We present a theoretical analysis of the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> within the chiral unitary approach, with particular emphasis on the dynamically generated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> resonance. In addition to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math>, our model incorporates contributions from other intermediate resonances including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1650</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1440</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1750</mn><mo stretchy="false">)</mo></math>. The calculated invariant mass distributions and Dalitz plot are in good agreement with the recent Belle measurements. Our analysis highlights the crucial role of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> state in this decay channel and supports its interpretation as a dynamically generated state arising from coupled-channel meson-baryon interactions.

China

Ying Li

En Wang

Li-Sheng Geng

Ju-Jun Xie

Dynamically generated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> state in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> decay

The fundamental theorem in renormalization group flows in two dimensions is the $\textit{c}$-theorem, which dictates that the number of degrees of freedom must decrease monotonically along the renormalization group flow. The $\textit{k}$-theorem claims that the number of charged degrees of freedom also decreases monotonically. Here, $\textit{k}$ is the current central charge defined by the two-point function of the current. A recent derivation of the c-theorem by Hartman and Mathys, which uses the three-point function sum rule and the positivity of the averaged null energy (ANE) operator, motivates us to seek a similar proof of the $\textit{k}$-theorem. In the case of the $\textit{k}$-theorem, the partial contact terms need to be taken into consideration. While ignoring the partial contact terms yields contradictory results, our careful analysis incorporating them leads to the correct sum rule and a complete proof based on the positivity of the ANE operator.

Japan

Nanami Nakamura

Yu Nakayama

Ung Nguyen

Revisiting the $\textit{k}$-theorem with the ANEC

We attempt to describe the moduli space of boundary states in the SU(2) WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to marginal deformations, our solutions exhibit a $\textit{g}$-function different from that of the background (typically lower). Thus, our method effectively combines features of both marginal and relevant deformations. After partially fixing an SU(2) symmetry of the equations of motion, we find families of solutions parameterized by the coefficient of the marginal field associated with the $\textit{J}$ current, and we identify them as Cardy boundary states with varying angle $\textit{θ}$. However, it turns out that these solutions become inconsistent once the marginal parameter exceeds a certain value, implying that they cover only a part of the moduli space. Finally, we also compare the relation between the marginal parameter and the angle $\textit{θ}$ for different solutions and we find evidence suggesting that this relation is universal for certain classes of solutions.

Czechia

Matěj Kudrna

Marginal deformations of SU(2) $\textit{k}$ WZW model boundary states in open string field theory

We utilize the universality of pion-pion (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>) final-state interactions at small invariant masses to understand the enhanced localized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, using a dispersive approach. From a fit to the integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> region, including the large localized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation enhanced by final-state interactions.

Germany

L.A. Heuser

Spain

A. Reyes-Torrecilla

C. Hanhart

B. Kubis

Brazil

P.C. Magalhães

T. Mannel

J.R. Peláez

Understanding Large Localized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> Using Dispersive Methods

Motivated by systematic observations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decays at LHCb, we analyze <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>T</mi><mo stretchy="false">)</mo></math> decays [where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> denotes axial-vector mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1260</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> denotes tensor mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1320</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>] within the perturbative QCD (pQCD) factorization framework. The framework employs light-cone distribution amplitudes to regulate nonperturbative dynamics, utilizing Sudakov suppression to control endpoint divergences. Our predictions indicate branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>T</mi></math> decays, which seem to be in the reach of future experiments. We also provide predictions for the polarization fractions of these decays. Based on quark helicity analysis, the longitudinal polarization amplitudes are expected to dominate the branching ratios.

Yun Zhao

Xian-Qiao Yu

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1260</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1235</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1320</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> decays with a perturbative QCD approach

We develop a general canonical quantization scheme for $\textit{k}$-essence cosmology in scalar–tensor theory. Utilizing the Dirac–Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the first- and second-class constraints. The introduction of appropriate canonically conjugate variables with respect to Dirac brackets, allows for the canonical quantization of the model. In these new variables, the Hamiltonian constraint reduces to a quadratic function with no potential term. Its quantum realization leads to a Wheeler–DeWitt equation reminiscent of the massless Klein–Gordon case. As an illustrative example, we consider the action of a tachyonic field and investigate the conditions under which a phantom crossing can occur as a quantum tunneling effect. For the simplified constant potential case, we investigate the consequences of different boundary conditions on the singularity avoidance and to the mean expansion rate.

Chile

Andrés Lueiza Colipí

South Africa

Andronikos Paliathanasis

Nikolaos Dimakis

Dirac–Bergmann algorithm and canonical quantization of $\textit{k}$-essence cosmology

