In the Wilson's lattice formulation of QCD, a fermionic Fock space of states can be explicitly built at each time slice using canonical creation and annihilation operators. The partition function $Z$ is then represented as the trace of the transfer matrix, and its usual functional representation as a path integral of $exp(- S)$ can be recovered in a standard way. However, applying a Bogoliubov transformation on the canonical operators before passing to the functional formalism, we can isolate a vacuum contribution in the resulting action which depends only on the parameters of the transformation and fixes them via a variational principle. Then, inserting in the trace defining $Z$ an operator projecting on the mesons subspace at each time slice and making the physical assumption that the true partition function is well approximate by the projected one, we can also write an effective quadratic action for mesons. We tested the method in the renowned 't Hooft model, namely QCD in two spacetime dimensions for large number of colours, in Coulomb gauge.
{"title":"Lattice QCD$_2$ effective action with Bogoliubov transformations","authors":"S. Caracciolo, M. Pastore","doi":"10.22323/1.336.0056","DOIUrl":"https://doi.org/10.22323/1.336.0056","url":null,"abstract":"In the Wilson's lattice formulation of QCD, a fermionic Fock space of states can be explicitly built at each time slice using canonical creation and annihilation operators. The partition function $Z$ is then represented as the trace of the transfer matrix, and its usual functional representation as a path integral of $exp(- S)$ can be recovered in a standard way. However, applying a Bogoliubov transformation on the canonical operators before passing to the functional formalism, we can isolate a vacuum contribution in the resulting action which depends only on the parameters of the transformation and fixes them via a variational principle. Then, inserting in the trace defining $Z$ an operator projecting on the mesons subspace at each time slice and making the physical assumption that the true partition function is well approximate by the projected one, we can also write an effective quadratic action for mesons. We tested the method in the renowned 't Hooft model, namely QCD in two spacetime dimensions for large number of colours, in Coulomb gauge.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132594160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In recent years, there have been important advances in understanding the far-from-equilibrium dynamics in different physical systems. In ultra-relativistic heavy-ion collisions, the combination of different methods led to the development of a weak-coupling description of the early-time dynamics. The numerical observation of a classical universal attractor played a crucial role for this. Such attractors, also known as non-thermal fixed points (NTFPs), have been now predicted for different scalar and gauge theories. An important universal NTFP emerges in scalar theories modeling ultra-cold atoms, inflation or dark matter, and its scaling properties have been recently observed in an ultra-cold atom experiment. In this proceeding, recent progress in selected topics of the far-from-equilibrium evolution in these systems will be discussed. A new method to extract the spectral function numerically is a particularly promising tool to better understand their microscopic properties.
{"title":"Understanding the dynamics of field theories far from equilibrium","authors":"K. Boguslavski","doi":"10.22323/1.336.0136","DOIUrl":"https://doi.org/10.22323/1.336.0136","url":null,"abstract":"In recent years, there have been important advances in understanding the far-from-equilibrium dynamics in different physical systems. In ultra-relativistic heavy-ion collisions, the combination of different methods led to the development of a weak-coupling description of the early-time dynamics. The numerical observation of a classical universal attractor played a crucial role for this. Such attractors, also known as non-thermal fixed points (NTFPs), have been now predicted for different scalar and gauge theories. An important universal NTFP emerges in scalar theories modeling ultra-cold atoms, inflation or dark matter, and its scaling properties have been recently observed in an ultra-cold atom experiment. In this proceeding, recent progress in selected topics of the far-from-equilibrium evolution in these systems will be discussed. A new method to extract the spectral function numerically is a particularly promising tool to better understand their microscopic properties.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117347484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the phase diagram and the thermodynamic properties of QCD at nonzero isospin asymmetry at physical quark masses with staggered quarks. In particular, continuum results for the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition are presented. Our findings indicate that the pion condensation phase is restricted to $Tlesssim170$~MeV for isospin chemical potentials up to 325~MeV. We also use the data to test the range of validity of the Taylor expansion method and show first results for the equation of state.
