We present a first-principles lattice QCD investigation of second-order fluctuations of and correlations among conserved charges—baryon number (B), electric charge (Q), and strangeness (S)—in the presence of external magnetic fields. Our study employs lattice simulations of (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD with physical pion masses using highly improved staggered fermions on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>48</mn><mn>3</mn></msup><mo>×</mo><mn>12</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>32</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> lattices, covering a wide range of magnetic field strengths up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi><mo>≃</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. We identify clear signals of magnetic field-induced modifications to these fluctuations and correlations, with the baryon-electric charge correlation, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mn>11</mn><mrow><mi>BQ</mi></mrow></msubsup></math>, exhibiting particularly strong sensitivity to the magnetic field. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas (HRG) model and construct proxy observables for fluctuations measurable in heavy-ion collision experiments. Our findings highlight <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mn>11</mn><mrow><mi>BQ</mi></mrow></msubsup></math> as a promising “magnetometer” for probing the presence of magnetic fields in QCD matter. Furthermore, we explore experimentally relevant ratios involving <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mn>11</mn><mrow><mi>BQ</mi></mrow></msubsup></math>, demonstrating their potential in mitigating volume effects and enhancing sensitivity to magnetic fields in collision environments. Additionally, we assess the limitations of the HRG model at strong magnetic fields, revealing deviations that indicate nontrivial modifications to hadronic degrees of freedom. These results offer new insights into the interplay between thermal and magnetic effects in the QCD phase diagram and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.

China

Heng-Tong Ding

Jin-Biao Gu

Arpith Kumar

Sheng-Tai Li

Second order fluctuations of conserved charges in external magnetic fields

We calculate the temperature dependence of bottomonium correlators in (2+1)-flavor lattice QCD with the aim to constrain in-medium properties of bottomonia at high temperature. The lattice calculations are performed using HISQ action with physical strange quark mass and light quark masses twenty times smaller than the strange quark mass at two lattice spacings $\textit{a}$ = 0$\textit{.}$0493 fm and 0$\textit{.}$0602 fm, and temporal extents $\textit{N}$ = 16 − 30, corresponding to the temperatures $\textit{T}$ = 133 − 250 MeV. We use a tadpole-improved NRQCD action including spin-dependent $\textit{v}$ corrections for the heavy quarks and extended meson operators in order to be sensitive to in-medium properties of the bottomonium states of interest. We find that within estimated errors the bottomonium masses do not change compared to their vacuum values for all temperatures under our consideration; however, we find different nonzero widths for the various bottomonium states.

Wei-Ping Huang

Germany

Rasmus Larsen

United States

Stefan Meinel

Swagato Mukherjee

Peter Petreczky

Zhanduo Tang

In-medium bottomonium properties from lattice NRQCD calculations with extended meson operators

The ultralight dark photon is an intriguing dark matter candidate. The interaction between visible and dark photons is introduced by the gauge kinetic mixing between the field strength tensors of the Abelian gauge groups in the Standard Model and dark sector. Relativistic electrodynamics was generalized to quantum electromagnetodynamics (QEMD) in the presence of both electric and magnetic charges. The photon is described by two four-potentials corresponding to two $ U(1) $ gauge groups and satisfying non-trivial commutation relations. In this work, we construct low-energy dark photon-photon interactions in the QEMD framework and obtain new dark photon-photon kinetic mixings. Then, we derive the consequent field and Maxwell's equations. We also investigate the detection strategies of dark photons as light dark matter and generic kinetic mixings at haloscope experiments.

Chang-Jie Dai

Tong Li

Rui-Jia Zhang

Dark photon dark matter in quantum electromagnetodynamics and detection at haloscope experiments * Li Tong is supported by the National Natural Science Foundation of China (12375096, 12035008, 11975129)

We investigate the effects of temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> and external magnetic fields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math> on the chiral condensates and screening masses of neutral pseudoscalar mesons, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>η</mi></mrow><mrow><mi>s</mi><mover accent="true"><mrow><mi>s</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math>, in (<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 physical quark masses. The chiral condensates are intrinsically connected to the screening masses via Ward-Takahashi identities, with the latter characterizing the inverse of the spatial correlation length in the pseudoscalar channel. Using highly improved staggered quark (HISQ), we perform simulations on lattices with temporal extents <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math>, 12, 16 and an aspect ratio of 4, covering five temperatures from 145 MeV to 166 MeV. For each temperature, eight magnetic field strengths are simulated, reaching up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>e</mi><mi>B</mi><mo>∼</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. These simulations allow us to provide continuum estimates for the chiral condensates and screening masses. We observe intricate behavior in the light (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mi>d</mi></math>), strange-light (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>s</mi></math>), and strange (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>) quark condensates as functions of the magnetic field and temperature, reflecting the competition between magnetic catalysis and inverse magnetic catalysis effects. This complex behavior is also mirrored in the screening masses of the neutral pseudoscalar mesons. Notably, the screening masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup></math> exhibit a nonmonotonic dependence on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math>, closely following the variations in their corresponding chiral condensates. Meanwhile, the screening mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>η</mi><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mn>0</mn></msubsup></math> decreases monotonically with increasing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math>. These findings provide valuable insights for understanding the behavior of QCD in a thermomagnetic medium and can serve as benchmarks for low-energy QCD models and effective theories.

Rishabh Thakkar

Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses

We present the determination of the charm quark mass, the masses, and decay constants of charmed mesons using thirteen <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor gauge ensembles at five different lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.05</mn><mo>,</mo><mn>0.11</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, 8 pion masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>∈</mo><mo stretchy="false">(</mo><mn>130</mn><mo>,</mo><mn>360</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and several values of the strange quark mass, which allows us to do the chiral and continuum extrapolation. These ensembles are generated through the stout smeared clover fermion action and Symanzik gauge actions with the tadpole improvement. By absorbing the discretization errors into the masses and field normalization of the charm quark, we manage to suppress the discretization error of the charmed meson mass and all the S-wave open charmed meson decay constants to a few percent or even less at lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∼</mo><mn>0.1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. Moreover, discretization errors for other quantities are also significantly reduced. The continuum extrapolated charm quark mass, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub><mo stretchy="false">(</mo><msub><mi>m</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>1.2933</mn><mo stretchy="false">(</mo><mn>72</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>95</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme, is determined using QED-subtracted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson mass and nonperturbative renormalization. Predictions of the open and close charm mesons using this charm quark mass agree with the experimental values at 0.1–0.5% level uncertainty. We obtained <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub></math> decay constants and also by far the most precise <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup></math> decay constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><msup><mi>D</mi><mo>*</mo></msup></msub><mo>=</mo><mn>0.2292</mn><mo stretchy="false">(</mo><mn>26</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>17</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></msub><mo>=</mo><mn>0.2691</mn><mo stretchy="false">(</mo><mn>30</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>03</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Hai-Yang Du

Bolun Hu

Mengchu Cai

Ying Chen

Xiangyu Jiang

Chuan Liu

Liuming Liu

Yu Meng

Peng Sun

Ji-Hao Wang

Yi-Bo Yang

Dian-Jun Zhao

Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles

In this work, we report a lattice calculation of -dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer − . The calculations are based on an = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer − .

Xiang Gao

Qi Shi

Sergey Syritsyn

Yong Zhao

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

We report the first lattice QCD computation of pion and kaon electromagnetic form factors, <math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math>, at large momentum transfer up to 10 and <math><mn>28</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, respectively. Utilizing physical masses and two fine lattices, we achieve good agreement with JLab experimental results at <math><msup><mi>Q</mi><mn>2</mn></msup><mo>≲</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>. For <math><msup><mi>Q</mi><mn>2</mn></msup><mo>≳</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, our results provide ab initio QCD benchmarks for the forthcoming experiments at JLab 12 GeV and future electron-ion colliders. We also test the QCD collinear factorization framework utilizing our high-<math><msup><mi>Q</mi><mn>2</mn></msup></math> form factors at next-to-next-to-leading order in perturbation theory, which relates the form factors to the leading Fock-state meson distribution amplitudes. Comparisons with independent lattice QCD calculations using the same framework demonstrate, within estimated uncertainties, the universality of these nonperturbative quantities.

Andrew D. Hanlon

Rui Zhang

QCD Predictions for Meson Electromagnetic Form Factors at High Momenta: Testing Factorization in Exclusive Processes

Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Japan

Okuto Morikawa

Soma Onoda

Hiroshi Suzuki

Yet Another Lattice Formulation of 2D (1) Chiral Gauge Theory via Bosonization David Tong: lectures on gauge theory

We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general “master pentagon identity” for group-like elements in the Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We prove this curious identity and discuss its implications.

Italy

Russia

Yegor Zenkevich

On pentagon identity in Ding-Iohara-Miki algebra

We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological vertex which is regarded as the intertwining operator of the Fock representation. The shift of the spectral parameter of the intertwiners is generated by the operator which is constructed from the universal R matrix. The solutions to the generalized KZ equation are factorized into the ratio of two point functions which are identified with generalizations of the Nekrasov factor for supersymmetric quiver gauge theories.

Panupong Cheewaphutthisakun

Hiroaki Kanno

MacMahon KZ equation for Ding-Iohara-Miki algebra