Gauge-invariant on-shellZ 2 in QED,QCD and the effective field theory of a static quark期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Gauge-invariant on-shellZ 2 in QED,QCD and the effective field theory of a static quark

Authors:

Affiliation:

1. Physics Department, Open University, MK 7 6AA, Milton Keynes, UK
2. Institut für Physik der Universit?t Mainz, Postfach 3980, W-6500, Mainz, Federal Republic of Germany

Abstract:

We calculate theon-shell fermion wave-function renormalization constantZ₂ of a general gauge theory, to two loops, inD dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ₂/da₀=i(2 pgr

)^–De₀²

d^Dk/k⁴=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension gamma

_F of the fermion field in minimally subtracted QCD, withN_L light-quark flavours, differs from the corresponding anomalous dimension $$tilde gamma _F $$

of the effective field theory of a static quark by the gauge-invariant amount

$begin{gathered} gamma _F - tilde gamma _F equiv mu frac{d}{{dmu }}log left( {frac{{Z_2^{MS} (mu )}}{{tilde Z_2^{MS} (mu )}}} right) hfill = 2frac{{bar alpha _s (mu )}}{pi } + left( {frac{{41}}{4} - frac{{11}}{{18}}N_L } right)frac{{bar alpha _s^2 (mu )}}{{pi ^2 }} + O(bar alpha _s^3 ) hfill end{gathered}$

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