Block persistence

We define a block persistence probability p _l (t) as the probability that the order parameter integrated on a block of linear size l has never changed sign since the initial time in a phase-ordering process at finite temperature T<T _c . We argue that in the scaling limit of large blocks, where z is the growth exponent (), is the global (magnetization) persistence exponent and f(x) decays with the local (single spin) exponent for large x. This scaling is demonstrated at zero temperature for the diffusion equation and the large-n model, and generically it can be used to determine easily from simulations of coarsening models. We also argue that and the scaling function do not depend on temperature, leading to a definition of at finite temperature, whereas the local persistence probability decays exponentially due to thermal fluctuations. These ideas are applied to the study of persistence for conserved models. We illustrate our discussions by extensive numerical results. We also comment on the relation between this method and an alternative definition of at finite temperature recently introduced by Derrida [Phys. Rev. E 55, 3705 (1997)]. Received: 25 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling

We study gravitational radiation reaction in the equations of motion for binary systems with spin-orbit coupling, at order (v/c)⁷ beyond Newtonian gravity, or O(v/c)² beyond the leading radiation reaction effects for non-spinning bodies. We use expressions for the energy and angular momentum flux at infinity that include spin-orbit corrections, together with an assumption of energy and angular momentum balance, to derive equations of motion that are valid for general orbits and for a class of coordinate gauges. We show that the equations of motion are compatible with those derived earlier by a direct calculation.     

Dark matter production at the LHC from black hole remnants

We study dark matter production at CERN LHC from black hole remnants (BHR). We find that the typical mass of these BHR at the LHC is ∼5–10 TeV which is heavier than other dark matter candidates, such as axion, axino, neutralino, etc. We propose the detection of this dark matter via single jet production in the process pp → jet + BHR (dark matter) at CERN LHC. We find that for zero impact parameter partonic collisions, the monojet cross section is not negligible in comparison to the standard model background and is much higher than the other dark matter scenarios studied so far. We also find that dσ/dp _T of jet production in this process increases as p _T increases, whereas in all other dark matter scenarios the dσ/dp _T decreases at CERN LHC. This may provide a useful signature for dark matter detection at the LHC. However, we find that when the impact parameter dependent effect of inelasticity is included, the monojet cross section from the above process becomes much smaller than the standard model background and may not be detectable at the LHC.     

BCS-BEC crossover and quantum hydrodynamics in <Emphasis Type="Italic">p</Emphasis>-wave superfluids with a symmetry of the <Emphasis Type="Italic">A</Emphasis>1 phase

We solve the Leggett equations for the BCS-BEC crossover in a three dimensional resonance p-wave superfluid with the symmetry of the A1 phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS domain (μ > 0), for the BEC domain (μ < 0), and close to the important point μ = 0 in the 100% polarized case. We find the indications of a quantum phase transition close to the point μ(T = 0) = 0. Deep in the BCS and BEC domains, the crossover ideas of Leggett, Nozieres, and Schmitt-Rink work quite well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and the complicated problem of chiral anomaly in the BCS A1 phase at T = 0. We present two different approaches to the chiral anomaly, based on supersymmetric hydrodynamics and on the formal analogy with the Dirac equation in quantum electrodynamics. We evaluate the damping of nodal fermions due to different decay processes in the superclean case at T = 0 and find that a ballistic regime ωτ ≫ 1 occurs. We propose to use aerogel or nonmagnetic impurities to reach the hydrodynamic regime ωτ ≪ 1 at T = 0. We discuss the concept of the spectral flow and exact cancelations between time derivatives of anomalous and quasiparticle currents in the equation for the total linear momentum conservation. We propose to derive and solve the kinetic equation for the nodal quasiparticles in both the hydrodynamic and ballistic regimes to demonstrate this cancelation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in the A phase of ³He at low temperatures.     

Computing the Loewner Driving Process of Random Curves in the Half Plane

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N ^1.35) rather than the usual O(N ²), where N is the number of points on the curve.     

Deeply virtual compton scattering at HERA – A probe of asymptotia

We demonstrate that the measurement of an azimuthal angle asymmetry in deeply virtual Compton scattering (DVCS) at HERA energies, is experimentally feasible and allows one to determine for the first time the ratio, η, of the real to imaginary part of the DIS amplitude. We further show that such measurements would discriminate between different scenarios for the energy dependence of F₂(x,Q²) at energies beyond those reachable at HERA.     

Associated production of a KK-graviton with a Higgs boson via gluon fusion at the LHC

In order to solve the hierarchy problem, several extra-dimensional models have received considerable attention. We have considered a process where a Higgs boson is produced in association with a KK-graviton (G _KK) at the LHC. At the leading order, this process occurs through the gluon fusion mechanism gg→hG _KK via a quark loop. We compute the cross section and examine some features of this process in the ADD model. We find that the quark in the loop does not decouple in the large quark-mass limit just as in the case of gg→h process. We compute the cross section of this process for the case of the RS model also. We examine the feasibility of this process being observed at the LHC.     

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose–Einstein Condensation (BEC) in the Infinite-Range-Hopping Bose–Hubbard model with repulsive on-site particle interaction in the presence of an ergodic random single-site external potential with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. We observe new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at certain fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the suppression of BEC at integer densities observed in Bru and Dorlas (J. Stat. Phys. 113:177–195, 2003) in the absence of a random potential, can disappear as the disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of the density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.     

