# QCD evolution with longitudinal fields and heavy quarks

Source: [QCD evolution with longitudinal fields and heavy quarks](<https://www.sota2.com/research/paper/68fa343d1e209131ce897224>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:32:22.295Z

Authors: A.Makhlin, E. Surdutovich

Published: 1996-10-31T22:27:26.000Z

## Abstract

QCD evolution equations that naturally include longitudinal (non-propagating) fields and heavy quarks are derived. We start with the integral equations of quantum field kinetics and obtain the master equations, similar to DGLAP evolution equations after several consecutive approximations. We demonstrate that in their primary form, the evolution equations include a new element, feed-back via longitudinal fields, leading to a low-x enhancement in the e-p DIS cross section. We show that the structure function F\_L is very sensitive to the dynamics of the longitudinal fields and that the heavy quarks in evolution equations make this effect even more pronounced.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-ph/9610554>)

[PDF](<https://arxiv.org/pdf/hep-ph/9610554.pdf>)