Studying heavy-quark hadrons is crucial due to the nonperturbative nature of low-energy QCD, with Heavy-Quark Symmetry (HQS) serving as a key framework for understanding their spin and flavor symmetries. However, a key issue is that the theoretically expected $$B^{(*)}\bar{K}$$ molecular states have not yet been observed, although they are considered the bottom-quark counterparts of the observed $$\bar{D}^{(*)}\bar{K}$$ molecular states (corresponding to $$D_{s0}(2317/2460)^{-}$$ ), which challenges the universality of HQS. The main goal of this work is to search for the theoretically predicted $$B\bar{K}$$ and $$B^{*}\bar{K}$$ molecular states, namely $$B_{s0}^{*}(5725)$$ and $$B_{s1}^{*}(5778)$$ , via the reactions $$K^{-}p \rightarrow \varLambda _{b}^{0} B_{s0}^{*}$$ and $$K^{-}p \rightarrow \varLambda _{b}^{0} B_{s1}^{*}$$ . Within an effective Lagrangian framework, we compute the relevant cross sections, considering $\textit{t}$-channel $$B^{(*)}$$ exchanges and $$K^{-}p$$ initial-state interactions (ISI). The results show that the production cross sections of $$B_{s0}^{*}(5725)$$ and $$B_{s1}^{*}(5778)$$ can reach the order of 0.01 nb, and we suggest that experiments searching for $$B_{s0}^{*}(5725)$$ are best performed at $$P_{K^{-}} = 12.18~\textrm{GeV}$$ , while higher energies are most favorable for producing $$B_{s1}^{*}(5778)$$ . The ISI play a crucial role, as they not only significantly enhance the production cross sections of $$B_{s0}^{*}(5725)$$ and $$B_{s1}^{*}(5778)$$ (by roughly one order of magnitude) but also markedly affect the angular distributions of the produced particles. We also calculated the production cross sections of the conventional quark–antiquark states $$B_{s0}^*(5700)$$ and $$B_{s1}^*(5720)$$ , which are found to be nearly the same as those of $$B_{s0}^{*}(5725)$$ and $$B_{s1}^{*}(5778)$$ . Although their internal structures remain ambiguous, these results can inform future experimental searches at CERN and J-PARC.

Min Yuan

Yin Huang

A search for $$B_{s0}^{*}$$ and $$B^{*}_{s1}$$ through the $$K^{-}p$$ interaction

In this work, we construct the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> coupled-channel Omn&#232;s matrix, formulated to satisfy unitarity, analyticity, and the appropriate asymptotic behavior. We employ a two-channel <italic>K</italic>-matrix model containing poles associated with the <italic>f</italic> <inf>2</inf>(1270) and <math altimg='si7.svg'><mrow><msubsup><mi>f</mi><mrow><mn>2</mn></mrow><mo>&#8242;</mo></msubsup><mrow><mo>(</mo><mn>1525</mn><mo>)</mo></mrow></mrow></math> resonances. The resulting unitary scattering matrix, which reproduces the experimental <italic>&#960;&#960;</italic>&#8239;&#8594;&#8239; <italic>&#960;&#960;</italic> and <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> data and PDG information, serves as input to the homogeneous two-channel Muskhelishvili-Omn&#232;s equation. We compare our Omn&#232;s matrix with previous constructions based on <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> phases extracted from sums of Breit-Wigner amplitudes. The Omn&#232;s matrix developed here provides a reliable dispersive input for form-factor calculations and resonance studies in the tensor-meson sector. As an application, we show that it enables a simultaneous and accurate description of the BESIII <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic> and <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic> spectra in the <math altimg='si2.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> electric-dipole (E1) partial wave.

Igor Danilkin

Oleksandra Deineka

United States

Emilie Passemar

Marc Vanderhaeghen

Coupled-channel Omnès matrix for the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> system and its application to <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic>,&#8201; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic>

An amplitude analysis of the decay $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$ is performed to determine the relative magnitudes and phases of different intermediate processes. The analysis uses $\textit{e}$ $\textit{e}$ collision data collected at the center-of-mass energy of 3.773 GeV by the BESIII detector corresponding to an integrated luminosity of 20.3 fb . The absolute branching fraction of $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$ is measured to be (1.026 $\textit{±}$ 0.008 $\textit{±}$ 0.009 )%. The dominant intermediate process is $$ {D}^0\to {\overline{K}}^{\ast }{(892)}^0\left(\to {K}_S^0{\pi}^0\right){\pi}^0 $$ , with a branching fraction of (4.10 $\textit{±}$ 0.10 $\textit{±}$ 0.07 ) $\textit{×}$ 10 .

M. Ablikim

Russia

M. Achasov

Sweden

P. Adlarson

X. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R. Briere

A. Brueggemann

H. Cai

M. Cai

X. Cai

A. Calcaterra

G. Cao

N. Cao

Türkiye

S. Cetin

X. Chai

J. Chang

G. Che

Y. Che

C. Chen

Chao Chen

G. Chen

H. Chen

M. Chen

S. Chen

T. Chen

X. Chen

Y. Chen

Z. Chen

J. Cheng

South Korea

S. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J. Cui

H. Dai

J. Dai

A. Dbeyssi

R. Boer

F. Mori

D. Dedovich

C. Deng

Z. Deng

A. Denig

I. Denysenko

M. Destefanis

B. Ding

X. Ding

Y. Ding

J. Dong

L. Dong

M. Dong

X. Dong

M. Du

S. Du

Y. Duan

Z. Duan

P. Egorov

G. Fan

J. Fan

Y. Fan

J. Fang

S. Fang

W. Fang

Y. Fang

L. Fava

F. Feldbauer

G. Felici

C. Feng

J. Feng

L. Feng

Amplitude analysis and branching fraction measurement of the decay $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$

Motivated by the interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></mrow></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state, heavy-quark spin symmetry predicts a spin-2 partner, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math>, which can be regarded as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecule with quantum numbers <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>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. Its experimental confirmation, however, remains elusive. In this work, we investigate the production mechanisms of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in the reactions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> within an effective Lagrangian framework. The production processes are modeled via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>/</mo><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> meson exchanges, while initial-state interactions (ISIs) mediated by Pomeron and Reggeon exchanges are also taken into account. Our calculations indicate that the total cross sections can reach the pb level, suggesting that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> may be accessible at current and future experiments such as AMBER@CERN and LHCb. Inclusion of ISIs enhances the cross sections by nearly 1 order of magnitude. The differential distributions show distinct angular behaviors for the two reactions: the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> reaction exhibits a forward-peaked distribution, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> reaction shows a dip near central angles. This study provides a quantitative theoretical benchmark for future experimental searches of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> and highlights the importance of ISIs in high-energy particle investigations.

Bo Nan Zhang

Search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions