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)

In this work, we investigate possible bound states in the $ D_s\bar{D}_s $ system using the Bethe-Salpeter (BS) formalism within both the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation with a kernel that incorporates contributions from $\textit{ϕ}$ and $ J/\psi $ meson exchanges, we confirm the existence of a loosely bound state. Furthermore, we explore the partial decay widths of the $ D_s\bar{D}_s $ bound state into the $ D\bar{D} $ , $ \eta_c\eta $ , and $ J/\psi\omega $ channels, and observe that these widths are sensitive to the model parameter $\textit{α}$. Notably, we find the dominant decay channel for the $ D_s\bar{D}_s $ bound state to be $ D\bar{D} $ .

Jing-Juan Qi

Zhen-Yang Wang

Zhu-Feng Zhang

Xin-Heng Guo

The properties of the $\textit{S}$-wave D$_{s}$ D $_{s}$ bound state * Supported by the National Natural Science Foundation of China (12405115, 12275024, 12105149)

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

K. Abeling

N. Abicht

S. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

H. Abreu

Y. Abulaiti

Italy

United Kingdom

B. Acharya

A. Ackermann

C. Bourdarios

Poland

L. Adamczyk

S. Addepalli

M. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A. Affolder

Y. Afik

Spain

M. Agaras

J. Agarwala

A. Aggarwal

Romania

C. Agheorghiesei

Azerbaijan

F. Ahmadov

Canada

W. Ahmed

S. Ahuja

X. Ai

G. Aielli

A. Aikot

M. Tamlihat

B. Aitbenchikh

M. Akbiyik

Sweden

T. Åkesson

A. Akimov

Japan

D. Akiyama

N. Akolkar

S. Aktas

K. Khoury

G. Alberghi

J. Albert

P. Albicocco

G. Albouy

S. Alderweireldt

Z. Alegria

Switzerland

M. Aleksa

I. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H. Ali

S. Ali

S. Alibocus

South Africa

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B. Allbrooke

J. Allen

Chile

C. Flores

P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

Z. Alsolami

M. Estevez

A. Fernandez

M. Cardoso

M. Alviggi

M. Aly

Brazil

Y. Coutinho

A. Ambler

C. Amelung

M. Amerl

C. Ames

D. Amidei

B. Amini

K. Amirie

Portugal

S. Santos

K. Amos

D. Amperiadou

S. An

V. Ananiev

C. Anastopoulos

T. Andeen

J. Anders

A. Anderson

S. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A. Anisenkov

A. Annovi

C. Antel

Erratum: Precision measurement of the $$B^0$$ meson lifetime using $$B^0 \rightarrow J/\psi K^{*0}$$ decays with the ATLAS detector

<p>An amplitude analysis 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><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><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> decay is performed in the mass regions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.30</mn><mo>&lt;</mo><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>&lt;</mo><mn>1.10</mn><mtext> </mtext><mtext> </mtext><mrow><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.75</mn><mo>&lt;</mo><msub><mrow><mi>m</mi></mrow><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></msub><mo>&lt;</mo><mn>1.20</mn><mtext> </mtext><mtext> </mtext><mrow><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></math>, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collision data recorded with the LHCb detector corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>9</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The polarization fractions and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries for <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><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> decays are measured. Violation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> is observed for the first time, with a significance exceeding 9 standard deviations. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>=</mo><mrow><mn>0.507</mn><mo>±</mo><mn>0.062</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.024</mn><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></mrow></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-averaged longitudinal polarization fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>L</mi></msub><mo>=</mo><mrow><mn>0.720</mn><mo>±</mo><mn>0.028</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.009</mn><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></math>. The measurements help to shed light on the polarization puzzle of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> mesons decaying to two vector mesons.</p>

Netherlands

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

J. Albrecht

R. Aleksiejunas

CERN

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

Costa Rica

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

First Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation and Measurement of Polarization in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> Decays