A search for the decay $ B^+\to D_s^+ K^+K^- $ has been reported by the LHCb Collaboration using $ pp $ collision data corresponding to an integrated luminosity of $4.8\;{\rm{fb}}^{-1}$ , collected at center-of-mass energies of 7, 8, and 13 TeV, in which no amplitude analysis of the $ K^+K^- $ subsystem was performed. In this work, we study the resonant contributions to the decay $ B^+\to D_s^+ K^+K^- $ within the perturbative QCD (PQCD) factorization framework. Contributions from the $\textit{S}$-wave resonances $ f_0(980) $ , $ f_0(1370) $ , and $ f_0(1500) $ , the $\textit{P}$-wave resonance $ \phi(1020) $ , and the $\textit{D}$-wave resonances $ f_2(1270) $ and $ f_2(1525) $ are taken into account. By introducing the corresponding two-meson distribution amplitudes for the $ K^+K^- $ system, we perform a complete perturbative analysis of the quasi-two-body decays $ B^+\to D_s^+(R\to)K^+K^- $ , where $\textit{R}$ denotes an intermediate resonance, and present the first PQCD predictions for the associated branching fractions. Using the narrow-width approximation, we further extract the branching fractions of the corresponding two-body decays $ B^+\to D_s^+R $ . Our results are consistent with the available experimental measurements and previous theoretical studies. Finally, we find that direct CP asymmetries vanish for these quasi-two-body decays within the Standard Model, so that any experimentally observed nonzero CP asymmetry would constitute a clear signal of physics beyond the Standard Model.

China

Zhi-Tian Zou

Jun-Peng Wang

Rui Zhou

Ying Li

Quasi-two-body decays $ {B^+\to D_s^+ (R\to) K^+K^-} $ in the perturbative QCD approach * Supported in part by the National Science Foundation of China (12375089, 12435004, 12075086), and the Natural Science Foundation of Shandong province (ZR2022ZD26, ZR2022MA035)

The recent measurement of the branching ratio of <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><mo>+</mo><mi>inv</mi></math> (where “inv” denotes invisible states) by the Belle II Collaboration is enhanced relative to the standard model expectation by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.7</mn><mi>σ</mi></mrow></math>. An older puzzle persists in measurements of the branching ratios and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>K</mi></math> decays. We address these two anomalies in flavor-changing neutral current <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays, with a short-lived axionlike particle (ALP) with mass close to that of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math>. In the model with the minimum number of new couplings, the ALP has couplings to the photon, top quark and a heavy sterile neutrino. The ALP contributes to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><mi>K</mi></math> decays by mixing with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math>. It contributes to <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><mo>+</mo><mi>inv</mi></math> by its off-shell coupling to sterile neutrino pairs. The model can explain the excess in the total rate, but not the observed distribution of signal events. We make predictions for all <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><mo>+</mo><mi>inv</mi></math> modes and for the rare kaon decays, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>+</mo><mi>inv</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><mo>+</mo><mi>inv</mi></math>. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>.

United States

Bhubanjyoti Bhattacharya

Alakabha Datta

Girish Kumar

Danny Marfatia

Axionlike particles and sterile neutrinos solve the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><mi>ν</mi><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>K</mi></mrow></math> puzzles

Based on the effective Lagrangian approach, we investigate 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><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> reaction. Within this framework, we provide a dynamical explanation by analyzing its total and differential cross sections, as well as the polarization of the produced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> hyperon. Incorporating the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel exchange of the scalar <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>700</mn><mo stretchy="false">)</mo></math> and pseudoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> mesons, complemented by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel contribution from the vector excited state, we can reproduce the current experimental data fairly well in a wide energy region. Compared to the conventional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> and <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> mesons exchange, the <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>700</mn><mo stretchy="false">)</mo></math> meson exchange plays a more essential role in simultaneously capturing the observed features of the total and differential cross sections. The introduction of the vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel resonance improves the description of the spin observables. This work gives a perspective to inspect the role of <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>700</mn><mo stretchy="false">)</mo></math> and serves as a test to search for the resonances in the reaction <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><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> at threshold.

Japan

Hao-Nan Wang

Cheng Chen

Xing-Yi Ji

De-Min Li

Yue Ma

En Wang

Ju-Jun Xie

Role of <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>700</mn><mo stretchy="false">)</mo></math> exchange 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><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> reaction

