arXiv subjects

N. Cardoso

Publications and source records attributed to N. Cardoso.

At least 19 recordsLinked to original sources

arXiv2021

Spectrum of very excited $Σ_g^+$ flux tubes in SU(3) gauge theory

Spectra with full towers of levels are expected due to the quantization of the string vibrations, however different theoretical models exist for the excitation spectra. First principle computations are important to test the different models and to search for novel phenomena, but so far only a few excited states of QCD flux tubes have been studied with pure gauge SU(3) lattice QCD in 3+1 dimensions. We thus aim to study a spectrum of flux tubes with static quark and antiquark sources up to a significant number of excitations. We specialize on the spectrum of the most symmetric case, namely $Σ_g^+$, where up to two levels are already published in the literature. To achieve the highest possible excitation level, we construct a large set of operators with the correct symmetry, solve the generalized eigenvalue problem and compare the results of different lattice QCD gauge actions with different lattice spacings and anisotropies.

hep-lat↗

arXiv2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $α$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(α^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_μ/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(α^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(α^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_μ^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$σ$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

hep-ph↗

arXiv2018

Colour field densities of the quark-antiquark excited flux tubes in SU(3) lattice QCD

We combine techniques previously utilised to study flux tube field density profiles and to study the excited spectrum of the gluonic fields produced by a static quark-antiquark pair. Working with pure gauge SU(3) fields discretised in a lattice, we utilise Wilson loops with a large basis of gluonic spacelike Wilson lines to include different excitations of the quark-antiquark flux tube. To increase the signal over noise ratio, we use the multihit technique in the temporal Wilson lines and the APE smearing in spatial Wilson lines. The number of gluonic operators combined with the space points where we compute the flux tube densities turns out to be very large, and we resort to GPUs and to CUDA codes. Computing the effective mass plot from the diagonalized correlation matrix, we separate the excitations with different two-dimensional angular momentum, parity and radial quantum numbers. We then compute the colour field density profiles for all the components of the colour electric and colour magnetic fields. We analyse our results for the first excitations of the flux tube and search for signals of novel phenomena beyond the Nambu-Goto string model, such as a longitudinal mode or an explicit gluon.

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arXiv2017

Pure gauge QCD flux tubes and their widths at finite temperature

We study the flux tubes produced by static quark-antiquark, quark-quark and quark-gluon charges at finite temperature in pure gauge SU(3) lattice QCD. Our sources are static and our lattice correlators are composed of fundamental and adjoint Polyakov loops. To signal the flux tubes, we compute the square densities of the chromomagnetic and chromoelectric fields with plaquettes, in a gauge invariant framework. We study the existence and non-existence of flux tubes both above and below the deconfinement phase transition temperature Tc. Using the Lagrangian density as a probability distribution, we also compute the widths of the flux tubes and study their widening as a function of the intercharge distance. We determine our results with both statistical and systematic errors. Our computations are performed in NVIDIA GPUs using the CUDA language.

hep-lat↗

arXiv2016

Gluons at finite temperature

The gluon propagator is investigated at finite temperature via lattice simulations. In particular, we discuss its interpretation as a massive-type bosonic propagator. Moreover, we compute the corresponding spectral density and study the violation of spectral positivity. Finally, we explore the dependence of the gluon propagator on the phase of the Polyakov loop.

hep-lat↗

arXiv2015

The lattice gluon propagator in renormalizable $ξ$ gauges

We study the SU(3) gluon propagator in renormalizable $R_ξ$ gauges implemented on a symmetric lattice with a total volume of (3.25 fm)$^4$ for values of the guage fixing parameter up to $ξ=0.5$. As expected, the longitudinal gluon dressing function stays constant at its tree-level value $ξ$. Similar to the Landau gauge, the transverse $R_ξ$ gauge gluon propagator saturates at a non-vanishing value in the deep infrared for all values of $ξ$ studied. We compare with very recent continuum studies and perform a simple analysis of the found saturation with a dynamically generated effective gluon mass.

