evanberkowitz / hadron_pdfs

Computing Hadronic PDFs with the FH technique.

Hadron_PDFs

Computing Hadronic PDFs with the FH technique.

We aim to compute hadronic parton distribution functions using the Feynman-Hellman technique.

Table of Contents

• Hadron_PDFs
• Table of Contents
• Introduction
• Method
• Code
  • Dependencies
  • Installation
  • Running
• Acknowledgements
• License

Introduction

Parton Distribution Functions, or PDFs, are functions that characterize the inner structure of hadrons, bound states quarks (and antiquarks) in QCD.

Below is a schematic of the correlation functions of interest.

The big black circles are supposed to represent baryons, black line on top an incident electron. The electron talks to valence quarks via photons. When hard enough, processes like this factorize, and we need only to worry about the behavior of the quarks. Here, one quark gets hit by a photon, goes a long for a bit, and emits a photon. Between the two photons we use a Wilson line to transport the quark, rather than letting it propagate according to the Dirac equation. We want to know the value of the matrix element as a function of the length of this Wilson line, the momenta injected at the electromagnetic interactions, and the asymptotic particle momentum.

Method

The Feynman-Hellman (FH) method is a technique for measuring hadronic matrix elements, normally requiring a three-point function, into a two-point function which can be analyzed with familiar effective-mass techniques. Here we apply this technique to PDFs.

The FH method works by computing sequential or Feynman-Hellman propagators---applying an operator to an already-computed propagator, and then using the result as a source for another propagator.

Here, the operator we apply is: injecting a given momentum, transporting a quark along a (spatial) path via the gauge links, and then emitting a (possibly-different) momentum.

Code

Dependencies

Hadron_PDFs is built on top of the USQCD software stack. In particular, it requires QMP, QDP++ with HDF5, and Chroma.

Installation

• Install the USQCD software stack.
• Construct a Makefile. The .gitignore automatically ignores Makefile; instead, write one in the Makefiles folder and symbolically link to it. Makefiles/mac provides what is needed, though your compiler and environment description needs to be customized, and the paths to the dependencies are needed in the DIR_* variables.
• make Hadron_PDFs.x

Running

Built on top of chroma, Hadron_PDFs.x needs a -i input_file argument. An example input file is provided.

Comments

When sensible, I've liberally sprinked comments into the code so that it's clear exactly what I'm doing. This includes drawing ASCII pictures, writing lots of comments for 2 lines of code, and the like.

Acknowledgements

This software was developed by Evan Berkowitz, Xiaonu Xiong, and Tom Luu at Forschungszentrum Jülich.

License

TBD.