Recently, a number of exotic hadrons have been reported in the experiments, and most of these states lie slightly below the threshold. Therefore, these states are considered to be hadronic molecules composed of mesons or baryons. In 2022, the doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was reported by the LHCb experiment, which is considered to be composed of two heavy quarks and two light antiquarks, and located slightly below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold. The observation motivates us to study the bound and resonant states of the doubly heavy tetraquarks as two meson systems. We employ the one boson exchange potential as an interaction between two mesons, where one free parameter has been determined to reproduce <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> reported by the LHCb experiment. In our previous work, bound states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> molecules were studied, where we respected the heavy quark spin symmetry (HQS). Using the same framework, we study not only bound but also resonant states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math> in this paper. Furthermore, we discuss the HQS partner structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> obtained in our study by introducing the light cloud basis.

Japan

Manato Sakai

Yasuhiro Yamaguchi

Analysis of bound and resonant states of doubly heavy tetraquarks with spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math>

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>, we analyze the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> in the improved perturbative QCD (iPQCD) formalism, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> denotes the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave charmonia with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">)</mo></math> denotes the pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> (the vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>). Our results <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>=</mo><mn>0.32</mn><mo>±</mo><mn>0.05</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>=</mo><mn>0.11</mn><mo>±</mo><mn>0.01</mn></math> at leading order in the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> agree well with the data within uncertainties. The result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.17</mn><mo>±</mo><mn>0.02</mn></math> is lower than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>1.41</mn><mrow><mo>−</mo><mn>0.45</mn></mrow><mrow><mo>+</mo><mn>0.50</mn></mrow></msubsup></math> inferred by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math> measurement. The large longitudinal polarization fractions imply that these components dominate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math>) mode, but not in the corresponding ones with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub></math> mesons. Inputting the BRs of the strong decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</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"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> reported by the BESIII Collaboration, we obtain those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>π</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> transitions.

China

Xin Liu

Hsiang-nan Li

Zhen-Jun Xiao

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo></math> decays in the improved perturbative QCD formalism

A partial-wave analysis is performed on the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> invariant-mass region below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.6</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>10.09</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> events collected with the BESIII detector. Significant isospin-violating decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></math> into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mi>π</mi><mn>0</mn></msup></math> are observed. For the first time, three axial vectors, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1510</mn><mo stretchy="false">)</mo></math>, are observed to decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>. The product branching fractions of these resonances are reported.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

Germany

O. Afedulidis

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

I. Balossino

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

G. Chelkov

C. Chen

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

South Korea

S.K. Choi

G. Cibinetto

F. Cossio

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. 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

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

H. Gao

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup></mrow></math>

Motivated by the deviations observed between the experimental measurements and the Standard Model (SM) predictions of the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> decays, we revisit the two-body hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>=</mo><mi>π</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo>,</mo><mi>ρ</mi></math>, both within the SM and beyond. Since these processes are also mediated by the quark-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></math> transitions and hence dominated by the color-allowed tree topology, the QCD factorization is generally expected to hold in the heavy-quark limit. First, we update the SM predictions of the observables of these decays by including the nonfactorizable vertex corrections to the hadronic matrix elements of the SM four-quark operators up to the next-to-next-to-leading order (NNLO) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>. It is found that, relative to the leading-order results, the branching ratios of these decays up to the next-to-leading-order (NLO) and NNLO corrections are always enhanced, with a relative amount given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>NLO</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mi>NLO</mi></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>6</mn><mo>%</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>NNLO</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mrow><mi>NNLO</mi></mrow></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>9</mn><mo>%</mo></math>, respectively. To minimize the uncertainties brought by the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub></math> as well as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we construct ratios of the nonleptonic decay rates with respect to the corresponding differential semileptonic decay rates evaluated at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><msubsup><mi>m</mi><mi>L</mi><mn>2</mn></msubsup></math> (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mi>L</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>) or integrated over the whole <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>), which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mi>π</mi><mo stretchy="false">(</mo><mi>K</mi><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> decays and the updated fitting results of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we find that the deviations can still be explained by the NP four-quark operators with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structures, while the solution with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>γ</mi><mi>μ</mi></msup><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><msub><mi>γ</mi><mi>μ</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structure does not work anymore, under the combined constraints from the ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>σ</mi></math> level. Furthermore, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>, once measured precisely, could provide complementary constraint on these NP Wilson coefficients allowed by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>. With the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> events expected at the Large Hadron Collider, we hope to obtain more precise measurements of these observables, which can be exploited to discriminate the different NP scenarios responsible for the deviations observed in the two-body nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays.

