351 research outputs found

    The method of global R* and its applications

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    The global R* operation is a powerful method for computing renormalisation group functions. This technique, based on the principle of infrared rearrangement, allows to express all the ultraviolet counterterms in terms of massless propagator integrals. In this talk we present the main features of global R* and its application to the renormalisation of QCD. By combining this approach with the use of the program Forcer for the evaluation of the relevant Feynman integrals, we renormalise for the first time QCD at five loops in covariant gauges.Comment: 10 pages, 6 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017

    Two dimensional SU(N) x SU(N) chiral models on the lattice

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    Lattice SU(N)×SU(N)SU(N)\times SU(N) chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. 12th12^{th} order strong coupling series for the free and internal energy are obtained for all N6N\geq 6. Three loop contributions to the internal energy and to the lattice β\beta-function are evaluated for all NN and non-universal corrections to the asymptotic Λ\Lambda parameter are computed in the ``temperature'' and the ``energy'' scheme. Numerical simulations confirm a faster approach to asymptopia of the energy scheme. A phenomenological correlation between the peak in the specific heat and the dip of the β\beta-function is observed. Tests of scaling are performed for various physical quantities, finding substantial scaling at ξ2\xi \gtrsim 2. In particular, at N=6N=6 three different mass ratios are determined numerically and found in agreement, within statistical errors of about 1\%, with the theoretical predictions from the exact S-matrix theory.Comment: pre-print IFUP 29/93, revised version, 12 pages, 10 figures avaliable on request by FAX or by mail. REVTE

    Four-loop splitting functions in QCD -- The gluon-to-quark case

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    We have computed the even-NN moments N20N \leq 20 of the gluon-to-quark splitting function PqgP_{\rm qg} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via physical cross sections. Using our new moments and all available endpoint constraints, we construct approximations for the four-loop Pqg(x)P_{\rm qg}(x) that should be sufficient for a wide range of collider-physics applications. The N3^3LO corrections resulting from these and the corresponding quark-quark splitting functions lead to a marked improvement of the perturbative accuracy for the scale derivative of the singlet quark distribution, with effects of 1% or less at x104x \gtrsim 10^{\,-4} at a standard reference scale with αs=0.2\alpha_s = 0.2.Comment: 17 pages latex, 3 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine

    Four-loop splitting functions in QCD -- The quark-quark case

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    We have computed the even-NN moments N20N\leq 20 of the pure-singlet quark splitting function PpsP_{\,\rm ps} at the fourth order of perturbative QCD via the anomalous dimensions of off-shell flavour-singlet operator matrix elements. Our results, derived analytically for a general gauge group, agree with all results obtained for this function so far, in particular with the lowest six even moments obtained via physical cross sections. Using these results and all available endpoint constraints, we construct approximations for PpsP_{\rm ps} at four loops that should be sufficient for most collider-physics applications. Together with the known results for the non-singlet splitting function Pns+P_{\rm ns}^{\,+} at this order, this effectively completes the quark-quark contribution for the evolution of parton distribution at N ⁣3^{\:\!3}LO accuracy. Our new results thus provide a major step towards fully consistent N ⁣3^{\:\!3}LO calculations at the LHC and the reduction of the residual uncertainty in the parton evolution to the percent level.Comment: 17 pages latex, 2 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine

    New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering

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    We present recent results on newly calculated 2- and 3-loop contributions to the heavy quark parts of the structure functions in deep-inelastic scattering due to charm and bottom.Comment: Contribution to the Proc. of Loops and Legs 2016, PoS, in prin

    Linear instability and statistical laws of physics

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    We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial conditions is given by ξ=[1+(1q)λqt]1/(1q) \xi =[1+(1-q)\lambda_q t]^{1/(1-q)} with q=0q=0; (ii) the statistical entropy Sq=(1ipiq)/(q1)(S1=ipilnpi)S_q=(1-\sum_i p_i^q)/(q-1) (S_1=-\sum_i p_i \ln p_i) in the infinitely fine graining limit (i.e., WW\equiv {\it number of cells into which the phase space has been partitioned} \to\infty), increases linearly with time only for q=0q=0; (iii) a nontrivial, qq-generalized, Pesin-like identity is satisfied, namely the limtlimWS0(t)/t=max{λ0}\lim_{t \to \infty} \lim_{W \to \infty} S_0(t)/t=\max\{\lambda_0\}. These facts (which are in analogy to the usual behaviour of strongly chaotic systems with q=1q=1), seem to open the door for a statistical description of conservative many-body nonlinear systems whose Lyapunov spectrum vanishes.Comment: 7 pages including 2 figures. The present version is accepted for publication in Europhysics Letter

    Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function

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    Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied to the evaluation of the two-point correlation function. The momentum-space lattice propagator is constructed with precision O(\beta^{10}) and an evaluation of the correlation length is obtained for several different definitions. Three-loop weak coupling contributions to the internal energy and to the lattice β\beta and γ\gamma functions are evaluated for all N, and the effect of adopting the ``energy'' definition of temperature is computed with the same precision. Renormalization-group improved predictions for the two-point Green's function in the weak coupling ( continuum ) regime are obtained and successfully compared with Monte Carlo data. We find that strong coupling is predictive up to a point where asymptotic scaling in the energy scheme is observed. Continuum physics is insensitive to the effects of the large N phase transition occurring in the lattice model. Universality in N is already well established for N10N \ge 10 and the large N physics is well described by a ``hadronization'' picture.Comment: Revtex, 37 pages, 16 figures available on request by FAX or mai

    The prediction of future from the past: an old problem from a modern perspective

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    The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability results to be hindered rather by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, regardless the regular or chaotic nature of the system, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.Comment: 9 pages, 4 figure

    Hadron Properties with FLIC Fermions

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    The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a)-improvement in lattice fermion actions offering near continuum results at finite lattice spacing. It provides computationally inexpensive access to the light quark mass regime of QCD where chiral nonanalytic behaviour associated with Goldstone bosons is revealed. The motivation and formulation of FLIC fermions, its excellent scaling properties and its low-lying hadron mass phenomenology are presented.Comment: 29 pages, 13 figures, 6 tables. Contribution to lecure notes in 2nd Cairns Topical Workshop on Lattice Hadron Physics 2003 (LHP 2003), Cairns, Australia, 22-30 Jul 200

    Library Design in Combinatorial Chemistry by Monte Carlo Methods

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    Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure
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