{"title":"QCD at nonzero isospin asymmetry","authors":"B. Brandt, G. Endrődi, S. Schmalzbauer","doi":"10.22323/1.336.0260","DOIUrl":"https://doi.org/10.22323/1.336.0260","url":null,"abstract":"We study the phase diagram and the thermodynamic properties of QCD at nonzero isospin asymmetry at physical quark masses with staggered quarks. In particular, continuum results for the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition are presented. Our findings indicate that the pion condensation phase is restricted to $Tlesssim170$~MeV for isospin chemical potentials up to 325~MeV. We also use the data to test the range of validity of the Taylor expansion method and show first results for the equation of state.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116194465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the $C=1$, $S=-2$, $I=0$ sector, where five excited $Omega_c$ states have been recently observed by the LHCb Collaboration. We start from a recently developed unitarized baryon-meson model that takes, as bare baryon-meson interaction, an extended Weinberg-Tomozawa kernel consistent with both chiral and heavy-quark spin symmetries. This ${rm SU(6)} times {rm HQSS}$ scheme leads to a successful description of the observed lowest-lying odd parity charmed $Lambda_c$(2595) and $Lambda_c$(2625) states, and bottomed $Lambda_b$(5912) and $Lambda_b$(5920) resonances. Within this model, five odd-parity $Omega_c$ states are dynamically generated, but with masses below 3 GeV, not allowing for an identification with the observed LHCb resonances. We revise this model and explore two different scenarios for the renormalization scheme, that is, using a modified common energy scale to perform the subtractions or utilizing a common ultraviolet cutoff to render finite the ultraviolet divergent loop functions in all channels. In both cases, we show that some (at least three) of the dynamically generated states can be identified with the experimental $Omega_c$, while having odd parity and $J=1/2$ or $J=3/2$. Two of these states turn out to be part of the same ${rm SU(6)} times {rm HQSS}$ multiplets as the charmed and bottomed $Lambda$ baryons.
我们研究了$C=1$, $S=-2$, $I=0$部门，其中五个激发态最近被LHCb合作观察到$Omega_c$。我们从最近发展的统一重子-介子模型开始，作为裸重子-介子相互作用，扩展Weinberg-Tomozawa核与手性和重夸克自旋对称一致。这个${rm SU(6)} times {rm HQSS}$方案成功地描述了观测到的最低奇宇称粲$Lambda_c$(2595)和$Lambda_c$(2625)态，以及最低$Lambda_b$(5912)和$Lambda_b$(5920)共振。在这个模型中，五个奇宇称$Omega_c$状态是动态生成的，但质量低于3 GeV，不允许与观测到的LHCb共振相识别。我们修改了该模型，并探索了重整化方案的两种不同方案，即使用修改的公共能量标度来执行减法或使用公共紫外线截止来在所有通道中呈现有限的紫外线发散回路函数。在这两种情况下，我们证明了一些(至少三个)动态生成的状态可以用实验$Omega_c$识别，同时具有奇宇称和$J=1/2$或$J=3/2$。结果证明，其中两个态是与被吸引的和底部的$Lambda$重子相同的${rm SU(6)} times {rm HQSS}$多重子的一部分。
{"title":"$Omega_c$ excited states with heavy-quark spin symmetry","authors":"L. Tolos, R. Pavão, J. Nieves","doi":"10.22323/1.336.0132","DOIUrl":"https://doi.org/10.22323/1.336.0132","url":null,"abstract":"We study the $C=1$, $S=-2$, $I=0$ sector, where five excited $Omega_c$ states have been recently observed by the LHCb Collaboration. We start from a recently developed unitarized baryon-meson model that takes, as bare baryon-meson interaction, an extended Weinberg-Tomozawa kernel consistent with both chiral and heavy-quark spin symmetries. This ${rm SU(6)} times {rm HQSS}$ scheme leads to a successful description of the observed lowest-lying odd parity charmed $Lambda_c$(2595) and $Lambda_c$(2625) states, and bottomed $Lambda_b$(5912) and $Lambda_b$(5920) resonances. Within this model, five odd-parity $Omega_c$ states are dynamically generated, but with masses below 3 GeV, not allowing for an identification with the observed LHCb resonances. We revise this model and explore two different scenarios for the renormalization scheme, that is, using a modified common energy scale to perform the subtractions or utilizing a common ultraviolet cutoff to render finite the ultraviolet divergent loop functions in all channels. In both cases, we show that some (at least three) of the dynamically generated states can be identified with the experimental $Omega_c$, while having odd parity and $J=1/2$ or $J=3/2$. Two of these states turn out to be part of the same ${rm SU(6)} times {rm HQSS}$ multiplets as the charmed and bottomed $Lambda$ baryons.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127958891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three phenomena.
