Scaling properties of direct photon yields in heavy ion collisions

A recent analysis from the PHENIX collaboration of available direct photon measurement results in collisions of various systems such as Au+Au, Cu+Cu, and Pb+Pb, at different beam energies ranging from 39 to 2760 GeV, has shown a universal, within experimental uncertainties, $multiplicity$ scaling, in which direct photon $p_{T}$-spectra for transverse momenta up to 2 GeV/$c$ are scaled with charged hadron pseudorapidity density at midrapidity raised to power $\alpha=1.25$. On the other hand, those direct photon $p_{T}$-spectra also exhibit $geometrical$ scaling in the similar $p_{T}$ range. Assuming power-law dependence of the scaled photon spectra for both scaling laws, we formulate two independent conditions for the power $\alpha$, which overshoot experimental data by $\sim 10\%$ on average. We discuss possible sources that might improve this estimate.Comment: 8 pages, 5 figures. The paper has been rewritten, title has been changed, new material and references added. Version accepted for publication in EPJ C. In v3 references updated, minor typos correcte

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

SIDIS-RC EvGen: a Monte-Carlo event generator of semi-inclusive deep inelastic scattering with the lowest-order QED radiative corrections

SIDIS-RC EvGen is a C++ standalone Monte-Carlo event generator for studies of semi-inclusive deep inelastic scattering (SIDIS) processes at medium to high lepton beam energies. In particular, the generator contains binary and library components for generating SIDS events and calculating cross sections for unpolarized or longitudinally polarized beam and unpolarized, longitudinally or transversely polarized target. The structure of the generator incorporates transverse momentum-dependent parton distribution and fragmentation functions, whereby we obtain multi-dimensional binned simulation results, which will facilitate the extraction of important information about the three-dimensional nucleon structure from SIDIS measurements. In order to build this software, we have used recent elaborate QED calculations of the lowest-order radiative effects, applied to the leading order Born cross section in SIDIS. In this paper, we provide details on the theoretical formalism as well as the construction and operation of SIDIS-RC EvGen, e.g., how we handle the event generation process and perform multi-dimensional integration. We also provide example programs, flowcharts, and numerical results on azimuthal transverse single-spin asymmetries.Comment: 53 pages, 10 figures, and 3 listing