We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <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><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <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><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

China

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

The LHCb Collaboration has recently found a large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating rate asymmetry in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. This is the first observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in baryon processes, opening a new window to test its standard model (SM) origin. Many more baryon decays are expected to exhibit observable signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. We show that there also exists large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the U-spin partner decay mode, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, with rate asymmetry <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><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><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><mfrac><mrow><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo stretchy="false">−</mo></msup><msup><mi>π</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow><mrow><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><msup><mi>K</mi><mo stretchy="false">+</mo></msup><msup><mi>K</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow></mfrac><mfrac><msup><mi>τ</mi><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></msup><msup><mi>τ</mi><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></msup></mfrac></math> in the U-spin symmetry limit. By neglecting a subleading contribution in the amplitudes, <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><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mo stretchy="false">(</mo><mn>12</mn><mo>±</mo><mn>6</mn><mo stretchy="false">)</mo><mo>%</mo></math>. These predictions can be tested in the near future.

Xiao-Gang He

Chia-Wei Liu

Jusak Tandean

Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and its <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>-spin partner decays

A search for the decay $\textit{B}$ $\textit{→ ϕϕ}$ is made using $\textit{pp}$ collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb . No significant signal is observed, and an upper limit on the branching fraction of 1$\textit{.}$3 (1$\textit{.}$4) × 10 at 90 (95)% confidence level is set. This result supersedes the previous LHCb study and improves the upper limit by a factor of two.

Netherlands

R. Aaij

United Kingdom

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

Z. Aliouche

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

C. Betancourt

F. Betti

J. Bex

Ia. Bezshyiko

Ukraine

O. Bezshyyko

J. Bhom

M. Bieker

N. Biesuz

P. Billoir

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

Canada

T. Blake

F. Blanc

J. Blank

Search for the decay $\textit{B}$

The observation of a wide peaking structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mi>γ</mi></math> mass spectrum is reported using proton-proton collision data collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total 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 statistical significance over the background-only hypothesis exceeds seven standard deviations. The width of the observed structure is larger than the expectation from a single-peak hypothesis, and is well described by an effective minimal model consisting of two narrow peaks located at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6704.8</mn><mo>±</mo><mn>5.5</mn><mo>±</mo><mn>2.8</mn><mo>±</mo><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mrow><mi>MeV</mi><mo>/</mo></mrow><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6752.4</mn><mo>±</mo><mn>9.5</mn><mo>±</mo><mn>3.1</mn><mo>±</mo><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mrow><mi>MeV</mi><mo>/</mo></mrow><msup><mi>c</mi><mn>2</mn></msup></math>. The uncertainty terms are statistical, systematic, and associated to the knowledge of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> mass, respectively. The measured peak locations are in line with theoretical predictions for lowest excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> states, marking the first observation of orbitally excited beauty-charm mesons and providing important insights into the internal dynamics of hadrons containing two heavy quarks.

A.S.W. Abdelmotteleb

A.A. Adefisoye

C.A. Aidala

CERN

J.L. Amey

J.A. Authier

J.J. Back

I.R. Barbosa

R.J. Barlow

P.B. Battista

I.B. Bediaga

N.A. Behling

M.S. Bieker

N.V. Biesuz

F.C.R. Bishop

J.E. Blank

S. Blusk

Observation of Orbitally Excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> States

The study of a wide peaking structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mi>γ</mi></math> mass spectrum is reported using a data sample of proton-proton collisions collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, 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 observed structure is consistent with the lowest excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> states and exhibits a statistical significance exceeding 7 standard deviations relative to the background-only hypothesis. A two-peak model serves as an effective description of the data, with various theory-constrained models further explored to provide physical interpretation. Based on the predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> spectrum, the relative production cross section of the overall <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> states with respect to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> ground state with the transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math> and rapidity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>y</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> mesons in the regions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub><mo>&lt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.0</mn><mo>&lt;</mo><mi>y</mi><mo>&lt;</mo><mn>4.5</mn></math> 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> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.20</mn><mo>±</mo><mn>0.03</mn><mo>±</mo><mn>0.02</mn><mo>±</mo><mn>0.03</mn></math>, where the uncertainty terms represent statistical, systematic, and uncertainties related to the choice of theoretical models, respectively. The results provide a test of theoretical models and deepen our understanding of quantum chromodynamics.

