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What does "light cone distribution" mean in QCD?

+ 3 like - 0 dislike
1038 views

I read that term in a paper recently and I wonder what it means. What's the difference between a normal distribution?

asked Oct 2, 2014 in Theoretical Physics by anonymous [ no revision ]

I think it means parton distribution function in a light cone frame, it has nothing to do with "normal distribution" in statistics, it's asking what the cross section for a particular perturbative QCD scattering will be if you smack together two protons. There are parton distribution functions that tell you the likelihood of a parton carrying a fraction of the momentum of the proton hitting another parton on the other proton. I'm not sure this is what is meant here, because you didn't link the paper.

1 Answer

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Without a specific reference it is difficult to determine the exact context the author meant with the phrase "light cone distribution".  However, since you mention QCD, it is worth discussing what it likely meant. 

The light-cone quantization of quantum chromodynamics [1] was developed in 1991 by Stanley Brodsky and Hans-Christian Pauli.  In that paper they contrast time-ordered perturbation theory (TOPTH) with light-cone perturbation theory (LCPTH).  The advantage of using LCPTH is that it eliminates the need for vacuum creation graphs in perturbative calculations.  Specifically,

In TOPTH, all intermediate states contribute to the total amplitude as long as three-momentum is conserved... The existence of vacuum creation and annihilation
graphs implies that one cannot even compute any current matrix element without
considering the effect of the currents arising from pair production from the
vacuum.

The light cone approach allows for calculation of interaction cross sections and jet distributions,

One of the most interesting applications of LCPTH would be the perturbative
calculation of the annihilation cross section \(R_{e^+e^-} \), since one would automatically
calculate, to the same order in perturbation theory, the quark and gluon jet distributions
appearing in the final state.

The light cone approach is sufficiently suitable for calculations that there is an organization which promotes its use in physics called the International Light Cone Advisory Committee (ILCAC) [2]. In its most modern form, the use of LCPTH is now referred to as Light Front Quantum Chromodynamics (LFQCD) [3].

So in answer to the question, the light cone distribution derived from LCPTH is not contrasted with the normal distribution, but with something one might call the time ordered distribution derived from TOPTH.

[1] Brodsky, S., Pauli, H.C., (1991) Light-Cone Quantization of Quantum Chromodymanics, SLAC-PUB-5558, http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-5558.pdf

[2] International Light Cone Advisory Committee, http://www.ilcacinc.org/

[3] Bakker et. al. (2013), Light Front Quantum Chromodynamics, SLAC-PUB-15745, JLAB-THY-13-1804, http://www.ilcacinc.org/ILCAC-WP-FINAL-201309.pdf

answered Nov 15, 2014 by Username (140 points) [ revision history ]
edited Nov 16, 2014 by Arnold Neumaier

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