Effect of m(c) on b quark chromomagnetic interaction and on-shell two loop integrals with two masses

The effect of non-zero c quark mass on b quark HQET Lagrangian, up to 1/m_b level, is calculated at two loops. The results are expressed in terms of dilogarithmic functions of m_c/m_b. This calculation involves on-shell two-loop propagator-type diagrams with two different masses, m_b and m_c. A general algorithm for reducing such Feynman integrals to the basis of two nontrivial and two trivial integrals is constructed.

HQET model
quantum chromodynamics: magnetic moment
bottom
charm
quark: mass
Feynman graph: higher-order
propagator
mass ratio: (beauty charm)
bibliography

References(44)

Figures(0)

Regularization and Renormalization of Gauge Fields

Gerard 't Hooft
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

- Nucl.Phys.B 44 (1972) 189-213,
- Also in *Lai, C. H. ( Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 322-346
•
DOI:
- 10.1016/0550-3213(72)90279-9

Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter

C.G. Bollini
(
- La Plata U.
)
,
J.J. Giambiagi
(
- La Plata U.
)

- Nuovo Cim.B 12 (1972) 20-26,
- Also in *Mohapatra, R. N. (ed.), Lai, C. H. (ed.): Gauge Theories Of Fundamental Interactions*, 259-264
•
DOI:
- 10.1007/BF02895558

A Method of Gauge Invariant Regularization

J.F. Ashmore
(
- ICTP, Trieste
)

- Lett.Nuovo Cim. 4 (1972) 289-290,
- Also in *Mohapatra, R. N. (ed.), Lai, C. H. (ed.): Gauge Theories Of Fundamental Interactions*, 265-266
•
DOI:
- 10.1007/BF02824407

Analytic renormalization via continuous space dimension

G.M. Cicuta
(
- Milan U. and
- INFN, Milan
)
,
E. Montaldi
(
- Milan U. and
- INFN, Milan
)

- Lett.Nuovo Cim. 4 (1972) 329-332
•
DOI:
- 10.1007/BF02756527

- Phys.Lett. 20 682

Three Loop Relation of Quark (Modified) Ms and Pole Masses

N. Gray
(
- Open U., England
)
,
David J. Broadhurst
(
- Open U., England
)
,
W. Grafe
(
- Mainz U., Inst. Phys.
)
,
K. Schilcher
(
- Mainz U., Inst. Phys.
)

- Z.Phys.C 48 (1990) 673-680
•
DOI:
- 10.1007/BF01614703

Gauge invariant on-shell Z(2) in QED, QCD and the effective field theory of a static quark

David J. Broadhurst
(
- Open U., England
)
,
N. Gray
(
- Open U., England
)
,
K. Schilcher
(
- Mainz U., Inst. Phys.
)

- Z.Phys.C 52 (1991) 111-122
•
DOI:
- 10.1007/BF01412333

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
)

- Phys.Rev.D 52 (1995) 4082-4098
•
e-Print:
- hep-ph/9410240
•
DOI:
- 10.1103/PhysRevD.52.4082

Two loop QCD corrections to b ---> c transitions at zero recoil: Analytical results

- Nucl.Phys.B 505 (1997) 65-83
•
e-Print:
- hep-ph/9703277
•
DOI:
- 10.1016/S0550-3213(97)00500-2

O(alpha-s**2) corrections to b ---> c decay at zero recoil

J. Franzkowski
(
- Mainz U., Inst. Phys.
)
,
J.B. Tausk
(
- Freiburg U.
)

- Eur.Phys.J.C 5 (1998) 517-524
•
e-Print:
- hep-ph/9712205
•
DOI:
- 10.1007/s100520050296

Threshold and pseudothreshold values of the sunset diagram

Frits A. Berends
(
- Leiden U.
)
,
Andrei I. Davydychev
(
- Leiden U. and
- Moscow State U.
)
,
N.I. Ussyukina
(
- Moscow State U.
)

- Phys.Lett.B 426 (1998) 95-104
•
e-Print:
- hep-ph/9712209
•
DOI:
- 10.1016/S0370-2693(98)00166-X

Threshold behavior of Feynman diagrams: The Master two loop propagator

- Phys.Lett.B 394 (1997) 211-217
•
e-Print:
- hep-ph/9608407
•
DOI:
- 10.1016/S0370-2693(96)01698-X

Pole masses of quarks in dimensional reduction

L.V. Avdeev
(
- Dubna, JINR
)
,
M.Yu. Kalmykov
(
- Dubna, JINR
)

- Nucl.Phys.B 502 (1997) 419-435
•
e-Print:
- hep-ph/9701308
•
DOI:
- 10.1016/S0550-3213(97)00404-5

A theorem on analytical calculability of 4-loop renormalization group functions

F.V. Tkachov
(
- Moscow, INR
)

- Phys.Lett.B 100 (1981) 65-68
•
DOI:
- 10.1016/0370-2693(81)90288-4

Integration by parts: The algorithm to calculate $\beta$ -functions in 4 loops

K.G. Chetyrkin
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Nucl.Phys.B 192 (1981) 159-204,
- Nucl. Phys. B192 ( 1981) 159-204
•
DOI:
- 10.1016/0550-3213(81)90199-1

Three loop on-shell charge renormalization without integration: Lambda-MS (QED) to four loops

David J. Broadhurst
(
- Open U., England
)

- Z.Phys.C 54 (1992) 599-606
•
DOI:
- 10.1007/BF01559486

Gauge invariant on-shell Z(1) in QED and QCD

J. Fleischer
(
- Bielefeld U.
)
,
O.V. Tarasov
(
- Bielefeld U.
)

- Phys.Lett.B 283 (1992) 129-134
•
DOI:
- 10.1016/0370-2693(92)91442-C

SHELL2: Package for the calculation of two loop on-shell Feynman diagrams in FORM

J. Fleischer
(
- Bielefeld U.
)
,
O.V. Tarasov
(
- Bielefeld U.
)

- Comput.Phys.Commun. 71 (1992) 193-205,
- Comput. Phys. Commun. 71 (1992) 193-205 and Bielefeld Univ. - BI-TP-91-42 (91/12,rec.Jan.92) 15 p
•
DOI:
- 10.1016/0010-4655(92)90083-B