Analytic form of the QCD instanton determinant for small quark mass

Journal Article · Sun Nov 15 04:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.105024· OSTI ID:21313414

Hur, Jin; Lee, Choonkyu; Min, Hyunsoo ^[1]

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1. School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-012 (Korea, Republic of)

We use a novel method to calculate analytically the QCD instanton prefactor due to a quark field carrying a small-mass parameter m. In the SU(2) instanton background of size {rho}, the spinor effective action {gamma}{sup F} (in the minimal subtraction scheme), which gives rise to the prefactor exp(-{gamma}{sup F}), is shown to have the small-m{rho} behavior {gamma}{sup F}=-ln(m/{mu})-ln({mu}{rho})/3 -2{alpha}(1/2)-(m{rho}){sup 2} {l_brace}ln(m{rho}/2)+{gamma}+1/2{r_brace} -2(m{rho}){sup 4}{l_brace}-ln{sup 2}(m{rho})/4 +ln(m{rho})(1/2-{gamma}+ln2)/2 +C{r_brace}+O((m{rho}){sup 6}), where {gamma}=0.577 216..., {alpha}(1/2)=0.145 873..., and our numerically evaluated value for the constant C is C=-0.382 727.... A good agreement between this form and the numerically exact calculation is found if (m{rho}) < or approx. 0.8.

• OSTI ID: 21313414
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CALCULATION METHODS
INSTANTONS
MASS
QUANTUM CHROMODYNAMICS
QUARKS
SU-2 GROUPS