Progress on Perturbative Matching Calculations for
the Charm Quark Mass using the HISQ Action
Emel Dalgic∗ ab, Kit Wongc, Christine Daviesc, Eduardo Follanad,Alistair Harte,Ron
Horganf, Peter Lepageg, Quentin Masonf, Junko Shigemitsud, Howard Trottieraand
aSimon Fraser University, Burnaby BC, Canada V5A 1S6
bTRIUMF, Vancouver BC, Canada V6T 2A3
cUniversity of Glasgow, Glasgow, UK G12 8QQ
dThe Ohio State University, Columbus OH, USA 43210
eUniversity of Edinburgh, Edinburgh, UK EH9 3JZ
fUniversity of Cambridge, Cambridge, UK CB3 0HE
gCornell University, Ithaca NY, USA 14853
E-mail: email@example.com, firstname.lastname@example.org,
email@example.com, R.R.Horgan@damtp.cam.ac.uk ,
The highly-improvedstaggeredquark(HISQ)action is the most accurate discretizationscheme to
date for the charm quark. Here we report on the progress of perturbative matching for the quark
mass using the HISQ action. The matching is done through O(α2
Carlo simulations at weak coupling and diagrammatic perturbation theory. When combined with
on-going simulation efforts using the HISQ action, a determination of the charm quark mass to a
few percent accuracy can be achieved. Of particular interest will be a comparison with the recent
sum rule determination of the charm mass due to Kühn et al. .
s) using a combination of Monte
The XXV International Symposium on Lattice Field Theory
July 30-4 August 2007
c ? Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence.
Charm Mass with HISQ
Figure 8: Convolution of two operators for two gluons.
to the pieces in all possible ways. Fig. 8 is a simple illustration with two operators and two gluons.
Once we perform the convolutions and reunitarize, we obtain an improved link variable. We need
to fatten this yet again. We therefore repeat the same process of convoluting, this time with the
already fattened and reunitarized link, to obtain the full HISQ vertices.
Our project involves performing perturbative matching calculations to find mcthrough O(α2
using the HISQ quark action. To achieve this, work is underway to do the fermionic part of the
calculation diagrammatically, while the gluonic part is computed using the weak coupling Monte
Carlo method. When both calculations are complete, the results will be combined to obtain per-
turbative coefficients for the mCmass renormalization. Our initial tests show that perturbative
coefficients can be obtained accurately using the weak coupling Monte Carlo method. For the
longer term goal of doing the entire calculation diagrammatically, the vertex functions necessary
to achieve this aim have been prepared.
 J.H. Kühn et al., arXiv:hep-ph/0702103v1.
 E. Follana et al., Phys.Rev.D75, 054502 (2007).
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 M. Göckeler et al., PoS LAT2005, 078 (2006).
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 W. M. Yao et al., J. Phys. G33, 1 (2006).
 C. Davies et al., PoS LAT2006, 082 (2006).
 Q. Mason et al., HPQCD Collaboration, Phys. Rev. Lett. 95, 052002 (2005).
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