Matching QCD and heavy-quark effective theory heavy-light currents at two loops and beyond

Broadhurst, David J.; Grozin, A.G.

doi:10.1103/PhysRevD.52.4082

Matching QCD and heavy-quark effective theory heavy-light currents at two loops and beyond

David J. Broadhurst
(
- Open U., England
)
,
A.G. Grozin
(
- Open U., England
)

Oct, 1994

25 pages

Published in:

Phys.Rev.D 52 (1995) 4082-4098

e-Print:

hep-ph/9410240 [hep-ph]

DOI:

10.1103/PhysRevD.52.4082

Report number:

OUT-4102-52

View in:

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Abstract:

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in

1/m

. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current

\bar{q}\gamma~{[\mu_1}\ldots\gamma~{\mu_n]}q

is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on

\gamma_5

prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in

f_{{\rm B}~*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}~2/\pi~2 +{\rm O}(\alpha_{\rm s}~3,1/m_b)

is

K_b=\frac{83}{12}+\frac{4}{81}\pi~2+\frac{2}{27}\pi~2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c

with

N_l=4

light flavours, and a correction,

\Delta_c=0.18\pm0.01

, that takes account of the non--zero ratio

m_c/m_b=0.28\pm0.03

. Fastest apparent convergence would entail

\alpha_{\rm s}(\mu)

at

\mu=370

MeV. ``Naive non--abelianization'' of large--

N_l

results, via

N_l\to N_l-\frac{33}{2}

, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large

\beta_0=11-\frac23N_l

. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.

quark: current
quark: flavor
quark: mass
mass: quark
expansion: mass
mass: expansion
renormalization
quantum chromodynamics
HQET model
correction: higher-order

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