351 research outputs found
The method of global R* and its applications
The global R* operation is a powerful method for computing renormalisation
group functions. This technique, based on the principle of infrared
rearrangement, allows to express all the ultraviolet counterterms in terms of
massless propagator integrals. In this talk we present the main features of
global R* and its application to the renormalisation of QCD. By combining this
approach with the use of the program Forcer for the evaluation of the relevant
Feynman integrals, we renormalise for the first time QCD at five loops in
covariant gauges.Comment: 10 pages, 6 figures, contribution to the proceedings of the 13th
International Symposium on Radiative Corrections (RADCOR 2017
Two dimensional SU(N) x SU(N) chiral models on the lattice
Lattice chiral models are analyzed by strong and weak
coupling expansions and by numerical simulations. order strong
coupling series for the free and internal energy are obtained for all . Three loop contributions to the internal energy and to the lattice
-function are evaluated for all and non-universal corrections to the
asymptotic parameter are computed in the ``temperature'' and the
``energy'' scheme. Numerical simulations confirm a faster approach to
asymptopia of the energy scheme. A phenomenological correlation between the
peak in the specific heat and the dip of the -function is observed.
Tests of scaling are performed for various physical quantities, finding
substantial scaling at . In particular, at three different
mass ratios are determined numerically and found in agreement, within
statistical errors of about 1\%, with the theoretical predictions from the
exact S-matrix theory.Comment: pre-print IFUP 29/93, revised version, 12 pages, 10 figures avaliable
on request by FAX or by mail. REVTE
Four-loop splitting functions in QCD -- The gluon-to-quark case
We have computed the even- moments of the gluon-to-quark
splitting function at the fourth order of perturbative QCD via the
renormalization of off-shell operator matrix elements. Our results, derived
analytically for a general gauge group, agree with all results obtained for
this function so far, in particular with the lowest five moments obtained via
physical cross sections. Using our new moments and all available endpoint
constraints, we construct approximations for the four-loop that
should be sufficient for a wide range of collider-physics applications. The
NLO corrections resulting from these and the corresponding quark-quark
splitting functions lead to a marked improvement of the perturbative accuracy
for the scale derivative of the singlet quark distribution, with effects of 1%
or less at at a standard reference scale with .Comment: 17 pages latex, 3 figures, 2 ancillary files (FORM file with results
and FORTRAN subroutine
Four-loop splitting functions in QCD -- The quark-quark case
We have computed the even- moments of the pure-singlet quark
splitting function at the fourth order of perturbative QCD via
the anomalous dimensions of off-shell flavour-singlet operator matrix elements.
Our results, derived analytically for a general gauge group, agree with all
results obtained for this function so far, in particular with the lowest six
even moments obtained via physical cross sections. Using these results and all
available endpoint constraints, we construct approximations for at
four loops that should be sufficient for most collider-physics applications.
Together with the known results for the non-singlet splitting function at this order, this effectively completes the quark-quark
contribution for the evolution of parton distribution at NLO
accuracy. Our new results thus provide a major step towards fully consistent
NLO calculations at the LHC and the reduction of the residual
uncertainty in the parton evolution to the percent level.Comment: 17 pages latex, 2 figures, 2 ancillary files (FORM file with results
and FORTRAN subroutine
New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering
We present recent results on newly calculated 2- and 3-loop contributions to
the heavy quark parts of the structure functions in deep-inelastic scattering
due to charm and bottom.Comment: Contribution to the Proc. of Loops and Legs 2016, PoS, in prin
Linear instability and statistical laws of physics
We show that a meaningful statistical description is possible in conservative
and mixing systems with zero Lyapunov exponent in which the dynamical
instability is only linear in time. More specifically, (i) the sensitivity to
initial conditions is given by with
; (ii) the statistical entropy in the infinitely fine graining limit (i.e., {\it
number of cells into which the phase space has been partitioned} ),
increases linearly with time only for ; (iii) a nontrivial,
-generalized, Pesin-like identity is satisfied, namely the . These facts (which are
in analogy to the usual behaviour of strongly chaotic systems with ), seem
to open the door for a statistical description of conservative many-body
nonlinear systems whose Lyapunov spectrum vanishes.Comment: 7 pages including 2 figures. The present version is accepted for
publication in Europhysics Letter
Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
Analytical and numerical methods are applied to principal chiral models on a
two-dimensional lattice and their predictions are tested and compared. New
techniques for the strong coupling expansion of SU(N) models are developed and
applied to the evaluation of the two-point correlation function. The
momentum-space lattice propagator is constructed with precision O(\beta^{10})
and an evaluation of the correlation length is obtained for several different
definitions. Three-loop weak coupling contributions to the internal energy and
to the lattice and functions are evaluated for all N, and the
effect of adopting the ``energy'' definition of temperature is computed with
the same precision. Renormalization-group improved predictions for the
two-point Green's function in the weak coupling ( continuum ) regime are
obtained and successfully compared with Monte Carlo data. We find that strong
coupling is predictive up to a point where asymptotic scaling in the energy
scheme is observed. Continuum physics is insensitive to the effects of the
large N phase transition occurring in the lattice model. Universality in N is
already well established for and the large N physics is well
described by a ``hadronization'' picture.Comment: Revtex, 37 pages, 16 figures available on request by FAX or mai
The prediction of future from the past: an old problem from a modern perspective
The idea of predicting the future from the knowledge of the past is quite
natural when dealing with systems whose equations of motion are not known. Such
a long-standing issue is revisited in the light of modern ergodic theory of
dynamical systems and becomes particularly interesting from a pedagogical
perspective due to its close link with Poincar\'e's recurrence. Using such a
connection, a very general result of ergodic theory - Kac's lemma - can be used
to establish the intrinsic limitations to the possibility of predicting the
future from the past. In spite of a naive expectation, predictability results
to be hindered rather by the effective number of degrees of freedom of a system
than by the presence of chaos. If the effective number of degrees of freedom
becomes large enough, regardless the regular or chaotic nature of the system,
predictions turn out to be practically impossible. The discussion of these
issues is illustrated with the help of the numerical study of simple models.Comment: 9 pages, 4 figure
Hadron Properties with FLIC Fermions
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of
nonperturbative O(a)-improvement in lattice fermion actions offering near
continuum results at finite lattice spacing. It provides computationally
inexpensive access to the light quark mass regime of QCD where chiral
nonanalytic behaviour associated with Goldstone bosons is revealed. The
motivation and formulation of FLIC fermions, its excellent scaling properties
and its low-lying hadron mass phenomenology are presented.Comment: 29 pages, 13 figures, 6 tables. Contribution to lecure notes in 2nd
Cairns Topical Workshop on Lattice Hadron Physics 2003 (LHP 2003), Cairns,
Australia, 22-30 Jul 200
Library Design in Combinatorial Chemistry by Monte Carlo Methods
Strategies for searching the space of variables in combinatorial chemistry
experiments are presented, and a random energy model of combinatorial chemistry
experiments is introduced. The search strategies, derived by analogy with the
computer modeling technique of Monte Carlo, effectively search the variable
space even in combinatorial chemistry experiments of modest size. Efficient
implementations of the library design and redesign strategies are feasible with
current experimental capabilities.Comment: 5 pages, 3 figure
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