Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at <math><mi>T</mi><mo>=</mo><mn>470</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> (<math><mo>∼</mo><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math>), as well as in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor QCD at <math><mi>T</mi><mo>=</mo><mn>220</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> (<math><mo>∼</mo><mn>1.2</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub></math>) with <math><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>320</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. In order to quantify the nonperturbative effects, the lattice correlator is compared with the corresponding <math><mi>NLO</mi><mo>+</mo><msup><mi>LPM</mi><mi>LO</mi></msup></math> estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian process regression. We find that the resulting photon rates agree within errors.

Germany

Pakistan

Sajid Ali

Dibyendu Bala

Taiwan

Anthony Francis

United States

France

Greg Jackson

Olaf Kaczmarek

Jonas Turnwald

Tristan Ueding

Nicolas Wink

Lattice QCD estimates of thermal photon production from the QGP

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple spatially-separated samples from each gauge field; in the extreme case, we arrive at the master-field approach in which a single gauge field is used. Here we develop techniques for studying hadronic observables using position-space correlators, which are more localized, and compare with the standard time-momentum representation. We also adapt methods for estimating the variance of an observable from autocorrelated Monte Carlo samples to the case of correlated spatially-separated samples.

Italy

Mattia Bruno

Switzerland

Marco Cè

Ireland

Patrick Fritzsch

Jeremy Green

United Kingdom

Maxwell Hansen

Denmark

Antonio Rago

Exploiting stochastic locality in lattice QCD: hadronic observables and their uncertainties

We calculate shear viscosity and bulk viscosity in <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> gauge theory on the lattice at <math><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math>. The viscosities are extracted via a Kubo formula from the reconstructed spectral function which we determine from the Euclidean time dependence of the corresponding channel of the energy-momentum tensor correlators. We obtain unprecedented precision for the correlators by applying gradient-flow and blocking methods. The correlators are extrapolated to the continuum and then to zero-flow time. To extract the viscosities we fit theoretically inspired models to the lattice data and cross-check the fit results using the Backus-Gilbert method. The final estimates for shear and bulk viscosity are <math><mrow><mi>η</mi><mo>/</mo><mi>s</mi><mo>=</mo><mn>0.15</mn><mi>–</mi><mn>0.48</mn></mrow></math> and <math><mi>ζ</mi><mo>/</mo><mi>s</mi><mo>=</mo><mn>0.017</mn><mi>–</mi><mn>0.059</mn></math>.

Luis Altenkort

Alexander M. Eller

Lukas Mazur

Guy D. Moore

Hai-Tao Shu

Viscosity of pure-glue QCD from the lattice

We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical m  π . We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have “good” scalar,   <math> <msub> <mover> <mn>3</mn> <mo>¯</mo> </mover> <mi>F</mi> </msub> </math>  $$ {\overline{3}}_F $$ ,   <math> <msub> <mover> <mn>3</mn> <mo>¯</mo> </mover> <mi>c</mi> </msub> </math>  $$ {\overline{3}}_c $$ , J  P  = 0+, and “bad” axial vector, 6 F ,   <math> <msub> <mover> <mn>3</mn> <mo>¯</mo> </mover> <mi>c</mi> </msub> </math>  $$ {\overline{3}}_c $$ , J  P  = 1+, quantum numbers, and a bad-good mass difference for ud flavors, 198(4) MeV, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the “good” diquark channel. We extract a corresponding diquark size of ∼ 0.6 fm and perform a first exploration of the “good” diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

CERN

Philippe Forcrand

Canada

Randy Lewis

Australia

Kim Maltman

Diquark properties from full QCD lattice simulations

As a simple model for dark matter, we propose a QCD-like theory based on SU(2) gauge theory with one flavor of dark quark. The model is confining at low energy and we use lattice simulations to investigate the properties of the lowest-lying hadrons. Compared to QCD, the theory has several peculiar differences: there are no Goldstone bosons or chiral symmetry restoration when the dark quark becomes massless; the usual global baryon number symmetry is enlarged to SU(2) B , resembling isospin; and baryons and mesons are unified together in SU(2) B  iso-multiplets. We argue that the lightest baryon, a vector boson, is a stable dark matter candidate and is a composite realization of the hidden vector dark matter scenario. The model naturally includes a lighter state, the analog of the η′ in QCD, for dark matter to annihilate into to set the relic density via thermal freeze-out. Dark matter baryons may also be asymmetric, strongly self-interacting, or have their relic density set via 3 → 2 cannibalizing transitions. We discuss some experimental implications of coupling dark baryons to the Higgs portal.

