1,395 research outputs found
Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-gluon scattering,
and for quark-antiquark annihilation into two gluons. These amplitudes are
relevant for next-to-next-to-leading order corrections to (polarized) jet
production at hadron colliders. We give the results in the `t Hooft-Veltman and
four-dimensional helicity (FDH) variants of dimensional regularization. The
transition rules for converting the amplitudes between the different variants
are much more intricate than for the previously discussed case of gluon-gluon
scattering. Summing our two-loop expressions over helicities and colors, and
converting to conventional dimensional regularization, gives results in
complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans.
We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric
Yang-Mills theory, obtained from the QCD amplitudes by modifying the color
representation and multiplicities, and verify supersymmetry Ward identities in
the FDH scheme.Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop
assembly; remaining results unaffecte
Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-quark and
quark-antiquark scattering. These amplitudes are relevant for
next-to-next-to-leading order corrections to (polarized) jet production at
hadron colliders. We give the results in the `t Hooft-Veltman and
four-dimensional helicity (FDH) variants of dimensional regularization and
present the scheme dependence of the results. We verify that the finite
remainder, after subtracting the divergences using Catani's formula, are in
agreement with previous results. We also provide the amplitudes for
gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We
describe ambiguities in continuing the Dirac algebra to D dimensions, including
ones which violate fermion helicity conservation. The finite remainders after
subtracting the divergences using Catani's formula, which enter into physical
quantities, are free of these ambiguities. We show that in the FDH scheme, for
gluino-gluino scattering, the finite remainders satisfy the expected
supersymmetry Ward identities.Comment: arXiv admin note: substantial text overlap with arXiv:hep-ph/030416
Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
We consider the singular behaviour of QCD scattering amplitudes in
kinematical configurations where two or more momenta of the external partons
become collinear. At the tree level, this behaviour is known to be controlled
by factorization formulae in which the singular collinear factor is universal
(process independent). We show that this strict (process-independent)
factorization is not valid at one-loop and higher-loop orders in the case of
the collinear limit in space-like regions (e.g., collinear radiation from
initial-state partons). We introduce a generalized version of all-order
collinear factorization, in which the space-like singular factors retain some
dependence on the momentum and colour charge of the non-collinear partons. We
present explicit results on one-loop and two-loop amplitudes for both the
two-parton and multiparton collinear limits. At the level of square amplitudes
and, more generally, cross sections in hadron--hadron collisions, the violation
of strict collinear factorization has implications on the non-abelian structure
of logarithmically-enhanced terms in perturbative calculations (starting from
the next-to-next-to-leading order) and on various factorization issues of mass
singularities (starting from the next-to-next-to-next-to-leading order).Comment: 81 pages, 5 figures, typos corrected in the text, few comments added
and inclusion of NOTE ADDED on recent development
Two-Loop g -> gg Splitting Amplitudes in QCD
Splitting amplitudes are universal functions governing the collinear behavior
of scattering amplitudes for massless particles. We compute the two-loop g ->
gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which
describe the limits of two-loop n-point amplitudes where two gluon momenta
become parallel. They also represent an ingredient in a direct x-space
computation of DGLAP evolution kernels at next-to-next-to-leading order. To
obtain the splitting amplitudes, we use the unitarity sewing method. In
contrast to the usual light-cone gauge treatment, our calculation does not rely
on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the
loop integrals contain some of the denominators typically encountered in
light-cone gauge. We reduce the integrals to a set of 13 master integrals using
integration-by-parts and Lorentz invariance identities. The master integrals
are computed with the aid of differential equations in the splitting momentum
fraction z. The epsilon-poles of the splitting amplitudes are consistent with a
formula due to Catani for the infrared singularities of two-loop scattering
amplitudes. This consistency essentially provides an inductive proof of
Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole
terms having non-trivial color structure. Finite terms in the splitting
amplitudes determine the collinear behavior of finite remainders in this
formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality
argument of hep-th/0404092, and additional explanation of cut-reconstruction
uniquenes
Two-Loop Correction to Bhabha Scattering
We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and
Bhabha scattering in dimensional regularization. The results are expressed in
