132 research outputs found

### Computation of Gr\"obner Bases for Two-Loop Propagator Type Integrals

The Gr\"obner basis technique for calculating Feynman diagrams proposed in
[O.V. Tarasov, Acta Physica Polonica, v. B29 (1998) 2655] is applied to the
two-loop propagator type integrals with arbitrary masses and momentum. We
describe the derivation of Gr\"obner bases for all integrals with 1PI
topologies and present elements of the Gr\"obner bases.Comment: 4 pages, LaTeX, to appear in the Proceedings of ACAT-03, Tsukuba,
Japa

### Massive two-loop Bhabha scattering -- the factorizable subset

The experimental precision that will be reached at the next generation of
colliders makes it indispensable to improve theoretical predictions
significantly. Bhabha scattering (e^+ e^- \to e^+ e^-) is one of the prime
processes calling for a better theoretical precision, in particular for
non-zero electron masses. We present a first subset of the full two-loop
calculation, namely the factorizable subset. Our calculation is based on DIANA.
We reduce tensor integrals to scalar integrals in shifted (increased)
dimensions and additional powers of various propagators, so-called
dots-on-lines. Recurrence relations remove those dots-on-lines as well as
genuine dots-on-lines (originating from mass renormalization) and reduce the
dimension of the integrals to the generic d = 4 - 2 \epsilon dimensions. The
resulting master integrals have to be expanded to ${\it O}(\epsilon)$ to ensure
proper treatment of all finite terms.Comment: 5 pages, Talk presented by A.W. at RADCOR and Loops and Legs 2002 in
Banz, Germany, to appear in the proceeding

### DIANA and selected applications

New developments concerning the extension of the Feynman diagram analyzer
DIANA are presented. We discuss new graphics facilities, different approaches
to automation of momenta distribution and parallel processing facilities.
Furthermore applications to $t\bar t$ production and Bhabha scattering are
shortly discussed.Comment: Latex, 5 pages, 4 eps figures, uses included npb.sty, presented by at
RADCOR and Loops and Legs 2002 8-13 September 2002, in Kloster Banz, German

### FIRCLA, one-loop correction to e+ e- to nu anti-nu H and basis of Feynman integrals in higher dimensions

An approach for an effective computer evaluation of one-loop multi-leg
diagrams is proposed. It's main feature is the combined use of several systems
- DIANA, FORM and MAPLE. As an application we consider the one-loop correction
to Higgs production in e+ e- to nu anti-nu H, which is important for future e+
e- colliders. To improve the stability of numerical evaluations a non-standard
basis of integrals is introduced by transforming integrals to higher
dimensions.Comment: 6 pages 1 figure, reference to G. Belanger et al. adde

### Non-renormalization of the full <VVA> correlator at two-loop order

By explicit calculation of the two-loop QCD corrections we show that for
singlet axial and vector currents the full off-shell correlation function
in the limit of massless fermions is proportional to the one-loop result, when
calculated in the MS-bar scheme. By the same finite renormalization which is
needed to make the one-loop anomaly exact to all orders, we arrive at the
conclusion that two-loop corrections are absent altogether, for the complete
correlator not only its anomalous part. In accordance with the one-loop nature
of the correlator, one possible amplitude, which seems to be missing by
accident at the one-loop level, also does not show up at the two-loop level.Comment: 6 pages, 1 figur

### Algebraic reduction of one-loop Feynman graph amplitudes

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.Comment: 18 pages, 1 figure, added references, expanded introduction, improved
tex

### Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems

Two-loop corrections for the correlator of the singlet axial and vector
currents in QCD are calculated in the chiral limit for arbitrary momenta.
Explicit calculations confirm the non-renormalization theorems derived recently
by Vainshtein and Knecht et.al. We find that as in the one-loop case also at
the two loops the correlator has only 3 independent form-factors instead
of 4. From the explicit results we observe that the two-loop correction to the
correlator is equal to the one-loop result times the constant factor C_2(R)
alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the
anomalous longitudinal as well as for the non- anomalous thansversal
amplitudes. The finite overall alpha_s dependent constant has to be normalized
away by renormalizing the axial current according to Witten's
algebraic/geometrical constraint on the anomalous Ward identity. Our
observations, together with known facts, suggest that in perturbation theory
the correlator is proportional to the one-loop term to all orders and
that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries
over to the full correlator.Comment: 10 pages, 2 Postscript figures, uses axodraw.st

### Decoupling of heavy quarks in HQET

Decoupling of c-quark loops in b-quark HQET is considered. The decoupling
coefficients for the HQET heavy-quark field and the heavy-light quark current
are calculated with the three-loop accuracy. The last result can be used to
improve the accuracy of extracting f_B from HQET lattice simulations (without
c-quark loops). The decoupling coefficient for the flavour-nonsinglet QCD
current with n antisymmetrized gamma-matrices is also obtained at three loops;
the result for the tensor current (n=2) is new.Comment: JHEP3 documentclass; the results in a computer-readable form can be
found at http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp06/ttp06-25/ V2:
a few typos corrected, a few minor text improvements, a few references added;
V3: several typos in formulas fixe

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