We systematically analyze the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">(</mo><msup><mi>V</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">)</mo><mi>V</mi><mi>P</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>V</mi><mo>*</mo></msup></math> represents a vector resonance (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ρ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ω</mi></mrow></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>), and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mi>P</mi></math> denotes the final-state meson pairs <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>K</mi></math>. The intermediate subprocesses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><msup><mi>V</mi><mo>*</mo></msup></math> are calculated in the factorization-assisted topological-amplitude approach, while the intermediate resonant states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>V</mi><mo>*</mo></msup></math> are modeled using a relativistic Breit-Wigner distribution, subsequently decaying into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mi>P</mi></math> through strong interactions. We predict the off-shell effects of the ground-state resonances (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup></math>) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">(</mo><msup><mi>V</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">)</mo><mi>V</mi><mi>P</mi></math>. Our results show that the virtual contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">→</mo><mi>ω</mi><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo stretchy="false">→</mo><mi>ρ</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>ρ</mi><mi>K</mi></math> are crucial for these three-body decays, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mi>V</mi><mi>P</mi></math>. In particular, the branching fractions arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math> virtual effects can be comparable to the total decay rates of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mi>ω</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mi>ρ</mi><mi>π</mi></math>, respectively. Decays with branching fractions of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> are expected to be measurable at Belle II and LHCb. Compared with previous perturbative QCD predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">→</mo><mo stretchy="false">)</mo><mi>ω</mi><mi>π</mi></math>, our results are consistent but exhibit higher precision.

China

Jing Ou-Yang

Run-Hui Li

Si-Hong Zhou

Analysis of three-body charmed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo stretchy="false">(</mo><msup><mi>V</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">)</mo><mrow><mi>V</mi><mi>P</mi></mrow></math>

This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of $$\sqrt{s_{\textrm{NN}}}~=~5.02$$ TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analysed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.

Italy

S. Acharya

India

A. Agarwal

Switzerland

G. Rinella

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

South Korea

S. Ahn

Slovakia

I. Ahuja

A. Akindinov

Germany

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H. Alfanda

Mexico

R. Molina

B. Ali

A. Alici

United States

N. Alizadehvandchali

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A. Altamura

I. Altsybeev

J. Alvarado

M. Anaam

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

France

C. Arata

S. Arcelli

R. Arnaldi

Brazil

J. Arneiro

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

D. Averyanov

M. Azmi

Japan

H. Baba

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

A. Baldisseri

Poland

B. Balis

S. Bangalia

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G. Barnaföldi

L. Barnby

E. Barreau

V. Barret

L. Barreto

K. Barth

E. Bartsch

N. Bastid

Sweden

S. Basu

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J. Bazo Alba

Denmark

I. Bearden

P. Becht

D. Behera

I. Belikov

A. Bell Hechavarria

F. Bellini

R. Bellwied

S. Belokurova

L. Beltran

Y. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

L. Bernardinis

L. Betev

P. Bhaduri

A. Bhasin

B. Bhattacharjee

Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at $$\sqrt{{{\varvec{s}}}_{{\textbf {NN}}}}={\textbf {5.02}}$$ TeV

We show that geometric scaling conjectured and observed at the ISR more than 50 years ago, still holds at the LHC. We discuss regularities of the dip - bump structures of the differential elastic cross sections, emphasizing the fact that the ratio of bump to dip positions is constant from the ISR to the LHC. Applying crossing and analyticity we identify imaginary and real parts of the scattering amplitude and compute the <math altimg='si3.svg'><mi>&#961;</mi></math> parameter and the ratio of bump to dip values of the differential <math altimg='si4.svg'><mrow><mi>p</mi><mi>p</mi></mrow></math> cross sections. We also discuss the energy dependence of the total elastic cross section and the violation of geometrical scaling outside the dip - bump region at the LHC.

