Search

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on N_t=6 and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found., Comment: 14 pages, 6 figures, 1 table

Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit., Comment: 15 pages, 7 figures, 2 tables; Version published in JHEP

The effect of an external magnetic field on the finite temperature transition of QCD is studied. We measure thermodynamic observables including the quark condensates and susceptibilities and the strange quark number susceptibility. We generate configurations at various values of the quantized magnetic flux with N_f=2+1 flavors of stout smeared staggered quarks at physical quark masses. We perform the renormalization of our observables and approach the continuum limit with N_t=6,8 and 10 lattices. We also check finite volume effects using various lattice volumes. Our main result is that the transition temperature significantly decreases with growing magnetic field, and that the transition remains an analytic crossover up to our largest external field eB ~ 1 GeV^2., Comment: 7 pages, 3 figures, talk presented at the XXIX International Symposium on Lattice Field Theory (Lattice 2011), July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA

The effect of an external (electro)magnetic field on the finite temperature transition of QCD is studied. We generate configurations at various values of the quantized magnetic flux with $N_f=2+1$ flavors of stout smeared staggered quarks, with physical masses. Thermodynamic observables including the chiral condensate and susceptibility, and the strange quark number susceptibility are measured as functions of the field strength. We perform the renormalization of the studied observables and extrapolate the results to the continuum limit using $N_t=6,8$ and 10 lattices. We also check for finite volume effects using various lattice volumes. We find from all of our observables that the transition temperature $T_c$ significantly decreases with increasing magnetic field. This is in conflict with various model calculations that predict an increasing $T_c(B)$. From a finite volume scaling analysis we find that the analytic crossover that is present at B=0 persists up to our largest magnetic fields $eB \approx 1 \textmd{GeV}^2$, and that the transition strength increases mildly up to this $eB\approx1 \textmd{GeV}^2$., Comment: 22 pages, 13 figures

In this paper, we will outline computations of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, for those deformations describable as deformations of toric Euler sequences. Quantum sheaf cohomology is a heterotic analogue of quantum cohomology, a quantum deformation of the classical product on sheaf cohomology groups, that computes nonperturbative corrections to analogues of (27*)^3 couplings in heterotic string computations. Previous computations have relied on either physics-based GLSM techniques or computation-intensive brute-force Cech cohomology techniques. This paper describes methods for greatly simplifying mathematical computations, and derives more general results than previously obtainable with GLSM techniques. We will outline recent results (rigorous proofs will appear elsewhere)., Comment: LaTeX, 39 pages; v2: references added

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to about 190 MeV in large volumes (M_\pi L > 4), and three values of the lattice spacing. Our main results are the nucleon sigma term \sigma_{\pi N} = 39(4)(^{+18}_{-7}) and the strangeness content y_{N} = 0.20(7)(^{+13}_{-17}). Under the assumption of validity of covariant baryon \chi PT in our range of masses one finds y_{N} = 0.276(77)(^{+90}_{-62})., Comment: LaTeX. 15 pages, 5 figures. Text and results corrected according to Erratum [Phys. Rev. D 93, 039905(E) (2016)]

We study the spectra of heavy-light and heavy-heavy mesons containing charm quarks, including higher spin states. We use two sets of $N_f = 2 + 1$ gauge configurations, one set from QCDSF using the SLiNC action, and the other configurations from the Budapest-Marseille-Wuppertal collaboration, using the HEX smeared clover action. To extract information about the excited states, we choose a suitable basis of operators to implement the variational method., Comment: 7 pages, 5 figures, Talk presented at the XXIX International Symposium on Lattice Field Theory, Lattice2011, July 11-16, 2011, The Village at Squaw Valley, California, USA

Indirect CP violation in K \rightarrow {\pi}{\pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from a\approx0.054 fm to a\approx0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data., Comment: 10 pages, 7 figures. v2: Added one reference and one figure, replaced 2 figures for better readability and updated ensembles, conclusions unchanged. Final, published version

