arXiv subjects

Stefano Lottini

Publications and source records attributed to Stefano Lottini.

At least 19 recordsLinked to original sources

arXiv2014

Spectral density of the Dirac operator in two-flavour QCD

We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeV, and with spacings in the range 0.05-0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is non-zero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of approximately 80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation.

hep-lat↗

arXiv2014

On the extraction of spectral quantities with open boundary conditions

We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by Lüscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.

hep-lat↗

arXiv2014

Chiral symmetry breaking in QCD Lite

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of (Mpi^2 Fpi^2)/2 with respect to the quark mass m in the chiral limit, where Mpi and Fpi are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use CLS lattices at three values of the lattice spacing in the range 0.05-0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks-Casher mechanism, and the rate of condensation agrees with the Gell-Mann-Oakes-Renner (GMOR) relation. For the renormalisation-group-invariant ratios we obtain [Σ^RGI]^(1/3)/F =2.77(2)(4) and Lambda^MSbar/F = 3.6(2), which correspond to [Σ^\MSbar(2 GeV)]^(1/3) =263(3)(4) MeV and F=85.8(7)(20) MeV if FK is used to set the scale by supplementing the theory with a quenched strange quark.

hep-ph↗

arXiv2014

Approaching the chiral point in two-flavour lattice simulations

We investigate the behaviour of the pion decay constant and the pion mass in two-flavour lattice QCD, with the physical and chiral points as ultimate goal. Measurements come from the ensembles generated by the CLS initiative using the O(a)-improved Wilson formulation, with lattice spacing down to about 0.05 fermi and pion masses as low as 190 MeV. The applicability of SU(2) chiral perturbation theory is investigated, and various functional forms, and their range of validity, are compared. The physical scale is set through the kaon decay constant, whose measurement is enabled by inserting a third, heavier valence strange quark.

hep-lat↗

arXiv2013

Chiral behaviour of the pion decay constant in $N_f=2$ QCD

As increased statistics and new ensembles with light pions have become available within the CLS effort, we complete previous work by inspecting the chiral behaviour of the pion decay constant. We discuss the validity of Chiral Perturbation Theory ($χ$PT) and examine the results concerning the pion decay constant and the ensuing scale setting, the pion mass squared in units of the quark mass, and the ratio of decay constants $f_K/f_π$; along the way, the relevant low-energy constants of SU(2) $χ$PT are estimated. All simulations were performed with two dynamical flavours of nonperturbatively O(a)-improved Wilson fermions, on volumes with $m_πL \geq 4$, pion masses $\geq$ 192 MeV and lattice spacings down to 0.048 fm. Our error analysis takes into account the effect of slow modes on the autocorrelations.

hep-lat↗

arXiv2013

Chiral condensate from the Banks-Casher relation

We report on our ongoing project of determining the chiral condensate of two-flavor QCD from the Banks-Casher relation. We compute the mode number of the O(a)-improved Wilson-Dirac operator for several values of Λ, and we discuss different fitting strategies to extract the chiral condensate from its mass and Λdependence. Our preliminary results haven been obtained at two different lattice spacings by using CLS-configurations.

hep-lat↗

arXiv2013

Quarkyonic Percolation and deconfinement at finite density and number of colors

We examine the interplay between the percolation and the deconfinement phase transitions of Yang-Mills matter at finite temperature, quark chemical potential $μ_Q$ and number of colors $N_c$. We find that, whereas the critical $N_c$ for percolation goes down with density, the critical $N_c$ for confinement generally goes up. Because of this, Yang-Mills matter falls into two qualitatively different regimes: the "low-$N_c$ limit", where percolation does not occur because matter deconfines before it percolates, and the high-$N_c$ limit, where there are three distinct phases characterizing Yang-Mills matter at finite temperature and density: confined, deconfined and confined but percolating matter. The latter can be thought of as the recently conjectured "quarkyonic phase". We attempt to estimate the critical $N_c$, to see if the percolating phase can occur in our world. We find that, while percolation will not occur at normal nuclear density as in the large-$N_c$ limit, a sliver of the phase diagram in $N_c$, energy density and baryonic density where percolation occurs while confinement persists is possible. We conclude by speculating on the phenomenological properties of such percolating "quarkyonic" matter, suggest avenues to study it quantitatively, and look for it in experiment.

