755 research outputs found
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
Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
We confirm by explicit computation the conjectured all-orders iteration of
planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of
five-point two-loop amplitudes. We compute the required unitarity cuts of the
integrand and evaluate the resulting integrals numerically using a
Mellin--Barnes representation and the automated package of ref.~[1]. This
confirmation of the iteration relation provides further evidence suggesting
that N=4 gauge theory is solvable.Comment: 4 pages, 3 figure
Three-jet cross sections in hadron-hadron collisions at next-to-leading order
We present a new QCD event generator for hadron collider which can calculate
one-, two- and three-jet cross sections at next-to-leading order accuracy. In
this letter we study the transverse energy spectrum of three-jet hadronic
events using the kT algorithm. We show that the next-to-leading order
correction significantly reduces the renormalization and factorization scale
dependence of the three-jet cross section.Comment: 4 pages, 4 figures, REVTEX
Expansion around half-integer values, binomial sums and inverse binomial sums
I consider the expansion of transcendental functions in a small parameter
around rational numbers. This includes in particular the expansion around
half-integer values. I present algorithms which are suitable for an
implementation within a symbolic computer algebra system. The method is an
extension of the technique of nested sums. The algorithms allow in addition the
evaluation of binomial sums, inverse binomial sums and generalizations thereof.Comment: 21 page
Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
We present an ansatz for the planar five-loop four-point amplitude in
maximally supersymmetric Yang-Mills theory in terms of loop integrals. This
ansatz exploits the recently observed correspondence between integrals with
simple conformal properties and those found in the four-point amplitudes of the
theory through four loops. We explain how to identify all such integrals
systematically. We make use of generalized unitarity in both four and D
dimensions to determine the coefficients of each of these integrals in the
amplitude. Maximal cuts, in which we cut all propagators of a given integral,
are an especially effective means for determining these coefficients. The set
of integrals and coefficients determined here will be useful for computing the
five-loop cusp anomalous dimension of the theory which is of interest for
non-trivial checks of the AdS/CFT duality conjecture. It will also be useful
for checking a conjecture that the amplitudes have an iterative structure
allowing for their all-loop resummation, whose link to a recent string-side
computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT
comparisons.Comment: 52 pages, 20 figures, revte
General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory
We evaluate all split helicity gluon tree amplitudes in open twistor string
theory. We show that these amplitudes satisfy the BCFW recurrence relations
restricted to the split helicity case and, hence, that these amplitudes agree
with those of gauge theory. To do this we make a particular choice of the
sextic constraints in the link variables that determine the poles contributing
to the contour integral expression for the amplitudes. Using the residue
theorem to re-express this integral in terms of contributions from poles at
rational values of the link variables, which we determine, we evaluate the
amplitudes explicitly, regaining the gauge theory results of Britto et al.Comment: 30 pages, minor misprints correcte
Antenna subtraction for gluon scattering at NNLO
We use the antenna subtraction method to isolate the double real radiation
infrared singularities present in gluonic scattering amplitudes at
next-to-next-to-leading order. The antenna subtraction framework has been
successfully applied to the calculation of NNLO corrections to the 3-jet cross
section and related event shape distributions in electron-positron
annihilation. Here we consider processes with two coloured particles in the
initial state, and in particular two-jet production at hadron colliders such as
the Large Hadron Collider (LHC). We construct a subtraction term that describes
the single and double unresolved contributions from the six-gluon tree-level
process using antenna functions with initial state partons and show numerically
that the subtraction term correctly approximates the matrix elements in the
various single and double unresolved configurations.Comment: 71 pages, JHEP3 class; corrected typos, equivalent but more compact
version of eq. (5.12), results unchange
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
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