Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on the examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma-models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a "memory" of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.Comment: 16 pages RevTeX, 14 figures; v2: Algorithm for the Weingarten model corrected; v3: published versio

Fermion loop simulation of the lattice Gross-Neveu model

We present a numerical simulation of the Gross-Neveu model on the lattice using a new representation in terms of fermion loops. In the loop representation all signs due to Pauli statistics are eliminated completely and the partition function is a sum over closed loops with only positive weights. We demonstrate that the new formulation allows to simulate volumes which are two orders of magnitude larger than those accessible with standard methods

Nucleon form factors and moments of parton distributions in twisted mass lattice QCD

We present results on the electroweak form factors and on the lower moments of parton distributions of the nucleon, within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Results are obtained on lattices with three different values of the lattice spacings, namely a=0.089 fm, a=0.070 fm and a=0.056 fm, allowing the investigation of cut-off effects. The volume dependence is examined by comparing results on two lattices of spatial length L=2.1 fm and L=2.8 fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the MS-scheme at a scale mu=2 GeV.Comment: Talk presented in the XXIst International Europhysics Conference on High Energy Physics, 21-27 July 2011, Grenoble, Rhones Alpes Franc

Nucleon Structure in Lattice QCD using twisted mass fermions

We present results on the nucleon form factors and moments of generalized parton distributions obtained within the twisted mass formulation of lattice QCD. We include a discussion of lattice artifacts by examining results at different volumes and lattice spacings. We compare our results with those obtained using different discretization schemes and to experiment.Comment: 4 pages, 3 Figures, Invited talk presented at the 35th International Conference of High Energy Physics - ICHEP 2010 July 22-28, 2010, Paris, Franc

Nucleon form factors with dynamical twisted mass fermions

The electromagnetic and axial form factors of the nucleon are evaluated in twisted mass QCD with two degenerate flavors of light, dynamical quarks. The axial charge g_A, magnetic moment and the Dirac and Pauli radii are determined for pion masses in the range 300 MeV to 500 MeV

Nucleon form factors with Nf=2 dynamical twisted mass fermions

We present results on the electromagnetic and axial nucleon form factors using two degenerate flavors of twisted mass fermions on lattices of spatial size 2.1 fm and 2.7 fm and a lattice spacing of about 0.09 fm. We consider pion masses in the range of 260-470 MeV. We chirally extrapolate results on the nucleon axial ch arge, the isovector Dirac and Pauli root mean squared radii and magnetic moment to the physical point and co mpare to experiment.Comment: Report no. added; typos corrected. ETM Collaboration, 7 pages, 10 figures, Talk given at the XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing, Chin

The low-lying baryon spectrum with two dynamical twisted mass fermions

The masses of the low lying baryons are evaluated using two degenerate flavors of twisted mass sea quarks corresponding to pseudo scalar masses in the range of about 270-500 MeV. The strange valence quark mass is tuned to reproduce the mass of the kaon in the physical limit. The tree-level Symanzik improved gauge action is employed. We use lattices of spatial size 2.1 fm and 2.7 fm at two values of the lattice spacing with $r_0/a=5.22(2)$ and $r_0/a=6.61(3)$. We check for both finite volume and cut-off effects on the baryon masses. We performed a detailed study of the chiral extrapolation of the octet and decuplet masses using SU(2) $\chi$PT. The lattice spacings determined using the nucleon mass at the physical point are consistent with the values extracted using the pion decay constant. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. The baryon masses that we find after taking the continuum limit and extrapolating to the physical limit are in good agreement with experiment.Comment: By the ETM Collaboration, 24 pages, 24 figure

Analysis of chemical composition stability of thermal water from Bańska PGP-1 well, Podhale

This paper presents an analysis of trends in the chemical composition of thermal waters exploited by Bańska PGP-1 well. Trends have been assessed for major ions (SOM4 2–, Cl –, Na+, Ca 2+), which determine the hydrogeochemical type of water. Assessment of trends was performed using GWSDAT software, using the results of the chemical composition conducted in the years 2001–2014. This assessment shows that the chemical composition of thermal water from Bańska PGP-1 can be classified as stable

Quantitative status of groundwater in small catchment area on example of Zawadka river catchment area

Niniejszy artykuł prezentuje wyniki badań, które przeprowadzone zostały na terenie obejmującym zlewnię potoku Zawadka w gminie Dębica w południowo-wschodniej Polsce. Wyniki badań terenowych oraz analiza dostępnych danych archiwalnych pozwoliły na określenie stanu ilościowego wód podziemnych regionu. W zestawieniu wielkości zasobów dyspozycyjnych z sumą szacunkowych poborów dokonano oceny stanu ilościowego badanej zlewni. Stan ten określony został jako dobry. Ocena stanu ilościowego pozwoliła wskazać najbardziej perspektywiczny obszar w obrębie badanej zlewni na potrzeby ustalenia potencjalnej lokalizacji ujęcia wód podziemnych. Jest to północna część zlewni. Wyniki badań oraz wnioski wynikające z oceny ilościowej wskazują na użyteczność przeprowadzania tego typu ocen dla małych zlewni w obszarach górskich.In this paper the results of field investigation in Zawadka river catchment area was presented. Based on that research quantitative status of groundwater was shown. Estimation of quantitative status is made on the base of comparison of quantity of disposable resources with the amount of estimated consumption and it was defined as good quantitative status. Taking into consideration the estimation of quantitative status , the north part of Zawadka catchment area is the most perspective for potential place of new groundwater capture. The result of research shows utility of carring out this type of research for small catchment areas

Analysis of the concentration stability of metasilic acid in the thermal water from the Bańska PGP-1 well

Niniejsza praca prezentuje ocenę stabilności stężenia kwasu metakrzemowego w wodach termalnych ujmowanych otworem Bańska PGP-1 opartą na wynikach analiz uzyskanych w latach 2012–2015. Analiza statystyczna danych została wykonana w programie IBM SPSS Statistics v.23, zaś analiza trendów za pomocą programu GWSDAT (Jones, Spence 2013). Wykonana ocena wykazuje, że stężenie kwasu metakrzemowego w wodach z ujęcia Bańska PGP-1 jest stabilne.This paper presents an analysis of the concentration stability of metasilic acid in the thermal waters exploited by the Bańska PGP-1 well, using the results of the chemical composition conducted in the years 2012–2015. The statistical analysis was performed using IBM SPSS v.23 and the assessment of trends was done by GWSDAT software (Jones, Spence 2013). This assessment shows that the concentration of metasilic acid in the thermal water from Bańska PGP-1 can be classified as stable