We compute next-to-leading power corrections in the zero-jettiness variable for the production of colorless final states at hadron colliders at next-to-leading order in QCD. To assess if the process-independence of leading power contributions can be extended, we attempt to construct generic expansions of phase spaces and matrix elements squared through next-to-leading power in the zero-jettiness. We highlight challenges associated with the collinear limit, where universality no longer holds at the subleading power, making the result process-dependent. We show that quantities that need to be calculated in the collinear limit can be obtained using Berends-Giele currents, enabling computation of power corrections to high-multiplicity final states. As a concrete example, we apply our method to compute power corrections in the zero-jettiness for lepton pair as well as multi-photon production in $$ q\overline{q} $$ collisions.

Germany

Prem Agarwal

Kirill Melnikov

Ivan Pedron

Philip Pfohl

Power corrections to the production of a color-singlet final state in hadron collisions in the $\textit{N}$-jettiness slicing scheme at NLO QCD

In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position 〈$\textit{n}$〉 defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments 〈$\textit{n}$ 〉 for $\textit{p >}$ 1, provide finer insights into the dynamics. We investigate the time evolution of generalized spread complexities following a quantum quench in random matrix theory. The quench is implemented by transitioning from an initial random Hamiltonian to a post-quench Hamiltonian obtained by dividing it into four blocks and flipping the sign of the off-diagonal blocks. This setup captures universal features of chaotic quantum quenches. When the initial state is the thermofield double state of the post-quench Hamiltonian, a peak in spread complexity preceding equilibration signals level repulsion, a hallmark of quantum chaos. We examine the robustness of this peak for other initial states, such as the ground state or the thermofield double state of the pre-quench Hamiltonian. To quantify this behavior, we introduce a measure based on the peak height relative to the late-time saturation value. In the continuous limit, higher-order complexities show increased sensitivity to the peak, supported by numerical simulations for finite-size random matrices.

South Korea

Hugo Camargo

Yichao Fu

Viktor Jahnke

Keun-Young Kim

Kuntal Pal

Higher-order Krylov state complexity in random matrix quenches

In relativistic heavy-ion collisions, charged particles are accelerated to nearly the speed of light, and their external electromagnetic fields can be effectively approximated as quasireal photons. These photons interact with another nucleus via photon-nuclear interactions, producing vector mesons. These vector mesons possess extremely low transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi>T</mi></msub><mo>∼</mo><mn>0.1</mn><mspace width="0.16em"></mspace><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></math>), distinguishing them from particles produced via hadronic interactions. STAR and ALICE have observed <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>ρ</mi><mn>0</mn></msup></math> and other vector mesons with very low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, which are well described by photoproduction models. This unique characteristic of having extremely low transverse momentum allows them to serve as a novel experimental probe. Recent STAR results show that the equivalent photons in photoproduction processes are fully linearly polarized, affecting the azimuthal distribution of final-state particles like <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>ρ</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></mrow></math>. Since the polarization links to the initial collision geometry, the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>ρ</mi><mn>0</mn></msup></math> azimuthal modulation can probe nuclear structure. However, the post-collision magnetic field may deflect these particles, distorting the azimuthal distribution and complicating structure measurements. We simulated the distribution of residual magnetic fields over time under different collision conditions using ultrarelativistic quantum molecular dynamics for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV and calculated their effects on the azimuthal modulation (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><mo form="prefix">cos</mo><mn>2</mn><mi>ϕ</mi><mo>〉</mo></mrow></math>) of photoproduced <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>ρ</mi><mn>0</mn></msup></math>. Our results show that in peripheral collisions, the field significantly alters the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><mo form="prefix">cos</mo><mn>2</mn><mi>ϕ</mi><mo>〉</mo></mrow></math> for photoproduced <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>ρ</mi><mn>0</mn></msup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi>T</mi></msub><mo>≈</mo><mspace width="0.16em"></mspace><mn>0.1</mn></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></math>. This provides key insights for future nuclear structure studies via photoproduction in peripheral collisions.

