3253782
On the efficient computation of high-order derivatives for implicitly defined functions
Abstract Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order derivatives. A technique based on algorithmic differentiation is presented which allows for a precise calculation of higher-order derivatives. The method can be widely applied even for the case of only numerically solvable, implicit dependencies which totally hamper a semi-analytical calculation of the derivatives. As a demonstration the method is applied to a quantum field theoretical physical model. The results are compared with standard numerical derivative methods.
17501397
Low-momentum hyperon-nucleon interactions
We present a first exploratory study for hyperon-nucleon interactions using renormalization group techniques. The effective two-body low-momentum potential ${V}_{\text{low}\phantom{\rule{0.3em}{0ex}}k}$ is obtained by integrating out the high-momentum components from realistic Nijmegen YN potentials. A T-matrix equivalence approach is employed, so that the low-energy phase shifts are reproduced by ${V}_{\text{low}\phantom{\rule{0.3em}{0ex}}k}$ up to a momentum scale $\ensuremath{\Lambda}~500$ MeV. Although the various bare Nijmegen models differ somewhat from each other, the corresponding ${V}_{\text{low}\phantom{\rule{0.3em}{0ex}}k}$ interactions show convergence in some channels, suggesting a possible model-independent YN interaction at low momenta.
62901349
Charge Fluctuations as Thermometer for Heavy-Ion Collisions
We present a determination of freeze-out conditions in heavy-ion collisions based on ratios of cumulants of net electric charge fluctuations obtained from lattice QCD. These ratios can reliably be calculated for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. We first determine the strangeness and electric charge chemical potentials that characterize the conditions in heavy ion collisions at RHIC and LHC. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature. We apply our method to preliminary data of the STAR and PHENIX collaborations.
118580235
Higher-order ratios of baryon number cumulants
The relevance of higher order cumulants of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy-ion collisions at LHC and RHIC is addressed. The sign structure of the higher order cumulants in the vicinity of the chiral crossover temperature might be a sensitive probe and may allow to elucidate their relation to the QCD phase transition. We calculate ratios of generalized quarknumber susceptibilities to high orders in three flavor QCD-like models and investigate their sign structure close to the chiral crossover line.
53496974
Towards finite density QCD with Taylor expansions
Abstract Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective N f = 2 + 1 flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective N f = 2 + 1 flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.
119170993
Thermodynamics of (2+1)-flavor QCD: Confronting models with lattice studies
The Polyakov-quark-meson model, which combines chiral as well as deconfinement aspects of strongly interacting matter, is introduced for three light quark flavors. An analysis of the chiral and deconfinement phase transition of the model and its thermodynamics at finite temperatures is given. Three different forms of the effective Polyakov-loop potential are considered. The findings of the 2+1 flavor model investigations are compared to corresponding recent QCD lattice simulations of the RBC-Bielefeld, HotQCD and Wuppertal-Budapest collaborations. The influence of the heavier quark masses, which are used in the lattice calculations, is taken into account. In the transition region the bulk thermodynamics of the Polyakov-quark-meson model agrees well with the lattice data.
27851457
Light hadrons from Nf=2+1+1 dynamical twisted mass fermions
7 pages, 5 figures, talk presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010 Villasimius, Italy
29909987
Fermions in the pseudoparticle approach
The pseudoparticle approach is a numerical technique to compute path integrals without discretizing spacetime. The basic idea is to integrate over those field configurations, which can be represented by a sum of a fixed number of localized building blocks (pseudoparticles). In a couple of previous papers we have successfully applied the pseudoparticle approach to pure SU(2) Yang-Mills theory. In this work I discuss how to incorporate fermionic fields in the pseudoparticle approach. To test the method, I compute the phase diagram of the 1 + 1-dimensional Gross-Neveu model in the large-N limit.
1888088
The pseudoparticle approach for solving path integrals in gauge theories
We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color orientations as degrees of freedom. Applied to Maxwell theory this technique results in a potential which is in excellent agreement with the Coulomb potential. For SU(2) Yang-Mills theory the same technique yields clear evidence of confinement. Varying the coupling constant exhibits the same scaling behavior for the string tension, the topological susceptibility and the critical temperature while their dimensionless ratios are similar to those obtained in lattice calculations.
7348824
The continuum limit of the static-light meson spectrum
We investigate the continuum limit of the low lying static-light meson spectrum using Wilson twisted mass lattice QCD with Nf = 2 dynamical quark flavours. We consider three values of the lattice spacing a ≈ 0.051 fm, 0.064 fm, 0.080 fm and various values of the pion mass in the range 280 MeV ≲ mPS 640 MeV. We present results in the continuum limit for light cloud angular momentum j = 1/2, 3/2, 5/2 and for parity $ \mathcal{P} = +, - $. We extrapolate our results to physical quark masses, make predictions regarding the spectrum of B and Bs mesons and compare with available experimental results.
3216251
Classes of confining gauge field configurations
We present a numerical method to compute path integrals in effective SU(2) Yang-Mills theories. The basic idea is to approximate the Yang-Mills path integral by summing over all gauge field configurations, which can be represented as a linear superposition of a small number of localized building blocks. With a suitable choice of building blocks many essential features of SU(2) Yang-Mills theory can be reproduced, particularly confinement. The analysis of our results leads to the conclusion that topological charge as well as extended structures are essential elements of confining gauge field configurations.