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J. Fleischer

Publications and source records attributed to J. Fleischer.

At least 37 records · Page 2Linked to original sources
arXiv2003

A New Hypergeometric Representation of One-Loop Scalar Integrals in $d$ Dimensions

A difference equation w.r.t. space-time dimension $d$ for $n$-point one-loop integrals with arbitrary momenta and masses is introduced and a solution presented. The result can in general be written as multiple hypergeometric series with ratios of different Gram determinants as expansion variables. Detailed considerations for $2-,3-$ and $4-$point functions are given. For the $2-$ point function we reproduce a known result in terms of the Gauss hypergeometric function $_2F_1$. For the $3-$point function an expression in terms of $_2F_1$ and the Appell hypergeometric function $F_1$ is given. For the $4-$point function a new representation in terms of $_2F_1$, $F_1$ and the Lauricella-Saran functions $F_S$ is obtained. For arbitrary $d=4-2ε$, momenta and masses the $2-,3-$ and $4-$point functions admit a simple one-fold integral representation. This representation will be useful for the calculation of contributions from the $ε-$ expansion needed in higher orders of perturbation theory. Physically interesting examples of $3-$ and $4-$point functions occurring in Bhabha scattering are investigated.

hep-ph↗
arXiv2003

Elektroweak one-loop corrections for e^+e^- annihilation into t\bar{t} including hard bremsstrahlung

We present the complete electroweak one-loop corrections to top-pair production at a linear e^+e^- collider in the continuum region. Besides weak and photonic virtual corrections, real hard bremsstrahlung with simple realistic kinematical cuts is included. For the bremsstrahlung we advocate a semi-analytical approach with a high numerical accuracy. The virtual corrections are parametrized through six independent form factors, suitable for Monte-Carlo implementation. Alternatively, our numerical package topfit, a stand-alone code, can be utilized for the calculation of both differential and integrated cross sections as well as forward--backward asymmetries.

hep-ph↗
arXiv2002

Status of Electroweak Corrections to Top Pair Production

We review the status of electroweak radiative corrections to top-pair production at a Linear Collider well above the production threshold. We describe the Fortran package topfit and present numerical results at sqrt(s) = 500 GeV, 1 TeV, and 3 TeV.

hep-ph↗
arXiv2002

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.

hep-ph↗
arXiv2002

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 εdimensions. The resulting master integrals have to be expanded to ${\it O}(ε)$ to ensure proper treatment of all finite terms.

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arXiv2002

Factorizing one-loop contributions to two-loop Bhabha scattering and automatization of Feynman diagram calculations

In higher order calculations a number of new technical problems arise: one needs diagrams in arbitrary dimension in order to obtain their needed $ε$-expansion, zero Gram determinants appear, renormalization produces diagrams with `dots' on the lines, i.e. higher order powers of scalar propagators. All these problems cannot be accessed by the `standard' Passarino-Veltman approach: there is not available what is needed for higher loops. We demonstrate our method of how to solve these problems.

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arXiv2002

A Feynman diagram analyzer DIANA: recent development

New developments concerning the extension of the Feynman diagram analyzer DIANA are presented. We discuss new graphic facilities, application of DIANA to processes with Majorana fermions and different approaches to automation of momenta distribution.

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arXiv2002

Complete electroweak one-loop radiative corrections to top-pair production at TESLA -- a comparison

Electroweak one-loop radiative corrections to the process e^+ e^- -> t tbar are revisited. Two groups from Karlsruhe and Bielefeld/Zeuthen performed independent calculations of both (virtual and soft) QED contributions and weak virtual corrections. For the angular distribution an agreement of at least eight digits for the weak corrections and of at least seven digits for additional photonic corrections is established.

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arXiv2002

One-loop corrections to the process e+ e- -> t tbar including hard bremsstrahlung

Radiative corrections to the process e+ e- to t tbar are calculated in one-loop approximation of the Standard Model. There exist results from several groups. This talk provides further comparisons of the complete elektroweak contributions, including hard bremsstrahlung. The excellent final agreement of the different groups allows to continue by working on a code for an event generator for TESLA and an extension to e+ e- to 6 fermions.

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arXiv2001

ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the Standard Model

A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations obtained from the integration-by-parts method, allows us to reduce diagrams with arbitrary indices (powers of scalar propagators) to a set of master integrals. The SHELL2 package is used for the calculation of special types of diagrams. Analytical results for master integrals are collected.

hep-ph↗
arXiv2001

Single mass scale diagrams: construction of a basis for the $ε$-expansion

Exploring the idea of Broadhurst on the ``sixth root of unity'' we present an ansatz for construction of a basis of transcendental numbers for the epsilon-expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.

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arXiv1999

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.

hep-ph↗
arXiv1999

Two-loop QCD corrections of the massive fermion propagator

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.

hep-ph↗
arXiv1999

Non factorizable $O(αα_s)$ corrections to the process $Z\to b\bar{b}$

We evaluate non factorizable $O(αα_s)$ corrections to the process $Z\to b\bar{b}$ due to the virtual t-quark. All two-loop vertex diagrams with $W$'s and charged ghosts $Φ$'s are included. They are evaluated in the large top-mass expansion up to the $10^{th}$ order. Gluon Bremsstrahlung is taken into account by integrating over the whole phase space. All calculations, including Bremsstrahlung, are done in dimensional regularization. The expansion coefficients of the large mass expansion are given in closed form. Their expansion in $y=m_Z^2/4m_W^2$ is in agreement with the coefficients up to $O(m_W^6/m_t^6)$ as given by Harlander et al.

hep-ph↗
arXiv1999

Recursion relations for two-loop self-energy diagrams on-shell

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2 package is used for the calculation of special types of diagrams. A method of calculation of higher order ε-expansion of master integrals is demonstrated.

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