Towards a NNLO calculation in hadronic heavy hadron production

We calculate the Laurent series expansion up to ${\cal O}(\epsilon^2)$ for all scalar one-loop one-, two-, three- and four-point integrals that are needed in the calculation of hadronic heavy flavour production. The Laurent series up to ${\cal O}(\epsilon^2)$ is needed as input to that part of the NNLO corrections to heavy hadron production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The ${\cal O}(\epsilon^2)$ expansion of the four-point integrals contains polylogarithms up to $Li_4$ and the multiple polylogarithms.Comment: 5 pages, 2 Postscript figure

Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose--Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L^3 the sum of the cycle probabilities of length k >> L^2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the \pi_k in the thermodynamic limit. We also determine the function \pi_k for arbitrary systems. Furthermore we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.Comment: 6 pages, extensive rewriting, new section on maximum-length cycle

Families of superhard crystalline carbon allotropes induced via cold-compressed graphite and nanotubes

We report a general scheme to systematically construct two classes of structural families of superhard sp3 carbon allotropes of cold compressed graphite through the topological analysis of odd 5+7 or even 4+8 membered carbon rings stemmed from the stacking of zigzag and armchair chains. Our results show that the previously proposed M, bct-C4, W and Z allotropes belong to our currently proposed families and that depending on the topological arrangement of the native carbon rings numerous other members are found that can help us understand the structural phase transformation of cold-compressed graphite and carbon nanotubes (CNTs). In particular, we predict the existence of two simple allotropes, R- and P-carbon, which match well the experimental X-ray diffraction patterns of cold-compressed graphite and CNTs, respectively, display a transparent wide-gap insulator ground state and possess a large Vickers hardness comparable to diamond.Comment: 5 pages, 4 figures, accepted by Phys. Rev. Let

Estimates for parameters and characteristics of the confining SU(3)-gluonic field in an η′\eta^\prime-meson

The confinement mechanism proposed earlier by the author is applied to estimate the possible parameters of the confining SU(3)-gluonic field in an $\eta^\prime$-meson. For this aim the electric form factor of an $\eta^\prime$-meson is nonperturbatively computed in an explicit analytic form. The estimates obtained are also consistent with the width of the electromagnetic decay $\eta^\prime\to2\gamma$. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the meson under consideration.Comment: 20 pages, LaTe

A record-driven growth process

We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node possessing a quality. The new incoming node connects to the preexisting node with best quality, that is, with record value for the quality. The emergent structure is that of a growing network, where groups are formed around record nodes (nodes endowed with the best intrinsic qualities). Special emphasis is put on the statistics of leaders (nodes whose degrees are the largest). The asymptotic probability for a node to be a leader is equal to the Golomb-Dickman constant omega=0.624329... which arises in problems of combinatorical nature. This outcome solves the problem of the determination of the record breaking rate for the sequence of correlated inter-record intervals. The process exhibits temporal self-similarity in the late-time regime. Connections with the statistics of the cycles of random permutations, the statistical properties of randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update

On leaders and condensates in a growing network

The Bianconi-Barabasi model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fitnesses, has the fundamental property to undergo a phase transition to a condensed phase below some finite critical temperature, for an appropriate choice of the distribution of fitnesses. At high temperature it exhibits a crossover to the Barabasi-Albert model, and at low temperature, where the fitness landscape becomes very rugged, a crossover to the recently introduced record-driven growth process. We first present an analysis of the history of leaders, the leader being defined as the node with largest degree at a given time. In the generic finite-temperature regime, new leaders appear endlessly, albeit on a doubly logarithmic time scale, i.e., extremely slowly. We then give a novel picture for the dynamics in the condensed phase. The latter is characterized by an infinite hierarchy of condensates, whose sizes are non-self-averaging and keep fluctuating forever.Comment: 29 pages, 13 figures, 3 tables. A few minor change

Pressure-induced phase transition in the electronic structure of palladium nitride

We present a combined theoretical and experimental study of the electronic structure and equation of state (EOS) of crystalline PdN2. The compound forms above 58 GPa in the pyrite structure and is metastable down to 11 GPa. We show that the EOS cannot be accurately described within either the local density or generalized gradient approximations. The Heyd-Scuseria-Ernzerhof exchange-correlation functional (HSE06), however, provides very good agreement with experimental data. We explain the strong pressure dependence of the Raman intensities in terms of a similar dependence of the calculated band gap, which closes just below 11 GPa. At this pressure, the HSE06 functional predicts a first-order isostructural transition accompanied by a pronounced elastic instability of the longitudinal-acoustic branches that provides the mechanism for the experimentally observed decomposition. Using an extensive Wannier function analysis, we show that the structural transformation is driven by a phase transition of the electronic structure, which is manifested by a discontinuous change in the hybridization between Pd-d and N-p electrons as well as a conversion from single to triple bonded nitrogen dimers. We argue for the possible existence of a critical point for the isostructural transition, at which massive fluctuations in both the electronic as well as the structural degrees of freedom are expected.Comment: 9 pages, 12 figures. Revised version corrects minor typographical error

Poisson's ratio in cryocrystals under pressure

We present results of lattice dynamics calculations of Poisson's ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches - the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are non-monotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed.Comment: Fizika Nizkikh Temperatur 41, 571 (2015

Electroweak Physics

The status of precision electroweak measurements as of summer 2002 is reviewed. The recent results on the anomalous magnetic moment of the muon and on neutrino-nucleon scattering are discussed. Precision results on the electroweak interaction obtained by the experiments at the SLC, LEP and TEVATRON colliders are presented. The experimental results are compared with the predictions of the minimal Standard Model and are used to constrain its parameters, including the mass of the Higgs boson. The final LEP results on the direct search for the Higgs boson of the Standard Model are presented.Comment: Plenary talk presented at the 31st ICHEP, Amsterdam, The Netherlands, July 24-31, 200

Quantum and Classical Orientational Ordering in Solid Hydrogen

We present a unified view of orientational ordering in phases I, II, and III of solid hydrogen. Phases II and III are orientationally ordered, while the ordering objects in phase II are angular momenta of rotating molecules, and in phase III the molecules themselves. This concept provides quantitative explanation of the vibron softening, libron and roton spectra, and increase of the IR vibron oscillator strength in phase III. The temperature dependence of the effective charge parallels the frequency shifts of the IR and Raman vibrons. All three quantities are linear in the order parameter.Comment: Replaced with the final text, accepted for publication in PRL. 1 Fig. added. Misc. text revision