Wei-Jun Deng

Fang-Min Cai

Xin-Qiang Li

Yan Shi

Ya-Dong Yang

Revisiting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays within the SM and beyond in QCD factorization

We present an update of HPQCD’s lattice quantum chromodynamics (QCD) determination of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector and axial-vector form factors, and provide new results for the tensor form factors. We use the highly improved staggered quark (HISQ) action for all valence quarks, together with the second generation MILC <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> HISQ gluon field configurations. This calculation includes two additional ensembles, one with physically light up and down quarks and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≈</mo><mn>0.06</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and one with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≈</mo><mn>0.03</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> on which we are able to reach the physical bottom quark mass. Our calculation uses nonperturbatively renormalized current operators and covers the full kinematical range of the decay. We use our recent results for the heavy-charm susceptibilities, as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mo>=</mo><msub><mi>m</mi><mi>c</mi></msub><mo>/</mo><msub><mi>m</mi><mi>h</mi></msub></math>, in order to employ the full dispersive parametrization for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in our physical-continuum extrapolation. We give updated Standard Model (SM) predictions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.2597</mn><mo stretchy="false">(</mo><mn>27</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><msub><mi>λ</mi><mi>τ</mi></msub></msub><mo>=</mo><mn>0.5093</mn><mo stretchy="false">(</mo><mn>42</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>F</mi><mi>L</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msubsup><mo>=</mo><mn>0.4421</mn><mo stretchy="false">(</mo><mn>55</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">A</mi><mi>FB</mi></msub><mo>=</mo><mo>−</mo><mn>0.0567</mn><mo stretchy="false">(</mo><mn>61</mn><mo stretchy="false">)</mo></math>, reducing uncertainties by 29%, 45%, 40%, and 50% respectively. Since our lattice form factors cover the full kinematic range we can use them to test extrapolations using data in a truncated range, at low-recoil. We investigate different physical continuum parametrization schemes, with lattice results in the first <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>3</mn></math> of the kinematic range near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>q</mi><mi>max</mi><mn>2</mn></msubsup></math>. We find that unexpectedly large systematic uncertainties near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math> can emerge when extrapolating synthetic data in the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region if higher order kinematical terms are omitted from the physical continuum extrapolation. This suggests a potentially underestimated systematic uncertainty entering extrapolations of synthetic lattice QCD data for the related <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>*</mo></msup><mo>ℓ</mo><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> decay from the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region into the low-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region.

United Kingdom

Judd Harrison

Improved lattice QCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> vector, axial-vector, and tensor form factors

