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)

This paper presents a thorough study of the local and nonlocal amplitudes in $\textit{B}$ → $\textit{K}$ $\textit{μ}$ $\textit{μ}$ transitions through an amplitude analysis of the dimuon mass spectrum of the decay. The analysis is based on $\textit{pp}$ collision data corresponding to an integrated luminosity of 8.4 fb collected by the LHCb experiment during Run1 and Run2. This measurement employs a model that describes both one-particle and two-particle nonlocal amplitudes across the entirety of the dimuon mass spectrum, enabling the determination of both short- and long-distance contributions to the decay. The compatibility of the Wilson coefficient combinations $$ {C}_9+{C}_9^{\prime } $$ and $$ {C}_{10}+{C}_{10}^{\prime } $$ with the Standard Model prediction is found to vary between 1$\textit{.}$6 $\textit{σ}$ and 4 $\textit{σ}$, depending on the choice of local form factors.

Netherlands

R. Aaij

United Kingdom

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J. 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. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

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. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P. Battista

Hungary

A. Bavarchee

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

E. Ben-Haim

G. Benane

G. Bencivenni

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

F. Betti

J. Bex

Ukraine

O. Bezshyyko

S. Bhattacharya

M. Bieker

N. Biesuz

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

Measurement of the local and nonlocal amplitudes in $\textit{B}$ + $\textit{→ K}$ + $\textit{μ}$ + $\textit{μ}$ $\textit{−}$ decays

<p>The LHCb Collaboration recently reported a measurement of the difference in direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries for the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>p</mi><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> (with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mo>=</mo><mi>K</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>π</mi></mrow></math>), offering new experimental constraints on the decay dynamics of heavy baryons into charmonium final states. Inspired by these findings, we explore the branching ratios and direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations for the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>4312</mn><mo>,</mo><mn>4440</mn><mo>,</mo><mn>4457</mn><mo stretchy="false">)</mo><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> within the framework of final-state rescattering. Our analysis indicates that the branching fractions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi>P</mi><mi>c</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math> lie around the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> level, with the corresponding direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries approaching approximately 1%. In contrast, the direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation for the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi>P</mi><mi>c</mi><mo>+</mo></msubsup><msup><mi>K</mi><mo>−</mo></msup></math> is found to be very small, while its branching ratios show a strong dependence on the spin assignments of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></math> states. These predictions may provide useful guidance for more precise <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> measurements and amplitude analyses in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></math> region in future experiments.</p>

Zhu-Ding Duan

Tian-Liang Feng

Run-Hui Li

Ming-Zhu Liu

Jian-Peng Wang

Fu-Sheng Yu

Probing direct <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><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mo>=</mo><mi>π</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi></mrow></math>) with final-state rescattering

<p>Using a sample 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 corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected with the BESIII detector at the BEPCII collider and produced at center-of-mass energies from 4600 to 4698 MeV, an amplitude analysis is performed of the singly Cabibbo-suppressed decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>. The branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1020</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo><msup><mi>K</mi><mo>+</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo><msup><mi>K</mi><mo>+</mo></msup></math> are measured, where the latter two modes are decays that are observed for the first time. At the same time, with the detection efficiency based on the results of the amplitude analysis, the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> is updated to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>9.94</mn><mo>±</mo><mn>0.6</mn><msub><mn>5</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.5</mn><msub><mn>0</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, which is consistent with the current world average value within one standard deviation. The result supersedes the previous BESIII measurement with precision improved by approximately a factor of 1.5.</p>

M. Ablikim

Russia

M.N. Achasov

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. 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

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

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Amplitude analysis of singly Cabibbo-suppressed decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>