## Conference Proceeding

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#### Institute

- Lower bounds for multi-pass processing of multiple data streams (2009)
- This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata. Two algorithms for solving the set disjointness problem with these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.

- Ambiguity and communication (2009)
- The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with size k poly(r) and ambiguity O(nk), but Lr,k has only NFA's with exponential size, if ambiguity o(nk) is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998).

- Towards a determination of the chiral critical surface of QCD (2009)
- The chiral critical surface is a surface of second order phase transitions bounding the region of first order chiral phase transitions for small quark masses in the fmu;d;ms;mg parameter space. The potential critical endpoint of the QCD (T;m)-phase diagram is widely expected to be part of this surface. Since for m = 0 with physical quark masses QCD is known to exhibit an analytic crossover, this expectation requires the region of chiral transitions to expand with m for a chiral critical endpoint to exist. Instead, on coarse Nt = 4 lattices, we find the area of chiral transitions to shrink with m, which excludes a chiral critical point for QCD at moderate chemical potentials mB < 500 MeV. First results on finer Nt = 6 lattices indicate a curvature of the critical surface consistent with zero and unchanged conclusions. We also comment on the interplay of phase diagrams between the Nf = 2 and Nf = 2+1 theories and its consequences for physical QCD.

- Lattice calculations at non-zero chemical potential: the QCD phase diagram (2009)
- The so-called sign problem of lattice QCD prohibits Monte Carlo simulations at finite baryon density by means of importance sampling. Over the last few years, methods have been developed which are able to circumvent this problem as long as the quark chemical potential is m=T <~1. After a brief review of these methods, their application to a first principles determination of the QCD phase diagram for small baryon densities is summarised. The location and curvature of the pseudo-critical line of the quark hardon transition is under control and extrapolations to physical quark masses and the continuum are feasible in the near future. No definite conclusions can as yet be drawn regarding the existence of a critical end point, which turns out to be extremely quark mass and cut-off sensitive. Investigations with different methods on coarse lattices show the lightmass chiral phase transition to weaken when a chemical potential is switched on. If persisting on finer lattices, this would imply that there is no chiral critical point or phase transition for physical QCD. Any critical structure would then be related to physics other than chiral symmetry breaking.

- Screened perturbation theory for 3d Yang-Mills theory and the magnetic modes of hot QCD : International Workshop on QCD Green’s Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT Trento, Italy (2009)
- Perturbation theory for non-abelian gauge theories at finite temperature is plagued by infrared divergences which are caused by magnetic soft modes ~ g2T, corresponding to gluon fields of a 3d Yang-Mills theory. While the divergences can be regulated by a dynamically generated magnetic mass on that scale, the gauge coupling drops out of the effective expansion parameter requiring summation of all loop orders for the calculation of observables. Some gauge invariant possibilities to implement such infrared-safe resummations are reviewed. We use a scheme based on the non-linear sigma model to estimate some of the contributions ~ g6 of the soft magnetic modes to the QCD pressure through two loops. The NLO contribution amounts to ~ 10% of the LO, suggestive of a reasonable convergence of the series.

- Dynamical lattice computation of the Isgur-Wise functions τ1/2 and τ3/2 (2009)
- We perform a two-flavor dynamical lattice computation of the Isgur-Wise functions t1/2 and t3/2 at zero recoil in the static limit. We find t1/2(1) = 0.297(26) and t3/2(1) = 0.528(23) fulfilling Uraltsev’s sum rule by around 80%. We also comment on a persistent conflict between theory and experiment regarding semileptonic decays of B mesons into orbitally excited P wave D mesons, the so-called “1/2 versus 3/2 puzzle”, and we discuss the relevance of lattice results in this context.

- First results of ETMC simulations with Nf = 2+1+1 maximally twisted mass fermions (2009)
- We present first results from runs performed with Nf = 2+1+1 flavours of dynamical twisted mass fermions at maximal twist: a degenerate light doublet and a mass split heavy doublet. An overview of the input parameters and tuning status of our ensembles is given, together with a comparison with results obtained with Nf = 2 flavours. The problem of extracting the mass of the K- and D-mesons is discussed, and the tuning of the strange and charm quark masses examined. Finally we compare two methods of extracting the lattice spacings to check the consistency of our data and we present some first results of cPT fits in the light meson sector.