new perspective on high-energy scattering in QCD.
  • The findings suggest a potential link to the Froissart-Martin bound, warranting further investigation.