Recent measurements of the charge-parity asymmetry in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> by CMS Collaboration, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><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>6.2</mn><mo>±</mo><mn>3.0</mn><mo>±</mo><mn>0.2</mn><mo>±</mo><mn>0.8</mn><mo stretchy="false">)</mo><mo>%</mo></math>, and by LHCb, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><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>1.86</mn><mo>±</mo><mn>1.04</mn><mo>±</mo><mn>0.41</mn><mo stretchy="false">)</mo><mo>%</mo></math>, suggest possible deviations from Standard Model expectations, which predict asymmetries below the percent level. This singly Cabibbo-suppressed decay is particularly sensitive to new physics, as the leading amplitudes vanish in the exact U-spin symmetry limit and the process is dominated by W-exchange topologies. We investigate scalar diquark contributions to this decay, comparing color-sextet and color-triplet representations. We find that the color-sextet diquark, characterized by a symmetric color structure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msubsup><mi>C</mi><mn>1</mn><mi>NP</mi></msubsup><mo>=</mo><msubsup><mi>C</mi><mn>2</mn><mi>NP</mi></msubsup><mo stretchy="false">)</mo></math>, avoids color suppression and can generate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> asymmetries in the range 0.5%–1.5% for a diquark mass of order 1 TeV. In contrast, the color-triplet contribution is strongly suppressed due to destructive interference from its antisymmetric color structure. We further show that a flavor hierarchy in the sextet couplings, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo>&gt;</mo><msub><mi>λ</mi><mrow><mi>u</mi><mi>s</mi></mrow></msub></math>, can simultaneously account for the observed deviation from the U-spin sum rule in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and the measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>. These results identify color-sextet scalar diquarks as viable candidates for explaining enhanced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in charm decays.

Mexico

David Delepine

Egypt

Shaaban Khalil

Colombia

Carlos A. Ramirez

<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"><mi>D</mi><mo stretchy="false">→</mo><mi>K</mi><mi>K</mi></math> decays: A comparative analysis of triplet and sextet diquarks

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collision data taken at the center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>3.773</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, we report the first experimental constraint on the scalar current in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> transitions, based on a simultaneous fit to the first measured forward-backward asymmetries and precisely determined partial decay rates. The parameters of the scalar current are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Re</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mn>0.017</mn><mo>±</mo><mn>0.00</mn><msub><mrow><mn>8</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Im</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo>±</mo><mo stretchy="false">(</mo><mn>0.077</mn><mo>±</mo><mn>0.01</mn><msub><mrow><mn>1</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>9</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math>, which deviates from the standard model by a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.3</mn><mi>σ</mi></math>. The branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, the hadronic form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math>, and the modulus of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo stretchy="false">→</mo><mi>s</mi></math> Cabibbo-Kobayahsi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> are also determined with improved precision. In addition, lepton flavor universality is tested via the ratios of the decay rates between semimuonic and semielectronic decays in the full momentum transfer range and in subranges.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Italy

C.S. Akondi

Germany

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

Poland

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

D. Cabiati

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

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. 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

Yi. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Shaoxu Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

Jin Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

First Experimental Constraint on the Scalar Current in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> Transition

In anticipation of the new wave of ALICE experiments on particle-resonance correlation functions, we study the interaction of a kaon with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> resonance. Assuming the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> to be a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> molecular state in isospin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>, we employ the fixed center approximation to describe the kaon scattering off the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> cluster, and implement elastic unitarity in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> amplitude via an optical potential and the Lippmann-Schwinger equation. We evaluate the scattering length, effective range, and correlation function, which exhibits a shape characteristic of a strongly attractive interaction. Notably, the amplitude develops a narrow resonant peak about 40 MeV below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></mrow></math> threshold, signaling a three-body bound state. We discuss the experimental feasibility of observing this state through the invariant mass distribution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mn>0</mn></msup></math>, and argue that such three-body states, predicted by various theoretical approaches, offer promising targets for future experimental searches, providing valuable insights into the nature of exotic hadronic resonances.

Wen-Hao Jia

Hai-Peng Li

Wei-Hong Liang

Jing Song

Spain

Eulogio Oset

Correlation function and bound state from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mtext> </mtext><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></mrow></math> interaction

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we present precise measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mspace linebreak="goodbreak"></mspace><msup><mi>K</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mo>=</mo><mi>e</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math>) decays. The branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mspace linebreak="goodbreak"></mspace><msup><mi>K</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.548</mn><mo>±</mo><mn>0.00</mn><msub><mn>6</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>7</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>3.445</mn><mo>±</mo><mn>0.00</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>8.928</mn><mo>±</mo><mn>0.02</mn><msub><mn>5</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.05</mn><msub><mn>0</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>8.770</mn><mo>±</mo><mn>0.02</mn><msub><mn>9</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.05</mn><msub><mn>3</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>, respectively. The partial decay rates of these four decays are measured with improved precision, and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to the measured partial decay rates and the forward-backward asymmetries of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, a search for a possible scalar current contribution in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> transition is performed. The results are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Re</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mn>0.017</mn><mo>±</mo><mn>0.00</mn><msub><mrow><mn>8</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Im</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo>±</mo><mo stretchy="false">(</mo><mn>0.077</mn><mo>±</mo><mn>0.01</mn><msub><mrow><mn>1</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>9</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math>, corresponding to a difference from the Standard Model (SM) with a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.3</mn><mi>σ</mi></math>. The product of the form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math> and the modulus of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo stretchy="false">→</mo><mi>s</mi></math> Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>cs</mi></mrow></msub><mo stretchy="false">|</mo></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mrow><mo>+</mo></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo stretchy="false">|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>cs</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mn>0.7183</mn><mo>±</mo><mn>0.000</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.001</mn><msub><mrow><mn>4</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math>. With the inputs <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>cs</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mn>0.97349</mn><mo>±</mo><mn>0.00016</mn></math> from the SM global fit or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.7452</mn><mo>±</mo><mn>0.0031</mn></math> from the lattice quantum chromodynamics calculation, we derive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.7383</mn><mo>±</mo><mn>0.000</mn><msub><mn>7</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.001</mn><msub><mn>4</mn><mrow><mi>syst</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>cs</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mn>0.9639</mn><mo>±</mo><mn>0.000</mn><msub><mn>9</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.001</mn><msub><mn>8</mn><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.004</mn><msub><mn>0</mn><mrow><mi>LQCD</mi></mrow></msub></math>. Combining with the results of the semimuonic and semielectronic decays, lepton flavor universality is tested via the ratios of the decay rates between semimuonic and semielectronic decays in the full and different momentum transfer ranges.

