135 research outputs found
On Glauber modes in Soft-Collinear Effective Theory
Gluon interactions involving spectator partons in collisions at hadronic
machines are investigated. We find a class of examples in which a mode, called
Glauber gluons, must be introduced to the effective theory for consistency.Comment: 19 pages, three figures. Uses JHEP3.cl
The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
Infrared divergences in scattering amplitudes arise when a loop momentum
becomes collinear with a massless external momentum . In gauge
theories, it is known that the L-loop logarithm of a planar amplitude has much
softer infrared singularities than the L-loop amplitude itself. We argue that
planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected
behavior as already at the level of the integrand. Moreover,
we conjecture that the four-point integrand can be uniquely determined, to any
loop-order, by imposing the correct soft-behavior of the logarithm together
with dual conformal invariance and dihedral symmetry. We use these simple
criteria to determine explicit formulae for the four-point integrand through
seven-loops, finding perfect agreement with previously known results through
five-loops. As an input to this calculation we enumerate all four-point dual
conformally invariant (DCI) integrands through seven-loops, an analysis which
is aided by several graph-theoretic theorems we prove about general DCI
integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive
non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica
files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7
corrected, Lemma 2 remove
On the renormalization of multiparton webs
We consider the recently developed diagrammatic approach to soft-gluon
exponentiation in multiparton scattering amplitudes, where the exponent is
written as a sum of webs - closed sets of diagrams whose colour and kinematic
parts are entangled via mixing matrices. A complementary approach to
exponentiation is based on the multiplicative renormalizability of intersecting
Wilson lines, and their subsequent finite anomalous dimension. Relating this
framework to that of webs, we derive renormalization constraints expressing all
multiple poles of any given web in terms of lower-order webs. We examine these
constraints explicitly up to four loops, and find that they are realised
through the action of the web mixing matrices in conjunction with the fact that
multiple pole terms in each diagram reduce to sums of products of lower-loop
integrals. Relevant singularities of multi-eikonal amplitudes up to three loops
are calculated in dimensional regularization using an exponential infrared
regulator. Finally, we formulate a new conjecture for web mixing matrices,
involving a weighted sum over column entries. Our results form an important
step in understanding non-Abelian exponentiation in multiparton amplitudes, and
pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure
Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
We calculate form factors of half-BPS operators in N=4 super Yang-Mills
theory at tree level and one loop using novel applications of recursion
relations and unitarity. In particular, we determine the expression of the
one-loop form factors with two scalars and an arbitrary number of
positive-helicity gluons. These quantities resemble closely the MHV scattering
amplitudes, including holomorphicity of the tree-level form factor, and the
expansion in terms of two-mass easy box functions of the one-loop result. Next,
we compare our result for these form factors to the calculation of a particular
periodic Wilson loop at one loop, finding agreement. This suggests a novel
duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde
Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
We consider the problem of soft gluon resummation for gauge theory amplitudes
and cross sections, at next-to-eikonal order, using a Feynman diagram approach.
At the amplitude level, we prove exponentiation for the set of factorizable
contributions, and construct effective Feynman rules which can be used to
compute next-to-eikonal emissions directly in the logarithm of the amplitude,
finding agreement with earlier results obtained using path-integral methods.
For cross sections, we also consider sub-eikonal corrections to the phase space
for multiple soft-gluon emissions, which contribute to next-to-eikonal
logarithms. To clarify the discussion, we examine a class of log(1 - x) terms
in the Drell-Yan cross-section up to two loops. Our results are the first steps
towards a systematic generalization of threshold resummations to
next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure
A next-to-next-to-leading order calculation of soft-virtual cross sections
We compute the next-to-next-to-leading order (NNLO) soft and virtual QCD
corrections for the partonic cross section of colourless-final state processes
in hadronic collisions. The results are valid to all orders in the dimensional
regularization parameter \ep. The dependence of the results on a particular
process is given through finite contributions to the one and two-loop
amplitudes. To evaluate the accuracy of the soft-virtual approximation we
compare it with the full NNLO result for Drell-Yan and Higgs boson production
via gluon fusion. We also provide a universal expression for the hard
coefficient needed to perform threshold resummation up to
next-to-next-to-leading logarithmic (NNLL) accuracy.Comment: 25 pages, 4 figure
Parton Fragmentation within an Identified Jet at NNLL
The fragmentation of a light parton i to a jet containing a light energetic
hadron h, where the momentum fraction of this hadron as well as the invariant
mass of the jet is measured, is described by "fragmenting jet functions". We
calculate the one-loop matching coefficients J_{ij} that relate the fragmenting
jet functions G_i^h to the standard, unpolarized fragmentation functions D_j^h
for quark and gluon jets. We perform this calculation using various IR
regulators and show explicitly how the IR divergences cancel in the matching.
We derive the relationship between the coefficients J_{ij} and the quark and
gluon jet functions. This provides a cross-check of our results. As an
application we study the process e+ e- to X pi+ on the Upsilon(4S) resonance
where we measure the momentum fraction of the pi+ and restrict to the dijet
limit by imposing a cut on thrust T. In our analysis we sum the logarithms of
tau=1-T in the cross section to next-to-next-to-leading-logarithmic accuracy
(NNLL). We find that including contributions up to NNLL (or NLO) can have a
large impact on extracting fragmentation functions from e+ e- to dijet + h.Comment: expanded introduction, typos fixed, journal versio
An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung
Two effects, jet broadening and gluon bremsstrahlung induced by the
propagation of a highly energetic quark in dense QCD matter, are reconsidered
from effective theory point of view. We modify the standard Soft Collinear
Effective Theory (SCET) Lagrangian to include Glauber modes, which are needed
to implement the interactions between the medium and the collinear fields. We
derive the Feynman rules for this Lagrangian and show that it is invariant
under soft and collinear gauge transformations. We find that the newly
constructed theory SCET recovers exactly the general result for the
transverse momentum broadening of jets. In the limit where the radiated gluons
are significantly less energetic than the parent quark, we obtain a jet
energy-loss kernel identical to the one discussed in the reaction operator
approach to parton propagation in matter. In the framework of SCET we
present results for the fully-differential bremsstrahlung spectrum for both the
incoherent and the Landau-Pomeranchunk-Migdal suppressed regimes beyond the
soft-gluon approximation. Gauge invariance of the physics results is
demonstrated explicitly by performing the calculations in both the light-cone
and covariant gauges. We also show how the process-dependent
medium-induced radiative corrections factorize from the jet production cross
section on the example of the quark jets considered here.Comment: 52 pages, 15 pdf figures, as published in JHE
Non-global Structure of the O({\alpha}_s^2) Dijet Soft Function
High energy scattering processes involving jets generically involve matrix
elements of light- like Wilson lines, known as soft functions. These describe
the structure of soft contributions to observables and encode color and
kinematic correlations between jets. We compute the dijet soft function to
O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on
terms not determined by its renormalization group evolution that have a
non-separable dependence on these masses. Our results include non-global single
and double logarithms, and analytic results for the full set of non-logarithmic
contributions as well. Using a recent result for the thrust constant, we
present the complete O({\alpha}_s^2) soft function for dijet production in both
position and momentum space.Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the
hard regime. v3: minor typos corrected, version published in JHEP. v4: typos
in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main
result, numerical results, or conclusion
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