The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in the phase space in multi-body decays of bottom and charmed mesons. In this study, we examine the CP violation in the decay channel $ {\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0} $ in the phase-space region where the intermediate resonances $ \overline{K}^{*}(892)^{0} $ and $ {\overline{K}^{*}_{0}(700)} $ dominate. In particular, the forward-backward asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are investigated. The nontrivial correlation between FBA and FB-CPA is analyzed. The analysis indicates that FB-CPAs around the resonance $ \overline{K}^{*}(892)^{0} $ can be as large as approximately 35%, which can be potentially accessible by Belle and Belle-II collaborations in the near future.

China

Jian-Yu Yang

Yu-Jie Zhao

Jing-Juan Qi

Zhen-Hua Zhang

The forward-backward asymmetry induced CP asymmetry in ${{\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0}}$ in phase space around the resonances ${{\overline{K}}^{*}(892)^{0}}$ and ${{\overline{K}}^{*}_{0}(700)}$ * Supported by National Natural Science Foundation of China (12475096, 12405115, 12192261) and Scientific Research Fund of Hunan Provincial Education Department (22A0319)

In double charmonium production, a long-standing challenge is that the theoretical predictions are not consistent with the measurements at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories. Within the Non-Relativistic Quantum Chromodynamics (NRQCD) framework, the next-to-leading order calculation has proved its power to cut down the discrepancy between theory and experiments. To further clarify this puzzle, we have performed the next-to-next-to-leading order calculation. The amplitude is obtained as an analytical asymptotic expansion in the ratio of the squared charm-quark mass over the squared center-of-mass energy, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>m</mi><mi>c</mi><mn>2</mn></msubsup><mo>/</mo><mi>s</mi></math>. We investigate the origin of the leading logarithms by performing a region analysis, revealing the intricate factorization structure in this process. We provide numerical predictions on the total cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mi>η</mi><mi>c</mi></msub></math> production, which agree with the experimental results. Extension of our computation to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo>+</mo><msub><mi>η</mi><mi>b</mi></msub></math> production is also discussed.

Xiang Chen

Xin Guan

Chuan-Qi He

Yan-Qing Ma

Jian Wang

Da-Jiang Zhang

Analytical two-loop amplitudes 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><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mi>η</mi><mi>c</mi></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories

In 2023, the Belle II Collaboration announced the observation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>ν</mi><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> decay channel for the first time. This decay channel provides a clean signal with high precision in theoretical calculations. However, we encounter a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.8</mn><mi>σ</mi></math> deviation from the Standard Model prediction. To resolve this excess, we study a scalar dark matter model with local discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math> symmetry. Assuming dark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>X</mi></msub><mo>≡</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> symmetry, this <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> symmetry is spontaneously broken into local discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math> by nonzero vacuum expectation value of dark Higgs boson. Considering a dark Higgs mass is 2 GeV, we can explain the recent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Br</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>ν</mi><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo></mrow></math> excess reported from the Belle II Collaboration and relic abundance at the same time.

Jongkuk Kim

Pyungwon Ko

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo></mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>ν</mi><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> excess and DM semi-annihilation

The first four-dimensional amplitude analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decay is performed with proton-proton collision data collected by the LHCb experiment at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.4</mn><mtext> </mtext><mtext> </mtext><mrow><mi mathvariant="normal">f</mi><msup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></mrow></math>. The data cannot be fully explained by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> contributions alone. A significantly better description of the data is obtained by adding a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow><mo>+</mo></msubsup></math> contribution decaying to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup></math>. The properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow><mo>+</mo></msubsup></math> structure are consistent with the exotic state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> reported in the isospin-related <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><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> decay. Effects of a possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup><mo stretchy="false">→</mo><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2600</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msup><mi>D</mi><mo>+</mo></msup></math> decay mode on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup></math> mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> structure using the triangle singularity mechanism is studied and also found to be consistent with the data.

R. Aaij

A.S.W. Abdelmotteleb

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

B. Adeva

M. Adinolfi

P. Adlarson

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

M. Akthar

P. Albicocco

J. Albrecht

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

S. Amato

J.L. 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

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.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.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

J. Bhom

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

Observation and investigation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> structure in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decays

We perform a detailed analysis of semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> decays mediated by flavor-changing neutral currents (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>d</mi></math>) with dilepton or dineutrino final states within the perturbative quantum chromodynamics (QCD) framework. All independent form factors including vector, axial-vector, tensor, and pseudotensor currents are calculated and are used to analyze the decay branching fractions and angular distributions. Our numerical results for the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Ξ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays suggest they are within measurable reach for the LHCb experiment in the near future. For the case of unpolarized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> baryons, we derive several angular observables, which can provide new and complementary constraints on Wilson coefficients in semileptonic flavor changing neutral current transitions compared to those from mesonic decays. Finally, we present a combined analysis of dilepton and dineutrino channels, comparing various observables in detail. Our results offer further insights into the long-standing anomalies observed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson decays.