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arXiv2014

Gluon screening mass at finite temperature from Landau gauge gluon propagator in lattice QCD

We address the interpretation of the Landau gauge gluon propagator at finite temperature as a massive type bosonic propagator. Using pure gauge SU(3) lattice simulations at a fixed lattice volume $\sim(6.5fm)^3$, we compute the electric and magnetic form factors, extract a gluon mass from Yukawa-like fits, and study its temperature dependence. This is relevant both for the Debye screening at high temperature $T$ and for confinement at low $T$.

hep-lat↗

arXiv2013

Flux tube widening in compact U (1) lattice gauge theory computed at T < Tc with the multilevel method and GPUs

We utilize Polyakov loop correlations to study d=3+1 compact U (1) flux tubes and the static electron-positron potential in lattice gauge theory. With the plaquette field operator, in U(1) lattice gauge theory, we probe directly the components of the electric and magnetic fields. In order to improve the signal-to-noise ratio in the confinement phase, we apply the Lüscher-Weiss multilevel algorithm. Our code is written in CUDA, and we run it in NVIDIA FERMI generation GPUs, in order to achieve the necessary efficiency for our computations. We measure in detail the quantum widening of the flux tube, as a function of the intercharge distance and at different finite temperatures T < Tc . Our results are compatible with the Effective String Theory.

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arXiv2013

Inside the SU(3) quark-antiquark QCD flux tube: screening versus quantum widening

In lattice QCD, colour confinement manifests in flux tubes. We compute in detail the quark-antiquark flux tube for pure gauge SU(3) dimension $D=3+1$ for quark-antiquark distances R ranging from 0.4 fm to 1.4 fm. To increase the signal over noise ratio, we apply the improved multihit and extended smearing techniques. We detail the gauge invariant squared components of the colour electric and colour magnetic fields both in the mediator plane between the static quark and static antiquark and in the planes of the sources. We fit the field densities with appropriate ansatze and we observe the screening of the colour fields in all studied planes together with the quantum widening of the flux tube in the mediator plane. All components squared of the colour fields are non-vanishing and are consistent with a penetration length lambda ~ 0.22 to 0.24 fm and an effective screening mass mu ~ 0.9 to 0.8 GeV. The quantum widening of the flux tube is well fitted with a logarithmic law in R.

hep-lat↗

arXiv2012

SU(3) gauge invariant lattice QCD exploration of the dual superconductor picture in flux tube fusion, in the dual gluon mass, and in the dual Ginzburg-Landau parameters

The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a $24^3\times 48$ lattice at $β=6.2$ and $a=0.07261(85)\,fm$. We compute the hybrid Wilson Loop including the cases when the gluon and the antiquark are superposed, i. e., the quark-antiquark case and when the quark and antiquark are superposed, i. e., the gluon-gluon case. The Casimir scaling is investigated, in the two gluon glueball case the Casimir scaling is consistent with the formation of an adjoint string. Measuring the decay of the tail in the mid section of the flux tube for the two gluon glueball and for the quark-antiquark meson, we determine the penetration length and present a gauge invariant effective dual gluon mass of $0.905\pm0.163\,\text{GeV}$. We also try to determine the coherence length comparing our results with the dual Ginzburg-Landau approach. With the penetration length and the possible coherence length we determine a putative Ginzburg-Landau dimensionless parameter, which is possibly consistent with a type II superconductor picture. These results are obtained at fixed quark-antiquark distance of 0.58 fm.

hep-lat↗

arXiv2012

Variational study of the flux tube recombination in the two quarks and two quarks system in Lattice QCD

The color fields in a system composed by two static quarks and two static antiquarks are studied. In particular, we consider the four particles in the corners of a rectangle, and two possible alignment of the particles, one in which the quarks are at the same side of the rectangle, and the other where they are at opposite sides. We use a variational method, to probe not only the ground state but also the first excited state. This results permit us to observe and interpret the flux-tube recombination in the mesons to mesons and the tetraquark to mesons transitions, for both states. The results are compared with previous results for the static potential and the Casimir scaling predictions.

hep-lat↗

arXiv2012

Lattice QCD computation of the SU(3) String Tension critical curve

We investigate the critical curve of the string tension sigma(T) as a function of temperature in quenched gauge invariant SU(3) lattice gauge theory. We extract sigma(T) from the colour averaged free energy of a static quark-antiquark pair. To compute the free energy, we utilize a pair of gauge invariant Polyakov loop and antiloop correlations, and apply the multihit procedure to enhance the signal to noise ratio. We find that the string tension departs from the zero temperature sigma(0) at T close to 0.5 Tc. We cover the relevant temperature range from 0.5 Tc up to the confinement temperature Tc using 57 different sets of pure gauge lattice configurations with four temporal extensions (4,6,8,12), different beta and a spatial volume of 48^3 in lattice units.

