QCD on the Light-Front -- A Systematic Approach to Hadron Physics

Light-Front Hamiltonian theory provides a rigorous frame-independent framework for solving nonperturbative QCD. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schr\"odinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. The valence LF meson wavefunctions for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable $\zeta^2=b^2_\perp x(1-x)$, which is conjugate to the invariant mass squared. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. The corresponding light-front Dirac equation provides a model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS_5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between amplitudes in the fifth dimension of AdS space and light-front wavefunctions. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting, and the implications of light-front quantization for the value of the cosmological constant.Comment: Invited talk, presented by SJB at LightCone 2013+, May 20- May 24, 2013, Skiathos, Greece. arXiv admin note: text overlap with arXiv:1309.4856, arXiv:1308.5251, arXiv:1302.539

Light-Front Holographic QCD and the Confinement Potential

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time \tau = t+z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the eigensolutions provide the light-front wavefunctions describing hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. The potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. The holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrodinger equation. It also gives a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions include a zero-mass pion in the chiral limit, and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics and the excitation spectra of light-quark hadrons in terms of a single mass parameter. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.Comment: Presented by SJB at Light-Cone 2012: Relativistic Hadronic and Particle Physics, 10 to 15 December, 2012 at the University of Delhi, New Delhi, Indi

Conformal Symmetry, Confinement, and Light-Front Holographic QCD

We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b) the properties of a field theory in one dimension under the full conformal group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent single-variable light-front Schr\"odinger equation for bound states all lead to the same result: a relativistic nonperturbative model which successfully incorporates salient features of hadronic physics, including confinement, linear Regge trajectories, and results which are conventionally attributed to spontaneous chiral symmetry breaking.Comment: Presented by SJB at the Third Workshop on the QCD Structure of the Nucleon (QCD-N'12), Bilbao, Spain, October 22-26, 2012. This work was supported by the Department of Energy contract DE--AC02--76SF0051

Spatiotemporal pulses in a liquid crystal optical oscillator

A nonlinear optical medium results by the collective orientation of liquid crystal molecules tightly coupled to a transparent photoconductive layer. We show that such a medium can give a large gain, thus, if inserted in a ring cavity, it results in an unidirectional optical oscillator. Dynamical regimes with many interacting modes are made possible by the wide transverse size and the high nonlinearity of the liquid crystals. We show the generation of spatiotemporal pulses, coming from the random superposition of many coexisting modes with different frequencies

The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models

The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c<1 including the unitary and non-unitary minimal series. Taking into account the half-integer angular momentum sectors - which correspond to chains with an odd number of sites - in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite XXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published back in 1993. It has been made available here because there has been recent interest in conformal twisted boundary conditions. The "duality-twisted" boundary conditions discussed in this paper are particular examples of such boundary conditions for quantum spin chains, so there might be some renewed interest in these result

Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure

An Emerging Model of Creative Game-based Learning

We consider the integration of creative approaches to problem solving into pervasive games is a natural extension of play for creative thinking – one that can innovatively drive technology-led changes to the facilitation of creative thinking and pose a new genre in serious gaming for learning. This paper presents an initial proposal of a new model of creative game-base learning (CGBL), which emerged through mapping of established characteristics of climates that encourage creativity and innovation to characteristics of effective serious games

DN interaction from meson exchange

A model of the DN interaction is presented which is developed in close analogy to the meson-exchange KbarN potential of the Juelich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (rho, omega) exchange and higher-order box diagrams involving D*N, D\Delta, and D*\Delta intermediate states. The coupling of DN to the pi-Lambda_c and pi-Sigma_c channels is taken into account. The interaction model generates the Lambda_c(2595) resonance dynamically as a DN quasi-bound state. Results for DN total and differential cross sections are presented and compared with predictions of an interaction model that is based on the leading-order Weinberg-Tomozawa term. Some features of the Lambda_c(2595) resonance are discussed and the role of the near-by pi-Sigma_c threshold is emphasized. Selected predictions of the orginal KbarN model are reported too. Specifically, it is pointed out that the model generates two poles in the partial wave corresponding to the Lambda(1405) resonance.Comment: 14 pages, 8 figure

Partial-wave analysis of the eta pi+ pi- system produced in the reaction pi-p --> eta pi+ pi- n at 18 GeV/c

A partial-wave analysis of 9082 eta pi+ pi- n events produced in the reaction pi- p --> eta pi+ pi- n at 18.3 GeV/c has been carried out using data from experiment 852 at Brookhaven National Laboratory. The data are dominated by J^{PC} = 0^{-+} partial waves consistent with observation of the eta(1295) and the eta(1440). The mass and width of the eta(1295) were determined to be 1282 +- 5 MeV and 66 +- 13 Mev respectively while the eta(1440) was observed with a mass of 1404 +- 6 MeV and width of 80 +- 21 MeV. Other partial waves of importance include the 1++ and the 1+- waves. Results of the partial wave analysis are combined with results of other experiments to estimate f1(1285) branching fractions. These values are considerably different from current values determined without the aid of amplitude analyses.Comment: 22 pages, 8 figure

A partial wave analysis of the π0π0\pi ^0\pi ^0 system produced in π−p\pi ^-p charge exchange collisions

A partial wave analysis of the of the $\pi ^0\pi ^0$ system produced in the charge exchange reaction: $\pi ^-p\to \pi ^0\pi ^0n$ at an incident momentum of $18.3 GeV/c$ is presented as a function of ${\pi ^0\pi ^0}$ invariant mass, $m_{\pi^0\pi^0}$, and momentum transfer squared, $| {t} |$, from the incident $\pi^-$ to the outgoing ${\pi ^0\pi ^0}$ system.Comment: 24 pages total,8 pages text, 14 figures, 1 table. Submitted to Phys Rev