Calculation of infrared divergent Feynman diagrams with zero mass threshold

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with zero mass thresholds is applied. On the other hand, a numerical method based on a two-fold integral representation is used. The application of the latter method is possible by using lightcone coordinates in the parallel space. The numerical data obtained with the two methods are in impressive agreement.

Feynman graph: higher-order
infrared problem
threshold: massless
expansion: momentum
regularization: dimensional
numerical calculations
tables

References(22)

Figures(7)

Calculation of Feynman diagrams from their small momentum expansion

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

- Z.Phys.C 64 (1994) 413-426
•
e-Print:
- hep-ph/9403230
•
DOI:
- 10.1007/BF01560102

Calculation of Feynman diagrams with zero mass threshold from their small momentum expansion

J. Fleischer
(
- Bielefeld U.
)
,
Vladimir A. Smirnov
(
- Moscow State U.
)
,
O.V. Tarasov
(
- Bielefeld U.
)

- Z.Phys.C 74 (1997) 379-386
•
e-Print:
- hep-ph/9605392
•
DOI:
- 10.1007/s002880050400

New representation of two loop propagator and vertex functions

Andrzej Czarnecki
(
- Mainz U., Inst. Phys.
)
,
Ulrich Kilian
(
- Mainz U., Inst. Phys.
)
,
Dirk Kreimer
(
- Tasmania U.
)

- Nucl.Phys.B 433 (1995) 259-275
•
e-Print:
- hep-ph/9405423
•
DOI:
- 10.1016/0550-3213(94)00455-N

Heavy Higgs lifetime at two loops

A. Frink
(
- Mainz U., Inst. Phys.
)
,
Bernd A. Kniehl
(
- Munich U.
)
,
D. Kreimer
(
- Mainz U., Inst. Phys.
)
,
K. Riesselmann
(
- Munich, Tech. U.
)

- Phys.Rev.D 54 (1996) 4548-4560
•
e-Print:
- hep-ph/9606310
•
DOI:
- 10.1103/PhysRevD.54.4548

Construction of Operator Expansions and Effective Theories in the Ms Scheme

S.G. Gorishnii
(
- Dubna, JINR
)

- Nucl.Phys.B 319 (1989) 633-666
•
DOI:
- 10.1016/0550-3213(89)90622-6

Operator Expansions in the Minimal Subtraction Scheme. 1: The Gluing Method

K.G. Chetyrkin
(
- Moscow, INR
)

- Theor.Math.Phys. 75 (1988) 346-356,
- Teor.Mat.Fiz. 75 (1988) 26-40
•
DOI:
- 10.1007/BF01017168

Operator Expansions in the Minimal Subtraction Scheme. 2: Explicit Formulas for Coefficient Functions

K.G. Chetyrkin
(
- Moscow, INR
)

- Theor.Math.Phys. 76 (1988) 809-817,
- Teor.Mat.Fiz. 76 (1988) 207-218
•
DOI:
- 10.1007/BF01028580

Coefficient Functions of Asymptotic Operator Expansions in Minimal Subtraction Scheme

S.G. Gorishnii
(
- Dubna, JINR
)
,
S.A. Larin
(
- Moscow, INR
)

- Nucl.Phys.B 283 (1987) 452
•
DOI:
- 10.1016/0550-3213(87)90283-5

The Large quark mass expansion of Gamma (Z0 ---> hadrons) and Gamma (tau- ---> tau-neutrino + hadrons) in the order alpha-s**3

S.A. Larin
(
- NIKHEF, Amsterdam
)
,
T. van Ritbergen
(
- NIKHEF, Amsterdam
)
,
J.A.M. Vermaseren
(
- NIKHEF, Amsterdam
)

- Nucl.Phys.B 438 (1995) 278-306
•
e-Print:
- hep-ph/9411260
•
DOI:
- 10.1016/0550-3213(94)00574-X

Asymptotic expansions in limits of large momenta and masses

Vladimir A. Smirnov
(
- Moscow State U.
)

- Commun.Math.Phys. 134 (1990) 109-137
•
DOI:
- 10.1007/BF02102092

Asymptotic expansions in momenta and masses and calculation of Feynman diagrams

Vladimir A. Smirnov
(
- Munich, Max Planck Inst.
)

- Mod.Phys.Lett.A 10 (1995) 1485-1500
•
e-Print:
- hep-th/9412063
•
DOI:
- 10.1142/S0217732395001617

Asymptotic expansions of Feynman diagrams on the mass shell in momenta and masses

Vladimir A. Smirnov
(
- Moscow State U.
)

- Phys.Lett.B 394 (1997) 205-210
•
e-Print:
- hep-th/9608151
•
DOI:
- 10.1016/S0370-2693(96)01697-8

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

Asymptotic expansions of two loop Feynman diagrams in the Sudakov limit

Vladimir A. Smirnov
(
- Moscow State U.
)

- Phys.Lett.B 404 (1997) 101-107
•
e-Print:
- hep-ph/9703357
•
DOI:
- 10.1016/S0370-2693(97)00545-5

New representation of the two loop crossed vertex function

- Nucl.Phys.B 488 (1997) 426-440
•
e-Print:
- hep-ph/9610285
•
DOI:
- 10.1016/S0550-3213(97)00026-6

Massive two loop vertex functions

Alexander Frink
(
- Mainz U., Inst. Phys.
)

- Nucl.Instrum.Meth.A 389 (1997) 339-342
•
e-Print:
- hep-ph/9611378
•
DOI:
- 10.1016/S0168-9002(97)00123-X

- ACM Trans.Math.Software 19 288

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

Zero threshold expansion of two loop selfenergy diagrams

Frits A. Berends
(
- Leiden U.
)
,
Andrei I. Davydychev
(
- Bergen U.
)
,
Vladimir A. Smirnov
(
- Moscow State U.
)
,
J.B. Tausk
(
- Durham U.
)

- Nucl.Phys.B 439 (1995) 536-560
•
e-Print:
- hep-ph/9410232
•
DOI:
- 10.1016/0550-3213(95)00018-N

The Two loop three point functions: General massive cases

D. Kreimer
(
- Mainz U., Inst. Phys.
)

- Phys.Lett.B 292 (1992) 341-347
•
DOI:
- 10.1016/0370-2693(92)91185-C

A New approach to the momentum expansion of multiloop Feynman diagrams

O.V. Tarasov
(
- DESY, Zeuthen
)

- Nucl.Phys.B 480 (1996) 397-412
•
e-Print:
- hep-ph/9606238
•
DOI:
- 10.1016/S0550-3213(96)00466-X