Motivated by the recent near-threshold enhancement in top-quark pair production reported by CMS and ATLAS, we study the $\textit{S}$-wave spectral structure of heavy-light systems containing a single top quark, namely $ t\bar{q} $ , $ t\bar{c} $ , and $ t\bar{b} $ , within the instantaneous Bethe-Salpeter formalism. Because the top quark decays on a timescale much shorter than the typical hadronization time, the discrete eigenvalues we obtain should be interpreted as model-dependent reference positions of possible quasi-bound heavy-light configurations, rather than as predictions for fully formed conventional hadrons. The numerical results indicate that the masses of these configurations lie close to the top-quark mass. For the $ t\bar{b} $ system, the masses of the first four $\textit{S}$-wave $ 0^{-} $ radial states are about $ 5.1 $ , $ 5.4 $ , $ 5.6 $ , and $ 5.7 $ GeV above the top-quark mass, respectively. For the $ t\bar{c} $ system, the corresponding values are about $ 1.9 $ , $ 2.2 $ , $ 2.5 $ , and $ 2.6 $ GeV. We also briefly discuss possible production and decay patterns at a qualitative level, which may serve as a reference for future dedicated phenomenological studies or for experimental constraints.

China

Jun-Hao Zhang

Shuo Yang

Bing-Dong Wan

The $\textit{S}$-wave topped meson * Supported in part by the National Natural Science Foundation of China (12575106, 12147214), and the Specific Fund of Fundamental Scientific Research Operating Expenses for Undergraduate Universities in Liaoning Province (LJ212410165019)

We analyze the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>P</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>D</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>S</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext> </mtext><mtext> </mtext><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>D</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>S</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext> </mtext><mtext> </mtext><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></mrow></math> charmed baryons, belonging to the flavor antitriplet (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mn mathvariant="bold">3</mn><mo stretchy="false">¯</mo></mover><mi mathvariant="normal">F</mi></msub></math>), using the constituent quark model. We compute electromagnetic transitions from ground and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave states to ground states, as well as from second-shell states to both ground and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave final states. Electromagnetic decay widths are especially valuable for identifying resonances when multiple states share similar mass and total decay width. We give branching ratios of several electromagnetic decay widths that can confirm the assignment of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3055</mn><mo stretchy="false">)</mo></math> reported by LHCb. Likewise, we provide branching-ratio predictions that can help guide the assignment of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3080</mn><mo stretchy="false">)</mo></math> states, and discuss their possible interpretation either as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>D</mi></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="bold">J</mi><mi mathvariant="bold">P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> or as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="bold">J</mi><mi mathvariant="bold">P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math>. For the first time, this work provides calculations of electromagnetic decays for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>ρ</mi></msub></math>-wave states, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>−</mo><mi>λ</mi></math> mixed configurations, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode radially excited states in singly charmed baryons of the flavor antitriplet. Both experimental and model-dependent uncertainties are taken into account throughout our analysis.

Mexico

R. Gamboa-Goni

H. García-Tecocoatzi

Italy

Ailier Rivero-Acosta

A. Gutierrez-Rodriguez

A. Ramirez-Morales

E. Santopinto

Carlos Alberto Vaquera-Araujo

Radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>P</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>D</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>S</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext> </mtext><mtext> </mtext><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mi>D</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>S</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext> </mtext><mtext> </mtext><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></mrow></math> charmed baryons

Using a dataset of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.33</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <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></math> annihilation data collected with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report an updated measurement of the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math> via four <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>τ</mi><mo>+</mo></msup></math> decay modes: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>τ</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>. The branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mrow><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></mrow><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>5.37</mn><mo>±</mo><mn>0.0</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mn>6</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>. The product of the modulus of the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> decay constant <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></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></msub><mo stretchy="false">|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mo stretchy="false">(</mo><mn>248.2</mn><mo>±</mo><msub><mrow><mn>1.9</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>1.4</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo>±</mo><msub><mrow><mn>0.6</mn></mrow><mrow><mtext>input</mtext></mrow></msub><mo>±</mo><msub><mrow><mn>0.8</mn></mrow><mrow><mi>EM</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. Both the branching fraction and the product <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 stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> are the most precise results yet obtained. Then, taking <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></math> from lattice quantum chromodynamics calculations results in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mn>0.993</mn><mo>±</mo><mn>0.00</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mn>6</mn><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mn>3</mn><mtext>input</mtext></msub><mo>±</mo><mn>0.00</mn><msub><mn>3</mn><mrow><mi>EM</mi></mrow></msub></math>. Conversely, one finds <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><mo stretchy="false">(</mo><mn>255.0</mn><mo>±</mo><msub><mn>1.9</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mn>1.4</mn><mrow><mi>syst</mi></mrow></msub><mo>±</mo><msub><mn>0.6</mn><mtext>input</mtext></msub><mo>±</mo><msub><mn>0.8</mn><mrow><mi>EM</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> when taking <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> from the CKMfitter group as an input. Combining with the world average value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math>, the ratio of the branching fractions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> is estimated to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>10.04</mn><mo>±</mo><mn>0.29</mn></math>, which is consistent with the Standard Model prediction of lepton flavor universality.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

C.S. Akondi

Germany

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

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

Chao 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

South Korea

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

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. 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

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

Updated measurement of the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math>

This paper proposes a novel mechanism based on the instantaneous Bethe-Salpeter (Salpeter) equation for investigating wave function mixing in vector mesons such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>. Conventional theories typically treat <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi><mo>−</mo><mn>1</mn><mi>D</mi></math> mixed state; however, considering only tensor forces or relativistic corrections alone often leads to mixing angles that are too small and inconsistent with experimental data. Phenomenological <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi><mo>−</mo><mn>1</mn><mi>D</mi></math> mixing requires experimental data as input to determine the mixing angles, resulting in limited theoretical studies on states like <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo>,</mo><mn>2</mn><mi>D</mi><mo stretchy="false">)</mo></math> in the absence of experimental data. To more accurately describe <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>−</mo><mi>D</mi></math> mixing and its relativistic effects, this paper systematically compares four relativistic wave function representations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>φ</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>φ</mi><mn>2</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>φ</mi><mn>3</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>φ</mi><mn>4</mn></msub></math>) by solving the Salpeter equation and calculates the mass spectra and dileptonic decay widths of charmonium and bottomonium. The study finds that the wave function representation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>φ</mi><mn>2</mn></msub></math> can simultaneously reproduce the experimental data of both charmonium and bottomonium well. Further analysis reveals that, in addition to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>−</mo><mi>D</mi></math> mixing, the wave functions of vector mesons contain a non-negligible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave component, meaning they are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>−</mo><mi>P</mi><mo>−</mo><mi>D</mi></math> mixed states. We predict the mixing angles for bottomonium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>D</mi><mo stretchy="false">)</mo></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1.7</mn><msubsup><mrow><mn>8</mn></mrow><mrow><mo>−</mo><mn>0.25</mn></mrow><mrow><mo>+</mo><mn>0.32</mn></mrow></msubsup><mo stretchy="false">)</mo><mi>°</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>5.4</mn><msubsup><mn>4</mn><mrow><mo>−</mo><mn>0.76</mn></mrow><mrow><mo>+</mo><mn>1.10</mn></mrow></msubsup><mo stretchy="false">)</mo><mi>°</mi></math>, with dileptonic decay widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2.29</mn><mrow><mo>−</mo><mn>0.69</mn></mrow><mrow><mo>+</mo><mn>0.86</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>10.5</mn><mrow><mo>−</mo><mn>3.1</mn></mrow><mrow><mo>+</mo><mn>4.2</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, respectively.

Wen-Yuan Ke

Qiang Li

Tianhong Wang

Tai-Fu Feng

Guo-Li Wang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>−</mo><mi>P</mi><mo>−</mo><mi>D</mi></math> mixing in vector quarkonia from the Salpeter equation with optimized wave function representations

In the present work, we investigate the molecular properties of the hidden charm pentaquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></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></math> with a coupled-channel framework that combines heavy quark spin symmetry and the local hidden gauge formalism. By solving the Bethe-Salpeter equation with the cutoff method, we obtain the pole trajectories, wave functions, and root-mean-square radii. For the hidden charm system, the full coupled-channel interactions respecting the heavy quark spin symmetry are essential to generate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></math> states, which significantly affect the poles’ widths. The dominant bound channels are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub></math>, which couple strongly to the lower decay channels. In contrast, for the hidden charm strange system, the full heavy quark spin symmetry treatment is not necessary, where the splitting pseudoscalar meson-baryon (PB) and vector meson-baryon (VB) sectors yield similar results. The main bound channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> couple strongly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math>, respectively, but weakly to the lower decay channels, different from the hidden charm case. The trajectories of the pole widths for the loosely bound channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup></math> exhibit distinct behaviors. Notably, all the primary bound channels have similar binding energies in the single-channel interactions due to equally attractive potentials. Furthermore, we also calculate the wave functions and root-mean-square radii of the corresponding poles. The wave functions are localized within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn><mo>∼</mo><mn>6</mn><mtext> </mtext><mi>fm</mi></mrow></math> and vanish fast beyond 4 fm. The root-mean-square radii, evaluated by two consistent methods, typically lie between 0.5 and 2 fm, comparable to the characteristic scale of molecular states. The root-mean-square radii depend on the pole trajectories and differ among the full coupled-channel case, the split PB and VB sectors, and the single-channel interactions.