China

Zhan Zhang

Xin Wu

Xinbai Li

Wangmei Zha

Zebo Tang

Influence of the residual magnetic field on the azimuthal distribution of final-state particles in photonuclear processes

The discovery of numerous new hadrons over the past two decades has provided unprecedented opportunities to understand the nonperturbative QCD and hadron structure. The hadronic molecule picture plays an important role in explaining these new hadrons and enriching the configurations of exotic hadronic states. In this Letter, using the model-independent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> potential extracted from the relevant experimental data, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> <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><mi>D</mi><mi>K</mi></math> three-body hadronic molecule is predicted with a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mn>4310</mn></mrow><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>14</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. This state shows decoupling to conventional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> charmonia or the <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><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> two-body molecular state. It can be regarded as a compelling three-body hadronic molecular candidate. We further demonstrate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>±</mo></mrow></msup><msup><mi>D</mi><mo>∓</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> decays could be promising channels for searching for the predicted state in future high-luminosity LHCb runs.

Tian-Wei Wu

Ming-Zhu Liu

Li-Sheng Geng

Implication of the Existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><mtext> </mtext><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><mi>D</mi><mi>K</mi></mrow></math> Bound State on the Nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></mrow></math>, and a New Configuration of Exotic State

Motivated by the updated analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> by the BESIII Collaboration, we perform a global analysis of the cross sections of the <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><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>, <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><mo stretchy="false">→</mo><mi>D</mi><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math>, <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><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> processes, especially focusing on the properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>. As the energy region of interest is limited by the next opening threshold, i.e., 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> threshold, we focus on the energy region [3.7, 4.25] GeV, where three charmonia <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>D</mi><mo stretchy="false">)</mo></math> explicitly contribute to the cross sections. By constructing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave contact interaction between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>D</mi><mo>,</mo><msup><mi>D</mi><mo>*</mo></msup><mo stretchy="false">)</mo></math> doublet and its antiparticle in the heavy quark limit, we extract the physical scattering amplitude by solving the Lippmann-Schwinger equation. No matter whether three or two charmonium states are included in our framework, we always find a dynamically generated state corresponding to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, which suggests it to be a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave dynamically generated state. We also predict several dynamically generated states in the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> channel. These states can be further searched for in the electron-positron annihilation process involving the emission of a single photon.

Quanxing Ye

Zhenyu Zhang

Meng-Lin Du

Ulf-G. Meißner

Peng-Yu Niu

Japan

Qian Wang

Resonance parameters of the vector charmoniumlike state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>

J-PARC E05 reported recently a hint of a <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>11</mn></mrow></msup><mi mathvariant='normal'>B</mi></math> nuclear state in the <math altimg='si17.svg'><mmultiscripts><mrow><mi mathvariant='normal'>C</mi></mrow><mprescripts /><none /><mrow><mn>12</mn></mrow></mmultiscripts><msubsup><mrow><mo stretchy='false'>(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mo>,</mo><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mo stretchy='false'>)</mo></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>12</mn></mrow></msubsup><mrow><mi mathvariant='normal'>Be</mi></mrow></math> spectrum, bound by <math altimg='si3.svg'><msub><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>8.9</mn><mo>&#177;</mo><msubsup><mrow><mn>1.4</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>3.1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>3.8</mn></mrow></msubsup></math> MeV. Using a density-dependent &#926;-nuclear optical potential <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math> we explore to what extent a <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> assignment of this nuclear state is compatible with <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> and <math altimg='si6.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>p</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> nuclear-state interpretations of <math altimg='si7.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></math> capture events in light emulsion-nuclei experiments. We find that the only acceptable <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> assignment at present, barring an abnormally strong repulsive <math altimg='si8.svg'><msup><mrow><mi>&#961;</mi></mrow><mrow><mn>2</mn></mrow></msup></math> component of <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math>, is that for the <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>11</mn></mrow></msup><mi mathvariant='normal'>B</mi></math> signal. This finding supports reassigning <math altimg='si7.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></math> capture events in 14N, originally assigned as <math altimg='si9.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>14</mn></mrow></msup><mi mathvariant='normal'>N</mi></math> nuclear states, to <math altimg='si10.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>14</mn></mrow></msup><mi mathvariant='normal'>C</mi></math> nuclear states. The depth of <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math> at nuclear-matter density <math altimg='si11.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mn>0</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.17</mn></math> fm &#8722;3 is then <math altimg='si12.svg'><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><msub><mrow><mi>&#961;</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy='false'>)</mo><mo>&#8776;</mo><mn>21</mn></math> MeV.