We present the results of our lattice QCD computation of the electric ( <math altimg='si18.svg'><msub><mi>E</mi><mn>1</mn></msub></math>) and magnetic <math altimg='si41.svg'><mrow><mo>(</mo><msub><mi>M</mi><mn>2</mn></msub><mo>)</mo></mrow></math> form factors relevant to the <math altimg='si42.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mspace width='0.16em' /><mi>&#947;</mi></mrow></math> decay by using the gauge field configurations produced by the Extended Twisted Mass Collaboration with <math altimg='si24.svg'><mrow><msub><mi>N</mi><mi>f</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn></mrow></math> dynamical Wilson-Clover twisted mass fermions at four different lattice spacings with physical dynamical <math altimg='si43.svg'><mi>u</mi></math>, <math altimg='si44.svg'><mi>d</mi></math>, <math altimg='si45.svg'><mi>s</mi></math> and <math altimg='si46.svg'><mi>c</mi></math> quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with <math altimg='si47.svg'><mrow><msub><mi>m</mi><mi>&#960;</mi></msub><mo>&#8771;</mo><mn>175</mn><mspace width='0.33em' /><mrow><mi mathvariant='normal'>MeV</mi></mrow></mrow></math>). In the continuum limit, we obtain <math altimg='si48.svg'><mrow><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mrow><mo>(</mo><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><mi>J</mi><mo linebreak='badbreak'>/</mo><mi>&#968;</mi><mspace width='0.33em' /><mi>&#947;</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>0.3265</mn><mrow><mo>(</mo><mn>79</mn><mo>)</mo></mrow><mspace width='0.33em' /><mrow><mi mathvariant='normal'>MeV</mi></mrow></mrow></math>, which agrees to <math altimg='si49.svg'><mrow><mo>(</mo><mn>1</mn><mo>&#247;</mo><mn>2</mn><mo>)</mo><mi>&#963;</mi></mrow></math> with the experimental results and disagrees with a previous (unquenched) lattice QCD calculation. Our result for the magnetic quadrupole fractional transition amplitude, <math altimg='si50.svg'><mrow><msub><mi>a</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>M</mi><mn>2</mn></msub><mo linebreak='goodbreak'>/</mo><msqrt><mrow><msubsup><mi>E</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup><mo linebreak='badbreak'>+</mo><msubsup><mi>M</mi><mrow><mn>2</mn></mrow><mn>2</mn></msubsup></mrow></msqrt><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>0.0666</mn><mrow><mo>(</mo><mn>22</mn><mo>)</mo></mrow></mrow></math>, is in agreement with the experiment and represents an improvement by a factor of about 30 with respect to the only existing (quenched) lattice QCD result.

France

Damir Bečirević

Roberto Di Palma

Roberto Frezzotti

Giuseppe Gagliardi

Vittorio Lubicz

Francesco Sanfilippo

Nazario Tantalo

Lattice QCD study of the <math altimg='si39.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi>&#947;</mi></mrow></math> decay

The first observation of the $${{{{\varXi } ^0_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{\pi } ^+} }}$$ decay and the most precise measurement of the branching fraction of the $${{{\varLambda } ^0_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{K} ^+} }$$ decay are reported, using proton-proton collision data from the LHCb experiment collected in 2016–2018 at a centre-of-mass energy of 13 $$\text {\,Te\hspace{-1.00006pt}V}$$ , corresponding to an integrated luminosity of 5.4 $$\text {\,fb} ^{-1}$$ . Using the $${{{{\varLambda } ^0_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {\varLambda } }}$$ and $${{{{\varXi } ^-_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} }}$$ decays as normalisation channels, the ratios of branching fractions are measured to be where the first uncertainty is statistical and the second systematic.

Netherlands

R. Aaij

A. Abdelmotteleb

Switzerland

C. Beteta

F. Abudinén

T. Ackernley

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

P. Albicocco

J. Albrecht

F. Alessio

M. Alexander

Z. Aliouche

P. Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

A. Andreianov

P. Andreola

M. Andreotti

D. Andreou

A. Anelli

D. Ao

F. Archilli

M. Argenton

Costa Rica

S. Cuendis

A. Artamonov

M. Artuso

E. Aslanides

R. Silva

M. Atzeni

B. Audurier

D. Bacher

I. Perea

S. Bachmann

M. Bachmayer

J. Back

P. Rodriguez

V. Balagura

A. Balboni

W. Baldini

L. Balzani

H. Bao

J. Souza Leite

Observation of the $${{{\varLambda } ^0_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{K} ^+} }$$ and $${{{{\varXi } ^0_{b}} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{\pi } ^+} }}$$ decays