We utilize Polyakov loop correlations to study d=3+1 compact U (1) flux tubes and the static elec... more 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.
Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)
We compute the spectra of flux tubes formed between a static quark antiquark pair up to a signifi... more We compute the spectra of flux tubes formed between a static quark antiquark pair up to a significant number of excitations and for eight symmetries of the flux tubes, up to Δ , using pure (3) gauge lattice QCD in 3+1 dimensions. To accomplish this goal, we use a large set of appropriate operators, an anisotropic tadpole improved action, smearing techniques, and solve a generalized eigenvalue problem. Moreover, we compare our results with the Nambu-Goto string model to evaluate possible tensions which could be a signal for novel phenomena.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), Mar 21, 2008
The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wils... more The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a 24 3 × 48 periodic lattice with β = 6.2, the potential energy of the system is measured for different geometries. For the medium range behaviour, when the quarks are far apart, we find a string tension which is compatible with two fundamental strings. On the other hand, when the quark and antiquark are nearby, the string tension is larger than two fundamental strings and is compatible with the Casimir scaling.
Proceedings of XLIX International Winter Meeting on Nuclear Physics — PoS(Bormio 2011), 2011
We study the chiral crossover, the spectra of light-light and of static-light mesons and the deco... more We study the chiral crossover, the spectra of light-light and of static-light mesons and the deconfinement crossover at finite temperature T. Our framework is the confining and chiral invariant quark model, related to truncated Coulomb gauge QCD. Since we are dealing with light quarks, where the linear potential dominates the quark condensate and the spectrum, we only specialize in the linear confining potential for the quark-antiquark interaction. We utilize T dependent string tensions previously fitted from lattice QCD data, and a fit of previously computed dynamically generated constituent quark masses. We scan the T effects on the constituent quark mass, on the meson spectra and on the polyakov loop.
The chromoelectric field generated by a static quark-antiquark pair, with its peculiar tube-like ... more The chromoelectric field generated by a static quark-antiquark pair, with its peculiar tube-like shape, can be nicely described, at zero temperature, within the dual superconductor scenario for the QCD confining vacuum. In this work we investigate, by lattice Monte Carlo simulations of the SU(3) pure gauge theory, the fate of chromoelectric flux tubes across the deconfinement transition. We find that, if the distance between the static sources is kept fixed at about 0.76 fm 1.6/ √ σ and the temperature is increased towards and above the deconfinement temperature T c , the amplitude of the field inside the flux tube gets smaller, while the shape of the flux tube does not vary appreciably across deconfinement. This scenario with flux-tube "evaporation" above T c has no correspondence in ordinary (type-II) superconductivity, where instead the transition to the phase with normal conductivity is characterized by a divergent fattening of flux tubes as the transition temperature is approached from below. We present also some evidence about the existence of flux-tube structures in the magnetic sector of the theory in the deconfined phase.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010
A large approximate degeneracy appears in the light meson spectrum measured at LEAR, suggesting a... more A large approximate degeneracy appears in the light meson spectrum measured at LEAR, suggesting a novel principal quantum number n + j in QCD spectra. We recently showed that the large degeneracy could not be understood with state of the art confining and chiral invariant quark models, derived in a truncated Coulomb gauge. To search for a solution to this problem, here we add the gluon or string degrees of freedom. Although independently the quarks or the gluons would lead to a 2n + j or 2n + l spectrum, adding them may lead to the desired n + j pattern.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012
The color fields in a system composed by two static quarks and two static antiquarks are studied.... more 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.
We explore the performance of CUDA in performing Landau gauge fixing in Lattice QCD, using the st... more We explore the performance of CUDA in performing Landau gauge fixing in Lattice QCD, using the steepest descent method with Fourier acceleration. The code performance was tested in a Tesla C2070, Fermi architecture. We also present a study of the string tension at finite temperature in the confined phase. The string tension is extracted from the color averaged free energy and from the color singlet using Landau gauge fixing.
We estimate the potential energy for a system of three static gluons in Lattice QCD. This is rele... more We estimate the potential energy for a system of three static gluons in Lattice QCD. This is relevant for the different models of three-body glueballs have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different colour structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is performed in a 24 3 × 48 periodic Lattice, with β = 6.2 and a ∼ 0.072 fm.
Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulti... more Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulting in the several successful theorems of PCAC. On the other hand scalar confinement is suggested both by the spectroscopy of hadrons and by the string picture of confinement. However these two evidences are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we reformulate the coupling of the quarks to the string, and we are able to comply with chiral symmetry breaking, using scalar confinement. The results are quite encouraging. 1 Open Problem Recently Bjorken asked, " how are the many disparate methods of describing hadrons which are now in use related to each other and to the first principles of QCD?". Chiral symmetry breaking and scalar confinement are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we try to solve this old conflict of hadronic physics, which remained open for many years. The QCD Lagrangian is chiral invariant in the limit of vanishing quark masses. This is crucial because Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, for the light flavors u, d and s, where, mu, md << ms < Λ QCD < M N /3. The techniques of current algebra led to beautifully correct theorems, the PCAC (Partially Conserved Axial Current) theorems. The QM (Quark Models) are widely used as a simplification of QCD, convenient to study quark bound states and hadron scattering. Recently 1 we have shown that these beautiful PCAC theorems, like the Weinberg theorem for π − π scattering, are reproduced by quark models with spontaneous chiral symmetry breaking. On the other hand the confining potential for constituent quarks is probably scalar. Scalar confinement is suggested both by the spectroscopy of hadrons, by lattice simulations and by the string picture of confinement. In a pertubative QCD scenario, the hadron spectroscopy would be qualitatively similar to electronic spectra of the lighter atoms. It is remarkable that the Spin-Orbit potential (also called fine interaction in atomic physics) turns out to be suppressed in hadronic spectra because it is smaller than the Spin-Spin potential (also called hyperfine interaction). This constitutes an evidence of non-pertubative QCD. Another evidence of nonpertubative QCD is present in the angular and radial excitations of hadrons, which fit linear trajectories in Regge plots, and suggest a long range, probably linear, confining potential for the quarks. This led Henriques, Kellet and Moorhouse, Isgur and Karl, and others 2,3 to develop a Quark Model where a short-range vector potential plus a long-range scalar potential partly cancel
Journal of Physics G: Nuclear and Particle Physics, 2006
Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon in... more Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon interaction complies with the Casimir scaling. The constituent gluon models have also been assuming the Casimir scaling. Nevertheless, inspired in type-II superconductors, we explore a new scenario for the gluon-gluon interaction where the adjoint string is replaced by a pair of fundamental strings, resulting in a factor of 2, smaller than 9/4. To test our proposal we construct a simple constituent gluon model, extrapolated from the funnel potential for quarkonium, and apply it to compute the wave-function of glueballs and of hybrid gluelumps. From the decay widths of quarkonium, we also extrapolate the decay widths of the glueballs. Our predictions apply to charmonia, lightonia, glueballs and hybrid gluelumps with large angular momentum.
We discuss how the steepest descent method with Fourier acceleration for Laudau gauge fixing in l... more We discuss how the steepest descent method with Fourier acceleration for Laudau gauge fixing in lattice SU(3) simulations can be implemented using CUDA. The scaling of the gauge fixing code was investigated using a Tesla C2070 Fermi architecture, and compared with a parallel CPU gauge fixing code.
The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(... more The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a 24 3 × 48 lattice at β = 6.2 and a = 0.07261(85) f m. 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 ± 0.163 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.
Flux tube spectra are expected to have full towers of levels due to the quantization of the strin... more Flux tube spectra are expected to have full towers of levels due to the quantization of the string vibrations. We study a spectrum of flux tubes with static quark and antiquark sources with pure gaugeSU(3) lattice QCD in 3+1 dimensions up to a significant number of excitations. To go high in the spectrum, we specialize in the most symmetric case Σg+, use a large set of operators, solve the generalized eigenvalue and compare different lattice QCD gauge actions and anisotropies.
We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with ... more We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with O(a) improved Wilson fermions. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 \cite{Bicudo:2019ymo}) to study quarkonium resonances and bound states.
