All charmless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><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"><mi>P</mi></math> denotes the light pseudoscalar meson and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math> denotes the vector meson) decays have not been experimentally observed to date, but some of them might be measured in the near future. The charmless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays with the axial-vector (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>) resonance states, the tensor (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>) resonance states, and the excited vector (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mrow><mi>E</mi><mo>,</mo><mi>D</mi></mrow></msub></math>) resonance states are studied based on flavor SU(3) analysis in this work, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mi>E</mi></msub></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>1450</mn><mo stretchy="false">)</mo><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1410</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ω</mi><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1680</mn><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math> with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>n</mi><mrow><mn>2</mn><mi>S</mi><mo>+</mo><mn>1</mn></mrow></msup><msub><mi>L</mi><mi>J</mi></msub><mo>=</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mi>D</mi></msub></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>1700</mn><mo stretchy="false">)</mo><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1680</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ω</mi><mo stretchy="false">(</mo><mn>1650</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mn>2170</mn><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math> with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>n</mi><mrow><mn>2</mn><mi>S</mi><mo>+</mo><mn>1</mn></mrow></msup><msub><mi>L</mi><mi>J</mi></msub><mo>=</mo><msup><mn>1</mn><mn>3</mn></msup><msub><mi>D</mi><mn>1</mn></msub></math>. The hadronic amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo>/</mo><mi>T</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays are related by the nonperturbative parameters, and the branching ratio predictions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo>/</mo><mi>T</mi><mo>/</mo><msub><mi>V</mi><mrow><mi>E</mi><mo>,</mo><mi>D</mi></mrow></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> are obtained, and then the branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><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"><mi>B</mi><mo stretchy="false">→</mo><mi>T</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><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"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>V</mi><mi>E</mi></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mi>E</mi></msub><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><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"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>V</mi><mi>D</mi></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mi>D</mi></msub><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> are obtained by the narrow width approximation or further considering the width effects. We find that most branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays and many branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays are on the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></math>, and all branching ratios with the tensor resonance states and the excited vector resonance states are small. Our results could be tested in the future Belle II and LHCb experiments.

China

Yi Qiao

Jin-Huan Sheng

Yuan-Guo Xu

Ru-Min Wang

Flavor SU(3) analysis of the charmless semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays

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 collected with the BESIII detector operating at the Beijing electron positron collider, the cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> is measured at 59 points with center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math> ranging from 4.009 to 4.950 GeV with a total integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>22.2</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The cross section between 4.3 and 4.45 GeV exhibits a plateaulike shape and drops sharply around 4.5 GeV, which cannot be described by two resonances only. Three coherent Breit-Wigner functions are used to parametrize the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>-dependent cross section line shape. The masses and widths are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mrow><mn>4223.6</mn></mrow><mrow><mo>−</mo><mn>3.7</mn><mo>−</mo><mn>2.9</mn></mrow><mrow><mo>+</mo><mn>3.6</mn><mo>+</mo><mn>2.6</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>58.5</mn></mrow><mrow><mo>−</mo><mn>11.4</mn><mo>−</mo><mn>6.5</mn></mrow><mrow><mo>+</mo><mn>10.8</mn><mo>+</mo><mn>6.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>4327.4</mn></mrow><mrow><mo>−</mo><mn>18.8</mn><mo>−</mo><mn>9.3</mn></mrow><mrow><mo>+</mo><mn>20.1</mn><mo>+</mo><mn>10.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>2</mn></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mn>244.1</mn><mrow><mo>−</mo><mn>27.1</mn><mo>−</mo><mn>18.3</mn></mrow><mrow><mo>+</mo><mn>34.0</mn><mo>+</mo><mn>24.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>4467.4</mn><mrow><mo>−</mo><mn>5.4</mn><mo>−</mo><mn>2.7</mn></mrow><mrow><mo>+</mo><mn>7.2</mn><mo>+</mo><mn>3.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>62.8</mn><mrow><mo>−</mo><mn>14.4</mn><mo>−</mo><mn>7.0</mn></mrow><mrow><mo>+</mo><mn>19.2</mn><mo>+</mo><mn>9.9</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The first uncertainties are statistical and the second are systematic. The inclusion of the relatively narrower third component proves crucial for reproducing the drop at around 4.5 GeV. The statistical significance of the three-resonance assumption over the two-resonance assumption is greater than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

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.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

Z.K. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

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

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. 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

L. Feng

Q.X. Feng

Y.T. Feng

Observation of Three Resonant Structures in the Cross Section 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><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>h</mi><mi>c</mi></msub></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.

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 measure the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> decays reconstructed in <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> collisions at the Belle II experiment using a dataset corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>428</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. A control sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> decays is used to correct for detection and production asymmetries. The result <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><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>1.8</mn><mo>±</mo><mn>0.9</mn><mo>±</mo><mn>0.1</mn><mo stretchy="false">)</mo><mo>%</mo></math>, where the first uncertainty is statistical and the second systematic, is the most precise determination to date. It agrees with the prediction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry from the standard model and with results of previous measurements.

I. Adachi

L. Aggarwal

H. Ahmed

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

P. Bambade

Sw. Banerjee

S. Bansal

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S. Choudhury

I. Consigny

L. Corona

J.X. Cui

S. Das

E. De La Cruz-Burelo

S.A. De La Motte

Measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> decays at Belle II