Z Areg

Study of <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><mn>1</mn><mi>P</mi><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> states in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mi>γ</mi></math> mass spectrum

Applying the light-cone sum rules approach, the next-to-leading-order corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi></math> form factors are calculated with the twist-two and twist-three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson light-cone distribution amplitudes (LCDAs) at leading power in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo>/</mo><msub><mi>m</mi><mi>b</mi></msub></math>. At one-loop level, the vacuum-to-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson correlation functions defined with interpolating currents for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave axial-vector meson are factorized into short-distance coefficients and the distribution amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson, among which the hard coefficients for A0-type currents and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>-dependent jet functions entering correlation functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Π</mi><mrow><mi>μ</mi><mo>,</mo><mo stretchy="false">∥</mo></mrow><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>+</mo><mover accent="true"><mi>T</mi><mo stretchy="false">˜</mo></mover><mo stretchy="false">)</mo></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Π</mi><mrow><mi>δ</mi><mi>μ</mi><mo>,</mo><mo>⊥</mo></mrow><mrow><mo stretchy="false">(</mo><mi>V</mi><mo>−</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Π</mi><mrow><mi>δ</mi><mi>μ</mi><mo>,</mo><mo>⊥</mo></mrow><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>+</mo><mover accent="true"><mi>T</mi><mo stretchy="false">˜</mo></mover><mo stretchy="false">)</mo></mrow></msubsup></math> are identical to the corresponding ones of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>V</mi></math> in soft-collinear effective theory (SCET). In addition, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Π</mi><mrow><mi>μ</mi><mo>,</mo><mo stretchy="false">∥</mo></mrow><mrow><mo stretchy="false">(</mo><mi>V</mi><mo>−</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Π</mi><mrow><mi>μ</mi><mo>,</mo><mo stretchy="false">∥</mo></mrow><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>+</mo><mover accent="true"><mi>T</mi><mo stretchy="false">˜</mo></mover><mo stretchy="false">)</mo></mrow></msubsup></math> coincide with the results of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mo>,</mo><mi>K</mi></math> under the limit <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>q</mi></msub><mo stretchy="false">→</mo><mn>0</mn></math> up to one-loop accuracy. Then the subleading-power corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi></math> form factors are computed with the higher-twist <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson LCDAs at tree level up to the twist-six accuracy. Furthermore, we predict the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> dependence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi></math> form factors via the Bourrely-Caprini-Lellouch <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-series expanding parametrization to compute several physical observables including branching ratios of semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo>ℓ</mo><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><msub><mi>ν</mi><mo>ℓ</mo></msub><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> processes, transverse asymmetries, forward-backward asymmetries, and lepton-flavor universality observables employing the given mixing angles <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mi>K</mi></msub><mo>=</mo><mo>−</mo><mn>3</mn><mn>4</mn><mi>°</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><msub><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></mrow></msub><mo>=</mo><mn>2</mn><mn>8</mn><mi>°</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><msub><mn>3</mn><msub><mi>P</mi><mn>1</mn></msub></msub></msub><mo>=</mo><mn>2</mn><mn>3</mn><mi>°</mi></math>. We also compare our theory calculations with the results from other methods.

Fang-Zhou Di

Yu-Hao Liu

Next-to-leading-order QCD calculations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi></math> form factors with higher-twist corrections

We present a comprehensive QCD analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> form factors within the framework of light-cone sum rules, employing two-pion light-cone distribution amplitudes (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mi>DA</mi></math>s). For the first time, we derive the twist-three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mi>DA</mi></math>s explicitly by exploiting the conformal symmetry of massless QCD. This breakthrough enables the first systematic calculation of higher-power corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math>-type transitions. Leveraging the recently measured partial decay fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math> by the Belle detector, we obtain <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><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>4.27</mn><mo>±</mo><mn>0.49</mn><msub><mo stretchy="false">|</mo><mrow><mi>data</mi></mrow></msub><mo>±</mo><mn>0.55</mn><msub><mo stretchy="false">|</mo><mtext>LCSRs</mtext></msub><mo stretchy="false">)</mo></mrow><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> within the dominant region of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> resonance. We clarify that the relatively small value of <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> extracted from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>ρ</mi><mi>l</mi><mi>ν</mi></math>, when compared to the golden channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>l</mi><mi>ν</mi></math>, arises due to the finite width and nonresonant effects. We anticipate future measurements of purely isovector and isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>l</mi><mn>4</mn></mrow></msub></math> decays, which will aid in reducing uncertainties by enhancing our understanding of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> phase shifts in the two-pion distribution amplitudes through heavy flavor decays.

Shan Cheng

QCD analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> form factors and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></mrow></math> extraction from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>l</mi><mn>4</mn></mrow></msub></math> decays

We study an alternative $$U(1)_{B-L}$$ model with singlet chiral fermions which can act as WIMP and FIMP type DM, which is anomaly-free by constructions in contrast to the well studied $$B-L$$ extension where three right handed neutrinos are needed for gauge anomaly cancellation. Fermion dark matter masses are generated after the $$U(1)_{B-L}$$ is broken spontaneously, so the Yukawa couplings for WIMP and FIMP components can be distinguished by the hierarchical values of the vacuum expectation values of the singlet scalar fields. Moreover, the $$U(1)_{B-L}$$ gauge boson receives a TeV-scale mass for a tiny extra gauge coupling, so it goes out of equilibrium from the rest of the model content in the early Universe. Both the $$U(1)_{B-L}$$ gauge boson and FIMP component are produced from the decays of the bath particles, and the former can decay into FIMP DM and/or WIMP DM before BBN. The WIMP component can reside in the resonance region of the Higgs bosons or dominantly annihilate into a pair of singlet-like scalars. Thus, there is a flexibility to choose a small mixing between the visible and dark sectors, thereby evading all the current direct and indirect detection bounds. Furthermore, we show that WIMP and FIMP components can coexist in suitable fractions, depending on the choice of model parameters, allowing for additional protection for WIMP DM against various experimental bounds. Finally, we identify the dimension-6 and dimension-7 operators for Majorana neutrino masses in our model, being consistent with the $$U(1)_{B-L}$$ gauge symmetry, and provide a possibility of extending the model with additional singlet fermions for neutrino masses.

South Korea

Sarif Khan

Hyun Lee

WIMP-FIMP option and neutrino masses via a novel anomaly-free $$B-L$$ symmetry

Inspired by the significant virtual contributions of the subprocesses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo>/</mo><msup><mi>B</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">→</mo><mi>ω</mi><mi>π</mi><mo>/</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> in the three-body hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson decays, we study the off-shell effects of the resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> decaying into the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mi>ρ</mi></math> system in the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi><mi>h</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><mi>ρ</mi><mi>h</mi></math> (with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>h</mi><mo>=</mo><mi>π</mi></mrow><mo>,</mo><mrow><mi>K</mi></mrow></mrow></math>) within the perturbative QCD approach. The strong coupling constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msup><mi>K</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msup><mi>K</mi><mo>*</mo></msup><mi>K</mi><mi>ρ</mi></mrow></msub></math> involved in this work are derived from the coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>ρ</mi><mi>ω</mi><mi>π</mi></mrow></msub></math> under the flavor SU(3) symmetry. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> averaged branching fractions for the quasi-two-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">[</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi><mo stretchy="false">]</mo><mi>h</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">[</mo><mo stretchy="false">→</mo><mi>K</mi><mi>ρ</mi><mo stretchy="false">]</mo><mi>h</mi></math> are predicted to be on the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>9</mn></mrow></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> in this study. And the branching fractions for the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">[</mo><mo stretchy="false">→</mo><mi>K</mi><mi>ρ</mi><mo stretchy="false">]</mo><mi>h</mi></math> are found to be around half of the corresponding results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">[</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi><mo stretchy="false">]</mo><mi>h</mi></math> channels, mainly due to the phase space difference between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math> pairs originating from the intermediate state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>. Experimental data for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> decaying into the final states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mi>ρ</mi></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson decays is expected to be obtained by the LHCb and Belle-II experiments in the near future.

Ai-Jun Ma

Wen-Fei Wang

Virtual contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi><mi>h</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><mi>ρ</mi><mi>h</mi></math> decays

Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

M. Ablikim

Russia

M.N. Achasov

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

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

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)