<p>Quarkonia, which are bound states of a heavy quark and antiquark, play a key role in probing the quark-gluon plasma (QGP). The dynamics of quarkonia in the QGP are encoded in their finite-temperature spectral functions. In this work, we estimate the quarkonium spectral functions in the pseudoscalar channel using (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD with a pion mass of 320 MeV, at temperatures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>220</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.2</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>251</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.4</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>293</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.6</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>. Reconstructing the spectral function from the Euclidean lattice correlator is a well-known ill-posed problem, requiring additional physics-motivated input. We address this by smoothly matching contributions from different frequency regions of the spectral function, using appropriate physics valid for each region. The spectral function around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>∼</mo><mn>2</mn><msub><mi>M</mi><mi>q</mi></msub></math> is obtained using a nonperturbative complex potential, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>≫</mo><mn>2</mn><msub><mi>M</mi><mi>q</mi></msub></math> it is modeled using results from vacuum perturbation theory. Since the pseudoscalar channel does not receive a transport contribution near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>∼</mo><mn>0</mn></math>, we find that the combination of these two regions already provides a good description of the relativistic lattice pseudoscalar correlator. We observe a substantial thermal width in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> state, indicating that pseudoscalar charmonium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>) is nearing dissolution at the studied temperatures. In comparison, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub></math> ground state exhibits little change and remains well defined.</p>

Germany

Pakistan

Sajid Ali

Dibyendu Bala

Olaf Kaczmarek

 Pavan

Thermal static potential and pseudoscalar quarkonium spectral functions from (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD

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.

Taiwan

Anthony Francis

United States

France

Greg Jackson

Jonas Turnwald

Tristan Ueding

Nicolas Wink

Lattice QCD estimates of thermal photon production from the QGP

We extend our analysis of bound states in  $${\mathcal {N}}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric Yang–Mills theory by the consideration of baryonic operators, which are composed of three gluino fields. The corresponding states are similar to the baryons in QCD, but due to the difference between gluino and quark fields, their properties and the fermion line contractions involved in their correlation functions are different from QCD. In this work, we first explain the derivation of these operators and the contractions needed in numerical calculations of their correlators. In contrast to QCD the correlators contain a spectacle piece, which requires methods for all-to-all propagators. We provide a first estimate of the two-point function and the mass of the lightest baryonic state in  $${\mathcal {N}}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric Yang–Mills theory.

Georg Bergner

Camilo López

Istvan Montvay

Gernot Münster

Stefano Piemonte

Baryonic states in  $$\mathbf {{\mathcal {N}}=1}$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric SU(2) Yang–Mills theory on the lattice

In $${\mathcal {N}}=1$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric Yang–Mills theory, regularised on a space-time lattice, in addition to the breaking by the gluino mass term, supersymmetry is broken explicitly by the lattice regulator. In addition to the parameter tuning in the theory, the supersymmetric Ward identities can be used as a tool to investigate lattice artefacts as well as to check whether supersymmetry can be recovered in the chiral and continuum limits. In this paper we present the numerical results of an analysis of the supersymmetric Ward identities for our available gauge ensembles at different values of the inverse gauge coupling $$\beta $$ <math><mi>β</mi></math>  and of the hopping parameter $$\kappa $$ <math><mi>κ</mi></math> . The results clearly indicate that the lattice artefacts vanish in the continuum limit, confirming the restoration of supersymmetry.

Henning Gerber

Philipp Scior

Continuum extrapolation of Ward identities in $${{\mathcal {N}}=1}$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric SU(3) Yang–Mills theory

The physical particles in supersymmetric Yang-Mills (SYM) theory are bound states of gluons and gluinos. We have determined the masses of the lightest bound states in SU(3) <math><mi>N</mi><mo>=</mo><mn>1</mn></math> SYM theory. Our simulations cover a range of different lattice spacings, which for the first time allows an extrapolation to the continuum limit. Our results show the formation of a supermultiplet of bound states, which provides a clear evidence for unbroken supersymmetry.

Numerical Results for the Lightest Bound States in <math><mi>N</mi><mo>=</mo><mn>1</mn></math> Supersymmetric SU(3) Yang-Mills Theory

We have calculated the masses of bound states numerically in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric Yang-Mills theory with gauge group SU(2). Using the suitably optimised variational method with an operator basis consisting of smeared Wilson loops and mesonic operators, we are able to obtain the masses of the ground states and first excited states in the scalar, pseudoscalar and spin-  <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \frac{1}{2} $$  sectors. Extrapolated to the continuum limit, the corresponding particles appear to be approximately mass degenerate and to fit into the predicted chiral supermultiplets. The extended operator basis including both glueball-like and mesonic operators leads to improved results compared to earlier studies, and moreover allows us to investigate the mixing content of the physical states, which we compare to predictions in the literature.

Simon Kuberski

Variational analysis of low-lying states in supersymmetric Yang-Mills theory

In numerical investigations of supersymmetric Yang–Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in $$\mathcal {N}=1$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric Yang–Mills theory with gauge group SU(3). The results indicate that lattice artefacts scale to zero as $$O(a^2)$$ <math><mrow><mi>O</mi><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo></mrow></math>  towards the continuum limit in agreement with theoretical expectations.

Analysis of Ward identities in supersymmetric Yang–Mills theory

In this article we summarise our results from numerical simulations of  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ supersymmetric Yang-Mills theory with gauge group SU(3). We use the formulation of Curci and Veneziano with clover-improved Wilson fermions. The masses of various bound states have been obtained at different values of the gluino mass and gauge coupling. Extrapolations to the limit of vanishing gluino mass indicate that the bound states form mass-degenerate supermultiplets.

Pietro Giudice

The light bound states of  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ supersymmetric SU(3) Yang-Mills theory on the lattice

In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein’s field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motion in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Second, we give a physical interpretation of new cosmological solutions which satisfy the positive energy condition and yield critical bounds on the expansion coefficient α , in which the underlying non-flat spacetimes have interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit t→∞ . In particular a non-flat spacetime is obtained that mimics the expansion in a flat FRW universe dominated by vacuum energy such that the expansion factor has the same form in both. However, the energy density is dynamical in the former.