{"title":"Localisation, chiral symmetry and confinement in QCD and related theories","authors":"M. Giordano","doi":"10.22323/1.336.0045","DOIUrl":"https://doi.org/10.22323/1.336.0045","url":null,"abstract":"I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three phenomena.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"64 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120983290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the renormalization of a class of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson-line (called Wilson-line operators). The matrix elements of these operators are involved in the recent "quasi-distribution" approach for computing light-cone distributions of Hadronic Physics on the lattice. We consider two classes of Wilson-line operators: straight-line and staple-shaped operators, which are related to the parton distribution functions (PDFs) and transverse momentum-dependent distributions (TMDs), respectively. We present our one-loop results for the conversion factors of straight-line operators between the RI' (appropriate for nonperturbative renormalization on the lattice) and MSbar (typically used in phenomenology) renormalization schemes in the presence of nonzero quark masses. In addition, we present the first results of our preliminary work for the renormalization of staple-shaped operators both in continuum (Dimensional Regularization) and lattice (Wilson/clover fermions and Symanzik improved gluons) regularizations. We identify the observed mixing pairs among these operators, which must be disentangled in the nonperturbative investigations of heavy-quark quasi-PDFs and of light-quark quasi-TMDs.
{"title":"Perturbative investigation of \"Wilson-line\"-type operators in Parton Physics","authors":"G. Spanoudes, H. Panagopoulos","doi":"10.22323/1.336.0094","DOIUrl":"https://doi.org/10.22323/1.336.0094","url":null,"abstract":"We investigate the renormalization of a class of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson-line (called Wilson-line operators). The matrix elements of these operators are involved in the recent \"quasi-distribution\" approach for computing light-cone distributions of Hadronic Physics on the lattice. We consider two classes of Wilson-line operators: straight-line and staple-shaped operators, which are related to the parton distribution functions (PDFs) and transverse momentum-dependent distributions (TMDs), respectively. We present our one-loop results for the conversion factors of straight-line operators between the RI' (appropriate for nonperturbative renormalization on the lattice) and MSbar (typically used in phenomenology) renormalization schemes in the presence of nonzero quark masses. In addition, we present the first results of our preliminary work for the renormalization of staple-shaped operators both in continuum (Dimensional Regularization) and lattice (Wilson/clover fermions and Symanzik improved gluons) regularizations. We identify the observed mixing pairs among these operators, which must be disentangled in the nonperturbative investigations of heavy-quark quasi-PDFs and of light-quark quasi-TMDs.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114781836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Local formulations of quantum field theory provide a powerful framework in which non-perturbative aspects of QCD can be analysed. Here we report on how this approach can be used to elucidate the general analytic features of QCD propagators, and why this is relevant for understanding confinement.
{"title":"On the analytic structure of QCD propagators","authors":"P. Lowdon","doi":"10.22323/1.336.0050","DOIUrl":"https://doi.org/10.22323/1.336.0050","url":null,"abstract":"Local formulations of quantum field theory provide a powerful framework in which non-perturbative aspects of QCD can be analysed. Here we report on how this approach can be used to elucidate the general analytic features of QCD propagators, and why this is relevant for understanding confinement.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128970007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum anomalies give rise to new non-dissipative transport phenomena in relativistic fluids induced by external electromagnetic fields and vortices. These phenomena can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We perform a computation in AdS/CFT of the anomalous transport coefficients in a holographic massive gravity model, and find that the anomalous conductivities turn out to be independent of the holographic disorder couplings of the model. To arrive at this result we suggest a new definition of the energy-momentum tensor in presence of the gauge-gravitational Chern-Simons coupling. We also compute the electric DC conductivity and find that it can vanish for certain values of the disorder couplings.
