Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

China

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

We propose a new extension of the Standard Model that incorporates a gauged $$ U(1)_{\mathrm{B-L}} $$ symmetry and the type-III seesaw mechanism to explain neutrino mass generation and provide a viable dark matter (DM) candidate. Unlike the type-I seesaw, the type-III seesaw extension under $$ U(1)_{\mathrm{B-L}} $$ is not automatically anomaly-free. We show that these anomalies can be canceled by introducing additional chiral fermions, which naturally emerge as DM candidates in the model. We thoroughly analyze the DM phenomenology, including relic density, direct and indirect detection prospects, and constraints from current experimental data. Furthermore, we explore the collider signatures of the model, highlighting the enhanced production cross-section of the triplet fermions mediated by the $$ \mathrm B-L $$ gauge boson, as well as the potential disappearing track signatures. Additionally, we investigate the gravitational wave signals arising from the first-order phase transition during $$ \mathrm B-L $$ symmetry breaking, offering a complementary cosmological probe of the framework.

South Korea

India

Satyabrata Mahapatra

Partha Paul

Narendra Sahu

Prashant Shukla

Verifiable type-III seesaw and dark matter in a gauged $$U(1)_{\mathrm{B-L}}$$ symmetric model

In this work, we derive a new class of analytic black hole solutions within the framework of <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math>, enabling a detailed exploration of how anisotropic pressures and different <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters ( <italic>&#946;</italic> <inf>1</inf>, <italic>&#946;</italic> <inf>2</inf>, <italic>&#946;</italic> <inf>3</inf>) under which the energy condition is satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian <math altimg='si9.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> and the trace <italic>T</italic> of the energy-momentum tensor.

Aniruddha Ghosh

Ujjal Debnath

The new black hole solution with anisotropic fluid in <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity: Thermodynamics

The observed matter–antimatter asymmetry of the Universe remains a fundamental challenge in modern physics. In this work, we explore gravitational baryogenesis within the framework of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity, where the gravitational Lagrangian depends on both the torsion scalar <italic>T</italic> and the matter Lagrangian <italic>L<inf>m</inf></italic>. We consider three representative models and examine their ability to generate the observed baryon-to-entropy ratio. Our analysis shows that couplings involving both torsion and the matter Lagrangian, <math altimg='si35.svg'><mrow><msub><mi>&#8706;</mi><mi>&#956;</mi></msub><mrow><mo>(</mo><mo>&#8722;</mo><mi>T</mi><mo linebreak='badbreak'>&#8722;</mo><mfrac><msub><mi>L</mi><mi>m</mi></msub><msub><mi>L</mi><mn>0</mn></msub></mfrac><mo>)</mo></mrow></mrow></math>, can successfully account for the baryon asymmetry for decoupling temperatures in the range 10 12&#8211;10 14&#8201;GeV, while remaining consistent with small deviations from General Relativity. These results highlight the capacity of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity to provide novel mechanisms for baryogenesis, demonstrating that the interplay between torsion and matter-sector contributions can naturally generate the observed asymmetry. The framework also remains compatible with late-time cosmological evolution, offering a unified setting for early- and late-time dynamics.

Portugal

Daniel F P Cruz

David S. Pereira

Francisco S N Lobo

Gravitational baryogenesis in <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity

We formulate a general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of $$\mathfrak{g}\mathfrak{l}(N)$$ . We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of $$\mathfrak{s}\mathfrak{u}(4)$$ .

Nan Bai

A general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains: application to the ABJM spin chain

We study the collider phenomenology of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> extension of the Standard Model (BLSM), focusing on the production and decay of a heavy neutral gauge boson (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math>) at the Large Hadron Collider (LHC). In this framework, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> can decay into pairs of heavy right-handed neutrinos (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math>), which subsequently decay into charged leptons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> bosons. These processes give rise to three distinctive final states: (i) two leptons plus four jets (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>ℓ</mo><mo>+</mo><mn>4</mn><mi>j</mi></math>), (ii) four leptons plus missing transverse energy (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>ℓ</mo><mo>+</mo><mi>MET</mi></math>), and (iii) three leptons plus two jets and MET (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>ℓ</mo><mo>+</mo><mn>2</mn><mi>j</mi><mo>+</mo><mi>MET</mi></math>). To enhance signal sensitivity and suppress Standard Model backgrounds, we employ multivariate analysis techniques based on boosted decision trees (BDTs), as well as selection optimizations using the xgboost framework. The classifiers are trained on kinematic observables sensitive to the masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math>. We demonstrate that all three final states offer significant discovery potential for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math> at the High-Luminosity LHC. Our results highlight the testability of the BLSM at current and future collider experiments, and provide a promising avenue for probing the origin of neutrino masses and the baryon asymmetry of the Universe.

