1,601 research outputs found
Recommended from our members
Locally compact abelian p-groups revisited
Even though the structure of locally compact abelian groups is generally considered to be rather thoroughly known through a wealth of publications, one keeps encountering corners that are not elucidated in up-to-date literature. In a study of a particular class of metabelian locally compact groups (see [HHR17]) we encountered some issues about noncompact locally compact abelian groups which do not appear to be discussed in the literature even though some of them were anticipated in Braconnier's article on his local product [Bra48]. Here we treat some of them, notably some aspects of totally disconnected torsion-free locally compact abelian groups which one might consider unexpected if not pathological. However, firstly we deal with some points concerning noncompact locally compact abelian torsion groups. For compact abelian groups we often refer to the monograph [HM13]. It will be convenient to use additive notation for abelian groups
Towards e+e- --> 3 jets at NNLO by sector decomposition
A method based on sector decomposition has been developed to calculate the
double real radiation part of the process e+e- to 3 jets at
next-to-next-to-leading order. It is shown in an example that the numerical
cancellation of soft and collinear poles works well. The method is flexible to
include an arbitrary measurement function in the final Monte Carlo program,
such that it allows to obtain differential distributions for different kinds of
observables. This is demonstrated by showing 3-, 4- and 5-jet rates at order
alpha_s^3 for a subpart of the process.Comment: 14 pages, 4 figure
Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
The three-loop form factors in massless QCD can be expressed as a linear
combination of master integrals. Besides a number of master integrals which
factorise into products of one-loop and two-loop integrals, one finds 16
genuine three-loop integrals. Of these, six have the form of a bubble insertion
inside a one-loop or two-loop vertex integral. We compute all master integrals
with these insertion topologies.Comment: 12 pages, 1 figur
Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
In this letter we continue the calculation of master integrals for massless
three-loop form factors by giving analytical results for those integrals which
are relevant for the fermionic contributions proportional to N_F^2, N_F*N, and
N_F/N. Working in dimensional regularisation, we express one of the integrals
in a closed form which is exact to all orders in epsilon, containing
Gamma-functions and hypergeometric functions of unit argument. In all other
cases we derive multiple Mellin-Barnes representations from which the
coefficients of the Laurent expansion in epsilon are extracted in an analytical
form. To obtain the finite part of the three-loop quark and gluon form factors,
all coefficients through transcendentality six in the Riemann zeta-function
have to be included.Comment: 12 pages, 1 figure. References added and updated. Appendix on
evaluation of Mellin-Barnes integrals added. Version to appear in PL
Two-Loop Photonic Corrections to Massive Bhabha Scattering
We describe the details of the evaluation of the two-loop radiative photonic
corrections to Bhabha scattering. The role of the corrections in the
high-precision luminosity determination at present and future electron-positron
colliders is discussed.Comment: 20 pages, Latex; discussion, references added; to appear in
Nucl.Phys.
Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
We complete the calculation of master integrals for massless three-loop form
factors by computing the previously-unknown three diagrams with nine
propagators in dimensional regularisation. Each of the integrals yields a
six-fold Mellin-Barnes representation which we use to compute the coefficients
of the Laurent expansion in epsilon. Using Riemann zeta functions of up to
weight six, we give fully analytic results for one integral; for a second,
analytic results for all but the finite term; for the third, analytic results
for all but the last two coefficients in the Laurent expansion. The remaining
coefficients are given numerically to sufficiently high accuracy for
phenomenological applications.Comment: 15 pages, 2 figures. Minor modifications and reference added. Matches
published versio
Tissue damage by laser radiation: an in vitro comparison between Tm:YAG and Ho:YAG laser on a porcine kidney model
An automatized algorithm to compute infrared divergent multi-loop integrals
We describe a constructive procedure to separate overlapping infrared
divergences in multi-loop integrals. Working with a parametric representation
in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in
epsilon, where the coefficients of the pole- and finite terms are sums of
regular parameter integrals which can be evaluated numerically. We fully
automatized this algorithm by implementing it into algebraic manipulation
programs and applied it to calculate numerically some nontrivial 2-loop 4-point
and 3-loop 3-point Feynman diagrams. Finally, we discuss the applicability of
our method to phenomenologically relevant multi--loop calculations such as the
NNLO QCD corrections for e^+e^- --> 3 jets.Comment: 14 pages, 5 eps figures. Replaced by slightly extended, published
version, typos correcte
- …