nucl-th↗

arXiv2013

Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results

A detailed study of the thermodynamics of the O(N=3) model in 1+1 dimensions is presented, employing a two-particle-irreducible resummation prescription as well as fully nonperturbative finite-temperature lattice simulations. The analytical results are computed using the Cornwall-Jackiw-Tomboulis (CJT) formalism and the auxiliary field method to one- and to two-loop order. The lattice results are obtained through Monte Carlo simulation for various lattice spacings. The analytical and lattice results for pressure, trace anomaly, and energy density, resembling closely those of four-dimensional Yang-Mills theories, are compared with each other. We find that to one-loop order there is a good correspondence between the CJT formalism and the lattice study for low temperatures. However, at high T the two-loop calculation fares better, correcting for the overestimation from the former approximation.

hep-ph↗

arXiv2013

Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks

Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by combined strong coupling and hopping expansions, which is valid for heavy but dynamical quarks and has a mild sign problem only. Its numerical evaluations agree between a standard Metropolis and complex Langevin algorithm, where the latter is free of the sign problem. Our continuum extrapolated data clearly show a first order phase transition building up at $μ_B \approx m_B$ as the temperature approaches zero. An excellent description of the data is achieved by an analytic solution in the strong coupling limit.

hep-lat↗

arXiv2012

Phenomenology of quarkyonic percolation at FAIR

We will give an introduction to the concept of quarkyonic matter, presenting an overview of what is meant by this term in the literature. We will then argue that the quarkyonic phase, as defined in the original paper, is a percolation-type phase transition whose phase transition line is strongly curved in $ρ_B-N_c$ space, where $N_c$ is the number of colors and $ρ_B$ the baryon density. With a toy model estimate, we show that it might be possible to obtain a percolating but confined phase at $N_c=3,N_f=2$ at densities larger than one baryon per one baryon size. We conclude by discussing how this phase can be observed at FAIR.

nucl-th↗

arXiv2012

Phase transitions in heavy-quark QCD from an effective theory

With combined hopping parameter and strong coupling expansions, we calculate a dimensionally reduced Polyakov-loop effective theory valid for heavy quarks at nonzero temperature and arbitrary chemical potential. We numerically compute the critical endpoint of the deconfinement transition as a function of quark masses and number of flavours. We also investigate the applicability of the model to the low-T and high density region, specifically in terms of baryon condensation phenomena.

hep-lat↗

arXiv2012

Pressure of the O(N) Model in 1+1 Dimensions

The O(N) model in 1+1 dimensions presents some features in common with Yang-Mills theories: asymptotic freedom, trace anomaly, non-petrurbative generation of a mass gap. An analytical approach to determine the termodynamical properties of the O(3) model is presented and compared to lattice results. Here the focus is on the pressure: it is shown how to derive the pressure in the CJT formalism at the one-loop level by making use of the auxiliary field method. Then, the pressure is compared to lattice results.

hep-ph↗

arXiv2012

Lattice versus 2PI: 2d O(N) model at nonzero T

The thermodynamics of the O(N) model in 1+1 dimensions is studied applying the CJT formalism and the auxiliary field method as well as fully nonperturbative finite temperature lattice simulations. The numerical results for the renormalized mass of the scalar particles, the pressure and the trace anomaly are presented and compared with the results from lattice simulation of the model. We find that when going to the two loop order we observe a good correspondence between the CJT formalism and the lattice study.

hep-ph↗

arXiv2012

Quarkyonic percolation in dense nuclear matter

We examine the phase diagram of hadronic matter when the number of colours $N_c$, as well as temperature and density, are varied. We show that in this regime a new percolation phase transition is possible, and examine the implications of this transition for extrapolations to physical QCD of the large-N_c limit.

hep-ph↗

arXiv2011

Strong coupling effective theory with heavy fermions

We extend the recently developed strong coupling, dimensionally reduced Polyakov-loop effective theory from finite-temperature pure Yang-Mills to include heavy fermions and nonzero chemical potential by means of a hopping parameter expansion. Numerical simulation is employed to investigate the weakening of the deconfinement transition as a function of the quark mass. The tractability of the sign problem in this model is exploited to locate the critical surface in the (M/T, mu/T, T) space over the whole range of chemical potentials from zero up to infinity.

hep-lat↗

arXiv2011

The QCD deconfinement transition for heavy quarks and all baryon chemical potentials

Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_τ\sim 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.

hep-lat↗

arXiv2011

Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series

We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters $N_τ,β$ of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings $β_c(N_τ)$ and find agreement with results from simulations of the 4d theory at the few percent level for $N_τ=4-16$.

hep-lat↗

arXiv2011

The phase diagram in $T-μ-N_c$ space

We examine the phase diagram of hadronic matter when the number of colors, as well as temperature and density, are varied. We show that in this regime several new phase transitions are possible, and we examine issues related to these transitions.

nucl-th↗