1,226 research outputs found
Eikonal methods applied to gravitational scattering amplitudes
We apply factorization and eikonal methods from gauge theories to scattering
amplitudes in gravity. We hypothesize that these amplitudes factor into an
IR-divergent soft function and an IR-finite hard function, with the former
given by the expectation value of a product of gravitational Wilson line
operators. Using this approach, we show that the IR-divergent part of the
n-graviton scattering amplitude is given by the exponential of the one-loop IR
divergence, as originally discovered by Weinberg, with no additional subleading
IR-divergent contributions in dimensional regularization.Comment: 16 pages, 3 figures; v2: title change and minor rewording (published
version); v3: typos corrected in eqs.(3.2),(4.1
On soft singularities at three loops and beyond
We report on further progress in understanding soft singularities of massless
gauge theory scattering amplitudes. Recently, a set of equations was derived
based on Sudakov factorization, constraining the soft anomalous dimension
matrix of multi-leg scattering amplitudes to any loop order, and relating it to
the cusp anomalous dimension. The minimal solution to these equations was shown
to be a sum over color dipoles. Here we explore potential contributions to the
soft anomalous dimension that go beyond the sum-over-dipoles formula. Such
contributions are constrained by factorization and invariance under rescaling
of parton momenta to be functions of conformally invariant cross ratios.
Therefore, they must correlate the color and kinematic degrees of freedom of at
least four hard partons, corresponding to gluon webs that connect four eikonal
lines, which first appear at three loops. We analyze potential contributions,
combining all available constraints, including Bose symmetry, the expected
degree of transcendentality, and the singularity structure in the limit where
two hard partons become collinear. We find that if the kinematic dependence is
solely through products of logarithms of cross ratios, then at three loops
there is a unique function that is consistent with all available constraints.
If polylogarithms are allowed to appear as well, then at least two additional
structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4;
added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11,
5.12 and 5.29); 38 pages, 3 figure
New differential equations for on-shell loop integrals
We present a novel type of differential equations for on-shell loop
integrals. The equations are second-order and importantly, they reduce the loop
level by one, so that they can be solved iteratively in the loop order. We
present several infinite series of integrals satisfying such iterative
differential equations. The differential operators we use are best written
using momentum twistor space. The use of the latter was advocated in recent
papers discussing loop integrals in N=4 super Yang-Mills. One of our
motivations is to provide a tool for deriving analytical results for scattering
amplitudes in this theory. We show that the integrals needed for planar MHV
amplitudes up to two loops can be thought of as deriving from a single master
topology. The master integral satisfies our differential equations, and so do
most of the reduced integrals. A consequence of the differential equations is
that the integrals we discuss are not arbitrarily complicated transcendental
functions. For two specific two-loop integrals we give the full analytic
solution. The simplicity of the integrals appearing in the scattering
amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation
to the conjectured underlying integrability of the theory. We expect these
differential equations to be relevant for all planar MHV and non-MHV
amplitudes. We also discuss possible extensions of our method to more general
classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic
polylogarithms adde
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
A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
Many observables in QCD rely upon the resummation of perturbation theory to
retain predictive power. Resummation follows after one factorizes the cross
section into the rele- vant modes. The class of observables which are sensitive
to soft recoil effects are particularly challenging to factorize and resum
since they involve rapidity logarithms. In this paper we will present a
formalism which allows one to factorize and resum the perturbative series for
such observables in a systematic fashion through the notion of a "rapidity
renormalization group". That is, a Collin-Soper like equation is realized as a
renormalization group equation, but has a more universal applicability to
observables beyond the traditional transverse momentum dependent parton
distribution functions (TMDPDFs) and the Sudakov form factor. This formalism
has the feature that it allows one to track the (non-standard) scheme
dependence which is inherent in any scenario where one performs a resummation
of rapidity divergences. We present a pedagogical introduction to the formalism
by applying it to the well-known massive Sudakov form factor. The formalism is
then used to study observables of current interest. A factorization theorem for
the transverse momentum distribution of Higgs production is presented along
with the result for the resummed cross section at NLL. Our formalism allows one
to define gauge invariant TMDPDFs which are independent of both the hard
scattering amplitude and the soft function, i.e. they are uni- versal. We
present details of the factorization and resummation of the jet broadening
cross section including a renormalization in pT space. We furthermore show how
to regulate and renormalize exclusive processes which are plagued by endpoint
singularities in such a way as to allow for a consistent resummation.Comment: Typos in Appendix C corrected, as well as a typo in eq. 5.6
Measurement of the Dipion Mass Spectrum in X(3872) -> J/Psi Pi+ Pi- Decays
We measure the dipion mass spectrum in X(3872)--> J/Psi Pi+ Pi- decays using
360 pb-1 of pbar-p collisions at 1.96 TeV collected with the CDF II detector.
