Global Analysis of Data on the Proton Structure Function g1 and Extraction of its Moments

Inspired by recent measurements with the CLAS detector at Jefferson Lab, we perform a self-consistent analysis of world data on the proton structure function g1 in the range 0.17 < Q2 < 30 (GeV/c)**2. We compute for the first time low-order moments of g1 and study their evolution from small to large values of Q2. The analysis includes the latest data on both the unpolarized inclusive cross sections and the ratio R = sigmaL / sigmaT from Jefferson Lab, as well as a new model for the transverse asymmetry A2 in the resonance region. The contributions of both leading and higher twists are extracted, taking into account effects from radiative corrections beyond the next-to-leading order by means of soft-gluon resummation techniques. The leading twist is determined with remarkably good accuracy and is compared with the predictions obtained using various polarized parton distribution sets available in the literature. The contribution of higher twists to the g1 moments is found to be significantly larger than in the case of the unpolarized structure function F2.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Black Hole Entropy from a Highly Excited Elementary String

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between black holes and strings.Comment: revtex, 4 page

Infinite Symmetry in the Fractional Quantum Hall Effect

We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the Laughlin wave functions. This generalization has a nice interpretation in Jain's composite fermion theory. Furthermore, for these models we have calculated the wave functions of the edge excitations viewing them as area preserving deformations of an incompressible quantum droplet, and have shown that the ${\cal W}_{1+\infty}$ is the underlying symmetry of the edge excitations in the fractional quantum Hall effect. Finally, we have applied this method to more general wave functions.Comment: 15pp. LaTeX, BONN-HE-93-2

Quantum Newtonian Dynamics on a Light Front

We recall the special features of quantum dynamics on a light-front (in an infinite momentum frame) in string and field theory. The reason this approach is more effective for string than for fields is stressed: the light-front dynamics for string is that of a true Newtonian many particle system, since a string bit has a fixed Newtonian mass. In contrast, each particle of a field theory has a variable Newtonian mass P^+, so the Newtonian analogy actually requires an infinite number of species of elementary Newtonian particles. This complication substantially weakens the value of the Newtonian analogy in applying light-front dynamics to nonperturbative problems. Motivated by the fact that conventional field theories can be obtained as infinite tension limits of string theories, we propose a way to recast field theory as a standard Newtonian system. We devise and analyze some simple quantum mechanical systems that display the essence of the proposal, and we discuss prospects for applying these ideas to large N_c QCD.Comment: 13 pages, 3 figures, LaTex, psfig, references added, APS copyrigh

Many-Body Superconformal Systems from Hamiltonian Reductions

We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with pairwise interaction starting from a composite system involving n(n-1)/2+1 copies of the ordinary (super)conformal mechanics. Applications of the scheme include an N=4 superconformal extension for a complexification of the Calogero model and a D(2,1|\alpha)-invariant n-particle system.Comment: 12 pages, no figures. v2: Title changed. New material and acknowledgements adde

Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent

We consider an inhomogeneous quantum phase transition across a multicritical point of the XY quantum spin chain. This is an example of a Lifshitz transition with a dynamical exponent z = 2. Just like in the case z = 1 considered in New J. Phys. 12, 055007 (2010) when a critical front propagates much faster than the maximal group velocity of quasiparticles vq, then the transition is effectively homogeneous: density of excitations obeys a generalized Kibble-Zurek mechanism and scales with the sixth root of the transition rate. However, unlike for z = 1, the inhomogeneous transition becomes adiabatic not below vq but a lower threshold velocity v', proportional to inhomogeneity of the transition, where the excitations are suppressed exponentially. Interestingly, the adiabatic threshold v' is nonzero despite vanishing minimal group velocity of low energy quasiparticles. In the adiabatic regime below v' the inhomogeneous transition can be used for efficient adiabatic quantum state preparation in a quantum simulator: the time required for the critical front to sweep across a chain of N spins adiabatically is merely linear in N, while the corresponding time for a homogeneous transition across the multicritical point scales with the sixth power of N. What is more, excitations after the adiabatic inhomogeneous transition, if any, are brushed away by the critical front to the end of the spin chain.Comment: 10 pages, 6 figures, improved version accepted in NJ

Scattering from Singular Potentials in Quantum Mechanics

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completenes

The Threshold Pion-Photoproduction of Nucleons In The Chiral Quark Model

In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order $\mu=m_{\pi}/M$ only in the isospin amplitude $A^{(-)}$. The role of the transitions between the nucleon and the resonance $P_{33}(1232)$ and P-wave baryons are also discussed, we find that the leading contributions to the isospin amplitudes at $O(\mu^2)$ are from the transition between the P-wave baryons and the nucleon and the charge radius of the nucleon. The leading contribution from the P-wave baryons only affects the neutral pion production, and improve the agreement with data significantly. The transition between the resonance $P_{33}(1232)$ and the nucleon only gives an order $\mu^3$ corrections to $A^{(-)}$

Smooth Bosonization as a Quantum Canonical Transformation

We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonization proposed by Damgaard et al. as well as an example of a quantum canonical transformation for a quantum field theory.Comment: 20 pages, revte

Updated resonance photo-decay amplitudes to 2 GeV

We present the results of an energy-dependent and set of single-energy partial-wave analyses of single-pion photoproduction data. These analyses extend from threshold to 2 GeV in the laboratory photon energy, and update our previous analyses to 1.8 GeV. Photo-decay amplitudes are extracted for the baryon resonances within this energy range. We consider two photoproduction sum rules and the contributions of two additional resonance candidates found in our most recent analysis of $\pi N$ elastic scattering data. Comparisons are made with previous analyses.Comment: Revtex, 26 pages, 3 figures. Postscript figures available from ftp://clsaid.phys.vt.edu/pub/pr or indirectly from http://clsaid.phys.vt.edu/~CAPS