{"title":"Anomalous transport, massive gravity theories and holographic momentum relaxation","authors":"E. Megías","doi":"10.22323/1.336.0255","DOIUrl":"https://doi.org/10.22323/1.336.0255","url":null,"abstract":"Quantum anomalies give rise to new non-dissipative transport phenomena in relativistic fluids induced by external electromagnetic fields and vortices. These phenomena can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We perform a computation in AdS/CFT of the anomalous transport coefficients in a holographic massive gravity model, and find that the anomalous conductivities turn out to be independent of the holographic disorder couplings of the model. To arrive at this result we suggest a new definition of the energy-momentum tensor in presence of the gauge-gravitational Chern-Simons coupling. We also compute the electric DC conductivity and find that it can vanish for certain values of the disorder couplings.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114529641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The property of color confinement ("C confinement"), meaning that all asymptotic particle states are color neutral, holds not only in QCD, but also in gauge-Higgs theories deep in the Higgs regime. In this talk we describe a new and stronger confinement criterion, separation-of-charge confinement or "S$_c$ confinement," which is an extension of the Wilson area-law criterion to gauge + matter theories. We will show that there is a transition between S$_c$ and C confinement in the phase plane of gauge-Higgs theories, and we will also explain what symmetry is actually broken in the Higgs phase of a gauge-Higgs theory.
{"title":"On the distinction between color confinement, and confinement","authors":"J. Greensite, Kazue Matsuyama","doi":"10.22323/1.336.0046","DOIUrl":"https://doi.org/10.22323/1.336.0046","url":null,"abstract":"The property of color confinement (\"C confinement\"), meaning that all asymptotic particle states are color neutral, holds not only in QCD, but also in gauge-Higgs theories deep in the Higgs regime. In this talk we describe a new and stronger confinement criterion, separation-of-charge confinement or \"S$_c$ confinement,\" which is an extension of the Wilson area-law criterion to gauge + matter theories. We will show that there is a transition between S$_c$ and C confinement in the phase plane of gauge-Higgs theories, and we will also explain what symmetry is actually broken in the Higgs phase of a gauge-Higgs theory.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124842381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Auvinen, K. Eskola, P. Huovinen, H. Niemi, R. Paatelainen, P. Petreczky
We perform a global model-to-data comparison on Au+Au collisions at $sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamics model with the EKRT initial state and a shear viscosity over entropy density ratio $(eta/s)(T)$ with a linear $T$ dependence. To quantify the amount of uncertainty due to the choice of the equation of state (EoS), we compare analysis results based on four different EoSs: the well known $s95p$ parametrisation, an updated parametrisation based on the same list of particles in hadron resonance gas, but using recent lattice results for the partonic part of the EoS, and two new parametrisations based on the Particle Data Group 2016 particle list and the recent lattice results. We find that the choice of the EoS does affect the favoured minimum value of $eta/s$, although within the confidence limits of the analysis. On the other hand, our analysis hardly constrains the temperature dependence of $eta/s$, no matter the EoS.
{"title":"Temperature dependence of $eta/s$: uncertainties from the equation of state","authors":"J. Auvinen, K. Eskola, P. Huovinen, H. Niemi, R. Paatelainen, P. Petreczky","doi":"10.22323/1.336.0135","DOIUrl":"https://doi.org/10.22323/1.336.0135","url":null,"abstract":"We perform a global model-to-data comparison on Au+Au collisions at $sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamics model with the EKRT initial state and a shear viscosity over entropy density ratio $(eta/s)(T)$ with a linear $T$ dependence. To quantify the amount of uncertainty due to the choice of the equation of state (EoS), we compare analysis results based on four different EoSs: the well known $s95p$ parametrisation, an updated parametrisation based on the same list of particles in hadron resonance gas, but using recent lattice results for the partonic part of the EoS, and two new parametrisations based on the Particle Data Group 2016 particle list and the recent lattice results. We find that the choice of the EoS does affect the favoured minimum value of $eta/s$, although within the confidence limits of the analysis. On the other hand, our analysis hardly constrains the temperature dependence of $eta/s$, no matter the EoS.","PeriodicalId":441384,"journal":{"name":"Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114382481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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