Related papers: Two-loop Sunset Integrals at Finite Volume
We compute the complete set of two-loop master integrals for the scattering of four massless particles and a massive one. Our results are ready for phenomenological applications, removing a major obstacle to the computation of complete…
We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants,…
A summary of recent progress in Chiral Perturbation Theory (ChPT) at the two-loop level is given. A short introduction to ChPT is included, along with an explanation of the usefulness of developing ChPT for partially quenched QCD. Further,…
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…
A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two loop sunrise master integrals.
We formulate quenched chiral perturbation theory for heavy-light mesons coupled to pions, and calculate the one-loop chiral logarithmic corrections to $f_B$, $f_{B_{s}}$, $B_B$ and $B_{B_{s}}$. We also calculate these corrections for…
We present the first step towards the estimation of finite volume effects in heavy-light meson systems using heavy meson chiral perturbation theory. We demonstrate that these effects can be amplified in both light-quark and heavy-quark mass…
The procedure to calculate masses and matrix-elements in the presence of mixing of the basis states is explained in detail. We then apply this procedure to the two-loop calculation in Chiral Perturbation Theory of pseudoscalar masses and…
We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation $\varepsilon$. This is done by introducing a class of functions…
A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of \sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior…
Chiral perturbation theory at finite four-volume V (=L^3T) is reconsidered with a view towards finding a computational scheme that can deal with any value of M_\pi L, where M_\pi is a generic Nambu-Goldstone mass. The momentum zero modes…
Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
We give the results of complete analytical computations of two- and three-point loop integrals ocurring in heavy particle theories, with and without velocity change, for arbitrary values of external momenta and masses.
We test the one-loop chiral perturbation theory formula on unquenched lattice data of pseudoscalar meson decay constants. The chiral extrapolation including the effect of the chiral logarithm is attempted and its uncertainty is discussed.
This paper presents a first study of the decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea quarks, in Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT). Explicit…
We present analytic results for one of two types of planar QED two-loop integrals for $\mu e$ scattering including finite lepton masses. No approximations are made, such that the results are valid not only in the limit of a small electron…
We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic…
We study the sunset graph defined as the scalar two-point self-energy at two-loop order. We evaluate the sunset integral for all identical internal masses in two dimensions. We give two calculations for the sunset amplitude; one based on an…