Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201

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

The quantum dilogarithm and representations quantum cluster varieties

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the cluster modular groups. The examples of the latter include the classical mapping class groups of punctured surfaces. One of applications is quantization of higher Teichmuller spaces. The constructed unitary representations can be viewed as analogs of the Weil representation. In both cases representations are given by integral operators. Their kernels in our case are the quantum dilogarithms. We introduce the symplectic/quantum double of cluster varieties and related them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version. To appear in Inventiones Math. The last Section of the previous versions was removed, and will become a separate pape

Restricted sum formula of alternating Euler sums

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Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering

We describe in detail the calculation of the two-loop corrections to the QED Bhabha scattering cross section due to the vacuum polarization by heavy fermions. Our approach eliminates one mass scale from the most challenging part of the calculation and allows us to obtain the corrections in a closed analytical form. The result is valid for arbitrary values of the heavy fermion mass and the Mandelstam invariants, as long as s,t,u >> m_e^2.Comment: 43 pages, 8 figures; added reference

Thermoelectric power of MgB2−x_{2-x}Bex_x

We investigated thermoelectric power $S(T)$ of MgB$_{2-x}$Be$_{x}$ ($x=0$, 0.2, 0.3, 0.4, and 0.6). $S(T)$ decreases systematically with $x$, suggesting that the hole density increases. Our band calculation shows that the increase occurs in the $\sigma$-band. With the hole-doping, $T_{c}$ decreases. Implication of this phenomenon is discussed within the BCS framework. While the Mott formula explains only the linear part of $S(T)$ at low temperature, incorporation of electron-phonon interaction enables us to explain $S(T)$ over wide temperature range including the anomalous behavior at high temperature.Comment: 4 pages, 4 figure

Vacuum fluctuations and topological Casimir effect in Friedmann-Robertson-Walker cosmologies with compact dimensions

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological parts coincide with those for a conformal coupling and they are related to the corresponding quantities in the flat spacetime by standard conformal transformation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values. In the monotonic regime and for nonconformally and nonminimally coupled fields the vacuum stresses are isotropic and the equation of state for the topological parts in the energy density and pressures is of barotropic type. In the oscillatory regime, the amplitude of the oscillations for the topological part in the expectation value of the field squared can be either decreasing or increasing with time, whereas for the energy-momentum tensor the oscillations are damping.Comment: 20 pages, 2 figure

The five-gluon amplitude in the high-energy limit

We consider the high energy limit of the colour ordered one-loop five-gluon amplitude in the planar maximally supersymmetric N=4 Yang-Mills theory in the multi-Regge kinematics where all of the gluons are strongly ordered in rapidity. We apply the calculation of the one-loop pentagon in D=6-2 eps performed in a companion paper to compute the one-loop five-gluon amplitude through to O(eps^2). Using the factorisation properties of the amplitude in the high-energy limit, we extract the one-loop gluon-production vertex to the same accuracy, and, by exploiting the iterative structure of the gluon-production vertex implied by the BDS ansatz, we perform the first computation of the two-loop gluon-production vertex up to and including finite terms.Comment: 24 pages, 1 figur