The last of the simple remainders

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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

Factorization Properties of Soft Graviton Amplitudes

We apply recently developed path integral resummation methods to perturbative quantum gravity. In particular, we provide supporting evidence that eikonal graviton amplitudes factorize into hard and soft parts, and confirm a recent hypothesis that soft gravitons are modelled by vacuum expectation values of products of certain Wilson line operators, which differ for massless and massive particles. We also investigate terms which break this factorization, and find that they are subleading with respect to the eikonal amplitude. The results may help in understanding the connections between gravity and gauge theories in more detail, as well as in studying gravitational radiation beyond the eikonal approximation.Comment: 35 pages, 5 figure

Large CP Violation in B_s Meson Mixing with EDM constraint in Supersymmetry

Motivated by the recent measurement of the like-sign dimuon charge asymmetry, we investigate anomalous CP violation in the B_s- bar{B}_s mixing within the supersymmetry. We show that when gluino diagrams dominate supersymmetry contributions, it is very difficult to realize a large B_s- bar{B}_s mixing phase under the constraint from electric dipole moments barring cancellations. This constraint can be ameliorated by supposing superparticles decoupled. In this limit, we find that it is possible to achieve the large CP asymmetry, and the branching ratio of B_s -> mu^+ mu^- tends to become sizable.Comment: 20 pages, 5 figure

Restrictive ID policies: implications for health equity

We wish to thank Synod Community Services for their critical work to develop, support, and implement a local government-issued ID in Washtenaw County, MI. We also thank Yousef Rabhi of the Michigan House of Representatives and Janelle Fa'aola of the Washtenaw ID Task Force, Lawrence Kestenbaum of the Washtenaw County Clerk's Office, Sherriff Jerry Clayton of the Washtenaw County Sherriff's Office, and the Washtenaw ID Task Force for their tireless commitment to developing and supporting the successful implementation of the Washtenaw ID. Additionally, we thank Vicenta Vargas and Skye Hillier for their contributions to the Washtenaw ID evaluation. We thank the Curtis Center for Research and Evaluation at the University of Michigan School of Social Work, the National Center for Institutional Diversity at the University of Michigan, and the University of California-Irvine Department of Chicano/Latino Studies and Program in Public Health for their support of the Washtenaw ID community-academic research partnership. Finally, we thank the reviewers for their helpful comments on earlier drafts of this manuscript. (Curtis Center for Research and Evaluation at the University of Michigan School of Social Work; National Center for Institutional Diversity at the University of Michigan; University of California-Irvine Department of Chicano/Latino Studies; Program in Public Health)https://link.springer.com/content/pdf/10.1007/s10903-017-0579-3.pdfPublished versio

Exact exchange-correlation potential of a ionic Hubbard model with a free surface

We use Lanczos exact diagonalization to compute the exact exchange-correlation (xc) potential of a Hubbard chain with large binding energy ("the bulk") followed by a chain with zero binding energy ("the vacuum"). Several results of density functional theory in the continuum (sometimes controversial) are verified in the lattice. In particular we show explicitly that the fundamental gap is given by the gap in the Kohn-Sham spectrum plus a contribution due to the jump of the xc-potential when a particle is added. The presence of a staggered potential and a nearest-neighbor interaction V allows to simulate a ionic solid. We show that in the ionic regime in the small hopping amplitude limit the xc-contribution to the gap equals V, while in the Mott regime it is determined by the Hubbard U interaction. In addition we show that correlations generates a new potential barrier at the surface

Controlling a magnetic Feshbach resonance with laser light

The capability to tune the strength of the elastic interparticle interaction is crucial for many experiments with ultracold gases. Magnetic Feshbach resonances are a tool widely used for this purpose, but future experiments would benefit from additional flexibility such as spatial modulation of the interaction strength on short length scales. Optical Feshbach resonances offer this possibility in principle, but suffer from fast particle loss due to light-induced inelastic collisions. Here we show that light near-resonant with a molecular bound-to-bound transition can be used to shift the magnetic field at which a magnetic Feshbach resonance occurs. This makes it possible to tune the interaction strength with laser light and at the same time induce considerably less loss than an optical Feshbach resonance would do

A molecular insight into algal-oomycete warfare : cDNA analysis of Ectocarpus siliculosus infected with the basal oomycete Eurychasma dicksonii

Peer reviewedPublisher PD

Single-valued harmonic polylogarithms and the multi-Regge limit

We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar N=4 super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, (w,w*). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables (\nu,n) which are related to (w,w*) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (\nu,n) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to NNNLLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.Comment: 71 pages, 2 figures, plus 10 ancillary files containing analytic expressions in Mathematica format. V2: Typos corrected and references added. V3: Typos corrected; assumption about single-Reggeon exchange made explici

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