Discrepancy and Signed Domination in Graphs and Hypergraphs

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepancy theory as shown by Fueredi and Mubayi [J. Combin. Theory, Ser. B 76 (1999) 223-239]. The signed domination number of G is the minimum of the sum of colours for all vertices, taken over all signed domination functions of G. In this paper, we present new upper and lower bounds for the signed domination number. These new bounds improve a number of known results.Comment: 12 page

Description of soft diffraction in the framework of reggeon calculus. Predictions for LHC

A model, based on Gribov's Reggeon calculus, is proposed and applied to processes of soft diffraction at high energies. It is shown that by accounting for absorptive corrections for all legs of triple-Regge and loop diagrams a good description of experimental data on inelastic soft diffraction can be obtained. In this paper we give a brief description of the model and of its predictions for LHC energies.Comment: Talk given at EDS'09 conferenc

Spectra of particles produced in high-mass diffraction dissociation in the Model of Quark-Gluon Strings

We calculate spectra of secondary particles produced in process of single diffraction dissociation in the Model of Quark-Gluon Strings. For description of diffractive dissociation process we use the reggeon model where all legs of triple-reggeon diagrams are eikonalized. Numerical calculation shows that the model gives a good description of data on charged particles pseudorapidity distribution in $p\bar{p}$ single diffractive dissociation

Geometric expansion of the log-partition function of the anisotropic Heisenberg model

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.Comment: 38 page

Measurement of π\pi, K, p transverse momentum spectra with ALICE in proton-proton collisions at s=\sqrt{s} = 0.9 and 7 TeV

Results of the measurement of the $\pi$, K, p transverse momentum ($p_{\mathrm{t}}$) spectra at mid-rapidity in proton-proton collisions at $\sqrt{s} = 7$ TeV are presented. Particle identification was performed using the energy loss signal in the Inner Tracking System (ITS) and the Time Projection Chamber (TPC), while information from the Time-of-Flight (TOF) detector was used to identify particles at higher transverse momentum. From the spectra at $\sqrt{s} = 7$ TeV the mean transverse momentum ($$) and particle ratios were extracted and compared to results obtained for collisions at $\sqrt{s} = 0.9$ TeV and lower energies.Comment: Quark Matter 2011 proceeding

Role of gluons in soft and semi-hard multiple hadron production in pp collisions at LHC

Hadron inclusive spectra in pp collisions are analyzed within the modified quark-gluon string model including both the longitudinal and transverse motion of quarks in the proton in the wide region of initial energies. The self-consistent analysis shows that the experimental data on the inclusive spectra of light hadrons like pions and kaons at ISR energies can be satisfactorily described at transverse momenta not larger than 1-2 GeV/c. We discuss some difficulties to apply this model at energies above the ISR and suggest to include the distribution of gluons in the proton unintegrated over the internal transverse momentum. It leads to an increase in the inclusive spectra of hadrons and allows us to extend the satisfactory description of the data in the central rapidity region at energies higher than ISR.Comment: 19 pages, 20 figure

Towards the NNLL precision in Bˉ→Xsγ\bar B \to X_s \gamma

The present NLL prediction for the decay rate of the rare inclusive process $\bar B \to X_s \gamma$ has a large uncertainty due to the charm mass renormalization scheme ambiguity. We estimate that this uncertainty will be reduced by a factor of 2 at the NNLL level. This is a strong motivation for the on-going NNLL calculation, which will thus significantly increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM. We also give a brief status report of the NNLL calculation.Comment: 5 pages, 2 figures, contribution to the proceedings of EPS-HEP 200

Abstract cluster expansion with applications to statistical mechanical systems

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions

Reduction of Charm Quark Mass Scheme Dependence in Bˉ→Xsγ\bar B \to X_s \gamma at the NNLL Level

The uncertainty of the theoretical prediction of the $\bar B \to X_s \gamma$ branching ratio at NLL level is dominated by the charm mass renormalization scheme ambiguity. In this paper we calculate those NNLL terms which are related to the renormalization of $m_c$, in order to get an estimate of the corresponding uncertainty at the NNLL level. We find that these terms significantly reduce (by typically a factor of two) the error on ${BR}(\bar B \to X_s \gamma)$ induced by the definition of $m_c$. Taking into account the experimental accuracy of around 10% and the future prospects of the $B$ factories, we conclude that a NNLL calculation would increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM significantly.Comment: 13 pages including 3 figure