3,030 research outputs found
Renormalisation of gauge theories on general anisotropic lattices and high-energy scattering in QCD
We study the renormalisation of gauge theories on general
anisotropic lattices, to one-loop order in perturbation theory, employing the
background field method. The results are then applied in the context of two
different approaches to hadronic high-energy scattering. In the context of the
Euclidean nonperturbative approach to soft high-energy scattering based on
Wilson loops, we refine the nonperturbative justification of the analytic
continuation relations of the relevant Wilson-loop correlators, required to
obtain physical results. In the context of longitudinally-rescaled actions, we
study the consequences of one-loop corrections on the relation between the
gauge theory and its effective description in terms of
two-dimensional principal chiral models.Comment: Revised version with minor corrections, matches published version; 40
pages, 4 figure
Hadronic total cross sections at high energy and the QCD spectrum
We show how to obtain the leading energy dependence of hadronic total cross
sections, in the framework of the nonperturbative approach to soft high-energy
scattering based on Wilson-loop correlation functions, if certain nontrivial
analyticity assumptions are satisfied. The total cross sections turn out to be
of "Froissart" type, for . We also discuss under which conditions the coefficient is
universal, i.e., independent of the hadrons involved in the scattering process.
In the most natural scenarios for universality, can be related to the
stable spectrum of QCD, and is predicted to be , in fair agreement with experimental results. If we consider, instead, the
stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite
larger value , suggesting (quite
surprisingly) large unquenching effects due to the sea quarks.Comment: Revised version; 43 pages, 3 figure
A reversible allelic partition process and Pitman sampling formula
We introduce a continuous-time Markov chain describing dynamic allelic
partitions which extends the branching process construction of the Pitman
sampling formula in Pitman (2006) and the birth-and-death process with
immigration studied in Karlin and McGregor (1967), in turn related to the
celebrated Ewens sampling formula. A biological basis for the scheme is
provided in terms of a population of individuals grouped into families, that
evolves according to a sequence of births, deaths and immigrations. We
investigate the asymptotic behaviour of the chain and show that, as opposed to
the birth-and-death process with immigration, this construction maintains in
the temporal limit the mutual dependence among the multiplicities. When the
death rate exceeds the birth rate, the system is shown to have reversible
distribution identified as a mixture of Pitman sampling formulae, with negative
binomial mixing distribution on the population size. The population therefore
converges to a stationary random configuration, characterised by a finite
number of families and individuals.Comment: 17 pages, to appear in ALEA , Latin American Journal of Probability
and Mathematical Statistic
Comments on high-energy total cross sections in QCD
We discuss how hadronic total cross sections at high energy depend on the
details of QCD, namely on the number of colours and the quark masses. We
find that while a "Froissart"-type behaviour is
rather general, relying only on the presence of higher-spin stable particles in
the spectrum, the value of depends quite strongly on the quark masses.
Moreover, we argue that is of order at large , and
we discuss a bound for which does not become singular in the chiral
limit, unlike the Froissart-\L ukaszuk-Martin bound.Comment: Revised version; matches published versio
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