In the present work, the strong decays of the discovered $ P_c(4380) $ , $ P_c(4440) $ , $ P_c(4457) $ and their possible isospin cousins are systematically studied via the assignment that they are meson-baryon molecular states. In detail, the strong decay constants and partial decay widths of their decay channels are calculated under the framework of QCD sum rules. The decay widths of the discovered $ P_c(4380) $ , $ P_c(4440) $ , and $ P_c(4457) $ are in good agreement with the experiments. The predictions of the decays of these three related possible isospin cousins are presented, which would shed light on their findings in experiments. In return, this may testify to the assignments of the discovered $ P_c $ states.

China

Xiu-Wu Wang

Xin Li

Zhi-Gang Wang

Systematic study of the strong decays of the $\textit{P}$ $\textit{c}$ states and their possible isospin cousins via the QCD sum rules * Supported by the National Natural Science Foundation of China (12575083) and the Natural Science Foundation of Hebei Province (A2024502002)

The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This study delves into the examination of $\textit{P}$ and $\rm CP$ symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $ \Omega_c $ . By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $ \Omega_c $ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $ \Omega_c\rightarrow \Omega^-\pi^+ $ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Phenomenological study of Ω $\textit{c}$ → Ω$^{−}$ $\textit{π}$ $^{+}$ at polarized electron-positron collider

Four-dimensional chiral gauge theory can be formulated as the boundary theory on a five-dimensional manifold in a manner that may be realized on a finite lattice. There are interesting features of these theories that defy a purely four-dimensional conception of universality. We find that QCD when embedded in a chiral gauge theory (the Standard Model) and regulated this way can simultaneously avoid both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>A</mi></msub></math> problem and the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem, with a central role played by fermion zero modes localized far away in the fifth dimension. In this way it differs from conventional lattice QCD formulated as a stand-alone theory, universality being violated by inaccessible light modes in the five-dimensional bulk. Our analysis builds on recent work by others that highlights the role of global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetries in five-dimensional formulations of four-dimensional chiral gauge theories, and the generic appearance of fermion zero modes in the bulk.

United States

David B. Kaplan

Srimoyee Sen

Regulated chiral gauge theory and the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem

In this work, to establish a more abundant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> baryon spectrum, we discuss the production potentials of the excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> baryons through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decays within a constituent quark model. Based on our successful explanations of the existing experimental data for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><msup><mi>π</mi><mo>−</mo></msup><mo>,</mo><msup><mi>K</mi><mo>−</mo></msup><mo>,</mo><msup><mi>D</mi><mo>−</mo></msup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><mo stretchy="false">)</mo></math> processes, we further calculate the decay rates of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> baryon into the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>D</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> excited states. It is found that these <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> excitations have large production rates in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decay process associated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup></math> meson emitting, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>*</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math>, their branching fractions can reach up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></math>. To search for the higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> states, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo>,</mo><mn>2</mn><mi>D</mi><mo>,</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math> decays are worth observing in future experiments.

Kai-Lei Wang

Ya-Mei Cao

Hui-Xiao Duan

Xian-Hui Zhong

Production of excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decays

The time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays is measured using proton-proton collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, collected with the LHCb detector at a center-of-mass energy of 13 TeV during the years 2015–2018. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violation parameters for this process are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><msubsup><mrow><mi>β</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>d</mi></mrow><mrow><mi>eff</mi></mrow></msubsup><mo>=</mo><mn>0.710</mn><mo>±</mo><mn>0.084</mn><mo>±</mo><mn>0.051</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><mi>λ</mi><mo stretchy="false">|</mo><mo>=</mo><mn>1.019</mn><mo>±</mo><mn>0.034</mn><mo>±</mo><mn>0.024</mn></mrow></math>, where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent <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"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays. Assuming approximate SU(3) flavor symmetry, these results are combined with the previous consistent LHCb measurement to set the most stringent constraint on the penguin contribution, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub></math>, to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mi>s</mi></msub></math> in <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><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1020</mn><mo stretchy="false">)</mo></math> decays, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub><mo>=</mo><mn>5.0</mn><mo>±</mo><mn>4.6</mn><mtext> </mtext><mtext> </mtext><mi>mrad</mi></math>.

Netherlands

R. Aaij

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Poland

M. Akthar

Italy

P. Albicocco

Germany

J. Albrecht

R. Aleksiejunas

CERN

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

Z.B. Bai

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bavarchee

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

S. Bhattacharya

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

Observation of <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"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> Decays

We investigate the effects of polarization on several physical observables in the semileptonic decay $$\Xi _{cc}^{++} \rightarrow \Xi _c^{+} \bar{\ell }\nu _{\ell }$$ . We analyze the polarization effects of the particles involved in the decay, namely $$\Xi _{cc}^{++}$$ , $$\Xi _c^{+}$$ , and the charged muon $$\ell $$ . Using the form factors obtained from QCD sum rules, we compute the $$q^{2}$$ -dependent observables including the differential branching ratio, forward–backward asymmetry, and polarization asymmetries for both longitudinal and transverse polarization states. We also define and examine several polarization ratios and discuss correlations among different observables. In addition, we evaluate the lepton flavor universality ratio defined as $$\mathcal {R}_{\Xi _c^+}(\mu /e) \equiv \mathcal {D}(\Xi _{cc}^{++}\rightarrow \Xi _c^+\mu ^+\nu _\mu )/\mathcal {D}(\Xi _{cc}^{++}\rightarrow \Xi _c^+e^+\nu _e)$$ and analyze its behavior over the available dynamical range. Our results show that these observables are quite sensitive to polarization effects, and can provide suitable probes for testing Standard Model predictions.

Pakistan

Qazi Salam

Anamta Asif

Ishtiaq Ahmed

Rizwan Khalid

The effects of polarization on the observables in the decay $$\Xi _{cc}^{++}\rightarrow \Xi _{c}^{+} \bar{\ell }\nu _{\ell }$$

The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> is studied at LHCb for the first time using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The branching ratio relative to the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> is measured to be [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>/</mo><mo stretchy="false">[</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><mn>0.53</mn><mo>±</mo><mn>0.05</mn><mo>±</mo><mn>0.05</mn></mrow></math> where the first uncertainty is statistical and the second is systematic. Evidence is found for contributions from two resonant states, <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>2923</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> and <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>2939</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, 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><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup></math> system. The two states show a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3.9</mn><mi>σ</mi></math> relative to the nonresonant hypothesis. These two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup></math> states are consistent with being the isospin partners of the states observed 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><msup><mi>K</mi><mo>−</mo></msup></math> system.

M. Abdelfatah

F. Blanc

J.E. Blank

S. Blusk

Study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decay

The three-body decays of charmonium states provide a valuable laboratory for probing non-perturbative QCD dynamics and investigating light meson resonances. Three-body decays <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> are studied in this work ( <italic>P</italic> denotes the light pseudoscalar meson). Branching ratio analysis is performed for the <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> decays incorporating light vector ( <italic>V</italic>) meson resonance, light tensor ( <italic>T</italic>) meson resonance and light scalar ( <italic>S</italic>) meson resonance contributions. Based on the SU(3) flavor symmetry approach, we calculate the branching ratios under both the narrow width approximation and the finite width effect, and provide the predict results in the <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239;( <italic>V</italic>/ <italic>T</italic>) <italic>P</italic> <inf>3</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> processes. Furthermore, based on the significant <math altimg='si401.svg'><mrow><msubsup><mi>a</mi><mn>0</mn><mo>+</mo></msubsup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow></mrow></math> resonance signal in <math altimg='si136.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mi>&#951;</mi></mrow></math> decay, the predict results for <italic>&#967;</italic> <inf><italic>c</italic>1</inf>&#8239;&#8594;&#8239; <italic>SP</italic> <inf>3</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> are also obtained. While the resonance signals observed in current experiments are mainly concentrated in the <math altimg='si136.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mi>&#951;</mi></mrow></math> decay, our results suggest potential resonance contributions in other channels. Especially in <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>KK&#960;</italic> channels, the predicted results show the significant resonance contributions from <italic>V</italic> mesons and <italic>T</italic> mesons, which is worth further experimental verification and exploration.

Bo Lan

Jie Zhu

Jin-Huan Sheng

Yuan-Guo Xu

Ru-Min Wang

Study of <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf> decays to <italic>PPP</italic> via light meson resonances

We present a search for the lepton number violating decay <math altimg='si9.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>+</mo><mi>c</mi><mo>.</mo><mi>c</mi><mo>.</mo></mrow></math> with (10087&#8239;&#177;&#8239;44)&#8239;&#215;&#8239;10 6 <italic>J</italic>/ <italic>&#968;</italic> events collected by the BESIII detector at the BEPCII collider, which provided a sample of <math altimg='si10.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><msup><mover accent='true'><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#175;</mo></mover><mo>+</mo></msup></mrow></math> pairs. Employing a blind analysis strategy, no significant signal is observed above the expected background yield. The upper limit on the branching fraction is determined to be <math altimg='si11.svg'><mrow><mrow><mrow><mi mathvariant='normal'>B</mi></mrow><mi>F</mi></mrow><mrow><mo>(</mo><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow><mo linebreak='goodbreak'>&lt;</mo><mn>2.0</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> at the 90% confidence level.

M. Ablikim

Russia

M.N. Achasov

Sweden

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

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

Search for the lepton number violating process <math altimg='si8.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>+</mo><mi>c</mi><mo>.</mo><mi>c</mi></mrow></math>