Algebraic reduction of one loop Feynman graph amplitudes

Fleischer, J.; Jegerlehner, F.; Tarasov, O.V.

doi:10.1016/S0550-3213(99)00678-1

Algebraic reduction of one loop Feynman graph amplitudes

J. Fleischer
(
- Bielefeld U.
)
,
F. Jegerlehner
(
- DESY, Zeuthen
)
,
O.V. Tarasov
(
- Bielefeld U. and
- Bern U. and
- DESY, Zeuthen
)

Jul, 1999

17 pages

Published in:

Nucl.Phys.B 566 (2000) 423-440

e-Print:

hep-ph/9907327 [hep-ph]

DOI:

10.1016/S0550-3213(99)00678-1

Report number:

BUTP-99-11,
BI-TP-99-08,
DESY-99-086

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Abstract:

An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic dimension. Also the integration-by-parts method is used to reduce indices (powers of scalar propagators) of the scalar diagrams. The obtained recurrence relations for one-loop integrals are explicitly evaluated for 5- and 6-point functions. In the latter case the corresponding Gram determinant vanishes identically for d=4, which greatly simplifies the application of the recurrence relations.

12.38.Bx
11.15.Bt
Feynman graph: tensor
n-point function
determinant

References(27)

Figures(0)

A Simple formula for reducing Feynman diagrams to scalar integrals

Andrei I. Davydychev
(
- Moscow State U.
)

- Phys.Lett.B 263 (1991) 107-111
•
DOI:
- 10.1016/0370-2693(91)91715-8

- J.Phys.C 10 L257

On Interaction of Color Objects at Large Distances

- Sov.J.Nucl.Phys. 40 (1984) 535,
- Yad.Fiz. 40 (1984) 836-845

Connection between Feynman integrals having different values of the space-time dimension

O.V. Tarasov
(
- DESY, Zeuthen
)

- Phys.Rev.D 54 (1996) 6479-6490
•
e-Print:
- hep-th/9606018
•
DOI:
- 10.1103/PhysRevD.54.6479

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

Hard bremsstrahlung processes at LEP-2

A. Aeppli
(
- Zurich U. and
- Brookhaven
)
,
D. Wyler
(
- Zurich U.
)

- Phys.Lett.B 262 (1991) 125-134
•
DOI:
- 10.1016/0370-2693(91)90655-A

O(alpha) 1-loop radiative corrections to e+ e- --> 4f

A. Vicini
(
- DESY, Zeuthen
)

- Acta Phys.Polon.B 29 (1998) 2847-2855

Analytic properties of npoint loops in perturbation theory

L.M. Brown
(
- Northwestern U.
)

- Nuovo Cim. 22 (1961) 1, 178-182
•
DOI:
- 10.1007/BF02829004

Reduction formula for the five-point function

Francis R. Halpern
(
- UC, San Diego
)

- Phys.Rev.Lett. 10 (1963) 310-312
•
DOI:
- 10.1103/PhysRevLett.10.310

Reduction of a one-loop Feynman diagram with n vertices in m-dimensional Lorentz space

Bengt Petersson
(
- Lund U.
)

- J.Math.Phys. 6 (1965) 1955-1959
•
DOI:
- 10.1063/1.1704747

A Narrow Resonance Model for a Two Current Two Particle Amplitude with Gauge Invariance and Scaling

C.S. Shukre
(
- Bern U.
)

- Nuovo Cim.A 40 (1977) 181-197
•
DOI:
- 10.1007/BF02776785

One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model

G. Passarino
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

- Nucl.Phys.B 160 (1979) 151-207
•
DOI:
- 10.1016/0550-3213(79)90234-7

LARGE LOOP INTEGRALS

W.L. van Neerven
(
- Dortmund U.
)
,
J.A.M. Vermaseren
(
- NIKHEF, Amsterdam
)

- Phys.Lett.B 137 (1984) 241-244
•
DOI:
- 10.1016/0370-2693(84)90237-5

Algebraic Reduction of One Loop Feynman Diagrams to Scalar Integrals

Robin G. Stuart
(
- Munich, Max Planck Inst.
)

- Comput.Phys.Commun. 48 (1988) 367-389,
- COMPUT. PHYS. COMMUN. 48 (1988) 367-389 AND MUENCHEN MPI PHYS. ASTROPHYS. - MPI-PAE-PTH 87-85 (87,REC.DEC.) 38 P. (801760)
•
DOI:
- 10.1016/0010-4655(88)90202-0

Algebraic Reduction of One Loop Feynman Diagrams to Scalar Integrals. 2.

Robin G. Stuart
(
- CINVESTAV, IPN
)
,
A. Gongora-T.
(
- Mexico U.
)

- Comput.Phys.Commun. 56 (1990) 337-350,
- Comput. Phys. Commun. 56 (1990) 337-350 and Mexico Nat. Polytech. Inst. - CINVESTAV-FIS-89-05 (89,rec.Aug.) 15 p. (911712)
•
DOI:
- 10.1016/0010-4655(90)90019-W