Precise measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first observation of the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><mi>ω</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mi>ω</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> with significances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>8.0</mn><mi>σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.8</mn><mi>σ</mi></math>, respectively. Their decay branching fractions are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><mi>ω</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>9.4</mn><mrow><mo>−</mo><mn>1.8</mn></mrow><mrow><mo>+</mo><mn>2.0</mn></mrow></msubsup><mo>±</mo><mn>0.6</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><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mi>ω</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>8.0</mn><mrow><mo>−</mo><mn>2.1</mn></mrow><mrow><mo>+</mo><mn>2.4</mn></mrow></msubsup><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.7</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. Combining these with the latest measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mrow><mo>−</mo><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> and assuming <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> to be the sole mediating resonance in all processes, the branching ratios are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">{</mo><mo stretchy="false">[</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo stretchy="false">+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>/</mo><mo stretchy="false">[</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">}</mo><mo>=</mo><msubsup><mrow><mn>3.4</mn></mrow><mrow><mo>−</mo><mn>0.7</mn></mrow><mrow><mo>+</mo><mn>0.8</mn></mrow></msubsup><mo>±</mo><mn>0.3</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">{</mo><mo stretchy="false">[</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mspace linebreak="goodbreak"></mspace><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo stretchy="false">+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>/</mo><mo stretchy="false">[</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">}</mo><mo>=</mo><msubsup><mrow><mn>7.9</mn></mrow><mrow><mo>−</mo><mn>2.1</mn></mrow><mrow><mo>+</mo><mn>2.4</mn></mrow></msubsup><mo>±</mo><mn>0.7</mn></mrow></math>. The combined branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>8.4</mn><mo>±</mo><mn>1.4</mn><mo>±</mo><mn>0.5</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, which is the most precise measurement from a collider experiment. Furthermore, for the first time based on a single vector-pseudoscalar decay channel, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> mass is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1336</mn><mo>±</mo><mn>9</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, providing unique experimental support for the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> resonance. The first uncertainties are statistical, and the second are systematic.

J.C. Cheng

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

First Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>ω</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> and Determination of the Branching Fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>ω</mi></math>

We investigate the production of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math> resonance in the charmed baryon weak decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>p</mi></mrow></math>, focusing on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>p</mi></mrow></math> final-state rescattering mechanism. The direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>+</mo></msup></math> exchange diagram is expected to be suppressed, hence we adopt the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>+</mo></msup></math> internal emission process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></mrow></math> followed by the subsequent decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> as the dominant source of the final state particles. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> resonance is then generated via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>p</mi></math> rescattering within a triangle loop mechanism. Our calculations incorporate both the tree-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></mrow></math> and the dynamically generated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> state arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mi>π</mi></math> final state interaction. We find that our theoretical results can reproduce the bump and peak structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> invariant mass distributions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></mrow></math>, respectively. Meanwhile, the peak for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>p</mi></math> invariant mass distributions is also well described. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> signal naturally emerges from rescattering effects, and adopting the pole parameters of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><mo stretchy="false">)</mo></math> resonance yields an improved description of the experimental data. In addition, we obtain a branching fraction ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">]</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>≈</mo><mn>0.5</mn></mrow></math>, which is lower than the experimentally measured value. This discrepancy suggests that interference effects are likely significant in this decay process. Future high-precision measurements will further verify the proposed rescattering mechanism.

Zu-Xin Cai

Si-Wei Liu

Xiang Wei

Gang Li

Xiao-Hai Liu

Final-state rescattering mechanism of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>p</mi></mrow></math> decay

This study examines the rare decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> as a possible probe for new physics beyond the standard model (SM). We first analyze this channel within the SM and then include scalar leptoquark contributions. We provide predictions for key observables, like differential decay rate, branching ratio, ratio of branching fractions at different channels, forward-backward asymmetry and different lepton polarizations, and assess their sensitivity to leptoquark scenarios, highlighting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> regions less affected by the long-distance charmonium effects. The results can be useful for future Belle II and LHCb measurements.

M. Dadashzadeh

K. Azizi

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decay in the standard model and scalar leptoquark scenario