Relativistic corrections to the rotation curves of disk galaxies

We present a method to investigate relativistic effects arising from large masses. The method is non-perturbative and employs a mean-field approximation and gravitational lensing. Using this method and a basic model of disk galaxy, we find that relativistic corrections to the rotation curves of disk galaxies are significant at large galactic radii. The model predicts a strong correlation between the inferred galactic dark mass and the galactic disk thickness, which we verified using two separate sets of observational data.Comment: 11 pages, 9 figures. Final version accepted in Eur. Phys. Jour.

Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies

The discrepancy between the visible mass in galaxies or galaxy clusters, and that inferred from their dynamics is well known. The prevailing solution to this problem is dark matter. Here we show that a different approach, one that conforms to both the current Standard Model of Particle Physics and General Relativity, explains the recently observed tight correlation between the galactic baryonic mass and its observed acceleration. Using direct calculations based on General Relativity's Lagrangian, and parameter-free galactic models, we show that the nonlinear effects of General Relativity make baryonic matter alone sufficient to explain this observation.Comment: Accepted for publication in the Astrophysical Journa

AdS/QCD, Light-Front Holography, and the Nonperturbative Running Coupling

The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable $\zeta$ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-$J$ modes in anti--de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling $\alpha_s^{AdS}(Q^2)$ which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $\sim 1$ GeV. The resulting $\beta$-function appears to capture the essential characteristics of the full $\beta$-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.Comment: Invited talk, presented by SJB at SCGT09, 2009 International Workshop on Strong Coupling Gauge Theories in the LHC Era, Nagoya, December 8-11, 2009, updated figur

Connecting the Hadron Mass Scale to the Fundamental Mass Scale of Quantum Chromodynamics

Establishing an explicit connection between the long distance physics of confinement and the dynamical interactions of quarks and gluons at short distances has been a long-sought goal of quantum chromodynamics. Using holographic QCD, we derive a direct analytic relation between the scale $\kappa$ which determines the masses of hadrons and the scale $\Lambda_{s}$ which controls the predictions of perturbative QCD at very short distances. The resulting prediction $\Lambda_{s}=0.341\pm0.032$ GeV in the $\overline{MS}$ scheme agrees well with the experimental average $0.339\pm0.016$ GeV. We also derive a relation between $\Lambda_{s}$ and the QCD string tension $\sigma$. This connection between the fundamental hadronic scale underlying the physics of quark confinement and the perturbative QCD scale controlling hard collisions can be carried out in any renormalization scheme.Comment: 11 pages, 4 figures. Final version published in Phys. Lett.

Hadron and Nuclear Physics on the Light Front

The QCD light-front (LF) Hamiltonian equation H_{LF}|\Psi> = M^2 |\Psi> derived from quantization at fixed LF time \tau = t+z/c provides a causal, frame-independent, method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The LF formalism also leads to novel nuclear phenomena, such as "hidden color", "color transparency", "nuclear-bound quarkonium" and the shadowing and antishadowing of nuclear structure functions. For example, there are five distinct color-singlet Fock state representations of the six color-triplet quarks of the deuteron. The hidden color Fock states become manifest when the deuteron is probed when it has small transverse size, as in measurements of the deuteron form factor at large momentum transfer. The QCD Lagrangian with zero quark mass has no explicit mass scale. However, as shown by de Alfaro, Fubini, and Furlan (dAFF), a mass scale can appear in the equations of motion without affecting the conformal invariance of the Action. When one applies the dAFF procedure to the QCD LF Hamiltonian, it leads to a color confining potential \kappa^4 \zeta^2 for mesons, where \zeta^2 is the LF radial variable conjugate to the qbar-q invariant mass squared. The same result, including spin terms, is obtained using LF holography (AdS/QCD) -- the duality between LF dynamics and AdS_5 -- if one modifies the AdS_5 Action by the dilaton exp{+\kappa^2 z^2} in the fifth dimension z. If this procedure is generalized using superconformal algebra, the resulting LF eigensolutions provide unified Regge spectroscopy of mesons, baryons, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons, baryons and tetraquarks with a universal Regge slope...Comment: 8 pages, 3 figures. Contribution to the proceedings of 13th International Conference on Nucleus-Nucleus Collisions (NN2018) in Omiya, Japan. Plenary talk given by S. J. Brodsky. arXiv admin note: text overlap with arXiv:1802.08552, arXiv:1709.01191, arXiv:1611.071

Effect of Orbital Angular Momentum on Valence-Quark Helicity Distributions

We study the quark helicity distributions at large x in perturbative QCD, taking into account contributions from the valence Fock states of the nucleon which have nonzero orbital angular momentum. These states are necessary to have a nonzero anomalous magnetic moment. We find that the quark orbital angular momentum contributes a large logarithm to the negative helicity quark distributions in addition to its power behavior, scaling as (1-x)^5\log^2(1-x) in the limit of x\to 1. Our analysis shows that the ratio of the polarized over unpolarized down quark distributions, \Delta d/d, will still approach 1 in this limit. By comparing with the experimental data, we find that this ratio should cross zero at x\approx 0.75.Comment: 10 pages, 3 eps figure