arXiv subjects
Publications and source records attributed to P. H. Tsang.
Using previously described functional techniques for some non-perturbative, gauge invariant, renormalized QCD processes, a simplified version of the amplitudes - in which forms akin to Pomerons naturally appear - provides fits to ISR and LHC-TOTEM pp elastic scattering data. Those amplitudes rely on a specific function $ϕ(b)$ which describes the fluctuations of the transverse position of quarks inside hadrons.
Using previously described functional techniques for some non--perturbative, gauge invariant, renormalized QCD processes, a simplified version of the amplitudes --- in which forms akin to Pomerons naturally appear --- provides fits to ISR and LHC--TOTEM $pp$ elastic scattering data. Those amplitudes rely on a specific function $φ(\vec b)$ which describes the fluctuations of the transverse position of quarks inside hadrons.
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no 'self-energy' to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion's chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to high energy elastic pp scattering is now underway.
We suggest a physical definition of the confinement mass scale in QCD in the framework of non-perturbative, gauge invariant QCD, where all possible gluons exchanged between any pair of quark lines are included; and we insist that a stable, quark bound state should not and must not have transverse quark fluctuations larger than the Compton wavelength of the bound state particle itself. This is possible in our QCD formulation because there are two parameters which describe confinement, a mass scale $μ$, and a "deformation parameter" $ξ$, which shrinks the transverse-quark-coordinate separation distribution $φ(b)$ away from Gaussian. With the mass scale $μ$ defined as equal to the mass of each quark bound state, we show that $ξ$ decreases with increasing bound state mass, $m_{BS}$, using order-of-magnitude estimates which agree with obvious intuition. Our $ξ$-values, including a calculation for the recently detected 4-quark system, display the predicted behavior: $ξ$ decreases with increasing $m_{BS}$. Our results for $φ(b)$, when the quark bound state is a nucleon or heavier, then show agreement with the form of Gaussian momentum-space fall-offs in recent Light-Front holographic analyses.