The weak decays of charmonium states such as $ J/\psi $ and $ \psi(2S) $ are instrumental in probing both nonperturbative QCD dynamics and the flavor structure of the Standard Model (SM). The extreme rarity of charmonium weak decays renders them highly sensitive to physics beyond the SM, particularly in channels that are heavily suppressed in the SM, such as flavor-changing neutral-current (FCNC) decays. This review highlights the critical role of the BESIII experiment, which leverages an unprecedented data sample of over $ 10^{10} $ $ J/\psi $ and $ 2.7\times10^{9} $ $ \psi(2S) $ events to achieve leading sensitivity in searches for charmonium weak decays. We present the latest and most stringent upper limits established by BESIII on various semileptonic, nonleptonic, and FCNC charmonium weak decay channels.

China

Xu-Ze Li

Kai-Xin Fan

Zheng-Yun You

Yu Zhang

Minggang Zhao

Mini-review of charmonium weak decays at BESIII * Supported in part by the National Key R&D Program of China (2023YFA1606000); the National Natural Science Foundation of China (NSFC) (12035009, 12175321, U1932101), and the National College Students' Science and Technology Innovation Project of Sun Yat-sen University

We investigate the direct $\rm CP $ violation in the decay $ D^\pm \to \pi^\pm \pi^+ \pi^- $ incorporating the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism. The integrated mixing intensities $ \overline \xi_{fa} $ and $ \overline \xi_{af} $ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $ \pi^+\pi^- $ pair lies near the $ f_0(980) $ resonance, this isospin-breaking mechanism can enhance the $\rm CP $ asymmetry. The enhancement is particularly pronounced when the $ f_0(980) $ carries a significant $ n\bar{n} $ quark component and the $ f_0(980) $ and $ \sigma(600) $ mixing angle is approximately $ 26^\circ $ . After accounting for non-factorizable effects, we find these corrections tend to partially cancel the leading-order contributions, resulting in a suppression of the $\rm CP $ violations relative to the naive factorization predictions. It is emphasized that the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism should be taken into account in both theoretical and experimental studies of $\rm CP $ violation in $\textit{B}$ or $\textit{D}$ meson decays.

Shi-Ji Cao

Jing-Juan Qi

Yi-Fan Zhao

Chao Wang

Zhen-Yang Wang

Xin-Heng Guo

Direct CP violation in ${ {\boldsymbol D}^{\bf\pm }\to {\boldsymbol\pi}^{\bf\pm} {\boldsymbol\pi}^{\bf +} {\boldsymbol\pi}^{\bf -}} $ with ${{\boldsymbol a}_{\bf 0}^{\bf 0}{\bf (980)-}{\boldsymbol f}_{\bf 0}{\bf (980)}} $ mixing * Supported by the National Natural Science Foundation of China (12405115, 12105149, 11805153, 12275024), and the High-Level Scientific Research Fund of Ningbo University (GJPY2026032)

We constructed a four-Higgs-doublet model (4HDM) invariant under $\textit{D}$ $_{5}$ symmetry and investigated its complete neutral vacuum structure in detail. Assuming explicit CP conservation in the scalar potential, we examined whether CP symmetry can be spontaneously broken. We provided a complete list of all possible real and complex vacua, along with the constraints on the potential parameters required for each vacuum solution to exist. We also discussed the positive-definiteness conditions that the Hessian must satisfy for each vacuum to be a local minimum of the potential. The results show that, after spontaneous symmetry breaking, some complex vacua lead to spontaneous CP violation in the potential, whereas the remaining complex vacua still preserve CP conservation. Among these CP-violating complex vacua, one can be regarded as the most general form. Furthermore, we discussed the relationship between real and complex vacua.

Dong-Ping Fu

Michihisa Takeuchi

Spontaneous CP violation in the $\textit{D}$ $_{5}$-symmetric four-Higgs-doublet models * Supported by the Fundamental Research Funds for the Central Universities, the One Hundred Talent Program of Sun Yat-sen University, China, and the Guangdong Natural Science Foundation (2026A1515012641)

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal {L}_{m},\Phi ,X)$$ class, an extension of $$f(R,\mathcal {L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi $$ , and its kinetic invariant $$X = g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi $$ . Working with the explicit model $$f = R + \mathcal {L}_{m} + (\lambda /2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi (x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$ , respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi \psi }<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal {L}_{m},\Phi ,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Türkiye

İzzet Sakallı

Are Petrov type-N and D spacetimes admitting CTCs valid in $$f(R,\mathcal {L}_m,\Phi ,X)$$ gravity?

