178 research outputs found
Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
We study the dynamic critical behavior of the Chayes-Machta dynamics for the
Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang
dynamics for the q-state Potts model to noninteger q, in two and three spatial
dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge
\alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in
d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q)
in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure
Feynman Rules for the Rational Part of the Standard Model One-loop Amplitudes in the 't Hooft-Veltman Scheme
We study Feynman rules for the rational part of the Standard Model
amplitudes at one-loop level in the 't Hooft-Veltman scheme.
Comparing our results for quantum chromodynamics and electroweak 1-loop
amplitudes with that obtained based on the Kreimer-Korner-Schilcher (KKS)
scheme, we find the latter result can be recovered when our
scheme becomes identical (by setting in our expressions)
with the KKS scheme. As an independent check, we also calculate Feynman rules
obtained in the KKS scheme, finding our results in complete agreement with
formulae presented in the literature. Our results, which are studied in two
different schemes, may be useful for clarifying the
problem in dimensional regularization. They are helpful to eliminate or find
ambiguities arising from different dimensional regularization schemes.Comment: Version published in JHEP, presentation improved, 41 pages, 10
figure
Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order
Results for next-to-leading order QCD corrections to the pp(p\bar{p}) -> t
\bar{t} -> W^+W^- b\bar{b} -> e^{+} \nu_{e} \mu^{-} \bar{\nu}_{\mu} b \bar{b}
+X processes with complete off-shell effects are presented for the first time.
Double-, single- and non-resonant top contributions of the order
{\cal{O}}(\alpha_{s}^3 \alpha^4) are consistently taken into account, which
requires the introduction of a complex-mass scheme for unstable top quarks.
Moreover, the intermediate W bosons are treated off-shell. Comparison to the
narrow width approximation for top quarks, where non-factorizable corrections
are not accounted for is performed. Besides the total cross section and its
scale dependence, several differential distributions at the TeVatron run II and
the LHC are given. In case of the TeVatron the forward-backward asymmetry of
the top is recalculated afresh. With inclusive selection cuts, the
forward-backward asymmetry amounts to A^{t}_{FB} = 0.051 +/- 0.0013.
Furthermore, the corrections with respect to leading order are positive and of
the order 2.3% for the TeVatron and 47% for the LHC. A study of the scale
dependence of our NLO predictions indicates that the residual theoretical
uncertainty due to higher order corrections is 8% for the TeVatron and 9% for
the LHC.Comment: 35 pages, 39 figures, 3 tables. References and note added, version to
appear in JHE
Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions
We study, via Monte Carlo simulation, the dynamic critical behavior of the
Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which
generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to
non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in
steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic
critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95
the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also
present plausible fits compatible with this conjecture. We show that the
Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire
range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of
our work, we also obtain evidence concerning the corrections to scaling in
static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure
Double Parton Scattering Singularity in One-Loop Integrals
We present a detailed study of the double parton scattering (DPS)
singularity, which is a specific type of Landau singularity that can occur in
certain one-loop graphs in theories with massless particles. A simple formula
for the DPS singular part of a four-point diagram with arbitrary
internal/external particles is derived in terms of the transverse momentum
integral of a product of light cone wavefunctions with tree-level matrix
elements. This is used to reproduce and explain some results for DPS
singularities in box integrals that have been obtained using traditional loop
integration techniques. The formula can be straightforwardly generalised to
calculate the DPS singularity in loops with an arbitrary number of external
particles. We use the generalised version to explain why the specific MHV and
NMHV six-photon amplitudes often studied by the NLO multileg community are not
divergent at the DPS singular point, and point out that whilst all NMHV
amplitudes are always finite, certain MHV amplitudes do contain a DPS
divergence. It is shown that our framework for calculating DPS divergences in
loop diagrams is entirely consistent with the `two-parton GPD' framework of
Diehl and Schafer for calculating proton-proton DPS cross sections, but is
inconsistent with the `double PDF' framework of Snigirev.Comment: 29 pages, 8 figures. Minor corrections and clarifications added.
Version accepted for publication in JHE
Photon Radiation with MadDipole
We present the automation of a subtraction method for photon radiation using
the dipole formalism within the MadGraph framework. The subtraction terms are
implemented both in dimensional regularization and mass regularization for
massless and massive cases and non-collinear-safe observables are accounted
for.Comment: 23 pages, 2 figures, minor additions, references added, version
published in JHE
Automation of one-loop QCD corrections
We present the complete automation of the computation of one-loop QCD
corrections, including UV renormalization, to an arbitrary scattering process
in the Standard Model. This is achieved by embedding the OPP integrand
reduction technique, as implemented in CutTools, into the MadGraph framework.
By interfacing the tool so constructed, which we dub MadLoop, with MadFKS, the
fully automatic computation of any infrared-safe observable at the
next-to-leading order in QCD is attained. We demonstrate the flexibility and
the reach of our method by calculating the production rates for a variety of
processes at the 7 TeV LHC.Comment: 64 pages, 12 figures. Corrected the value of m_Z in table 1. In table
2, corrected the values of cross sections in a.4 and a.5 (previously computed
with mu=mtop/2 rather than mu=mtop/4). In table 2, corrected the values of
NLO cross sections in b.3, b.6, c.3, and e.7 (the symmetry factor for a few
virtual channels was incorrect). In sect. A.4.3, the labeling of the
four-momenta was incorrec
Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
SAMURAI is a tool for the automated numerical evaluation of one-loop
corrections to any scattering amplitudes within the dimensional-regularization
scheme. It is based on the decomposition of the integrand according to the
OPP-approach, extended to accommodate an implementation of the generalized
d-dimensional unitarity-cuts technique, and uses a polynomial interpolation
exploiting the Discrete Fourier Transform. SAMURAI can process integrands
written either as numerator of Feynman diagrams or as product of tree-level
amplitudes. We discuss some applications, among which the 6- and 8-photon
scattering in QED, and the 6-quark scattering in QCD. SAMURAI has been
implemented as a Fortran90 library, publicly available, and it could be a
useful module for the systematic evaluation of the virtual corrections oriented
towards automating next-to-leading order calculations relevant for the LHC
phenomenology.Comment: 35 pages, 7 figure
On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations
An improved method is presented for the numerical evaluation of multi-loop
integrals in dimensional regularization. The technique is based on
Mellin-Barnes representations, which have been used earlier to develop
algorithms for the extraction of ultraviolet and infrared divergencies. The
coefficients of these singularities and the non-singular part can be integrated
numerically. However, the numerical integration often does not converge for
diagrams with massive propagators and physical branch cuts. In this work,
several steps are proposed which substantially improve the behavior of the
numerical integrals. The efficacy of the method is demonstrated by calculating
several two-loop examples, some of which have not been known before.Comment: 13 pp. LaTe
Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude
When using dimensional regularization/reduction the epsilon-dimensional
numerator of the 1-loop Feynman diagrams gives rise to rational contributions.
I list the set of fundamental rules that allow the extraction of such terms at
the integrand level in any theory containing scalars, vectors and fermions,
such as the electroweak standard model, QCD and SUSY.Comment: 19 pages, 14 figures, uses axodraw.sty. Version accepted for
publication in JHE
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