Michał Praszałowicz

Geometric scaling of elastic <math altimg='si4.svg'><mrow><mi>p</mi><mi>p</mi></mrow></math> cross section at the LHC

We present a method to measure time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup></math> decays produced in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">→</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mrow><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></mrow></math> events at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories without reconstructing the signal decay vertex. The method exploits the sensitivity of the tag <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></math> decay time to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup></math> signal. It relies on a compact <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> interaction region and excellent vertex resolution, which enable precise measurement of the displacement between production and decay vertices of the tag meson. We study an application to <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>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> decays using a simplified simulation that approximates the conditions of the Belle II experiment at the SuperKEKB collider. Our approach achieves a sensitivity on mixing-induced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation that would require 20 times larger samples with standard approaches. When incorporated into 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> isospin analysis, the expected results would reduce the degeneracy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mn>2</mn></msub></math> solutions and significantly increase precision. This work opens a path to previously inaccessible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violation studies enhancing and accelerating the reach of Belle II and future flavor physics programs.

M. Dorigo

S. Raiz

D. Tonelli

R. Žlebčík

Unlocking time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation without signal vertexing at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi></mrow></math> factories

We study phases and propagation of closed $\textit{p}$-brane within the framework of effective field theory with higher-form global symmetries, i.e., $\textit{brane-field theory}$. We extend our previous studies by including the kinetic term of the center-of-mass motion as well as the kinetic term for the relative motions constructed by the area derivatives. This inclusion gives rise to another scalar Nambu-Goldstone mode in the broken phase, enriching the phase structures of $\textit{p}$-brane. For example, when the higher-form global symmetries are discrete ones, we show that the low-energy effective theory in the broken phase is described by a topological field theory of the axion $\textit{φ}$($\textit{X}$) and $\textit{p}$-form field $\textit{A}$ ($\textit{X}$) with multiple (emergent) higher-form global symmetries. After the mean-field analysis, we investigate the propagation of $\textit{p}$-brane in the present framework. We find the (functional) plane-wave solutions for the kinetic terms and derive a path-integral representation of the brane propagator. This representation motivates us to study the brane propagation within the Born-Oppenheimer approximation, where the volume of $\textit{p}$-brane is treated as constant. In the volume-less limit (i.e. point-particle limit), the propagator reduces to the ordinary propagator of relativistic particle, whereas it describes the propagation of the area elements in the large-volume limit. Correspondingly, it is shown that the Hausdorff dimension of $\textit{p}$-brane varies from 2 to 2($\textit{p}$ + 1) as we increase the $\textit{p}$-brane volume within the Born-Oppenheimer approximation. Although these results are quite intriguing, we also point out that the Born-Oppenheimer approximation is invalid in the point-particle limit, highlighting the quantum nature of $\textit{p}$-brane as an extended object in spacetime.

Kiyoharu Kawana

Phases and propagation of closed $\textit{p}$-brane

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>, we analyze the 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>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> in the improved perturbative QCD (iPQCD) formalism, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> denotes the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave charmonia with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">)</mo></math> denotes the pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> (the vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>). Our results <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>=</mo><mn>0.32</mn><mo>±</mo><mn>0.05</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>=</mo><mn>0.11</mn><mo>±</mo><mn>0.01</mn></math> at leading order in the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> agree well with the data within uncertainties. The result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.17</mn><mo>±</mo><mn>0.02</mn></math> is lower than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>1.41</mn><mrow><mo>−</mo><mn>0.45</mn></mrow><mrow><mo>+</mo><mn>0.50</mn></mrow></msubsup></math> inferred by the <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>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math> measurement. The large longitudinal polarization fractions imply that these components dominate the <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>χ</mi><mrow><mi>c</mi><mn>1</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the <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>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> (<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>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math>) mode, but not in the corresponding ones with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub></math> mesons. Inputting the BRs of the strong decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> reported by the BESIII Collaboration, we obtain those of <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>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>π</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> transitions.