The <italic>&#947;d</italic>&#8239;&#8594;&#8239; <italic>K</italic> 0&#923; <italic>p</italic> reaction has been studied to search for a <math altimg='si30.svg'><mrow><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover><mi>N</mi><mi>N</mi></mrow></math> quasi-bound state using the LEPS2 solenoid spectrometer at SPring-8. A localized enhancement concentrated at low <italic>q</italic> is observed in the ( <italic>M</italic> <inf>&#923;<italic>p</italic></inf>, <italic>q</italic>) distribution below the <math altimg='si8.svg'><mrow><msup><mi>K</mi><mo>&#8722;</mo></msup><mi>p</mi><mi>p</mi></mrow></math> mass threshold, where <italic>M</italic> <inf>&#923;<italic>p</italic></inf> is the &#923; <italic>p</italic> invariant mass and <math altimg='si31.svg'><mrow><mrow><mi>q</mi><mo>&#8801;</mo><mo>|</mo></mrow><msub><mover accent='true'><mi>p</mi><mo>&#8594;</mo></mover><mi>&#947;</mi></msub><mo linebreak='goodbreak'>&#8722;</mo><msub><mover accent='true'><mi>p</mi><mo>&#8594;</mo></mover><msup><mi>K</mi><mn>0</mn></msup></msub><mrow><mo>|</mo><mo>=</mo><mo>|</mo></mrow><msub><mover accent='true'><mi>p</mi><mo>&#8594;</mo></mover><mrow><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mi>p</mi></mrow></msub><mrow><mo>|</mo></mrow></mrow></math> is the momentum transfer. A two-dimensional ( <italic>M</italic> <inf>&#923;<italic>p</italic></inf>, <italic>q</italic>) fit demonstrates that the enhancement near the threshold is statistically significant, yielding a local significance of 7.3&#8201; <italic>&#963;</italic>. The enhancement is characterized by effective shape parameters including the Breit&#8211;Wigner mass <italic>M</italic> and width &#915;, and a Gaussian form-factor momentum scale <italic>Q</italic>: <math altimg='si32.svg'><mrow><mi>M</mi><mo linebreak='goodbreak'>=</mo><mn>2.354</mn><mo>&#177;</mo><mn>0.011</mn><msubsup><mrow><mo>(</mo><mrow><mtext>stat</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>&#8722;</mo><mn>0.005</mn></mrow><mrow><mo>+</mo><mn>0.009</mn></mrow></msubsup><mrow><mo>(</mo><mrow><mtext>syst</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mspace width='0.33em' /><mtext>GeV</mtext><mo linebreak='goodbreak'>/</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></math>, <math altimg='si33.svg'><mrow><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mo linebreak='goodbreak'>=</mo><mn>0.055</mn><mo>&#177;</mo><mn>0.023</mn><msubsup><mrow><mo>(</mo><mrow><mtext>stat</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>&#8722;</mo><mn>0.009</mn></mrow><mrow><mo>+</mo><mn>0.031</mn></mrow></msubsup><mrow><mo>(</mo><mrow><mtext>syst</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mspace width='0.33em' /><mtext>GeV</mtext><mo linebreak='goodbreak'>/</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></math>, and <math altimg='si34.svg'><mrow><mi>Q</mi><mo linebreak='goodbreak'>=</mo><mn>0.350</mn><mo>&#177;</mo><mn>0.041</mn><msubsup><mrow><mo>(</mo><mrow><mtext>stat</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>&#8722;</mo><mn>0.010</mn></mrow><mrow><mo>+</mo><mn>0.035</mn></mrow></msubsup><mrow><mo>(</mo><mrow><mtext>syst</mtext><mo>.</mo></mrow><mo>)</mo></mrow><mspace width='0.33em' /><mtext>GeV</mtext><mo linebreak='goodbreak'>/</mo><mi>c</mi></mrow></math>. The obtained results support the existence of a <math altimg='si30.svg'><mrow><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover><mi>N</mi><mi>N</mi></mrow></math> quasi-bound state in photoproduction.

Japan

R. Kobayakawa

South Korea

J.K. Ahn

S. Ajimura

Taiwan

W.C. Chang

M.L. Chu

S. Daté

T. Gogami

T.A. Hashimoto

T. Hotta

T. Ishikawa

H. Katsuragawa

H. Kohri

Y. Ma

M. Miyabe

K. Mizutani

N. Muramatsu

T. Nakano

Vietnam

T.H. Nam

M. Niiyama

Y. Nozawa

Y. Ohashi

H. Ohkuma

H. Ohnishi

T. Ohta

Canada

C. Rangacharyulu

S.Y. Ryu

Y. Sada

H. Shimizu

M. Sumihama

S. Suzuki

S. Tanaka

A.O. Tokiyasu

N. Tomida

K. Watanabe

T. Yorita

C. Yoshida

M. Yosoi

Evidence for a <math altimg='si30.svg'><mrow><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover><mi>N</mi><mi>N</mi></mrow></math> quasi-bound state in the <italic>&#947;d</italic>&#8239;&#8594;&#8239; <italic>K</italic> 0&#923; <italic>p</italic> reaction

We investigate the vacuum-induced current density for a charged scalar field in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional cosmic dispiration spacetime threaded by a magnetic flux. This background combines a cosmic string and a screw dislocation, yielding a nontrivial helical geometry. By constructing the normalized mode functions of the Klein-Gordon equation, we evaluate the Wightman function and obtain the vacuum expectation value of the current density. We show that, in addition to the azimuthal component describing a persistent current around the defect, a nonvanishing axial component is induced as a direct consequence of the helical structure of the spacetime. Both components are periodic functions of the magnetic flux depending only on its fractional part, reflecting the Aharonov-Bohm nature of the effect. Closed expressions are obtained for massive and massless fields in arbitrary dimensions. We demonstrate that the screw dislocation parameter plays a crucial role in the behavior of the induced currents, leading to the regularization of the components at the origin and controlling their magnitude. Their asymptotic behavior is also analyzed in detail. Our results reduce to known expressions in the absence of the screw dislocation, providing a consistency check. In particular, we examine the physically relevant (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional case, where numerical analysis reveals nontrivial features arising from the interplay between topology and gauge effects.

Brazil

Herondy Mota

Vacuum-induced current density from a magnetic flux threading a cosmic dispiration in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>+</mo><mn>1</mn></math>)-dimensional spacetime

We present a lattice quantum chromodynamics calculation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math>-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>d</mi><mo stretchy="false">˜</mo></mover><mn>2</mn></msub></math> moment of the twist-3 PDF <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>T</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> for the first time in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.076</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>z</mi></msub><mo>=</mo><mo stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>0.25</mn><mo>,</mo><mn>1.02</mn><mo>,</mo><mn>1.53</mn><mo stretchy="false">}</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>T</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>d</mi><mo stretchy="false">˜</mo></mover><mn>2</mn><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.0024</mn><mo stretchy="false">(</mo><mn>46</mn><mo stretchy="false">)</mo></math> at next-to-leading order in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math>. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.25</mn><mo>,</mo><mn>0.75</mn><mo stretchy="false">]</mo></math>. The end-point regions are then parametrized, combined with the LaMET prediction at moderate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, and fitted to the short-distance matrix elements in coordinate space.

United States

Xiang Gao

Andrew D. Hanlon

Swagato Mukherjee

Peter Petreczky

Hai-Tao Shu

Fei Yao

Rui Zhang

Yong Zhao

Proton isovector helicity PDF at NNLO and the twist-3 moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow><mn>2</mn></msub></mrow></math> from lattice QCD at physical quark masses

We investigate the reaction mechanism of strangeness production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math> within a hybrid Regge framework, taking into account <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>-Reggeon exchanges. We present results for the total cross section, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-dependent differential cross sections, and spin-density matrix elements (SDMEs), and compare them with the available experimental data. We find that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>-Reggeon exchange provides the dominant contribution, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-Reggeon exchange remains non-negligible, particularly in describing the SDMEs. In contrast, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>-channel nucleon exchanges are negligible. To obtain reliable predictions for the open-charm production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math>, we employ a quark-gluon-string-model-motivated Regge prescription that incorporates both pseudoscalar- and vector-Reggeon exchanges. Within this prescription, the Regge trajectories <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and energy-scale parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>s</mi><mn>0</mn></msub></math> are determined consistently, thereby constraining the model and reducing theoretical ambiguities. For the hidden-charm production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>, we use the same quark-level diagrammatic correspondence. The total cross sections for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> are suppressed by approximately 4–6 and 8–9 orders of magnitude, respectively, compared with that for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math>. We also examine possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel contributions from the hidden-charm pentaquark states with strangeness, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4338</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, to both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> production.

Sang-Ho Kim

Production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> in kaon-induced reactions off the nucleon

We investigate how the temperature influences the threshold cusps in meson-meson scatterings, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover></mrow></math>) scatterings, using the production rates and propagators obtained at finite temperature. The line shape of production rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> at different temperatures demonstrates that the cusp structure in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> scattering is mildly enhanced as the temperature increases. For the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> propagator, which includes isospin symmetry breaking, the line shape displays a unique plateaulike structure, and this structure will also be enhanced as the temperature increases. For comparison, the line shape of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> propagator including isospin symmetry breaking is also investigated at different temperatures. As the temperature increases, its line shape shows a similar plateaulike structure but with some different properties when the temperature modifications to the masses and widths of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> are considered.

Ying Zhang

Atsushi Hosaka

Qian Wang

Shigehiro Yasui

Finite-temperature effects on the threshold cusps in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> scatterings from relativistic heavy-ion collisions

We investigate a non-Abelian SU(2) quantum link model in $$2+1$$ dimensions on a hexagonal lattice using tensor network methods. We determine the static quark potential for a wide range of bare coupling values and find that the theory is confining. We also probe the existence of a Lüscher term and find a clear signal with a $$g^2$$ dependent coefficient, in qualitative agreement with a strong coupling expansion. Correspondingly, the width of the strings scales logarithmically with the string length again for all $$g^2$$ -values, providing evidence for a rough string, with no indication for a roughening transition.