We present the equation of state (pressure, trace anomaly, energy density and entropy density) of the SU(3) gauge theory from lattice field theory in an unprecedented precision and temperature range. We control both finite size and cut-off effects. The studied temperature window ($0.7... 1000 T_c$) stretches from the glueball dominated system into the perturbative regime, which allows us to discuss the range of validity of these approaches. From the critical couplings on fine lattices we get $T_c/\Lambdamsbar=1.26(7)$ and use this ratio to express the perturbative free energy in $T_c$ units. We also determine the preferred renormalization scale of the Hard Thermal Loop scheme and we fit the unknown $g^6$ order perturbative coefficient at extreme high temperatures $T>100T_c$. We furthermore quantify the nonperturbative contribution to the trace anomaly using two simple functional forms., Comment: 7 pages, Contribution to the The XXVIII International Symposium on Lattice Field Theory; June 14 - 19, 2010, Villasimius, Sardinia, Italy

We determine the phase diagram of QCD on the \mu-T plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility. The calculations are carried out on N_t =6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavor staggered fermion action using physical quark masses. After carrying out the continuum extrapolation we find that both quantities result in a similar curvature of the transition line. Furthermore, our results indicate that in leading order the width of the transition region remains essentially the same as the chemical potential is increased., Comment: 12 pages, 6 figures

Based on a series of lattice calculations we determine the ratio FK/Fpi in QCD. With experimental data from kaon decay and nuclear double beta decay, we obtain a precise determination of |Vus|. Our simulation includes 2+1 flavours of sea quarks, with three lattice spacings, large volumes and a simulated pion mass reaching down to about 190 MeV for a full control over the systematic uncertainties., Comment: 6 pages, 2 figures. Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 6-10 September 2010

A status report is given for a joint project of the Budapest-Marseille-Wuppertal collaboration and the Regensburg group to study the quark mass-dependence of octet baryons in SU(3) Baryon XPT. This formulation is expected to extend to larger masses than Heavy-Baryon XPT. Its applicability is tested with 2+1 flavor data which cover three lattice spacings and pion masses down to about 190 MeV, in large volumes. Also polynomial and rational interpolations in M_\pi^2 and M_K^2 are used to assess the uncertainty due to the ansatz. Both frameworks are combined to explore the precision to be expected in a controlled determination of the nucleon sigma term and strangeness content., Comment: Lattice 2010

At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. We will present preliminary results for electromagnetic corrections to light hadron masses, based on simulations in which a $\mathrm{U}(1)$ degree of freedom is superimposed on $N_f=2+1$ QCD configurations from the BMW collaboration., Comment: 7 pages, 2 figures, The XXVIII International Symposium on Lattice Field Theory, June 14-19,2010, Villasimius, Sardinia Italy

While the masses of light hadrons have been extensively studied in lattice QCD simulations, there exist only a few exploratory calculations of the strong decay widths of hadronic resonances. We will present preliminary results of a computation of the rho meson width obtained using $N_f=2+1$ flavor simulations. The work is based on L\"uscher's formalism and its extension to moving frames., Comment: The XXVIII International Symposium on Lattice Field Theory, June 14-19,2010, Villasimius, Sardinia Italy

We give details of our precise determination of the light quark masses m_{ud}=(m_u+m_d)/2 and m_s in 2+1 flavor QCD, with simulated pion masses down to 120 MeV, at five lattice spacings, and in large volumes. The details concern the action and algorithm employed, the HMC force with HEX smeared clover fermions, the choice of the scale setting procedure and of the input masses. After an overview of the simulation parameters, extensive checks of algorithmic stability, autocorrelation and (practical) ergodicity are reported. To corroborate the good scaling properties of our action, explicit tests of the scaling of hadron masses in N_f=3 QCD are carried out. Details of how we control finite volume effects through dedicated finite volume scaling runs are reported. To check consistency with SU(2) Chiral Perturbation Theory the behavior of M_\pi^2/m_{ud} and F_\pi as a function of m_{ud} is investigated. Details of how we use the RI/MOM procedure with a separate continuum limit of the running of the scalar density R_S(\mu,\mu') are given. This procedure is shown to reproduce the known value of r_0m_s in quenched QCD. Input from dispersion theory is used to split our value of m_{ud} into separate values of m_u and m_d. Finally, our procedure to quantify both systematic and statistical uncertainties is discussed., Comment: 45 pages