hep-lat↗

arXiv2011

Colour Fields Computed in SU(3) Lattice QCD for the Static Tetraquark System

The colour fields created by the static tetraquark system are computed in quenched SU(3) lattice QCD, in a 24^3 x 48 lattice at beta=6.2 corresponding to a lattice spacing a=0.07261(85) fm. We find that the tetraquark colour fields are well described by a double-Y, or butterfly, shaped flux tube. The two flux tube junction points are compatible with Fermat points minimizing the total flux tube length. We also compare the diquark-diantiquark central flux tube profile in the tetraquark with the quark-antiquark fundamental flux tube profile in the meson, and they match, thus showing that the tetraquark flux tubes are composed of fundamental flux tubes.

hep-lat↗

arXiv2011

Colour field flux tubes and Casimir scaling for various SU(3) representations

We investigate the QCD flux tubes linking static colour charges of different SU(3) representations, relevant to the understanding of confinement and of the Lund strings of Heavy Ion Collisions. The colour field densities, the Casimir scaling factors and the widths for the flux tubes of the first five different representations are computed in quenched SU(3) lattice QCD. This study is relevant to understand the mechanisms of confinement and also the flux tubes utilized in the Lund Model and in other models of Heavy Ion Collisions.

hep-lat↗

arXiv2011

QCD confinement and chiral crossovers, two critical points

We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. We present the confinement of quark fields into a flux tube, obtained in SU(3) quenched lattice QCD, to illustrate the importance of the confining quark-antiquark potential. Our finite temperature con-fining potential is extracted from the Lattice QCD data of the Bielefeld group. Our formalism, the Coulomb gauge hamiltonian of QCD, is presently the only one able to microscopically include both a quark-antiquark confining potential and a vacuum condensate of quark-antiquark pairs. This model is able to address all the excited hadrons, and chiral symmetry breaking, at the same token. Our order parameters are the Polyakov loop and the quark mass gap. We address how the quark masses affect the critical point location in the phase diagram.

hep-lat↗

arXiv2010

Tetraquark resonances, flip-flop and cherry in a broken glass model

We develop a formalism to study tetraquarks using the generalized flip-flop potential, which include the tetraquark potential component. Technically this is a difficult problem, needing the solution of the Schrödinger equation in a multidimensional space. Since the tetraquark may at any time escape to a pair of mesons, here we study a simplified two-variable toy model and explore the analogy with a cherry in a glass, but a broken one where the cherry may escape from. We also compute the decay width in this two-variable picture, solving the Schrödinger equation for the outgoing spherical wave.

hep-ph↗

arXiv2009

Lattice QCD computation of the colour fields for the static hybrid quark-gluon-antiquark system, and microscopic study of the Casimir scaling

The chromoelectric and chromomagnetic fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a $24^3\times 48$ lattice at $β=6.2$ and $a=0.07261(85) fm$. We compute the hybrid Wilson Loop with two spatial geometries, one with a U shape and another with an L shape. The particular cases of the two gluon glueball and quark-antiquark are also studied, and the Casimir scaling is investigated in a microscopic perspective. This microscopic study of the colour fields is relevant to understand the structure of hadrons, in particular of the hybrid excitation of mesons. This also contributes to understand confinement with flux tubes and to discriminate between the models of fundamental versus adjoint confining strings, analogous to type-II and type-I superconductivity.

hep-lat↗

arXiv2009

Schwinger-Dyson equations and the quark-antiquark static potential

In lattice QCD, a confining potential for a static quark-antiquark pair can be computed with the Wilson loop technique. This potential, dominated by a linear potential at moderate distances, is consistent with the confinement with a flux tube, an extended and scalar system also directly observable in lattice QCD. Quantized flux tubes have also been observed in another class of confinement, the magnetic confinement in type II superconductors. On the other hand the solution of Schwinger Dyson Equations, say with the Landau gauge fixing and the truncation of the series of Feynman diagrams, already at the rainbow level for the self energy and at the ladder level for the Bethe Salpeter equation, provides a signal of a possible inverse quartic potential in momentum space derived from one gluon and one ghost exchange, consistent with confinement. Here we address the successes, difficulties and open problems of the matching of these two different perspectives of confinement, the Schwinger-Dyson perspective versus the flux tube perspective.

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