The spectrum is fit with predictions for odd C-parity (3S1, 1P1, and 3DJ)
charmonia decaying to J/Psi Pi+ Pi-, as well as even C-parity states in which
the pions are from Rho0 decay. The latter case also encompasses exotic
interpretations, such as a D0-D*0Bar molecule. Only the 3S1 and J/Psi Rho
hypotheses are compatible with our data. Since 3S1 is untenable on other
grounds, decay via J/Psi Rho is favored, which implies C=+1 for the X(3872).
Models for different J/Psi-Rho angular momenta L are considered. Flexibility in
the models, especially the introduction of Rho-Omega interference, enable good
descriptions of our data for both L=0 and 1.Comment: 7 pages, 4 figures -- Submitted to Phys. Rev. Let
Search for Higgs Boson Decaying to b-bbar and Produced in Association with W Bosons in p-pbar Collisions at sqrt{s}=1.96 TeV
We present a search for Higgs bosons decaying into b-bbar and produced in
association with W bosons in p-pbar collisions at sqrt{s}=1.96 TeV. This search
uses 320 pb-1 of the dataset accumulated by the upgraded Collider Detector at
Fermilab. Events are selected that have a high-transverse momentum electron or
muon, missing transverse energy, and two jets, one of which is consistent with
a hadronization of a b quark. Both the number of events and the dijet mass
distribution are consistent with standard model background expectations, and we
set 95% confidence level upper limits on the production cross section times
branching ratio for the Higgs boson or any new particle with similar decay
kinematics. These upper limits range from 10 pb for mH=110 GeV/c2 to 3 pb for
mH=150 GeV/c2.Comment: 7 pages, 3 figures; updated title to published versio
Measurement of the Inclusive Jet Cross Section using the Kt algorithm in pp-bar Collisions at sqrt(s) = 1.96 TeV
We report on a measurement of the inclusive jet production cross section in
pp-bar collisions at sqrt{s} = 1.96 TeV using data collected with the upgraded
Collider Detector at Fermilab in Run II (CDF II) corresponding to an integrated
luminosity of 385 pb^-1. Jets are reconstructed using the kt algorithm. The
measurement is carried out for jets with rapidity 0.1 < | yjet | < 0.7 and
transverse momentum in the range 54 < ptjet < 700 GeV/c. The measured cross
section is in good agreement with next-to-leading order perturbative QCD
predictions after the necessary non-perturbative parton-to-hadron corrections
are included.Comment: Submitted to Phys. Rev. Let
Search for Second-Generation Scalar Leptoquarks in Collisions at =1.96 TeV
Results on a search for pair production of second generation scalar
leptoquark in collisions at =1.96 TeV are reported. The
data analyzed were collected by the CDF detector during the 2002-2003 Tevatron
Run II and correspond to an integrated luminosity of 198 pb. Leptoquarks
(LQ) are sought through their decay into (charged) leptons and quarks, with
final state signatures represented by two muons and jets and one muon, large
transverse missing energy and jets. We observe no evidence for production
and derive 95% C.L. upper limits on the production cross sections as well
as lower limits on their mass as a function of , where is the
branching fraction for .Comment: 9 pages (3 author list) 5 figure
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