Quantum chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>16</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math>) dataset that we generated at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math> with our 4HEX staggered action. We extend the canonical ensemble to noninteger net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g., for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub><mo>≈</mo><mn>500</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

Germany

Alexander Adam

Szabolcs Borsányi

United States

Hungary

Zoltán Fodor

Jana N. Guenther

Italy

Paolo Parotto

Attila Pásztor

Ludovica Pirelli

Chik Him Wong

Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">⟩</mo></mrow></math> of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> flavor tree-level improved Wilson clover fermions coupling via two-level HEX smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. This is the first direct calculation of these observables performed at the physical pion mass.

Emilio Taggi

Michael Engelhardt

Jeremy R. Green

Stefan Krieg

Stefan Meinel

John W. Negele

Andrew Pochinsky

Marcel Rodekamp

Sergey Syritsyn

Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

The work was motivated by the numerical result that, in a pure SU(2) gauge theory, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> of the effective noncompact and compact lattice spacing is larger than 1 and increases with decreasing gauge coupling, with the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at a given number of lattice sites and comparable scaling, one can obtain a larger physical volume whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of noncompact pure SU(2) and Abelian gauge theories, but we find in addition that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> reaches the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mn>2</mn></msqrt></math>. Including matter fields, we find that R increases (still up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mn>2</mn></msqrt></math>) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

F. Palumbo

Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice

The observed fluid behavior of the matter produced in heavy ion and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions implies that the strings stretched between the constituents of the projectile and target should have a hard core giving rise to a repulsion between them. It is shown that in these collisions there are two critical string densities, one corresponding to the well-studied percolation of strings and another to the percolation of the hard core of the strings. These two critical densities are related to two critical temperatures, one <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi><mspace width="4pt"></mspace><mo>≈</mo><mspace width="4pt"></mspace><mn>160</mn></mrow></math> MeV would correspond to the restoration of chiral symmetry and partial deconfinement and a second transition <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi><mspace width="4pt"></mspace><mo>≈</mo><mspace width="4pt"></mspace><mn>220</mn></mrow></math> MeV form the fluid behavior of quantum chromodynamics matter strongly interacting to a quasi free gas of quarks and gluons. This argument is supported by the recently published results on the sudden increase in the degrees of freedom above the deconfinement temperature in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mtext>−</mtext><mi>A</mi></mrow></math> collisions [Mishra et al., <a href="http://dx.doi.org/10.1016/j.nuclphysa.2024.122865">Nucl. Phys. A 1046, 122865 (2024)</a>].

Spain

C. Pajares

R.P. Scharenberg

B.K. Srivastava

Existence of a second phase transition in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mtext>−</mtext><mi>A</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider: A physical interpretation

Based on $ (10087\pm44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, the $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ J/\psi\rightarrow \gamma \pi^{0}\pi^{0}\eta $ processes are studied. The $ X(2370) $ is observed in both the $ K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ \pi^{0}\pi^{0}\eta $ invariant mass spectra, with statistical significances greater than $ 14\sigma $ and $ 20\sigma $ , respectively. By combining measurements from these processes with those from the previously reported $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\eta^{\prime} $ process, the mass and width of the $ X(2370) $ are determined to be $ 2359^{+13}_{-14}\; \text{MeV}/c^{2} $ and $ 170^{+44}_{-29}\; \text{MeV} $ , respectively. In addition, the decay $ X(2370)\to a_{0}(980)^{0}\pi^{0} $ with $ a_{0}(980)^{0}\to \pi^{0}\eta $ is observed with a statistical significance exceeding $ 9\sigma $ . The properties of the $ X(2370) $ —decay pattern similarities to that of $ \eta_{c} $ , are consistent with those of a pseudoscalar glueball.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

