The processes of $ K^-p \to \pi^0 \pi^0 \Sigma^0 $ and $ K^- p \to \pi^0 \Lambda(1405) $ are studied within the effective Lagrangian approach. In addition to the “background” contribution from the $\textit{u}$-channel nucleon pole term, the contribution from the $ \Sigma(1660) $ resonance with spin-parity $ J^P=1/2^+ $ is also considered. For the $ K^-p \to \pi^0 \pi^0 \Sigma^0 $ reaction, we perform a calculation for the total and differential cross sections by considering the contribution from the $ \Sigma(1660) $ intermediate resonance decaying into $ \pi^0 \Lambda(1405) $ with $ \Lambda(1405) $ decaying into $ \pi^0 \Sigma^0 $ . With our model parameters, the available experimental data on both the $ K^-p \to \pi^0 \pi^0 \Sigma^0 $ and $ K^- p \to \pi^0 \Lambda(1405) $ reactions can be fairly well reproduced. It is shown that the contribution from the $ \Sigma(1660) $ resonance is necessary, and that these experimental measurements could be used to determine some properties of the $ \Sigma(1660) $ resonance.

China

Xing-Yi Ji

Si-Wei Liu

Wen-Tao Lyu

De-Min Li

En Wang

Ju-Jun Xie

Role of Σ(1660) in the $\textit{K}$ $^{−}$ $\textit{p}$ → $\textit{π}$ $^{0}$ $\textit{π}$ $^{0}$Σ$^{0}$ reaction * Supported by the National Key R&D Program of China (2023YFA1606703, 2024YFE0105200), the National Natural Science Foundation of China (12435007, 12475086, 12192263, 12361141819, 1252200936), the Natural Science Foundation of Henan (232300421140, 252300423951) and the Zhengzhou University Young Student Basic Research Projects (PhD students) (ZDBJ202522)

Using a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></mrow></math> events collected by the BESIII detector at the BEPCII collider, we measure the branching fractions of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi><mo>,</mo><mi>ϕ</mi><mi>ϕ</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2). The obtained branching fractions are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>7.40</mn><mo>±</mo><mn>0.23</mn><mo>±</mo><mn>0.55</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>3.33</mn><mo>±</mo><mn>0.14</mn><mo>±</mo><mn>0.25</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>5.46</mn><mo>±</mo><mn>0.17</mn><mo>±</mo><mn>0.40</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.96</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.23</mn><mo>±</mo><mn>0.29</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.69</mn><mo>±</mo><mn>0.10</mn><mo>±</mo><mn>0.08</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.65</mn><mo>±</mo><mn>0.09</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.23</mn><mo>±</mo><mn>0.08</mn><mo>±</mo><mn>0.10</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.00</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.07</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.82</mn><mo>±</mo><mn>0.09</mn><mo>±</mo><mn>0.14</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> is not from the decay of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> meson, the first uncertainties are statistical and the second systematic. The branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi></math> are measured with precision improved by factors of 1.5–1.9, and those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><msup><mi>η</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi></math> are measured for the first time.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. 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

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J.C. 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.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

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

Measurements of the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mi>η</mi><mo>,</mo><mtext> </mtext><mi>ϕ</mi><mi>ϕ</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>η</mi></math>

Using a data sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events collected with the BESIII detector operating at the BEPCII collider, we report the first observation of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mn>2</mn><msup><mi>K</mi><mo>+</mo></msup><mn>2</mn><msup><mi>K</mi><mo>−</mo></msup><mi>ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>ω</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) via the radiative transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math>. The branching fractions of these decays are measured for the first time, and the statistical significance for each signal exceeds <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>10</mn><mi>σ</mi></math>.

X.L. Bao

W. Chen

J. Cheng

Measurements of the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mn>2</mn><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mn>2</mn><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>ω</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>ω</mi></math> decays

Motivated by the observations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2900</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2900</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>, we propose to search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></mrow><mn>0</mn></msup></math> in the cleaner process <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>D</mi><mn>0</mn></msup><msup><mi>K</mi><mn>0</mn></msup></math>. In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> molecular picture, our estimates suggest that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2900</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> should contribute significantly to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><msup><mi>K</mi><mn>0</mn></msup></math> invariant mass distribution 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>D</mi><mn>0</mn></msup><msup><mi>K</mi><mn>0</mn></msup></math>, as reported by the Belle II Collaboration. The corresponding fit fraction is estimated to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>9.72</mn><mo>±</mo><mn>3.92</mn><mo stretchy="false">)</mo><mo>%</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>7.09</mn><mo>±</mo><mn>5.88</mn><mo stretchy="false">)</mo><mo>%</mo></math> in different fitting schemes. Further precise measurements of this process at Belle II and LHCb could be helpful for clarifying the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math>.

Man-Yu Duan

Guan-Ying Wang

Yun Liang

Xiang Liu

Dian-Yong Chen

Finding the clean process <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><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> to probe absolutely exotic four-quark states

An amplitude analysis of the $${{{B} ^0} \!\rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}} $$ decays with $${\eta _{c}} (1S) \rightarrow {p} {\overline{{p}}} $$ is performed using a sample corresponding to an integrated luminosity of 9 $$\,\text {fb} ^{-1}$$ of $$p $$ $$p $$ collision data collected by the LHCb detector at centre-of-mass energies of $$\sqrt{s}$$ = 7, 8 and 13 $$\,\text {Te\hspace{-1.00006pt}V}$$ . The data are described with a model including only intermediate contributions from known $${K} ^{*0}$$ resonances. Evidence for an exotic resonance in the $${\eta _{c}} (1S) {{\pi } ^-} $$ system, reported in a previous analysis of this decay channel, is not confirmed. The inclusive branching fraction of the $${{B} ^0} \rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-} $$ decays is measured to be where the first uncertainty is statistical, the second systematic, and the third arises from the limited knowledge of external branching fractions.

Netherlands

R. Aaij

A.S.W. Abdelmotteleb

Switzerland

C. Beteta

F. Abudinén

T. Ackernley

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

P. Albicocco

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

P. Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Silva

M. Atzeni

B. Audurier

J. Authier

D. Bacher

I. Perea

S. Bachmann

M. Bachmayer

J. Back

P. Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Souza Leite

C. Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

Amplitude analysis of $$B^0 \rightarrow \eta _c(1S) K^+ \pi ^- $$ decays