Renwick Hudspith

Sean Tulin

Dark matter from strong dynamics: the minimal theory of dark baryons

We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><msup><mn>1</mn><mo>+</mo></msup><mo>)</mo></math> <math><mi>u</mi><mi>d</mi><mover><mi>c</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover></math> tetraquark with mass in the range of 15 to 61 MeV below <math><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>B</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> threshold. Since this range includes the electromagnetic <math><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>B</mi><mi>γ</mi></mrow></math> decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically or only weakly. We also perform a study at fixed pion mass, with non-relativistic QCD (NRQCD) for the heavy quarks, simulating <math><mi>q</mi><msup><mi>q</mi><mo>′</mo></msup><msup><mover><mi>b</mi><mo>¯</mo></mover><mo>′</mo></msup><mover><mi>b</mi><mo>¯</mo></mover></math> and <math><mi>q</mi><msup><mi>q</mi><mo>′</mo></msup><msup><mover><mi>b</mi><mo>¯</mo></mover><mo>′</mo></msup><msup><mover><mi>b</mi><mo>¯</mo></mover><mo>′</mo></msup></math> tetraquarks with <math><mrow><mi>q</mi></mrow></math>, <math><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>u</mi><mi>d</mi></mrow></math> or <math><mrow><mo>ℓ</mo><mi>s</mi></mrow></math> and variable, unphysical <math><msub><mi>m</mi><msup><mi>b</mi><mo>′</mo></msup></msub></math> in order to investigate the heavy mass dependence of such tetraquark states. We find that the dependence of the binding energy follows a phenomenologically expected form and that, though NRQCD breaks down before <math><msub><mi>m</mi><msup><mi>b</mi><mo>′</mo></msup></msub><mo>=</mo><msub><mi>m</mi><mi>c</mi></msub></math> is reached, the results at higher <math><msub><mi>m</mi><msup><mi>b</mi><mo>′</mo></msup></msub></math> clearly identify the <math><mi>u</mi><mi>d</mi><msup><mover><mi>b</mi><mo>¯</mo></mover><mo>′</mo></msup><mover><mi>b</mi><mo>¯</mo></mover></math> channel as the most likely to support a strong-interaction-stable tetraquark state at <math><msub><mi>m</mi><msup><mi>b</mi><mo>′</mo></msup></msub><mo>=</mo><msub><mi>m</mi><mi>c</mi></msub></math>. This observation serves to motivate the direct <math><mrow><mi>u</mi><mi>d</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> simulation. Throughout we use dynamical <math><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> ensembles with pion masses <math><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>415</mn></math>, 299, and 164 MeV reaching down almost to the physical point, a relativistic heavy quark prescription for the charm quark and NRQCD for the bottom quark(s).

Renwick J. Hudspith

Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD

We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using O ( a )-improved Wilson quarks. Temperature scans are performed at a fixed value of N t = ( aT ) −1 = 16, where a is the lattice spacing and T the temperature, at three fixed zero-temperature pion masses between 200 MeV and 540 MeV. In this range we find that the transition is consistent with a broad crossover. As a probe of the restoration of chiral symmetry, we study the static screening spectrum. We observe a degeneracy between the transverse isovector vector and axial-vector channels starting from the transition temperature. Particularly striking is the strong reduction of the splitting between isovector scalar and pseudoscalar screening masses around the chiral phase transition by at least a factor of three compared to its value at zero temperature. In fact, the splitting is consistent with zero within our uncertainties. This disfavours a chiral phase transition in the O (4) universality class.

Bastian Brandt

Harvey Meyer

Owe Philipsen

Daniel Robaina

Hartmut Wittig

On the strength of the U A (1) anomaly at the chiral phase transition in N f = 2 QCD

We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N f = 2 + 1 flavors of non-perturbatively improved Wilson fermions in the sea with the Lüscher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t 0 .

Dalibor Djukanovic

Georg Engel

Spain

Gregorio Herdoiza

Hanno Horch

Piotr Korcyl

Tomasz Korzec

Mauro Papinutto

Stefan Schaefer

Enno Scholz

Jakob Simeth

Hubert Simma

Wolfgang Söldner

Simulation of QCD with N f = 2 + 1 flavors of non-perturbatively improved Wilson fermions