Egypt

Kareem Ezzat

Syria

Germany

Nidal Chamoun

Shaaban Khalil

Rhitaja Sengupta

Exploring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and right-handed neutrinos in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> symmetric SM at the Large Hadron Collider

A search for a dark baryon is performed for the first time in the two-body decay <math altimg='si14.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>+</mo><mrow><mrow><mi mathvariant='normal'>i</mi></mrow><mi>n</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>l</mi><mi>e</mi></mrow></mrow></math> using (10.087&#8239;&#177;&#8239;0.044)&#8239;&#215;&#8239;10 9 <italic>J</italic>/ <italic>&#968;</italic> events collected at a center-of-mass energy of <math altimg='si23.svg'><mrow><msqrt><mi>s</mi></msqrt><mo linebreak='goodbreak'>=</mo><mn>3.097</mn><mspace width='0.16em' /><mtext>GeV</mtext></mrow></math> with the BESIII detector at the BEPCII collider. No significant signal is observed, and the 90% (95%) confidence level upper limits on the branching fraction <math altimg='si24.svg'><mrow><mi mathvariant='script'>B</mi><mo>(</mo><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>+</mo><mrow><mrow><mi mathvariant='normal'>i</mi></mrow><mi>n</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>l</mi><mi>e</mi></mrow><mo>)</mo></mrow></math> are determined to be <math altimg='si25.svg'><mrow><mn>4.2</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> ( <math altimg='si26.svg'><mrow><mn>5.2</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math>), <math altimg='si27.svg'><mrow><mn>6.9</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> ( <math altimg='si28.svg'><mrow><mn>8.4</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math>), <math altimg='si29.svg'><mrow><mn>6.5</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math> ( <math altimg='si30.svg'><mrow><mn>7.6</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math>), <math altimg='si31.svg'><mrow><mn>1.1</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math> ( <math altimg='si32.svg'><mrow><mn>1.3</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math>) and <math altimg='si33.svg'><mrow><mn>4.5</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> ( <math altimg='si34.svg'><mrow><mn>5.5</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math>), under the dark baryon mass hypotheses of 1.07&#8201;GeV/ <italic>c</italic> 2, 1.10&#8201;GeV/ <italic>c</italic> 2, <math altimg='si19.svg'><msub><mi>m</mi><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></msub></math> (1.116&#8201;GeV/ <italic>c</italic> 2), 1.13&#8201;GeV/ <italic>c</italic> 2, and 1.16&#8201;GeV/ <italic>c</italic> 2, respectively. The constraints obtained on the Wilson coefficients <math altimg='si17.svg'><msubsup><mi>C</mi><mrow><mi>u</mi><mi>s</mi><mo>,</mo><mi>s</mi></mrow><mi>L</mi></msubsup></math> and <math altimg='si18.svg'><msubsup><mi>C</mi><mrow><mi>u</mi><mi>s</mi><mo>,</mo><mi>s</mi></mrow><mi>R</mi></msubsup></math> are more stringent than the previous limits derived from the LHC searches for the colored mediators.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

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. Chen

Z.J. Chen

Z.K. Chen

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

Search for a dark baryon in the <math altimg='si14.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>+</mo><mrow><mrow><mi mathvariant='normal'>i</mi></mrow><mi>n</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>l</mi><mi>e</mi></mrow></mrow></math> decay

This study rigorously examines the influence of dark matter within the framework of <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity, with a particular emphasis on its critical role in facilitating traversable wormhole solutions. By employing anisotropic matter sources modeled through Bose-Einstein condensates and Einasto density profiles, we derive a novel class of wormhole solutions. The construction of the shape function relies on the density profile equation in conjunction with modified field equations, thereby establishing a theoretical foundation for these solutions. Careful selection of parameters ensures that the proposed solutions satisfy all requisite conditions for traversability. Moreover, we conduct a systematic evaluation of energy conditions across two distinct scenarios, further validating the physical viability of the models. The investigation also extends to analyzing anisotropic effects, exoticity parameters, and active gravitational mass. This work presents a comprehensive exploration of the physical feasibility and stability of wormhole structures within the context of <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> modified gravity theories, offering significant contributions to our understanding of the interplay between dark matter and advanced gravitational phenomena.

H Aruna Kumara

Chaitra Chooda Chalavadi

V. Venkatesha

Investigating wormhole structures in <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity: Implications for dark matter

We present a 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>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> from the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> <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 mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson is reconstructed in the modes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><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"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. Charge conjugation is implied. The second <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi><mo>=</mo><msub><mi>v</mi><mi>B</mi></msub><mo>·</mo><msub><mi>v</mi><mi>D</mi></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>B</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>D</mi></msub></math> are the four-velocities of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> mesons. We measure the total decay branching fractions to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.06</mn><mo>±</mo><mn>0.05</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.10</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.31</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.09</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We probe lepton flavor universality by measuring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>1.020</mn><mo>±</mo><mn>0.020</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.022</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo></mrow></math>. Fitting the partial decay branching fraction as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi></math> and using the average of lattice QCD calculations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi></math> form factor, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>39.2</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.6</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.5</mn><mo stretchy="false">(</mo><mrow><mi>th</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>.

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

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

B. Bhuyan

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mi>l</mi></msub></math> decays at Belle II