Topological Charge Screening and the `Proton Spin' Beyond the Chiral Limit

The theory of the `proton spin' effect proposed in our earlier papers is extended to include the chiral SU(3) symmetry breaking and flavour mixing induced by non-vanishing quark masses in QCD. The theoretical basis is the derivation of exact, unified Goldberger-Treiman (GT) relations valid beyond the chiral limit. The observed suppression in the flavour singlet axial charge $a^0(Q^2)$ is explained by an anomalously small value for the slope of the singlet current correlation function <0|T~\pl^\m J_{\m 5}^0 ~ \pl^\n J_{\n 5}^0 |0>, a consequence of the screening of topological charge in the QCD vacuum. Numerical predictions are obtained by evaluating the current correlation functions using QCD spectral sum rules. The results, $a^0(Q^2) = 0.31 \pm 0.02$ and $\int dx ~g_1^p(x,Q^2) = 0.141 \pm 0.005$ (at Q^2=10 \~\GV^2), are in good agreement with current experimental data on the polarised proton structure function $g_1^p$.Comment: 44 pages, plain TeX, 2 ps figure

CFT, Holography, and Causal Entropy Bound

The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension $D$. For CFT's with a large number of fields, $N$, the CEB is found to be valid for temperatures not exceeding a value of order $M_P/N^{{1\over D-2}}$, in agreement with large $N$ bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFT's and strongly coupled CFT's with AdS duals, the CEB, despite the fact that it relates extensive quantities, is equivalent to (a generalization of) a purely holographic entropy bound proposed by E. Verlinde.Comment: 14 pages, 2 figure

Radiation Problem in Transplanckian Scattering

We investigate hard radiation emission in small-angle transplanckian scattering. We show how to reduce this problem to a quantum field theory computation in a classical background (gravitational shock wave). In momentum space, the formalism is similar to the flat-space light cone perturbation theory, with shock wave crossing vertices added. In the impact parameter representation, the radiating particle splits into a multi-particle virtual state, whose wavefunction is then multiplied by individual eikonal factors. As a phenomenological application, we study QCD radiation in transplanckian collisions of TeV-scale gravity models. We derive the distribution of initial state radiation gluons, and find a suppression at large transverse momenta with respect to the standard QCD result. This is due to rescattering events, in which the quark and the emitted gluon scatter coherently. Interestingly, the suppression factor depends on the number of extra dimensions and provides a new experimental handle to measure this number. We evaluate the leading-log corrections to partonic cross-sections due to the initial state radiation, and prove that they can be absorbed into the hadronic PDF. The factorization scale should then be chosen in agreement with an earlier proposal of Emparan, Masip, and Rattazzi. In the future, our methods can be applied to the gravitational radiation in transplanckian scattering, where they can go beyond the existing approaches limited to the soft radiation case.Comment: 41 pp, v2: minor changes and added refs, conforms with published versio

The cosmology with the Dp-brane gas

We study the effect of the Dp-brane gas in string cosmology. When one kind of Dp-brane gas dominates, we find that the cosmology is equivalent to that of the Brans-Dicke theory with the perfect fluid type matter. We obtain $\gamma$, the equation of state parameter, in terms of p and the space-time dimension.Comment: 12 pages, 3 figure

Perturbations in a Bouncing Brane Model

The question of how perturbations evolve through a bounce in the Cyclic and Ekpyrotic models of the Universe is still a matter of ongoing debate. In this report we show that the collision between boundary branes is in most cases singular even in the full 5-D formalism, and that first order perturbation theory breaks down for at least one perturbation variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, non singular solution be found. It is then possible to follow the perturbations explicitly until the actual collision. In this case, we find that if a scale invariant spectrum developed on the hidden brane, it will get transferred to the visible brane during the bounce.Comment: 15 pages, minor modifications, a few typos correcte

Target Independence of the Emc-SMC Effect

An approach to deep inelastic scattering is described in which the matrix elements arising from the operator product expansion are factorised into composite operator propagators and proper vertex functions. In the case of polarised \m p scattering, the composite operator propagator is identified with the square root of the QCD topological susceptibility $\sqrt{\chi^{\prime}(0)}$, while the corresponding proper vertex is a renormalisation group invariant. We estimate $\chi^{\prime}(0)$ using QCD spectral sum rules and find that it is significantly suppressed relative to the OZI expectation. Assuming OZI is a good approximation for the proper vertex, our predictions, \int_{0}^{1}dx g_1^p (x;Q^2=10\GV^2)= 0.143 \pm 0.005 and $G^{(0)}_A \equiv \Delta \Sigma = 0.353 \pm 0.052$, are in excellent agreement with the new SMC data. This result, together with one confirming the validity of the OZI rule in the \hp radiative decay, supports our earlier conjecture that the suppression in the flavour singlet component of the first moment of $g_1^p$ observed by the EMC-SMC collaboration is a target-independent feature of QCD related to the $U(1)$ anomaly and is not a property of the proton structure. As a corollary, we extract the magnitude of higher twist effects from the neutron and Bjorken sum rules.Comment: 22 pages, 8 figures available on request

The explicit Mordell conjecture for families of curves

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are small enough to successfully implement a computer search. As an evidence of the simplicity of its application, we present a variety of explicit examples and explain how to produce many others. In the appendix our method is compared in detail to the classical method of Manin-Demjanenko and the analysis of our explicit examples is carried to conclusion

The eta-prime propagator in quenched QCD

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa<kappa_c in the quark propagators to the critical value of hop ping parameter. By this method, the eta-prime propagator can be accurately calculated even for very light quark mass. A determination of the topological susceptibility for quenched QCD is also obtained, using the fermionic method of Smit and Vink to calculate winding numbers.Comment: 3 pages, 3 postscript figure

Trialogue on the number of fundamental constants

This paper consists of three separate articles on the number of fundamental dimensionful constants in physics. We started our debate in summer 1992 on the terrace of the famous CERN cafeteria. In the summer of 2001 we returned to the subject to find that our views still diverged and decided to explain our current positions. LBO develops the traditional approach with three constants, GV argues in favor of at most two (within superstring theory), while MJD advocates zero.Comment: Version appearing in JHEP; 31 pages late

A Stringy Correspondence Principle in Cosmology

We study a d-dimensional FRW universe, containing a perfect fluid with p = w \rho and \frac{1} {d - 1} \le w \le 1, and find a correspondence principle similar to that of Horowitz and Polchinski in the black hole case. This principle follows quite generally from thermodynamics and the conservation of energy momentum tensor, and can be stated along similar lines as in the black hole case: ``When the temperature T of the universe becomes of order string scale the universe state becomes a highly excited string state. At the transition, the entropies and energies of the universe and strings differ by factors of {\cal O}(1).'' Such a matching is absent for w \ne 1 if the transition is assumed to be when the curvature or the horizon length is of order string scale.Comment: 14 pages. V2: More references added and some minor textual modifications mad