We utilize Polyakov loop correlations to study d=3+1 compact U (1) flux tubes and the static elec... more 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.
Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)
We compute the spectra of flux tubes formed between a static quark antiquark pair up to a signifi... more We compute the spectra of flux tubes formed between a static quark antiquark pair up to a significant number of excitations and for eight symmetries of the flux tubes, up to Δ , using pure (3) gauge lattice QCD in 3+1 dimensions. To accomplish this goal, we use a large set of appropriate operators, an anisotropic tadpole improved action, smearing techniques, and solve a generalized eigenvalue problem. Moreover, we compare our results with the Nambu-Goto string model to evaluate possible tensions which could be a signal for novel phenomena.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), Mar 21, 2008
The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wils... more The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a 24 3 × 48 periodic lattice with β = 6.2, the potential energy of the system is measured for different geometries. For the medium range behaviour, when the quarks are far apart, we find a string tension which is compatible with two fundamental strings. On the other hand, when the quark and antiquark are nearby, the string tension is larger than two fundamental strings and is compatible with the Casimir scaling.
Proceedings of XLIX International Winter Meeting on Nuclear Physics — PoS(Bormio 2011), 2011
We study the chiral crossover, the spectra of light-light and of static-light mesons and the deco... more We study the chiral crossover, the spectra of light-light and of static-light mesons and the deconfinement crossover at finite temperature T. Our framework is the confining and chiral invariant quark model, related to truncated Coulomb gauge QCD. Since we are dealing with light quarks, where the linear potential dominates the quark condensate and the spectrum, we only specialize in the linear confining potential for the quark-antiquark interaction. We utilize T dependent string tensions previously fitted from lattice QCD data, and a fit of previously computed dynamically generated constituent quark masses. We scan the T effects on the constituent quark mass, on the meson spectra and on the polyakov loop.
The chromoelectric field generated by a static quark-antiquark pair, with its peculiar tube-like ... more The chromoelectric field generated by a static quark-antiquark pair, with its peculiar tube-like shape, can be nicely described, at zero temperature, within the dual superconductor scenario for the QCD confining vacuum. In this work we investigate, by lattice Monte Carlo simulations of the SU(3) pure gauge theory, the fate of chromoelectric flux tubes across the deconfinement transition. We find that, if the distance between the static sources is kept fixed at about 0.76 fm 1.6/ √ σ and the temperature is increased towards and above the deconfinement temperature T c , the amplitude of the field inside the flux tube gets smaller, while the shape of the flux tube does not vary appreciably across deconfinement. This scenario with flux-tube "evaporation" above T c has no correspondence in ordinary (type-II) superconductivity, where instead the transition to the phase with normal conductivity is characterized by a divergent fattening of flux tubes as the transition temperature is approached from below. We present also some evidence about the existence of flux-tube structures in the magnetic sector of the theory in the deconfined phase.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010
A large approximate degeneracy appears in the light meson spectrum measured at LEAR, suggesting a... more A large approximate degeneracy appears in the light meson spectrum measured at LEAR, suggesting a novel principal quantum number n + j in QCD spectra. We recently showed that the large degeneracy could not be understood with state of the art confining and chiral invariant quark models, derived in a truncated Coulomb gauge. To search for a solution to this problem, here we add the gluon or string degrees of freedom. Although independently the quarks or the gluons would lead to a 2n + j or 2n + l spectrum, adding them may lead to the desired n + j pattern.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012
The color fields in a system composed by two static quarks and two static antiquarks are studied.... more 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.
We explore the performance of CUDA in performing Landau gauge fixing in Lattice QCD, using the st... more We explore the performance of CUDA in performing Landau gauge fixing in Lattice QCD, using the steepest descent method with Fourier acceleration. The code performance was tested in a Tesla C2070, Fermi architecture. We also present a study of the string tension at finite temperature in the confined phase. The string tension is extracted from the color averaged free energy and from the color singlet using Landau gauge fixing.
We estimate the potential energy for a system of three static gluons in Lattice QCD. This is rele... more We estimate the potential energy for a system of three static gluons in Lattice QCD. This is relevant for the different models of three-body glueballs have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different colour structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is performed in a 24 3 × 48 periodic Lattice, with β = 6.2 and a ∼ 0.072 fm.
Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulti... more Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulting in the several successful theorems of PCAC. On the other hand scalar confinement is suggested both by the spectroscopy of hadrons and by the string picture of confinement. However these two evidences are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we reformulate the coupling of the quarks to the string, and we are able to comply with chiral symmetry breaking, using scalar confinement. The results are quite encouraging. 1 Open Problem Recently Bjorken asked, " how are the many disparate methods of describing hadrons which are now in use related to each other and to the first principles of QCD?". Chiral symmetry breaking and scalar confinement are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we try to solve this old conflict of hadronic physics, which remained open for many years. The QCD Lagrangian is chiral invariant in the limit of vanishing quark masses. This is crucial because Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, for the light flavors u, d and s, where, mu, md << ms < Λ QCD < M N /3. The techniques of current algebra led to beautifully correct theorems, the PCAC (Partially Conserved Axial Current) theorems. The QM (Quark Models) are widely used as a simplification of QCD, convenient to study quark bound states and hadron scattering. Recently 1 we have shown that these beautiful PCAC theorems, like the Weinberg theorem for π − π scattering, are reproduced by quark models with spontaneous chiral symmetry breaking. On the other hand the confining potential for constituent quarks is probably scalar. Scalar confinement is suggested both by the spectroscopy of hadrons, by lattice simulations and by the string picture of confinement. In a pertubative QCD scenario, the hadron spectroscopy would be qualitatively similar to electronic spectra of the lighter atoms. It is remarkable that the Spin-Orbit potential (also called fine interaction in atomic physics) turns out to be suppressed in hadronic spectra because it is smaller than the Spin-Spin potential (also called hyperfine interaction). This constitutes an evidence of non-pertubative QCD. Another evidence of nonpertubative QCD is present in the angular and radial excitations of hadrons, which fit linear trajectories in Regge plots, and suggest a long range, probably linear, confining potential for the quarks. This led Henriques, Kellet and Moorhouse, Isgur and Karl, and others 2,3 to develop a Quark Model where a short-range vector potential plus a long-range scalar potential partly cancel
Journal of Physics G: Nuclear and Particle Physics, 2006
Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon in... more Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon interaction complies with the Casimir scaling. The constituent gluon models have also been assuming the Casimir scaling. Nevertheless, inspired in type-II superconductors, we explore a new scenario for the gluon-gluon interaction where the adjoint string is replaced by a pair of fundamental strings, resulting in a factor of 2, smaller than 9/4. To test our proposal we construct a simple constituent gluon model, extrapolated from the funnel potential for quarkonium, and apply it to compute the wave-function of glueballs and of hybrid gluelumps. From the decay widths of quarkonium, we also extrapolate the decay widths of the glueballs. Our predictions apply to charmonia, lightonia, glueballs and hybrid gluelumps with large angular momentum.
We discuss how the steepest descent method with Fourier acceleration for Laudau gauge fixing in l... more We discuss how the steepest descent method with Fourier acceleration for Laudau gauge fixing in lattice SU(3) simulations can be implemented using CUDA. The scaling of the gauge fixing code was investigated using a Tesla C2070 Fermi architecture, and compared with a parallel CPU gauge fixing code.
The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(... more The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a 24 3 × 48 lattice at β = 6.2 and a = 0.07261(85) f m. 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 ± 0.163 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.
Flux tube spectra are expected to have full towers of levels due to the quantization of the strin... more Flux tube spectra are expected to have full towers of levels due to the quantization of the string vibrations. We study a spectrum of flux tubes with static quark and antiquark sources with pure gaugeSU(3) lattice QCD in 3+1 dimensions up to a significant number of excitations. To go high in the spectrum, we specialize in the most symmetric case Σg+, use a large set of operators, solve the generalized eigenvalue and compare different lattice QCD gauge actions and anisotropies.
We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with ... more We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with O(a) improved Wilson fermions. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 \cite{Bicudo:2019ymo}) to study quarkonium resonances and bound states.
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Papers by Pedro Bicudo