Divergences in the quark number susceptibility: The origin and a cure

Rajiv V. Gavai (Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India) ; Sayantan Sharma (Fakultät für Physik, Universität Bielefeld, Bielefeld, D-33615, Germany)

Quark number susceptibility on the lattice, obtained by merely adding a μN term with μ as the chemical potential and N as the conserved quark number, has a quadratic divergence in the cut-off a . We show that such a divergence already exists for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory.

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      "value": "Quark number susceptibility on the lattice, obtained by merely adding a \u03bcN term with \u03bc as the chemical potential and N as the conserved quark number, has a quadratic divergence in the cut-off a . We show that such a divergence already exists for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory."
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Published on:
21 July 2015
Publisher:
Elsevier
Published in:
Physics Letters B (2015)

DOI:
https://doi.org/10.1016/j.physletb.2015.07.036
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: