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

Search for Second-Generation Scalar Leptoquarks in ppˉ\bm{p \bar{p}} Collisions at s\sqrt{s}=1.96 TeV

Results on a search for pair production of second generation scalar leptoquark in $p \bar{p}$ collisions at $\sqrt{s}$=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$^{-1}$. 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 $LQ$ production and derive 95% C.L. upper limits on the $LQ$ production cross sections as well as lower limits on their mass as a function of $\beta$, where $\beta$ is the branching fraction for $LQ \to \mu q$.Comment: 9 pages (3 author list) 5 figure

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