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Higher order perturbative corrections to b ---> c transitions at zero recoil

Matthias Neubert
(
- CERN
)

Sep, 1994

9 pages

Published in:

Phys.Lett.B 341 (1995) 367-371

e-Print:

hep-ph/9409453 [hep-ph]

DOI:

Report number:

CERN-TH-7454-94

View in:

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Abstract:

We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents

\bar c\,\gamma~\mu b

and

\bar c\,\gamma~\mu\gamma_5\,b

by calculating the terms of order

n_f\,\alpha_s~2

and substituting the dependence on the number of flavours by the first coefficient of the

\beta

-function. Both for vector and axial vector currents, we find moderate two-loop corrections below 1\% in magnitude. Using the Brodsky--Lepage--Mackenzie prescription to set the scale in the order-

\alpha_s

corrections in the

\overline{\rm MS}

scheme, we obtain

\mu_V\simeq 0.92\sqrt{m_b m_c}

and

\mu_A\simeq 0.51\sqrt{m_b m_c}

in the two cases. These scales are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of

|\,V_{cb}|

are briefly discussed.

anti-B: semileptonic decay
semileptonic decay: anti-B
D*(2010)
bottom
charm
current: flavor changing
current: vector
current: axial-vector
HQET model
correction: mass

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