Ordinary matter is described by six fundamental parameters: three couplings (gravitational, electromagnetic and strong) and three masses: the electron's (m_e) and those of the up (m_u) and down (m_d) quarks. An additional mass enters through quantum fluctuations: the strange quark mass (m_s). The three couplings and m_e are known with an accuracy of better than a few per mil. Despite their importance, $m_u$, $m_d$ (their average m_{ud}) and m_s are relatively poorly known: e.g. the Particle Data Group quotes them with conservative errors close to 25%. Here we determine these quantities with a precision below 2% by performing ab initio lattice quantum chromodynamics (QCD) calculations, in which all systematics are controlled. We use pion and quark masses down to (and even below) their physical values, lattice sizes of up to 6 fm, and five lattice spacings to extrapolate to continuum spacetime. All necessary renormalizations are performed nonperturbatively., Comment: 9 pages, 2 figures, 1 table. v2: published version, one reference added

We determine the ratio FK/Fpi in QCD with Nf=2+1 flavors of sea quarks, based on a series of lattice calculations with three different lattice spacings, large volumes and a simulated pion mass reaching down to about 190 MeV. We obtain FK/Fpi=1.192 +/- 0.007(stat) +/- 0.006(syst). This result is then used to give an updated value of the CKM matrix element |Vus|. The unitarity relation for the first row of this matrix is found to be well observed., Comment: 15 pages, 4 figures, 2 tables

Recent results on the QCD phase diagram are reviewed. We begin with a detailed introduction of lattice techniques. Then results at vanishing chemical potential are presented. The order of the phase transition, the transition temperature and the equation of state are discussed. At non-vanishing chemical potential we study the mu-T phase line, the critical point as well as the equation of state., Comment: 48 pages, 33 figures. Accepted for publication in Landolt-Boernstein Volume 1-23A. Originally submitted Nov.08; note added

More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab-initio calculation of the masses of protons, neutrons and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega electronvolts are used to extrapolate to the physical point with lattice sizes of approximately four times the inverse pion mass. Three lattice spacings are used for a continuum extrapolation. Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties., Comment: 22 pages, 3 Tables, 8 Figures. Published in Science (21 November 2008) with Supporting Online Material. Submission to arXiv has been delayed by 6 months to respect the journal's embargo policy

We extend our previous study [Phys. Lett. B643 (2006) 46] of the cross-over temperatures (T_c) of QCD. We improve our zero temperature analysis by using physical quark masses and finer lattices. In addition to the kaon decay constant used for scale setting we determine four quantities (masses of the \Omega baryon, K^*(892) and \phi(1020) mesons and the pion decay constant) which are found to agree with experiment. This implies that --independently of which of these quantities is used to set the overall scale-- the same results are obtained within a few percent. At finite temperature we use finer lattices down to a <= 0.1 fm (N_t=12 and N_t=16 at one point). Our new results confirm completely our previous findings. We compare the results with those of the 'hotQCD' collaboration., Comment: 19 pages, 8 figures, 3 tables

We determine the curvature of the phase transition line in the mu-T plane through an analysis of various observables, including the Polyakov loop, the quark number susceptibilities and the susceptibility of the chiral condensate. The second derivative of these quantities with respect to mu was calculated. The measurements were carried out on N_T = 4,6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavour staggered fermion action using physical quark masses., Comment: Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA. 7 pages, 6 figures

We present a framework for phenomenological lattice QCD calculations which makes use of a tree level Symanzink improved action for gluons and stout-link Wilson fermions. We give details of our efficient HMC/RHMC algorithm and present a scaling study of the low-lying N_f=3 baryon spectrum. We find a scaling region that extends to a~<0.16fm and conclude that our action and algorithm are suitable for large scale phenomenological investigations of N_f=2+1 QCD. We expect this conclusion to hold for other comparable actions., Comment: 11 pages, 7 figures, aps style. Final published version

Some algorithmic details of our $N_f=2+1$ QCD mixed action simulations with overlap valence and improved Wilson sea quarks are presented., Comment: 7 pages, 6 figures. Presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany

We present preliminary results for the chiral behavior of charged pseudo-Goldstone-boson masses and decay constants. These are obtained in simulations with N_f=2+1 flavors of tree-level, O(a)-improved Wilson sea quarks. In these simulations, mesons are composed of either valence quarks discretized in the same way as the sea quarks (unitary simulations) or of overlap valence quarks (mixed-action simulations). We find that the chiral behavior of the pseudoscalar meson masses in the mixed-action calculations cannot be explained with continuum, partially-quenched chiral perturbation theory. We show that the inclusion of O(a^2) unitarity violations in the chiral expansion resolves this discrepancy and that the size of the unitarity violations required are consistent with those which we observe in the zero-momentum, scalar-isotriplet-meson propagator., Comment: 7 pages, 3 figures, talk by L. Lellouch at the XXV International Symposium on Lattice Field Theory (LATTICE 2007), 30 July - 4 August 2007, Regensburg, Germany

We present results for the equation of state upto previously unreachable, high temperatures. Since the temperature range is quite large, a comparison with perturbation theory can be done directly., Comment: 7 pages, 5 figures, Lattice 2007

We determine the static quark free energies around the transition temperature using 2+1 flavors of staggered fermions. Simulations are carried out on N_t=4,6,8 and 10 lattices using physical quark masses. The free energies extracted from Polyakov-loop correlators are extrapolated to the continuum limit., Comment: 7 pages, talk presented at Lattice 2007, Regensburg, 30th July-4th August, 2007

The finite temperature QCD transition for physical quark masses is a crossover. For smaller quark masses a first-order phase transition is expected. Using Symanzik improved gauge and stout improved fermion action for 2+1 flavour staggered QCD we give estimates/bounds for the phase line separating the first-order region from the crossover one. The calculations are carried out on two different lattice spacings. Our conclusion for the critical mass is $m_0 \lesssim 0.07 \cdot m_{phys}$ for $N_T=4$ and $m_0 \lesssim 0.12 \cdot m_{phys}$ for $N_T=6$ lattices., Comment: Talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany. 7 pages, 6 figures

We determine the nature of the QCD transition using lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities.No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations., Comment: 7 pages, 4 figures

The transition temperature ($T_c$) of QCD is determined by Symanzik improved gauge and stout-link improved staggered fermionic lattice simulations. We use physical masses both for the light quarks ($m_{ud}$) and for the strange quark ($m_s$). Four sets of lattice spacings ($N_t$=4,6,8 and 10) were used to carry out a continuum extrapolation. It turned out that only $N_t$=6,8 and 10 can be used for a controlled extrapolation, $N_t$=4 is out of the scaling region. Since the QCD transition is a non-singular cross-over there is no unique $T_c$. Thus, different observables lead to different numerical $T_c$ values even in the continuum and thermodynamic limit. The peak of the renormalized chiral susceptibility predicts $T_c$=151(3)(3) MeV, wheres $T_c$-s based on the strange quark number susceptibility and Polyakov loops result in 24(4) MeV and 25(4) MeV larger values, respectively. Another consequence of the cross-over is the non-vanishing width of the peaks even in the thermodynamic limit, which we also determine. These numbers are attempted to be the full result for the $T$$\neq$0 transition, though other lattice fermion formulations (e.g. Wilson) are needed to cross-check them., Comment: 13 pages 5 figures. Final version, published in Phys.Lett.B

We study the density of states method to explore the phase diagram of the chiral transition on the temperature and quark chemical potential plane. Four quark flavors are used in the analysis. Though the method is quite expensive small lattices show an indication for a triple-point connecting three different phases on the phase diagram., Comment: 5 pages, 6 figures, talk given at 'Extreme QCD', August 2-5 2005, Swansea, Wales, UK

The grand canonical potential for a static quark-antiquark pair at non-vanishing chemical potential was determined at several temperatures. The dynamical staggered simulations were carried out with 2+1 physical quarks along the Lines of Constant Physiscs (LCP)., Comment: 6 pages, Presented at 23rd International Symposium on Lattice Field Theory: Lattice 2005, Trinity College, Dublin, Ireland, 25-30 Jul 2005

Recent results on the equation of state from lattice QCD are reviewed. The lattice technique and previous results are shortly discussed. New results for physical quark masses and two sets of lattice spacings are presented. The pressure, energy density, entropy density, speed of sound and quark number susceptibilities are determined., Comment: 10 pages, 11figures. Plenary talk presented at the Quark Matter 2005 conference

