464 research outputs found
Generalized Unitarity and Six-Dimensional Helicity
We combine the unitarity method with the six-dimensional helicity formalism
of Cheung and O'Connell to construct loop-level scattering amplitudes. As a
first example, we construct dimensionally regularized QCD one-loop four-point
amplitudes. As a nontrivial multiloop example, we confirm that the recently
constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory,
including nonplanar contributions, is valid for dimensions less than or equal
to six. We comment on the connection of our approach to the recently discussed
Higgs infrared regulator and on dual conformal properties in six dimensions.Comment: 38 pages, 7 figures, typos correcte
The Last of the Finite Loop Amplitudes in QCD
We use on-shell recursion relations to determine the one-loop QCD scattering
amplitudes with a massless external quark pair and an arbitrary number (n-2) of
positive-helicity gluons. These amplitudes are the last of the unknown
infrared- and ultraviolet-finite loop amplitudes of QCD. The recursion
relations are similar to ones applied at tree level, but contain new
non-trivial features corresponding to poles present for complex momentum
arguments but absent for real momenta. We present the relations and the compact
solutions to them, valid for all n. We also present compact forms for the
previously-computed one-loop n-gluon amplitudes with a single negative helicity
and the rest positive helicity.Comment: 45 pages, revtex, 7 figures, v2 minor correction
All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
We compute the non-MHV one-loop seven-gluon amplitudes in N=4
super-Yang-Mills theory, which contain three negative-helicity gluons and four
positive-helicity gluons. There are four independent color-ordered amplitudes,
(- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV
amplitudes containing two negative-helicity and five positive-helicity gluons
were computed previously, so all independent one-loop seven-gluon helicity
amplitudes are now known for this theory. We present partial information about
an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three
negative-helicity and n-3 positive-helicity gluons, and the color ordering (- -
- + + ... + +); we give a new coefficient of one class of integral functions
entering this amplitude. We discuss the twistor-space properties of the
box-integral-function coefficients in the amplitudes, which are quite simple
and suggestive.Comment: 54 pages, v3 minor correction
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
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
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
Basics of Generalized Unitarity
We review generalized unitarity as a means for obtaining loop amplitudes from
on-shell tree amplitudes. The method is generally applicable to both
supersymmetric and non-supersymmetric amplitudes, including non-planar
contributions. Here we focus mainly on N=4 Yang-Mills theory, in the context of
on-shell superspaces. Given the need for regularization at loop level, we also
review a six-dimensional helicity-based superspace formalism and its
application to dimensional and massive regularizations. An important feature of
the unitarity method is that it offers a means for carrying over any identified
tree-level property of on-shell amplitudes to loop level, though sometimes in a
modified form. We illustrate this with examples of dual conformal symmetry and
a recently discovered duality between color and kinematics.Comment: 37 pages, 10 figures. Invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R.
Roiban(ed), M. Spradlin(ed), A. Volovich(ed
Memory Phenotype CD4 T Cells Undergoing Rapid, Nonburst-Like, Cytokine-Driven Proliferation Can Be Distinguished from Antigen-Experienced Memory Cells
Contrary to the current paradigm that nearly all memory T cells proliferate in response to antigenic stimulation, this paper shows that an important population of CD4 T lymphocytes achieves memory/effector status independent of antigenic stimulation
- …