M.S. Anderson

Y. Bai

O. Bakina

H.R. Bao

X.L. Bao

M. Barbagiovanni

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R. Briere

A. Brueggemann

D. Cabiati

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

C. Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

E. Di Fiore

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

Z.J. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

Observation of the ${\boldsymbol X(2370)}$ in ${{\boldsymbol J}/\boldsymbol\psi\rightarrow\gamma K^{0}_{S}K^{0}_{S}\pi^{0}}$ and ${J/\psi\rightarrow\gamma \pi^{0}\pi^{0}\eta}$ * This work is supported in part by the National Key R&D Program of China under Contracts Nos. 2025YFA1613900, 2023YFA1606000, 2023YFA1606704; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12342502, 12361141819, 12535005; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the Strategic Priority Research Program of Chinese Academy of Sciences under Contract No. XDA0480600; CAS under Contract No. YSBR-101; 100 Talents Program of CAS; China Postdoctoral Science Foundation under Contracts Nos. GZC20252256, 2025M773423; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile under Contract No. ANID CCTVal CIA250027; ERC under Contract No. 758462; German Research Foundation DFG under Contract No. FOR5327; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation under Contracts Nos. 2021.0174, 2021.0299, 2023.0315; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; Polish National Science Centre under Contract No. 2024/53/B/ST2/00975; STFC (United Kingdom); Swedish Research Council under Contract No. 2019.04595; U. S. Department of Energy under Contract No. DE-FG02-05ER41374

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Derived a novel representation of 2&#8239;&#8594;&#8239;2 scattering left-hand cuts using right-hand cut imaginary parts.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Provides exact extraction of logarithmic branch left-cuts for arbitrary isospin and angular momentum partial waves.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Enables systematic quantification of left-hand cut uncertainties in unitarization methods like IAM and <italic>N</italic>/<italic>D</italic>.</para></list-item></list>

Alexandre Salas-Bernárdez

The left-cut for partial waves in terms of physical amplitudes

In generally covariant theories, evolution in coordinate time is a gauge transformation, so that a symmetry made manifest in a gauge-fixed description need not be a symmetry of the physical dynamics. At the same time, deparametrisation removes gauge redundancies but may hide physical symmetries, in particular those that depend on the chosen physical clock. We investigate the relation between gauge and hidden physical symmetries in flat FLRW geometry coupled to an arbitrary number $\textit{n}$ of free massless scalar fields. We show that conformal Killing vectors of the minisuperspace metric generate conserved charges that are Dirac observables and hence gauge-invariant. Their Poisson algebra realises the maximal conformal algebra $$ \mathfrak{conf}\left(n,1\right)\simeq \mathfrak{so}\left(n+1,2\right) $$ , extending previous single-field results to arbitrary $\textit{n}$. We then revisit the Eisenhart-Duval lift in a family of gauges and show that the resulting symmetry algebra is gauge dependent. Only in the harmonic gauge does the algebra enlarge to the Schrödinger algebra, which is thus not a physical symmetry. Finally, we show that deparametrisation maps the lifted charges to gauge-invariant Dirac observables, which always realise a subalgebra of $$ \mathfrak{conf}\left(n,1\right) $$ , recovering it in full in the harmonic gauge. Our results provide a systematic framework for disentangling gauge from physical symmetries in minisuperspace models, recovering charges to which reduced phase-space descriptions are structurally blind, and extending naturally to models with potentials.

Andrea Calcinari

France

Adrià Delhom

Federico Greco

Daniele Oriti

Néstor Rivero

Gauge versus (hidden) physical symmetries of FLRW cosmologies

We consider a quenched <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> gauge Higgs theory on the lattice, coupled to a static vectorlike fermion which, in this case, is in the same gauge group representation as the Higgs field. Physical (i.e., locally gauge invariant) electrically charged and electrically neutral states of matter particles in the electroweak theory were described decades ago, but those constructions do not exhaust all the possibilities, and new types of electrically charged/neutral states, orthogonal to former constructions, are described here. The difference has to do with how the static source, which by itself does not create a physical state, is dressed by dynamical fields. We find that, unsurprisingly, the neutral static fermion is much lighter than any of the charged fermion states. But a lattice study of the propagation of the charged fermion states indicates the existence of (at least) two particle states with different masses in charged particle spectrum.

Jeff Greensite

Varieties of electrically charged physical states in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> lattice gauge Higgs theory

We study classical background electric fields and the Schwinger effect in de Sitter space. We show that a constant electric field in de Sitter requires the photon to have a tachyonic mass proportional to the Hubble scale. This has physical implications for the induced Schwinger current that affect its IR behaviour. To study this, we recompute the Schwinger current in de Sitter space for charged fermions and minimally coupled scalars, imposing a physically consistent renormalization condition. We find a $\textit{finite and positive}$ Schwinger current even in the massless limit. This is in contrast to previous calculations in the literature, which found a negative IR divergence. We also obtain the first result for the Schwinger current of a non-minimally coupled scalar, including the conformally coupled case, which we find exhibits behaviour very similar to that of the fermion current. Our results may have physical implications for both magnetogenesis and inflationary dark matter production.

Mar Bastero-Gil

Portugal

Paulo B. Ferraz

António Torres Manso

Slovenia

Lorenzo Ubaldi

Roberto Vega-Morales

Schwinger current in de Sitter space * This work has been partially supported by Junta de Andalucía Projects P21-00199 and A-FQM-472-UGR20 (FEDER funds); SRA (10.13039/501100011033) and ERDF (PID2022-139466NB-C21) (R.V.M.); PID2022-140831NB-I00, funded by MICIU/AEI/10.13039/501100011033 and FEDER, UE (M.B.G., A.T.M.); by FCT CERN (10.54499/2024.00252.CERN) (M.B.G., A.T.M., P.F.); FCT Grant No. SFRH/BD/151475/2021 and 10.54499/SFRH/BD/151475/2021 (P.F.). LU is supported by the Slovenian Research Agency under research core funding No. P1-0035 and by research grants J1-60026 and J1-4389. This article is based upon work from COST Action COSMIC WISPers CA21106, supported by COST (European Cooperation in Science and Technology). R.V.M. thanks the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA$^{+}$ (Project ID 390831469) for its hospitality and partial support during the completion of this work

In this work, we investigate the physical viability and structural properties of compact stars within the framework of modified gravity, specifically <italic>f</italic>( <italic>R</italic>) gravity. Three distinct functional forms of the gravitational Lagrangian are considered, namely <math altimg='si8.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>R</mi><mn>2</mn></msup></mrow></math>, <math altimg='si10.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>R</mi><mn>2</mn></msup><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>+</mo><mi>&#947;</mi><mi>R</mi><mo>)</mo></mrow></mrow></math>, and <math altimg='si12.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>R</mi><mrow><mo stretchy='true'>(</mo><msup><mi>e</mi><mrow><mo>&#8722;</mo><mi>R</mi><mo>/</mo><mi>&#947;</mi></mrow></msup><mo linebreak='badbreak'>&#8722;</mo><mn>1</mn><mo stretchy='true'>)</mo></mrow></mrow></math>, which allow us to explore both polynomial and exponential corrections to General Relativity. The interior spacetime is modeled using a static and spherically symmetric anisotropic fluid distribution, and the corresponding modified field equations are solved to obtain the energy density, radial pressure, and tangential pressure profiles. To assess the astrophysical relevance of the proposed models, we apply them to ten observed compact stellar candidates, namely Her X-1, SAX J1808.4&#8211;3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. The obtained solutions are examined through several physical acceptability criteria, including regularity conditions, energy conditions, causality, equilibrium via the generalized Tolman&#8211;Oppenheimer&#8211;Volkoff equation, and stability analyses. Furthermore, key observable quantities such as mass&#8211;radius relations, compactness, surface redshift, and anisotropy are discussed in detail for each model. Our results indicate that all three <italic>f</italic>( <italic>R</italic>) gravity models can support realistic and stable astrophysical compact star configurations, with noticeable deviations from General Relativity, particularly for higher curvature regimes, suggesting that modified gravity effects may play a significant role in describing ultra-dense stellar objects.

Saudi Arabia

Shah Muhammad

Azerbaijan

Pakistan

M. Ilyas

Greece

Euaggelos E. Zotos

Physical viability of dark energy compact stars in <italic>f</italic>( <italic>R</italic>) gravity using Durgapal-Fuloria solutions