Zhou Rui

Zhi-Tian Zou

Ya Li

Ying Li

Semileptonic neutral current decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> with dileptons or dineutrinos in the final state

In all previous calculations of the nonlocal subleading contribution to the inclusive penguin decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi></math> due to the interference of the electroweak operators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">O</mi><mn>1</mn><mi>c</mi></msubsup><mo>−</mo><msub><mi mathvariant="script">O</mi><mrow><mn>7</mn><mi>γ</mi></mrow></msub></math> the local Voloshin term was subtracted. In view of the ongoing analysis at order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>, we present a calculation of the complete nonlocal contribution which takes into account the high correlation between the uncertainties of the local Voloshin and the nonlocal term of the previous analyses. The new calculation has a high impact on the range of the nonlocal contribution.

Michael Benzke

Maria Vittoria Garzelli

Tobias Hurth

Addendum to “Resolved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>m</mi><mi>b</mi></msub></math> contributions to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mrow><mi>s</mi><mo>,</mo><mi>d</mi></mrow></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi></math>”

We systematically investigate the dibaryons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> (di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> (di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math>), with various isospin-spin configurations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo></math> in a nonrelativistic quark model. For the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system, only the single channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> are capable of forming deuteronlike bound states, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> meson exchange playing a decisive role. Those states have binding energies of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>3.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and sizes of 2.37 fm and 1.87 fm, respectively. The coupled channel effect in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> enhances the attraction. As a result, this di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system can establish a deuteronlike configuration, with the binding energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>7.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> relative to the threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and the size of approximately 1.40 fm. For the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system, the single channels with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>3</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> can give rise to deuteronlike bound states with binding energies ranging from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>6.1</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>14.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Additionally, the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> can also establish deuteronlike bound states with binding energies of around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. When considering the coupled channel effect in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>, a compact hexaquark state is formed, exhibiting a binding energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>21.2</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> relative to the threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> and a size of 0.53 fm. In this state, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> meson exchange provides a very powerful attractive force. The meson exchange interactions in the quark model is dispensable in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> bound states, except for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mo>*</mo></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mo>*</mo></msubsup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>.

An-Su Lu

Mao-Jun Yan

Chun-Sheng An

Cheng-Rong Deng

Heavy dibaryons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>

We present the nonrelativistic QCD (NRQCD) calculations at the next-to-leading order (NLO) of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> for <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>η</mi><mi>c</mi></msub></math> vector, axial-vector, tensor, and axial-tensor form factors, and obtain complete analytical expressions for the form factors, along with their asymptotic forms in the hierarchical heavy quark limit. Our results show that the NLO corrections are both sizable and well behaved in the low squared transfer momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> region. Using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>NRQCD</mi><mo>+</mo><mtext>lattice</mtext></mrow><mo>+</mo><mi>z</mi></math>-series method, we further provide theoretical predictions for <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>η</mi><mi>c</mi></msub></math> form factors across the full physical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range. Based on these predicted form factors, we finally compute the decay widths and branching fractions for the semileptonic 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>η</mi><mi>c</mi></msub><mo>+</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>.

Wei Tao

Ya-Hui Zhao

Li-Ting Wang

Qin Chang

Zhen-Jun Xiao

Form factors for <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>η</mi><mi>c</mi></msub><mo>+</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math> at NLO in QCD

Exclusive semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> mesons to the ground, radially and orbitally excited states of light mesons are investigated in the framework of the relativistic quark model based on the quasipotential approach. Such decays are very important for the determination of the 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>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> and testing the nature of the excited light mesons. The mixing schemes for the isoscalar light mesons are considered. The possible assignment of the experimentally observed excited light mesons to the particular states is discussed. The form factors parametrizing weak decay matrix elements between the initial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson and final light mesons are calculated with the complete account of the relativistic effects, including contributions of the intermediate negative energy states and relativistic transformations of the meson wave functions from rest to the moving reference frame. As a result, the transferred momentum squared, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math>, dependence of the form factors is explicitly determined in the whole accessible kinematical range. On the basis of the helicity formalism, the decay branching fractions and asymmetry and polarization parameters are calculated. The obtained results for the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays to the ground states of light mesons are confronted with available experimental data. On this basis, the value of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> matrix element is determined. It is found in good agreement with the value extracted from inclusive decays. Predictions for the branching fractions of the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays to radially (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>) and orbitally (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>) excited light mesons are given. Comparison with the previous calculations is performed. It is found that several decays to the excited light mesons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>1450</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1235</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1260</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1170</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1320</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1700</mn><mo stretchy="false">)</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>) have branching fractions of the order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> and, thus, they can be measured at existing and future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories.

V.O. Galkin

Xian-Wei Kang

Exclusive semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays to the ground and excited states of light mesons

We investigate the physics reach and potential for the study of $\textit{B}$-meson decays to invisible final states at the Future Circular Collider running electron-positron collisions at the $\textit{Z}$ pole (FCC-ee). Signal and background candidates are simulated for a proposed multipurpose detector, including inclusive contributions from $\textit{Z}$ decays to leptons or quarks. Signal candidates are selected by a mixture of rectangular cuts and a multiclass boosted decision tree classifier.

United Kingdom

M. Kenzie

R. Mangrulkar

A. Wiederhold

E. Wood

Prospects of searches for invisible $\textit{B}$-meson decays at FCC-ee