Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10^{15} is achieved for arbitrary real values of the momentum transfer.Comment: 11 pages, LaTeX. The complete paper is also available via the www at http://www-ttp.physik.uni-karlsruhe.de/Preprints/ and the program can be downloaded from http://www-ttp.physik.uni-karlsruhe.de/Progdata

Electroweak Fermion-loop Contributions to the Muon Anomalous Magnetic Moment

The two-loop electroweak corrections to the anomalous magnetic moment of the muon, generated by fermionic loops, are calculated. An interesting role of the top quark in the anomaly cancellation is observed. New corrections, including terms of order $G_\mu \alpha m_t^2$, are computed and a class of diagrams previously thought to vanish are found to be important. The total fermionic correction is $-(23\pm 3) \times 10^{-11}$ which decreases the electroweak effects on $g-2$, predicted from one-loop calculations, by 12\%. We give an updated theoretical prediction for $g-2$ of the muon.Comment: Corrected versio

Charm and Bottom Quark Masses from Perturbative QCD

Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. We assume that the continuum contribution to the sum rules is adequately described by pQCD. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of $m_c$ is related to the experimental data. On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision.Comment: 5 pages, 2 figures, final version as publishe

Differential equations and massive two-loop Bhabha scattering: the B5l2m3 case

The two-loop box contributions to massive Bhabha scattering may be reduced to two-loop box master integrals (MIs) with five, six, and seven internal lines, plus vertices and self energies. The self-energy and vertex MIs may be solved analytically by the differential equations (DE) method. This is true for only few of the box masters. Here we describe some details of the analytical determination, including constant terms in ep=(4-d)/2, of the complicated topology B5l2m3 (with 5 lines, 2 of them being massive). With the DE approach, three of the four coupled masters have been solved in terms of (generalized) standard Harmonic Polylogarithms.Comment: 5 pages, 2 figures, contribution to RADCOR 2005, Oct 2-7, 2005, Shonan Village, Japan, to appear in Nucl. B (Proc. Suppl.

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions

We consider the Z Q Qbar vertex to second order in the QCD coupling for an on-shell massive quark-antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 57 pages, 5 figures. All the results in Section 6 of the paper are available in an electronic form in the file formulas.in

Reduze - Feynman Integral Reduction in C++

Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel.Comment: 18 pages, 2 figure

Precise mass-dependent QED contributions to leptonic g-2 at order alpha^2 and alpha^3

Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and tau lepton are presented. The Standard Model prediction for the electron (g-2) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the tau lepton, differences with previously published results are found and discussed. An updated value of the fine-structure constant is presented in "Note added after publication."Comment: 6 pages, 1 figure. v2: New determination of alpha presented (based on the recent electron g-2 measurement). v3: New formulae added in Sec.IIB. v4: Updated value of alpha presente

Using differential equations to compute two-loop box integrals

The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop calculations can be reduced to a small number of master integrals. An efficient method to compute these master integrals is to derive and solve differential equations in the external invariants for them. As an application of the differential equation method, we compute the ${\cal O}(\epsilon)$-term of a particular combination of on-shell massless planar double box integrals, which appears in the tensor reduction of $2 \to 2$ scattering amplitudes at two loops.Comment: 5 pages, LaTeX, uses espcrc2.sty; presented at Loops and Legs in Quantum Field Theory, April 2000, Bastei, German

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions

We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.Comment: 24 pages, 6 figure

Coherent tunneling by adiabatic passage in an optical waveguide system

We report on the first experimental demonstration of light transfer in an engineered triple-well optical waveguide structure which provides a classic analogue of Coherent Tunnelling by Adiabatic Passage (CTAP) recently proposed for coherent transport in space of neutral atoms or electrons among tunneling-coupled optical traps or quantum wells [A.D. Greentree et al., Phys. Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)]. The direct visualization of CTAP wavepacket dynamics enabled by our simple optical system clearly shows that in the counterintuitive passage scheme light waves tunnel between the two outer wells without appreciable excitation of the middle well.Comment: submitted for publicatio