Based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2.712</mn><mo>±</mo><mn>0.014</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>9</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, 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><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) are observed for the first time with statistical significances exceeding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>. The measured branching fractions are <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>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>7.25</mn><mo>±</mo><mn>0.28</mn><mo>±</mo><mn>0.35</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</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>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.33</mn><mo>±</mo><mn>0.12</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</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>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.51</mn><mo>±</mo><mn>0.16</mn><mo>±</mo><mn>0.12</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, where the first uncertainties are statistical and the second systematic. In addition, no significant structures are observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> mass spectra.

China

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

Observation and branching fraction measurements 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>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>

In this paper we study Krylov complexity in the presence of single and multiple operators in the DSSYK model, where we can use the analytical techniques coming from chord diagrammatics. One of the results we obtain is that it showcases the switchback effect, when the appropriate “triple-scaling limit” is taken, under which the model becomes dual to semiclassical JT gravity. We build on previous work, where it was shown that, in the continuum limit, Krylov complexity is defined as the sum of expectations value of right and left chord number operators. Here we argue that this property signals the emergence of the geometric nature of this notion of K-complexity. We show that in the regime where DSSYK is dual to semi-classical gravity, the light matter chord corresponds to a shockwave insertion in JT gravity. We identify the geodesic-length dual of the operator complexity and extend the relevant holographic dictionary to describe the details of the matter insertions. Additionally, we define a class of two-sided perturbations of the Lanczos algorithm that allows to analyze the switchback effect. In the appropriate semi-classical limit, this perturbed operator complexity is dual to an ERB length in JT gravity with corresponding shockwave insertions. We thus establish that K-complexity exhibits the expected switchback effect and universal late-time linear growth, consistent with previous findings regarding its geometric nature in the holographic bulk-boundary map.

Switzerland

Marco Ambrosini

Israel

Eliezer Rabinovici

Julian Sonner

Holography of K-complexity: switchbacks and shockwaves

Recent Belle II data on <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><msub><mi>E</mi><mrow><mi>miss</mi></mrow></msub></math> show an excess consistent with a two-body decay involving a light invisible particle with mass around 2.1 GeV. We present a UV-complete explanation based on a Higgsed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math> gauge symmetry with a light vector boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and a vectorlike top partner, which naturally enhances <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi></math> transitions. While the minimal model can reproduce the required <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>Z</mi><mo>′</mo></msup></math> rate, it is excluded by LHCb searches for resonant dimuon decays due to unavoidable loop-induced couplings of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> to charged leptons. We show that a minimal extension with an additional light <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math>-charged singlet fermion allows <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> to decay dominantly invisibly, evades existing constraints coming also from dark photon and collider searches as well as Higgs measurements, and can simultaneously account for the Belle II excess and the observed dark matter abundance through resonant thermal freeze-out.

Slovenia

Patrick D. Bolton

Jernej F. Kamenik

Spain

Martín Novoa-Brunet

Dark light shining on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msub><mrow><mi>E</mi></mrow><mrow><mrow><mi>miss</mi></mrow></mrow></msub></mrow></math>

Based on a data sample corresponding to an integrated luminosity of 6.4 fb of $\textit{e}$ $\textit{e}$ annihilation and collected with the BESIII detector at 13 center-of-mass energy points ranging between 4.600 GeV and 4.950 GeV, we report the first observation of the singly Cabibbo-suppressed decay $$ {\Lambda}_c^{+}\to {\Sigma}^0{K}_S^0{\pi}^{+} $$ with a statistical significance of 5.9$\textit{σ}$. The branching fraction is determined to be $$ B\left({\Lambda}_c^{+}\to {\Sigma}^0{K}_S^0{\pi}^{+}\right)=\left(0.58\pm 0.{14}_{\mathrm{stat}.}\pm 0.0{4}_{\mathrm{syst}.}\right)\times 1{0}^{-3} $$ . In addition, the decay $$ {\Lambda}_c^{+}\to {\Sigma}^0{K}_S^0{K}^{+} $$ has also been investigated, and the evidence for this decay is obtained with a statistical significance of 3.7$\textit{σ}$.

M. Achasov

X. Ai

C. Akondi

Y. An

X. Bao

M. Bertani

R. Briere

M. Cai

G. Cao

S. Cetin

X. Chai

J. Chang

T. Chang

G. Che

Y. Che

C. Chen

H. Chen

M. Chen

S. Chen

W. Chen

X. Chen

Y. Chen

Z. Chen

J. Cheng

L. Cheng

S. Choi

H. Dai

J. Dai

X. Dai

R. Boer

F. Mori

C. Deng

Z. Deng

X. Ding

Yi. Ding

L. Dong

M. Dong

M. Du

S. Du

Shaoxu Du

X. Du

Y. Du

Y. Duan

Z. Duan

G. Fan

J. Fan

Y. Fan

Jin Fang

S. Fang

W. Fang

Y. Fang

Measurements of branching fractions of $$ {\Lambda}_c^{+}\to {\Sigma}^0{K}_S^0{\pi}^{+} $$ and $$ {\Lambda}_c^{+}\to {\Sigma}^0{K}_S^0{K}^{+} $$

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.

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.

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

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

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