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Habilitationsordnung der Mathematisch–Naturwissenschaftlichen Fachbereiche der Johann Wolfgang Goethe-Universität Frankfurt am Main vom 04.02.1992 (ABl. 1992, S.816 ff.), zuletzt geändert am 28. April 2002 (StAnz. 41/2003, S. 4024 – 4025) : genehmigt durch Beschluss des Präsidiums der Johann Wolfgang Goethe-Universität Frankfurt am Main am 27. Januar 2009 ; hier: Änderung bzw. Ergänzung (2009)

Promotionsordnung der Mathematisch-Naturwissenschaftlichen Fachbereiche der Johann Wolfgang Goethe-Universität in Frankfurt am Main vom 26. Mai 1993 (ABL.1/94, S. 21) zuletzt geändert am 05.09.2007 (Uni-Report 13.11.2008) : genehmigt durch Beschluss des Präsidiums der Johann Wolfgang Goethe-Universität Frankfurt am Main am 27. Januar 2009 ; hier: Änderung (2009)

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)

Owe Philipsen Daniel Bieletzki York Schröder

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.

Lattice calculations at non-zero chemical potential: the QCD phase diagram (2009)

Owe Philipsen

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.

Towards a determination of the chiral critical surface of QCD (2009)

Owe Philipsen

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.

Dynamical lattice computation of the Isgur-Wise functions τ1/2 and τ3/2 (2009)

Benoit Blossier Marc Wagner Olivier Pène

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.

fB and fBs with maximally twisted Wilson fermions (2009)

Gregorio Herdoiza Karl Jansen Vittorio Lubicz Cecilia Tarantino Francesco Sanfilippo Chris Michael Andrea Shindler Silvano Simula Carsten Urbach

We present a lattice QCD calculation of the heavy-light decay constants fB and fBs performed with Nf = 2 maximally twisted Wilson fermions, at four values of the lattice spacing. The decay constants have been also computed in the static limit and the results are used to interpolate the observables between the charmand the infinite-mass sectors, thus obtaining the value of the decay constants at the physical b quark mass. Our preliminary results are fB = 191(14)MeV, fBs = 243(14)MeV, fBs/ fB = 1.27(5). They are in good agreement with those obtained with a novel approach, recently proposed by our Collaboration (ETMC), based on the use of suitable ratios having an exactly known static limit.

First results of ETMC simulations with Nf = 2+1+1 maximally twisted mass fermions (2009)

Rémi Baron Benoit Blossier Philippe Boucaud Albert Deuzeman Vincent Drach Federico Farchioni Vicent Gimenez Gregorio Herdoiza Karl Jansen Chris Michael István Montvay David Palao Elisabetta Pallante Olivier Pène Siebren Reker Carsten Urbach Marc Wagner Urs Wenger

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.

Jahresbericht 2008/2009 / Institut für Kernphysik am Fachbereich Physik der Goethe-Universität Frankfurt am Main (2009)

The O(N=2) model in polar coordinates at nonzero temperature (2009)

Martin Grahl

Chapter 1 contains the general background of our work. We briefly discuss important aspects of quantum chromodynamics (QCD) and introduce the concept of the chiral condensate as an order parameter for the chiral phase transition. Our focus is on the concept of universality and the arguments why the O(4) model should fall into the same universality class as the effective Lagrangian for the order parameter of (massless) two-flavor QCD. Chapter 2 pedagogically explains the CJT formalism and is concerned with the WKB method. In chapter 3 the CJT formalism is then applied to a simple Z(2) symmetric toy model featuring a one-minimum classical potential. As for all other models we are concerned with in this thesis, we study the behavior at nonzero temperature. This is done in 1+3 dimensions as well as in 1+0 dimensions. In the latter case we are able to compare the effective potential at its global minimum (which is minus the pressure) with our result from the WKB approximation. In chapter 4 this program is also carried out for the toy model with a double-well classical potential, which allows for spontaneous symmetry breaking and tunneling. Our major interest however is in the O(2) model with the fields treated as polar coordinates. This model can be regarded as the first step towards the O(4) model in four-dimensional polar coordinates. Although in principle independent, all subjects discussed in this thesis are directly related to questions arising from the investigation of this particular model. In chapter 5 we start from the generating functional in cartesian coordinates and carry out the transition to polar coordinates. Then we are concerned with the question under which circumstances it is allowed to use the same Feynman rules in polar coordinates as in cartesian coordinates. This question turns out to be non-trivial. On the basis of the common Feynman rules we apply the CJT formalism in chapter 6 to the polar O(2) model. The case of 1+0 dimensions was intended to be a toy model on the basis of which one could more easily explore the transition to polar coordinates. However, it turns out that we are faced with an additional complication in this case, the infrared divergence of thermal integrals. This problem requires special attention and motivates the explicit study of a massless field under topological constraints in chapter 8. In chapter 7 we investigate the cartesian O(2) model in 1+0 dimensions. We compare the effective potential at its global minimum calculated in the CJT formalism and via the WKB approximation. Appendix B reviews the derivation of standard thermal integrals in 1+0 and 1+3 dimensions and constitutes the basis for our CJT calculations and the discussion of infrared divergences. In chapter 9 we discuss the so-called path integral collapse and propose a solution of this problem. In chapter 10 we present our conclusions and an outlook. Since we were interested in organizing our work as pedagogical as possible within the narrow scope of a diploma thesis, we decided to make extensive use of appendices. Appendices A-H are intended for students who are not familiar with several important concepts we are concerned with. We will refer to them explicitly to establish the connection between our work and the general context in which it is settled.

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