Israel

E. Friedman

A. Gal

Compatibility of recent Ξ-nuclear bound state signals

In this letter, we present the intrinsic state formalism of the Interacting Boson-Fermion Model incorporating both 0p-0h and 2p-2h (regular and intruder) configurations. The framework allows to deal with the unpaired fermion in either a single-j or multi-j orbital and is applicable to both axial and triaxial nuclear shapes. The formalism is applied to a schematic transitional region where regular and intruder configurations coexist and cross. We show that the boson-fermion part of the Hamiltonian can either enhance or suppress the emergence of a type II Quantum Phase Transition.

Spain

Esperanza Maya-Barbecho

José-Enrique García-Ramos

An intrinsic-state formalism for the Interacting Boson-Fermion Model with configuration mixing

This study examines the black hole developed from multi-polytropic equations of state by investigating particle dynamics and various related properties, such as the radius of the horizon, the effective force, the innermost stable circular orbit radius, the photon radius, quasi-periodic oscillations, and the weak plasma lensing in uniform plasma fields, singular isothermal sphere (SIS), and non-singular isothermal gas sphere (NSIS). Furthermore, we examine the image magnification for the black hole solution. An important parameter in this black hole solution is $$c_1$$ , which significantly impacts the results. Our study shows that particle dynamics features and deflection of light are affected by the black hole parameter.

Azerbaijan

Pakistan

Allah Ditta

Farzan Mushtaq

Thailand

Phongpichit Channuie

Saudi Arabia

Awad Ibraheem

Asifa Ashraf

India

Rana Zulqarnain

Studying the properties of particle motion and plasma lensing in regular black holes from multi-polytropic equations of state

We systematically discuss the decay patterns of the hidden-strange hadronic molecular state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mo>(</mo><mn>2270</mn><mo>)</mo></mrow></math> which is assumed to be an <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></mrow></math> shallow bound state with possible quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mi>P</mi></msup></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup><mo>,</mo><mo> </mo><msup><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></math>. By using the effective Lagrangian approach and considering pseudoscalar meson and vector meson exchanges, we thoroughly calculate and discuss the decay behavior of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mo>(</mo><mn>2270</mn><mo>)</mo></mrow></math> molecular state, including hadronic and radiative decay and the cutoff dependence, for different <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mi>P</mi></msup></math> values. For all three cases, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><mi mathvariant="normal">Λ</mi></mrow></math> final state is always included as the main decay channel. However, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>K</mi><mi mathvariant="normal">Σ</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>K</mi><mi mathvariant="normal">Λ</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>K</mi><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi mathvariant="normal">Δ</mi></mrow></math> final states exhibit notable differences. These different decay properties will provide valuable guidance for future experimental searches and aid in distinguishing different <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mi>P</mi></msup></math> assumptions and understanding their internal structures.

Di Ben

Shu-Ming Wu

Decay behavior of hidden-strange hadronic molecular state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mo>(</mo><mn>2270</mn><mo>)</mo></mrow></math>

We study the direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries in the decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>, emphasizing the critical role of final-state interactions (FSIs). In these channels, the small energy release and annihilation topology suppress short-distance contributions while enhancing long-distance effects. By separating the decay amplitudes into S and P waves, we show that the P-wave component, carrying only a single weak phase, contributes negligibly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries. In contrast, the S-wave amplitude—strongly modified by FSIs—acquires a substantial strong phase that enables interference among multiple weak phases, producing large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating effects. Numerically, we find sizable asymmetries of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>dir</mi></msubsup><mo>=</mo><mn>0.88</mn><mo>±</mo><mn>0.05</mn><mo>±</mo><mn>0.10</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>dir</mi></msubsup><mo>=</mo><mo>−</mo><mn>0.106</mn><mo>±</mo><mn>0.019</mn><mo>±</mo><mn>0.010</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>, where the first and second uncertainties stem from the poorly known hadron couplings and the omission of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> rescattering process. For practical feasibility, we restrict our analysis to intermediate states involving pseudoscalar mesons, which yield tractable loop integrals. Excited intermediate states, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math>, are omitted because their inclusion would require handling nonrenormalizable interactions, introducing substantial ambiguity. These results, combined with the relatively large branching fractions, make these modes prime targets for experimental searches at LHCb and Belle II, potentially offering new insights into strong dynamics and nonperturbative QCD in heavy-hadron decays.

Chao-Qiang Geng

Xiang-Nan Jin

Chia-Wei Liu

Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries from final-state interactions in charmful baryonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>