Jing-Zhi Cao

Huan-Yu Wei

Jiao-Xue Yang

Jian Sun

Chu-Wen Xiao

Study of the molecular properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></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></math> states

We investigate the elliptic-flow splitting between prompt <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> mesons within a heavy-quark transport framework with sequential hadronization, in which <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> forms at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.2</mn><mspace width="0.16em"></mspace><msub><mi>T</mi><mi>c</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>c</mi></msub></math>. We present model calculations for the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>-differential <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> yield ratio in O-O <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mo>–</mo><mspace width="0.16em"></mspace><mn>20</mn><mo>%</mo></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msup><mi>D</mi><mn>0</mn></msup><mo>)</mo></mrow><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>)</mo></mrow></mrow></math> ordering and predicts an enhanced <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> ratio at low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> ordering is driven by the late-stage flow accumulated by <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math>-parent charm quarks during the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.2</mn><mspace width="0.16em"></mspace><msub><mi>T</mi><mi>c</mi></msub><mo>→</mo><msub><mi>T</mi><mi>c</mi></msub></mrow></math> interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O-O and Pb-Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><mo>–</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></mrow></math> flow splitting as a hadronization chronometer of the QGP at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV.

Hui Du

Xiao-Wei Hao

Wei Dai

Jiaxing Zhao

Ben-Wei Zhang

Enke Wang

System-size dependence of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><mtext>−</mtext><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></mrow></math> flow splitting from early <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> formation at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV

Although heavy-quark symmetry implies a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> molecular partner of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>1</mn></msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> molecule, no such state has been observed experimentally to date. In this work, we propose that the experimentally observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math> may be a candidate for such a molecular state, although it may also contain a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> component. To explore whether the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math> can be interpreted as an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>–</mi><msub><mi>B</mi><mn>1</mn></msub><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> molecule, we calculate its strong decay widths within this molecular scenario using the compositeness condition and effective Lagrangians. The coupling of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math> to its constituents <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> is determined by fitting the available experimental data on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub><mi>π</mi><mi>π</mi><mi>π</mi></math> decays. With the extracted coupling, we compute the partial decay widths of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math> into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mi>n</mi><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mi>n</mi><mi>P</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>b</mi><mn>1</mn></mrow></msub></math> via hadronic loops, as well as the three-body <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>π</mi><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> decays via tree-level diagrams. Our results suggest that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math> can indeed be interpreted as an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>–</mi><msub><mi>B</mi><mn>1</mn></msub><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> molecule with a dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>1</mn></msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> component, whose main decay channel is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math>. Moreover, the partial widths for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mi>n</mi><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mi>n</mi><mi>P</mi><mo stretchy="false">)</mo></math> are found to be only a few eV. In contrast, the widths for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></math> are considerably larger, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>b</mi><mn>1</mn></mrow></msub></math> reaching up to 0.167 MeV, while the yet-unobserved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> channel could be as large as 0.754 keV. These distinctive decay patterns could serve as experimental signatures of the molecular nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></math>, and their confirmation would provide a test of the applicability of heavy-quark symmetry.

Qing Lu

Cai Cheng

Yin Huang

Interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>11020</mn><mo stretchy="false">)</mo></mrow></math> as an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mn>1</mn></msub><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>−</mo><msub><mrow><mi>B</mi></mrow><mn>1</mn></msub><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> gauge symmetry under which one right-handed neutrinolike Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> doublet, while a discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector that can contain a potential dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.

P.S. Bhupal Dev

Julia Gehrlein

Japan

Amartya Sengupta

Amarjit Soni

Minimal dark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> origin of a massless Dirac neutrino

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>

Nucleon-nucleon systems in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channels are studied in lattice quantum chromodynamics at a pion mass of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>292</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, employing three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> ensembles with the same pion mass and lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.10530</mn><mo stretchy="false">(</mo><mn>18</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> but different spatial volumes. Finite-volume energies of the nucleon-nucleon systems are determined in both the rest frame and a moving frame. The distillation quark smearing method is applied to improve the precision and to ensure the symmetric correlators by using the same interpolating operators at sink and source. The scattering amplitudes are extracted from the finite-volume spectra using the Lüscher’s finite-volume method. At the studied pion mass, both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> (deuteron) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> (dineutron) channels exhibit a virtual state pole, with binding energies of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>6</mn><mrow><mo>−</mo><mn>3</mn></mrow><mrow><mo>+</mo><mn>5</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>11</mn><mrow><mo>−</mo><mn>5</mn></mrow><mrow><mo>+</mo><mn>6</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, respectively. To investigate the effects of the left-hand cut, an alternative method—the nonperturbative Hamiltonian framework—is used for the scattering analysis and yields consistent results with those from the Lüscher method.

Kuan Zhang

Kang Yu

Yiqi Geng

Chuan Liu

Liuming Liu

Peng Sun

Jia-Jun Wu

Ruilin Zhu

Two-nucleon systems at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>292</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> from lattice QCD