Vanishing cycles and analysis of singularities of Feynman diagrams

In this work, we analyze vanishing cycles of Feynman loop integrals by means of the Mayer-Vietoris spectral sequence. A complete classification of possible vanishing geometries are obtained. We employ this result for establishing an asymptotic expansion for the loop integrals near their singularity locus, then give explicit formulas for the coefficients of such an expansion. The further development of this framework may potentially lead to exact calculations of one- and two-loop Feynman diagrams, as well as other next-to-leading and higher-order diagrams, in studies of radiative corrections for upcoming lepton-hadron scattering experiments.Comment: 22 pages and 3 figure

Lowest-order QED radiative corrections in unpolarized elastic electron-deuteron scattering beyond the ultra-relativistic limit for the proposed deuteron charge radius measurement at Jefferson Laboratory

Analogous to the well-known proton charge radius puzzle, a similar puzzle exists for the deuteron charge radius, $r_{d}$. There are discrepancies observed in the results of $r_{d}$, measured from electron-deuteron ($e-d$) scattering experiments, as well as from atomic spectroscopy. In order to help resolve the charge radius puzzle of the deuteron, the PRad collaboration at Jefferson Lab has proposed an experiment for measuring $r_{d}$, named DRad. This experiment is designed to measure the unpolarized elastic $e-d$ scattering cross section in a low-$Q^{2}$ region. To extract the cross section with a high precision, having reliable knowledge of QED radiative corrections is important. In this paper, we present complete numerical calculations of the lowest-order radiative corrections in $e-d$ scattering for the DRad kinematics. The calculations have been performed within a covariant formalism and beyond the ultra-relativistic approximation ($m_{e}^{2} \ll Q^{2}$). Besides, we present a systematic uncertainty on $r_{d}$ arising from higher-order radiative corrections, estimated based on our cross-section results.Comment: 16 pages and 6 figure

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

44 pages, ReVTeX, White Paper on EIC Theory AllianceWe outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance