Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

Investigating the electromagnetic characteristics of unconventional states may offer new insights into their internal structures. In particular, the magnetic moment attributes may serve as a crucial physical observable for differentiating exotic states with disparate configurations or spin-parity quantum numbers. As a promising avenue for research, encompassing both opportunities and challenges, an in-depth examination of the electromagnetic properties of exotic states is crucial for advancing our understanding of unconventional states. Motivated by this, in this study, the magnetic moments of ${I(J^{P})} = 1(1^{+})$ $ Z_{\bar{b} c} $ tetraquark states are analyzed in the framework of QCD light-cone sum rules by considering the diquark-antidiquark approximation, designated as type $ 3_c \otimes \bar{3}_c $ . Although the tetraquark states examined in this study have nearly identical masses, their magnetic moment results exhibit noticeable discrepancies. This may facilitate the differentiation between quantum numbers associated with states with identical quark content. The results show that heavy quarks overcoming light quarks can determine both the sign and magnitude of the magnetic moments of these tetraquark states. The numerical results obtained in this study suggest that the magnetic moments of $ Z_{\bar{b} c} $ tetraquark states may reveal aspects of their underlying structure, which could distinguish between their spin-parity quantum numbers and internal structure. The results obtained regarding the magnetic moments of the $ Z_{\bar{b} c} $ tetraquark states may be checked within the context of different phenomenological approaches.

Ulaş Özdem

Elucidating the nature of axial-vector charm-antibottom tetraquark states

The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in the phase space in multi-body decays of bottom and charmed mesons. In this study, we examine the CP violation in the decay channel $ {\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0} $ in the phase-space region where the intermediate resonances $ \overline{K}^{*}(892)^{0} $ and $ {\overline{K}^{*}_{0}(700)} $ dominate. In particular, the forward-backward asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are investigated. The nontrivial correlation between FBA and FB-CPA is analyzed. The analysis indicates that FB-CPAs around the resonance $ \overline{K}^{*}(892)^{0} $ can be as large as approximately 35%, which can be potentially accessible by Belle and Belle-II collaborations in the near future.

Jian-Yu Yang

Yu-Jie Zhao

Jing-Juan Qi

Zhen-Hua Zhang

The forward-backward asymmetry induced CP asymmetry in ${{\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0}}$ in phase space around the resonances ${{\overline{K}}^{*}(892)^{0}}$ and ${{\overline{K}}^{*}_{0}(700)}$ * Supported by National Natural Science Foundation of China (12475096, 12405115, 12192261) and Scientific Research Fund of Hunan Provincial Education Department (22A0319)

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

The weak decays of the $$D_{(s)}$$ meson provide a pivotal platform to advance our understanding of the Standard Model (SM) and to explore New Physics (NP). In recent years, experiments have collected a significant amount of data on the $$D_{(s)}$$ meson decays, particularly from BESIII, which provides substantial support for theoretical research. In this work, we systematically investigate the semi-leptonic decays of $$D_{(s)}$$ meson to pseudoscalar (P), scalar (S), vector (V), and axial-vector (A) mesons within the framework of the covariant light-front quark model (CLFQM). We calculate the form factors of the transitions $$D_{(s)}\rightarrow P,S,V,A$$ and the branching ratios of the corresponding semi-leptonic decays, then compare them with experimental data and results from other theoretical models. The form factor values of the transitions $$D_{(s)}\rightarrow P, V$$ obtained from the CLFQM are consistent with those of other theoretical models and available data in most cases. However, significant discrepancies are found in some specific $$D_{(s)}\rightarrow S,A$$ transitions, such as $$D\rightarrow a_0(980), a_0(1450)$$ and $$D_{(s)} \rightarrow K_{1B}$$ , compared to other theoretical calculations. The predicted branching ratios for the semi-leptonic decays $$D\rightarrow P(V)\ell \nu _\ell $$ with $$\ell =e,\mu $$ agree well with experimental data and other theoretical results in most decay channels, validating the reliability of the model. However, for some $$D\rightarrow S(V)\ell \nu _\ell $$ decays, tension exists among different theoretical predictions and experimental results. Further clarification of such differences is necessary. Our study provides important insights into the internal structures for some scalar and axial-vector mesons and serves as a theoretical reference for future experiments.

Hao Yang

Shao-Qin Guo

Zhi-Qing Zhang

Systematic analysis of $$D_{(s)}$$ meson semi-leptonic decays in the covariant light-front quark model

In the experiment to study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>n</mi><mover accent="true"><mi>n</mi><mo stretchy="false">¯</mo></mover></math> process at the VEPP-2000 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> collider, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>G</mi><mi>E</mi></msub><mo stretchy="false">|</mo><mo>/</mo><mo stretchy="false">|</mo><msub><mi>G</mi><mi>M</mi></msub><mo stretchy="false">|</mo></math> of the neutron timelike electric and magnetic form factors has been measured. The experiment was carried out with the SND detector in the center-of-mass energy range 1890–2000 MeV in eight energy points with an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>83</mn><mtext> </mtext><mtext> </mtext><msup><mi>pb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>G</mi><mi>E</mi></msub><mo stretchy="false">|</mo><mo>/</mo><mo stretchy="false">|</mo><msub><mi>G</mi><mi>M</mi></msub><mo stretchy="false">|</mo></math> ratio is determined by the analyzing the distribution of the polar angle of the produced antineutron. The measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>G</mi><mi>E</mi></msub><mo stretchy="false">|</mo><mo>/</mo><mo stretchy="false">|</mo><msub><mi>G</mi><mi>M</mi></msub><mo stretchy="false">|</mo></math> value in the energy range under study is between 1.0 and 1.5 with an average value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.21</mn><mo>±</mo><mn>0.13</mn></math>.

M.N. Achasov

A.E. Alizzi

A. Yu. Barnyakov

E.V. Bedarev

K.I. Beloborodov

A.V. Berdyugin

A.G. Bogdanchikov

A.A. Botov

T.V. Dimova

V.P. Druzhinin

R.A. Efremov

V.N. Zhabin

V.V. Zhulanov

P.V. Zhulanova

L.V. Kardapoltsev

A.S. Kasaev

A.A. Kattsin

D.P. Kovrizhin

I.A. Koop

A.A. Korol

A.S. Kupich

A.P. Kryukov

N.A. Melnikova

N. Yu. Muchnoi

A.E. Obrazovsky

A.A. Oorzhak

I.V. Ovtin

E.V. Pakhtusova

I.A. Polomoshnov

K.V. Pugachev

S.A. Rastigeev

Yu. A. Rogovsky

A.I. Senchenko

S.I. Serednyakov

Z.K. Silagadze

K.D. Sungurov

I.K. Surin

Yu. V. Usov

A.G. Kharlamov

D.E. Chistyakov

D.A. Shtol

Measurement of the neutron timelike electric and magnetic form factor ratio at the VEPP-2000 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> collider

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>10087</mn><mo>±</mo><mn>44</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> events collected with the BESIII detector, we present a study of resonant structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>γ</mi></math> processes, reporting the first observation of the electromagnetic radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup></math>, with a statistical significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>16.6</mn><mi>σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>23.2</mn><mi>σ</mi></math>, respectively. The ratio of the branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">{</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="normal">Λ</mi><mo stretchy="false">]</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo><mo stretchy="false">}</mo></mrow></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.19</mn><mo>±</mo><mn>0.34</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.19</mn><mo stretchy="false">(</mo><mrow><mi>syst</mi></mrow><mo stretchy="false">)</mo></mrow></math>, which is in agreement with flavor SU(3) symmetry within two standard deviations. The branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><mn>2.66</mn><mo>±</mo><mn>0.28</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.50</mn><mo stretchy="false">(</mo><mrow><mi>syst</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, corresponding to a partial width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><mn>46.8</mn><mo>±</mo><mn>6.6</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>9.3</mn><mo stretchy="false">(</mo><mrow><mi>syst</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>keV</mi></mrow></math>, which is inconsistent with predictions from the relativized constituent quark model and the Algebraic model. Additionally, we observe a clear resonant structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup></math> mass spectrum near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.7</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math>. The product branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">]</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo></mrow></math> is measured for the first time as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">[</mo><mn>6.05</mn><mo>±</mo><mn>0.42</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.39</mn><mo stretchy="false">(</mo><mrow><mi>syst</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>. However, no corresponding structure is seen in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi mathvariant="normal">Λ</mi></math> mass spectrum, so an upper limit on the product branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">]</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="normal">Λ</mi><mo stretchy="false">]</mo></mrow></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.08</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> at the 90% confidence level.

M. Ablikim

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

V. Batozskaya

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Observation of the Electromagnetic Radiative Decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></mrow></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math>

We study the nonrelativistic (NR) limit of Hohm-Siegel-Zwiebach (HSZ) theory, a higher-derivative theory of gravity with exact and manifest T-duality invariance. Since the theory can be formulated using the generalized metric formalism, the HSZ Lagrangian remains convergent to all orders in derivatives when taking the NR limit. In this work, we analyze the three-derivative corrections to the symmetry transformations of the fields in the NR case, as well as the terms in the four-derivative action depending on the b field. Interestingly, the corrections to the metric degrees of freedom cannot be fully trivialized, as in the relativistic case, in order to preserve the convergence of the theory. As HSZ theory interpolates order by order between heterotic and bosonic string theories, the results of this work can be interpreted as a truncation of the four-derivative structure of heterotic supergravity in the NR limit.

Eric Lescano

Nonrelativistic limit of Hohm-Siegel-Zwiebach theory

Based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></mrow></math> events collected with the BESIII detector, we present a high-precision study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass spectrum in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays. A clear resonancelike structure is observed near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass threshold for the first time. A fit with a Breit-Wigner function yields a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>285.6</mn><mo>±</mo><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and a width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>16.3</mn><mo>±</mo><mn>0.9</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> with a statistical significance exceeding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>10</mn><mi>σ</mi></mrow></math>. To interpret the data, we incorporate final-state interactions (FSI) within two theoretical frameworks: chiral perturbation theory (ChPT) and QCD multipole expansion (QCDME). ChPT describes the spectrum above <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> but fails to reproduce the threshold enhancement. In contrast, the QCDME model—assuming the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> is an admixture of S- and D-wave charmonium—reproduces the data well. The pronounced dip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> offers new insight into the interplay between chiral dynamics and low-energy QCD.

M.B. Bertani

T.T. Chang

J.C. Cheng

L.N. Cheng

X.C. Dai

I. Denisenko

X.L. Du

Z.H. Duan

Y.T. Feng

M. Fritsch

Observation of a Threshold Enhancement in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> Spectrum in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Decays