We perform dynamical QCD simulations with $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3\times 16$ lattices. We study the problem of topological sector changing. A new method is proposed which works without topological sector changes. We use this new method to determine the topological susceptibility at various quark masses., Comment: 15 pages, 3 figures

The equation of state of QCD at vanishing chemical potential as a function of temperature is determined for two sets of lattice spacings. Coarser lattices with temporal extension of N_t=4 and finer lattices of N_t=6 are used. Symanzik improved gauge and stout-link improved staggered fermionic actions are applied. The results are given for physical quark masses both for the light quarks and for the strange quark. Pressure, energy density, entropy density, quark number susceptibilities and the speed of sound are presented., Comment: 14 pages, 9 figures. Version published in JHEP: discussions added in Sects. 1, 2. Fig. 1 changed and a new figure for the interaction measure added. Information on statistics added in Table 1. Raw values of the pressure added in Table 3. A few references added

We study spin 1/2 isoscalar and isovector, even and odd parity candidates for the $\Theta^+(1540)$ pentaquark particle using large scale lattice QCD simulations. Previous lattice works led to inconclusive results because so far it has not been possible to unambiguously identify the known scattering spectrum and tell whether additionally a genuine pentaquark state also exists. Here we carry out this analysis using several possible wave functions (operators). Linear combinations of those have a good chance of spanning both the scattering and pentaquark states. Our operator basis is the largest in the literature, and it also includes spatially non-trivial ones with unit orbital angular momentum. The cross correlator we compute is 14$\times$14 with 60 non-vanishing elements. We can clearly distinguish the lowest scattering state(s) in both parity channels up to above the expected location of the pentaquark, but we find no trace of the latter. Based on that we conclude that there are most probably no pentaquark bound states at our quark masses, corresponding to $m_\pi$=400--630 MeV. However, we cannot rule out the existence of a pentaquark state at the physical quark mass corresponding to $m_\pi$=135 MeV or pentaquarks with a more exotic wave function., Comment: 18 pages, 2 figures

We present numerical results on the static quark--anti-quark grand canonical potential in full QCD at non-vanishing temperature ($T$) and quark chemical potential ($\mu$). Non-zero $\mu$-s are reached by means of multi-parameter reweighting. The dynamical staggered simulations were carried out for $n_f=2+1$ flavors with physical quark masses on $4\times 12^3$ lattices., Comment: Lattice2004(non-zero)

Extraterrestrial neutrinos can initiate deeply developing air showers, and those that traverse the atmosphere unscathed may produce cascades in the ice or water. Up to now, no such events have been observed. This can be translated into upper limits on the diffuse neutrino flux. On the other hand, the observation of cosmic rays with primary energies > 10^{10} GeV suggests that there is a guaranteed flux of cosmogenic neutrinos, arising from the decay of charged pions (and their muon daughters) produced in proton interactions with the cosmic microwave background. In this work, armed with these cosmogenic neutrinos and the increased exposure of neutrino telescopes we bring up-to-date model-independent upper bounds on the neutrino-nucleon inelastic cross section. Uncertainties in the cosmogenic neutrino flux are discussed and taken into account in our analysis. The prospects for improving these bounds with the Pierre Auger Observatory are also estimated. The unprecedented statistics to be collected by this experiment in 6 yr of operation will probe the neutrino-nucleon inelastic cross section at the level of Standard Model predictions., Comment: To be published in JCAP

We present results of a hybrid Monte-Carlo algorithm for dynamical, $n_f=2$, four-dimensional QCD with overlap fermions. The fermionic force requires careful treatment, when changing topological sectors. The pion mass dependence of the topological susceptibility is studied on $6^4$ and $12\cdot 6^3$ lattices. The results are transformed into physical units., Comment: Lattice2004(chiral)

The present work is a summary of the status of lattice pentaquark calculations. After a pedagogic introduction to the basics of lattice hadron spectroscopy we give a critical comparison of results presently available in the literature. Special emphasis is put on presenting some of the possible pitfalls of these calculations. In particular we discuss at length the choice of the hadronic operators and the separation of genuine five-quark states from meson-baryon scattering states., Comment: 13 pages LaTeX, 1 eps figure

In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way., Comment: 51 pages, LaTeX; v2: typos fixed; v3: more typos fixed

After a short review of the ultrahigh energy cosmic ray puzzle - the apparent observation of cosmic rays originating from cosmological distances with energies above the expected Greisen-Zatsepin-Kuzmin cutoff 4x10^{19} eV - we consider strongly interacting neutrino scenarios as an especially interesting solution. We show that all features of the ultrahigh energy cosmic ray spectrum from 10^{17} eV to 10^{21} eV can be described to originate from a simple power-like injection spectrum of protons, under the assumption that the neutrino-nucleon cross-section is significantly enhanced at center of mass energies above ~ 100 TeV. In such a scenario, the cosmogenic neutrinos produced during the propagation of protons through the cosmic microwave background initiate air showers in the atmosphere, just as the protons. The total air shower spectrum induced by protons and neutrinos shows excellent agreement with the observations. We shortly discuss TeV-scale extensions of the Standard Model which may lead to a realization of a strongly interacting neutrino scenario. We emphasize, however, that such a scenario may even be realized within the standard electroweak model: electroweak instanton/sphaleron induced processes may get strong at ultrahigh energies. Possible tests of strongly interacting neutrino scenarios range from observations at cosmic ray facilities and neutrino telescopes to searches at lepton nucleon scattering experiments., Comment: 20 pages, 12 figures, ws-procs975x65.cls included, invited talk given at the 10th Marcel Grossmann Meeting, 20-26 July 2003, Rio de Janeiro, Brazil

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (\mu) plane. Using a recently proposed lattice method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices. Our result for the critical point is T_E=162 \pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing m_{u,d} decreased \mu_E. Note, that the continuum extrapolation is still missing, Comment: 10 pages, 2 figures

We present results on lattice QCD at finite temperature (T) and chemical potential (\mu). We apply the overlap-improving multi-parameter reweighting technique for n_f=4 and 2+1 staggered QCD. We use semi-realistic masses on L_t=4 lattices. The critical endpoint (E) of 2+1 flavour QCD on the \mu-T plane is located. Our results are based on {\cal{O}}(10^3-10^4) configurations., Comment: 7 pages, 4 figures, talk given at Finite Density QCD at Nara, Nara, Japan, 10-12 July 2003

We present N_t=4 lattice results for the equation of state of 2+1 flavour staggered, dynamical QCD at finite temperature and chemical potential. We use the overlap improving multi-parameter reweighting technique to extend the equation of state for non-vanishing chemical potentials. The results are obtained along the line of constant physics. Our physical parameters extend in temperature and baryon chemical potential upto \approx 500-600 MeV., Comment: 13 pages 9 figures, talk given at Finite Density QCD at Nara, Nara, Japan, 10-12 July 2003

We present an N_t=4 lattice study for the equation of state of 2+1 flavour staggered, dynamical QCD at finite temperature and chemical potential. We use the overlap improving multi-parameter reweighting technique to extend the equation of state for non-vanishing chemical potentials. The results are obtained on the line of constant physics and our physical parameters extend in temperature and baryon chemical potential upto \approx 500-600 MeV., Comment: 28 pages, 15 figures

We introduce a numerical method for generating the approximating polynomials used in fermionic calculations with smeared link actions. We investigate the stability of the algorithm and determine the optimal weight function and the optimal type of discretization. The achievable order of polynomial approximation reaches several thousands allowing fermionic calculations using the Hypercubic Smeared Link action even with physical quark masses., Comment: 12 pages, 9 figures, Final version appeared in Comp.Phys.Comm

We present first, exploratory results of a hybrid Monte-Carlo algorithm for dynamical, n_f=2, four-dimensional QCD with overlap fermions. As expected, the computational requirements are typically two orders of magnitude larger for the dynamical overlap formalism than for the more conventional (Wilson or staggered) formulations., Comment: 13 pages, 2 figures

Recent results of lattice QCD at finite temperature and density are reviewed. At vanishing density the transition temperature, the equation of state and hadron properties are discussed both for the pure gauge theory and for dynamical staggered, Wilson and overlap fermions. The second part deals with finite density. There are recent results for full QCD at finite temperature and moderate density, while at larger densities QCD-like models are studied., Comment: 14 pages, 19 figures, lattice2003(plenary). Minor corrections