Xin Liu

Hsiang-nan Li

Zhen-Jun Xiao

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo></math> decays in the improved perturbative QCD formalism

Motivated by the recent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation observation, we investigate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon charmless four-body decays under the U-spin symmetry. However, we find that only U-spin symmetry cannot provide effective predictions, particularly for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> decays. For giving more useful predictions, we also give a simple dynamic analysis. By counting the power (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>λ</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>QCD</mi></mrow></msub></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfrac></mrow></msqrt></mrow></math>) of each topological diagram, we find that for the specific decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">→</mo><mi>R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>M</mi></mrow><mrow><mover accent="true"><mrow><mn>2</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msup><mo stretchy="false">)</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, only one U-spin amplitude can contribute in the leading power, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">→</mo><mi>R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mi>M</mi></mrow><mrow><mover accent="true"><mrow><mn>2</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msup><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>, only two U-spin amplitudes can contribute in this leading power. Then the most effective prediction can be given as <a class="disp-formula xref" name="und1"></a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>dir</mi></mrow></msubsup><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><mi>R</mi><mo stretchy="false">(</mo><mi>p</mi><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><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>12.99</mn><mo>±</mo><mn>2.83</mn><mo>±</mo><mn>2.59</mn><mo>±</mo><mn>0.65</mn><mo stretchy="false">)</mo><mo>%</mo><mo>.</mo></mrow></math>Considering the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> can effectively be produced in LHCb, we strongly encourage a more precise experimental investigation of it.

Qi Chen

Xin Wu

Zhi-Peng Xing

Ruilin Zhu

Implications of recent LHCb data on <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"><mi>b</mi></math>-baryon four-body decays

We continue the study of 2D gravity—“matrix model” duality on the example of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></math> minimal string. We propose a reformulation of the duality, related to a more conventional one by “<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi><mtext>−</mtext><mi>y</mi></mrow></math> swap” in the language of topological recursion. This formulation elucidates some conceptual and technical difficulties in the dictionary of the duality and relation to other examples. In particular, it allows to circumvent the necessity to use “resonance transformations,” which were previously introduced to match the world sheet and “matrix model” correlators, and the expressions for minimal string amplitudes in this approach are reminiscent of the ones obtained recently for “complex Liouville string” theory. Using this new approach, we also formulate a conjecture on how one can compute amplitudes with operators other than tachyons in the dual theory.

Russia

Aleksandr Artemev

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi><mtext>−</mtext><mi>y</mi></mrow></math> swap for a (2, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn></mrow></math>) minimal string

In view of the recent observation of <math altimg='si50.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math>-violation in bottom baryon decays, we explore <math altimg='si50.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math>-asymmetry relations in charmless four-body decays of bottom baryons featuring fully charged hadronic final states. Starting with a general effective Hamiltonian, we derive amplitude relations among various decay modes within the framework of <math altimg='si31.svg'><mi>U</mi></math>-spin symmetry. These relations lead to symmetry-based predictions for <math altimg='si50.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating rate asymmetries in <math altimg='si31.svg'><mi>U</mi></math>-spin conjugate decay channels. Furthermore, we demonstrate that all leading-order amplitude relations are violated once <math altimg='si31.svg'><mi>U</mi></math>-spin breaking effects are taken into account.

Shibasis Roy

<math altimg='si50.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math>-violation and <math altimg='si31.svg'><mi>U</mi></math>-spin symmetry in four-body bottom baryon decays

The nucleon matrix elements (NMEs) associated with quark chromomagnetic dipole moments (cMDMs) play a crucial role in determining the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="italic">CP</mi></mrow></math>-odd pion-nucleon couplings induced by quark chromoelectric dipole moments. In recent years, it has been argued that the NMEs of cMDMs can be related to the third moment of the nucleon's higher-twist (specifically, twist-3) parton distribution function (PDF) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, which can, in principle, be measured through dihadron production in semi-inclusive deep inelastic scattering processes. By applying the spin-flavor expansion to the cMDM operators in the large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> limit, where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> is the number of quark colors, we show that the NMEs receive contributions not only from the twist-3 PDF <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math> but also from an additional, previously neglected nucleon form factor. Incorporating constraints from the spin-flavor expansion, recent experimental data on <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, as well as model calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, we estimate the NMEs of the cMDM operators. Our analysis indicates that the NMEs are dominated by the nucleon form factors, and the cMDM contributions to pion-nucleon couplings can be comparable to those from the quark sigma terms.

Shohini Bhattacharya

Kaori Fuyuto

Emanuele Mereghetti

Thomas R. Richardson

Toward the determination of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd pion-nucleon couplings