Aspects of φ-meson production in proton-proton collisions

We analyze near-threshold cross-section data for the reaction pp → ppφ published by the DISTO Collaboration and recent, still preliminary results presented by the ANKE Collaboration. We formulate a procedure to evaluate the OZI ratio at low energies by taking into account corrections from the kinematics and the final-state interaction. Combining the new data with the few measurements available at higher energies we give a limit for the OZI rule violation. We also demonstrate and discuss the effect of a possible contribution from a five-quark baryonic resonance coupled to the φp system on the pp → ppφ cross-section and the φp and pp invariant mass spectra.     

Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall

A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v _c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v<v _c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→v _c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.     

On Fusion Algebras and Modular Matrices

We consider the fusion algebras arising in e.g. Wess–Zumino–Witten conformal field theories, affine Kac–Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the A _r fusion algebra at level k. We prove that for many choices of rank r and level k, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most r and k. We also find new, systematic sources of zeros in the modular matrix S. In addition, we obtain a formula relating the entries of S at fixed points, to entries of S at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of S, and by the fusion (Verlinde) eigenvalues. Received: 7 October 1997 / Accepted: 7 March 1999     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Higher-order constraints on the Higgs production rate from fixed-target DIS data

The constraints of fixed-target DIS data in fits of parton distributions including QCD corrections to next-to-next-to leading order are studied. We point out a potential problem in the analysis of the NMC data which can lead to inconsistencies in the extracted value for α _s (M _Z ) and the gluon distribution at higher orders in QCD. The implications for predictions of rates for Standard Model Higgs boson production at hadron colliders are investigated. We conclude that the current range of excluded Higgs boson masses at the Tevatron appears to be much too large.     

Charm and hidden charm scalar mesons in the nuclear medium

We study the renormalization of the properties of low-lying charm and hidden charm scalar mesons in a nuclear medium, concretely of the D _s0(2317) and the theoretical hidden charm state X(3700) . We find that for the D _s0(2317) , with negligible width at zero density, the width becomes about 100MeV at normal nuclear-matter density, while in the case of the X(3700) the width becomes as large as 200MeV. We discuss the origin of this new width and trace it to reactions occurring in the nucleus, while offering a guideline for future experiments testing these changes. We also show how those medium modifications will bring valuable information on the nature of the scalar resonances and the mechanisms of the interaction of D mesons with nucleons and nuclei.     

CMS overview

We discuss the production of γπ⁰ and π⁰ π⁰ pairs with a large invariant mass at collider energies. We present a study based on a perturbative QCD calculation at full next-to-leading order accuracy, implemented in the computer programme DIPHOX. We give estimations for various observables, which concern the reducible background to the Higgs boson search in the channel H → γγ, in the mass range 80-140 GeV at the LHC. We critically discuss the reliability of these estimates due to our imperfect knowledge of fragmentation functions at high z and a subtle interplay between higher order corrections and realistic experimental cuts. Whereas the invariant mass spectrum of photon-pion pairs is theoretically better under control, in the dipion case large uncertainties remain. Finally we comment on the impact of our findings on Higgs boson searches at the LHC. We conclude that the qualitative statement that the pion backgrounds should not be dangerous for the H → γγ search channel remains true at the next-to-leading order level.     

Perturbative QCD results on pion production in <Emphasis Type="Italic">pp,pA</Emphasis> and <Emphasis Type="Italic">AA</Emphasis> collisions

We summarize new pQCD results on pion production in proton–proton (pp), proton–nucleus (pA) and nucleus–nucleus (AA) collisions. Our calculation introduces intrinsic parton transverse momentum (k_T) and is performed effectively at next-to-leading order (NLO), applying a K factor extracted for jet events. Two different factorization scales, Q = p_Tjet/2 and p_Tjet are used. Experimental data in pA collisions imply a preference for the latter choice at NLO level. We display our results at CERN SPS for AA collisions.     

Some results on the quantum dynamics of a particle in a Markovian potential

We consider the quantum dynamics of a particle in a time dependent potentialV(t), assuming it to be a Markovian random function of time. We derive a formula for the density matrix at timet averaged over the realisations of the potential. We then obtain a kind of RAGE theorem for the time evolution of compact observables, and some information on the phase space behaviour of the system.     

Estimating the effect of NNLO contributions on global parton analyses

We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function and the cross sections for W and Z hadroproduction as examples. For we find relatively poor convergence, with increasing order, at small x; whereas are much more reliably predicted. Received: 7 September 2000 / Published online: 13 November 2000     

Spin waves,vortices, and the structure of equilibrium states in the classicalXY model

We prove that, for spin systems with a continuous symmetry group on lattices of arbitrary dimension, the surface tension vanishes at all temperatures. For the classicalXY model in zero magnetic field, this result is shown to imply absence of interfaces in the thermodynamic limit, at arbitrary temperature. We show that, at values of the temperature at which the free energy of that model is continuously differentiable, i.e. at all except possibly countably many temperatures, there iseither aunique translation-invariant equilibrium state, or all such states are labelled by the elements of the symmetry group, SO(2). Moreover, there areno non-translation-invariant, but periodic equilibrium states. We also reconsider the representation of theXY model as a gas of spin waves and vortices and discuss the possibility that, in four or more dimensions, translation invariance may be broken by imposing boundary conditions which force an (open) vortex sheet through the system. Among our main tools are new correlation inequalities.