terms of polylogarithms. The form of the infrared divergences agrees with
previous expectations. These results are a crucial ingredient in the complete
next-to-next-to-leading order QED corrections to these processes. A future
application will be to reduce theoretical uncertainties associated with
luminosity measurements at e^+ e^- colliders. The calculation also tests
methods that may be applied to analogous QCD processes.Comment: Latex, 22 pages, 1 figur
Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
We compute the leading-color (planar) three-loop four-point amplitude of N=4
supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent
expansion about epsilon = 0 including the finite terms. The amplitude was
constructed previously via the unitarity method, in terms of two Feynman loop
integrals, one of which has been evaluated already. Here we use the
Mellin-Barnes integration technique to evaluate the Laurent expansion of the
second integral. Strikingly, the amplitude is expressible, through the finite
terms, in terms of the corresponding one- and two-loop amplitudes, which
provides strong evidence for a previous conjecture that higher-loop planar N =
4 amplitudes have an iterative structure. The infrared singularities of the
amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on
resummation. Based on the four-point result and the exponentiation of infrared
singularities, we give an exponentiated ansatz for the maximally
helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole
in the four-point amplitude determines the soft, or cusp, anomalous dimension
at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a
prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the
leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and
Vogt. Following similar logic, we are able to predict a term in the three-loop
quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words
about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on
multiloop ansatz; remark that form-factor prediction is now confirmed by
other work; minor typos correcte
ProbCD: enrichment analysis accounting for categorization uncertainty
As in many other areas of science, systems biology makes extensive use of statistical association and significance estimates in contingency tables, a type of categorical data analysis known in this field as enrichment (also over-representation or enhancement) analysis. In spite of efforts to create probabilistic annotations, especially in the Gene Ontology context, or to deal with uncertainty in high throughput-based datasets, current enrichment methods largely ignore this probabilistic information since they are mainly based on variants of the Fisher Exact Test. We developed an open-source R package to deal with probabilistic categorical data analysis, ProbCD, that does not require a static contingency table. The contingency table for
the enrichment problem is built using the expectation of a Bernoulli Scheme stochastic process given the categorization probabilities. An on-line interface was created to allow usage by non-programmers and is available at: http://xerad.systemsbiology.net/ProbCD/. We present an analysis framework and software tools to address the issue of uncertainty in categorical data analysis. In particular, concerning the enrichment analysis, ProbCD can accommodate: (i) the stochastic nature of the high-throughput experimental techniques and (ii) probabilistic gene annotation
Svestka's Research: Then and Now
Zdenek Svestka's research work influenced many fields of solar physics,
especially in the area of flare research. In this article I take five of the
areas that particularly interested him and assess them in a "then and now"
style. His insights in each case were quite sound, although of course in the
modern era we have learned things that he could not readily have envisioned.
His own views about his research life have been published recently in this
journal, to which he contributed so much, and his memoir contains much
additional scientific and personal information (Svestka, 2010).Comment: Invited review for "Solar and Stellar Flares," a conference in honour
of Prof. Zden\v{e}k \v{S}vestka, Prague, June 23-27, 2014. This is a
contribution to a Topical Issue in Solar Physics, based on the presentations
at this meeting (Editors Lyndsay Fletcher and Petr Heinzel
Correlation property of length sequences based on global structure of complete genome
This paper considers three kinds of length sequences of the complete genome.
Detrended fluctuation analysis, spectral analysis, and the mean distance
spanned within time are used to discuss the correlation property of these
sequences. The values of the exponents from these methods of these three kinds
of length sequences of bacteria indicate that the long-range correlations exist
in most of these sequences. The correlation have a rich variety of behaviours
including the presence of anti-correlations. Further more, using the exponent
, it is found that these correlations are all linear (). It is also found that these sequences exhibit noise in some
interval of frequency (). The length of this interval of frequency depends
on the length of the sequence. The shape of the periodogram in exhibits
some periodicity. The period seems to depend on the length and the complexity
of the length sequence.Comment: RevTex, 9 pages with 5 figures and 3 tables. Phys. Rev. E Jan. 1,2001
(to appear
- …