Alfred S. Goldhaber’s research while affiliated with State University of New York and other places

Hidden-color configurations are a key prediction of QCD with important physical consequences. In this work we examine a QCD color-singlet configuration in nuclei formed by combining six scalar [ud] diquarks in a strongly bound SU(3)C channel. The resulting hexadiquark state is a charge-2, spin-0, baryon number-4, isospin-0, color-singlet state. It contributes to alpha clustering in light nuclei and to the additional binding energy not saturated by ordinary nuclear forces in He4 as well as the alpha-nuclei sequence of interest for nuclear astrophysics. We show that the strongly bound combination of six scalar isospin-0 [ud] diquarks within the nuclear wave function - relative to free nucleons - provides a natural explanation of the EMC effect measured by the CLAS collaboration's comparison of nuclear parton distribution function ratios for a large range of nuclei. These experiments confirmed that the EMC effect; i.e., the distortion of quark distributions within nuclei, is dominantly identified with the dynamics of neutron-proton (“isophobic”) short-range correlations within the nuclear wave function rather than proton-proton or neutron-neutron correlations.

A central feature of deep inelastic lepton-nucleus scattering is the EMC effect, a distortion of quark distributions within nuclei in the domain $0.3 < x_{B} < 0.7$, first measured by the European Muon Collaboration in 1983. The CLAS collaboration recently compared nuclear parton distribution functions for a large range of nuclei and confirmed that the EMC effect is dominantly isophobic; i.e., it could be identified with the dynamics of neutron-proton short-range correlations (SRCs) within the nuclear wave function rather than proton-proton or neutron-neutron SRCs. In this article we analyze the EMC deviation of leading twist nuclear structure functions from nucleon additivity directly in terms of the underlying quark and gluon QCD degrees of freedom. We show that an increased number of scalar isospin-0 [ud] diquarks within the nuclear wavefunction, relative to free nucleons, provides a natural explanation of the isophobic EMC effect. The primary feature is the formation of a novel color-singlet $|[ud][ud][ud][ud][ud][ud]\rangle$ hexa-diquark state in the nuclear wavefunction. The hexa-diquark state is a charge-2, spin-0, baryon number-4, isospin-0, color singlet state created from 6 strongly bound scalar diquarks. The hexa-diquark may be broken into smaller diquark clusters in the high energy diffractive dissociation of nuclei to final states with multiple color diquark jets. Additional states may be created in the multi-diquark core, e.g., a tetra-diquark with one valence quark, leading to qualitative predictions for the A=3 nuclei targets of the MARATHON experiment.

One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two “ridges”, opposite in azimuthal angle ϕ, with approximately flat rapidity distributions. This phenomenon can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper, we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic tube string collisions in the context of two examples: electron-proton scattering at a future electron-ion collider or the peripheral scattering of protons accessible at the LHC. A striking prediction of our analysis is that the azimuthal angle of the produced ridges will be correlated with the scattering plane of the electron or proton producing the virtual photon. In the case of ep→eX, the final state X is expected to exhibit maximal multiplicity when the elliptic flow in X is aligned with the electron scattering plane. In the pp→ppX example, the multiplicity and elliptic flow in X are estimated to exhibit correlated oscillations as functions of the azimuthal angle Φ between the proton scattering planes. In the minimum-bias event samples, the amplitude of oscillations is expected to be on the order of 2% to 4% of the mean values. In the events with highest multiplicity, the oscillations can be three times larger than in the minimum-bias event samples.

One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two "ridges", opposite in azimuthal angle $\phi$, with approximately flat rapidity distributions. This phenomena can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic tube string collisions in the context of two examples: electron-proton scattering at a future electron-ion collider or the peripheral scattering of protons accessible at the LHC. A striking prediction of our analysis is that the azimuthal angle of the produced ridges will be correlated with the scattering plane of the electron or proton producing the virtual photon. In the case of $ep \to eX$, the final state X is expected to exhibit maximal multiplicity when the elliptic flow in X is aligned with the electron scattering plane. In the $pp \to ppX$ example, the multiplicity and elliptic flow in X are estimated to exhibit correlated oscillations as functions of the azimuthal angle $\Phi$ between the proton scattering planes. In the minimum-bias event samples, the amplitude of oscillations is expected to be on the order of 2 to 4 percent of the mean values. In the events with highest multiplicity, the oscillations can be three times larger than in the minimum-bias event samples.

Dirac in 1931 gave a beautiful argument for the quantization of electric charge, which required only the existence in the universe of one magnetic monopole, because gauge invariance of the interaction between the pole and any charge could hold only if the product of the charge and the pole strength were quantized in half-integer multiples of the reduced Planck constant. However, if the photon had a nonzero mass, implying exponential decrease of the flux out of an electric charge, then Dirac's argument might seem to fail. We demonstrate that the result still should hold. The key point is that magnetic charge, unlike electric charge, cannot be screened, so that on any surface enclosing the pole Dirac's string, or equally the Wu-Yang gauge shift, must be present, and to make either of these invisible to charged particles the quantization condition is required.

An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are distributed as two "ridges", approximately flat in rapidity and opposite in azimuthal angle. We propose that the origin of these events is due to the inelastic collisions of aligned gluonic flux tubes that underly the color confinement of the quarks in each proton. We predict that high-multiplicity hadronic ridges will also be produced in the high energy photon-photon collisions accessible at the LHC in ultra-peripheral proton-proton collisions or at a high energy electron-positron collider. We also note the orientation of the flux tubes between the $q \bar q$ of each high energy photon will be correlated with the plane of the scattered proton or lepton. Thus hadron production and ridge formation can be controlled in a novel way at the LHC by observing the azimuthal correlations of the scattering planes of the ultra-peripheral protons with the orientation of the produced ridges. Photon-photon collisions can thus illuminate the fundamental physics underlying the ridge effect and the physics of color confinement in QCD.

In reply to Robert P Crease's article "The spot in the shadow" (February p16, http://ow.ly/ulHSX).

The CMS collaboration at the LHC has reported a remarkable and unexpected phenomenon in very high-multiplicity high energy proton-proton collisions: a positive correlation between two particles produced at similar azimuthal angles, spanning a large range in rapidity. We suggest that this "ridge"-like correlation may be a reflection of the rare events generated by the collision of aligned flux tubes connecting the valence quarks in the wave functions of the colliding protons. The "spray" of particles resulting from the approximate line source produced in such inelastic collisions then gives rise to events with a strong correlation between particles produced over a large range of both positive and negative rapidity. We suggest an additional variable that is sensitive to such a line source which is related to a commonly used measure, ellipticity.