Based on available experimental results on $ \chi _{cJ}(J=0,1,2) $ decays, we investigated the $ \chi_{cJ}\to PP $ , $ VV $ , $ PV $ , and $ PT $ decays using the $\textit{SU}$(3) flavor symmetry/breaking approach, where $\textit{P}$, $\textit{V}$, and $\textit{T}$ denote light pseudoscalar, vector, and tensor mesons, respectively. With the decay amplitude relations determined by $\textit{SU}$(3) flavor symmetry/breaking, we present the branching ratios for all $ \chi_{cJ}\to PP $ and $ \chi_{cJ}\to VV $ modes, including those without experimental data. While theoretical considerations strongly suppress or even forbid most $ \chi_{cJ}\to PV $ and $ PT $ decays, we also provide quantitative predictions constrained by existing experimental data. Our results are expected to be accessible in future experiments at BESIII and the planned Super Tau-Charm Facility.

China

Bo Lan

Qin-Ze Song

Jin-Huan Sheng

Yi Qiao

Ru-Min Wang

Study of χ$_{cJ}$ ($\textit{J}$ = 0,1,2) decays to light meson pairs based on $\textit{SU}$(3) flavor symmetry/breaking analysis * Supported by the National Natural Science Foundation of China (12175088, 12305100, 12365014) and Graduate Innovation Fund Project of Jiangxi Provincial Department of Education (YJS2024091)

The impact of the inclusion of transverse-momentum-dependent (TMD) shape functions on the transverse momentum spectrum in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production at the electron-ion collider (EIC) is investigated by considering the matching of the TMD factorization description at low transverse momentum with the collinear factorization description at high transverse momentum by means of the inverse-error weighting method. Despite large uncertainties from scale variations and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> long-distance matrix elements, predictions for the differential cross section and its <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mi>ϕ</mi><mi>ψ</mi></msub><mo stretchy="false">)</mo></math> modulation are obtained. We find that physical constraints are satisfied in case a process-dependent term is included for color octet production, but not in all cases when it is excluded. These numerical results support the analytic calculations in the work by Boer et al. [<a href="http://dx.doi.org/10.1007/JHEP08(2023)105">J. High Energy Phys. 08 (2023) 105</a>.]. Future experimental data can thus test the validity of TMD factorization in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production and explore the presence of nontrivial process-dependent effects in the soft-gluon resummation. This will be crucial in the extraction of gluon unpolarized and linearly polarized TMD distributions of the proton. In addition, we suggest how the sign of the latter can be determined by investigating the presence of a node in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mi>ϕ</mi><mi>ψ</mi></msub><mo stretchy="false">)</mo></math> modulation as a function of transverse momentum.

Netherlands

France

Luca Maxia

Daniël Boer

Jelle Bor

Impact of the TMD shape function on matching the transverse momentum spectrum in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production at the EIC

We, using an effective Lagrangian approach, investigated the dipionic transition of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> newly well established in the process <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><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>. In this study, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> was considered as a mixture of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>5</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>4</mn><msub><mrow><mmultiscripts><mrow><mi>D</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow></math>, and its dipionic decay to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> was assumed to occur via charmed meson loops including box and two kinds of triangle loops. The calculated invariant mass spectra due to the different loop mechanisms exhibit distinct differences. These spectrum patterns are found to be nearly independent of the cutoff parameter, especially for the box and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">R</mi></math> loops. By means of comparing our calculated results with the future experimental measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>±</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> invariant mass distributions, we could judge which loop mechanism is of more importance in this dipionic transition. The interference among the different kinds of loops is also exhibited. Despite the unknown phase angles between different kinds of loop diagrams, the partial decay width for the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is estimated to be 250–700 keV, aligning with the estimation obtained by combining BESIII Collaboration measurements and theoretical predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>. We hope that the present calculations would be tested by the future BESIII or Belle II experiments.

Shi-Dong Liu

Qi Wu

Gang Li

Dipionic transitions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math>

Hidden-charm decays provide irreplaceable platforms for probing the structures of charmoniumlike states, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4260</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, and their heavy-quark-symmetry partners. In the hadronic molecular scenario, these hidden-charm decays are dominated by intermediate meson loops (IMLs), and the couplings of <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>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> are essential building blocks of the amplitudes for the pionic and radiative transitions of the charmoniumlike states to the <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math> states, e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>,</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>,</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4260</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>h</mi><mi>c</mi></msub><mo>,</mo><mi>η</mi><msub><mi>h</mi><mi>c</mi></msub></math>. These couplings cannot be extracted from the partial decay widths of the <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> directly and only have estimated values from the vector meson dominance (VMD) model. Utilizing the recent precise determination of the pole position and the isospin breaking properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, we give an estimation on the upper bounds of the absolute values of the <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>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> couplings. Our results show that the VMD model may overestimate the <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>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> couplings considering the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> hadronic molecule with a binding energy about tens of keV. These upper limits can be used and tested in other hidden-charm transitions of the charmoniumlike states to the <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math>.

Zhao-Sai Jia

Zhen-Hua Zhang

Constrain the <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>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> effective couplings via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> decays

We present the first calculation of the high-energy corrections to the process of isolated photon production in association with two jets. These corrections both stabilise the perturbative behaviour in $$ {m}_{j_1{j}_2} $$ and lead to a significantly improved description of data from a recent ATLAS measurement.

United Kingdom

Switzerland

Jeppe Andersen

Spain

Andreas Maier

Malina Rosca

Germany

Giacomo Ruisi

Stable perturbative predictions for isolated photon production with a jet pair at large $$ {m}_{j_1{j}_2} $$

The low-lying light tetraquark states are investigated in the nonrelativistic quark model including the pseudoscalar meson exchange, where two different confinement potential schemes, the Cornell potential and the linear potential, are employed, along with the instanton-induced interaction serving as the residual spin-dependent interaction. The numerical results show agreement with masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1500</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2020</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2200</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1170</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1595</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1900</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1965</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2215</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1640</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1810</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>2010</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>2150</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1450</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1950</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1260</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1640</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1700</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1950</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1440</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1650</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1980</mn><mo stretchy="false">)</mo></math>. The results shed light on the spectrum of these mesons and offer guidance to search for the tetraquarks in the future.

Hao Wu

Mao-Jun Yan

Chun-Sheng An

Cheng-Rong Deng

Low-lying light tetraquark states with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mo>+</mo></msup></math>

A time-integrated angular analysis of the decay $$ {B}_s^0\to J/\psi {\overline{K}}^{\ast }{(892)}^0 $$ , with $\textit{J}$/$\textit{ψ}$ → $\textit{μ}$ $\textit{μ}$ and $$ {\overline{K}}^{\ast }{(892)}^0\to {K}^{-}{\pi}^{+} $$ , is presented. The analysis employs a sample of proton-proton collision data collected by the LHCb experiment during 2015–2018 at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb . A simultaneous maximum-likelihood fit is performed to the angular distributions in bins of the $\textit{K}$ $\textit{π}$ mass. This fit yields measurements of the $\textit{CP}$-averaged polarisation fractions and $\textit{CP}$ asymmetries for the P-wave component of the $\textit{K}$ $\textit{π}$ system. The longitudinal and parallel polarisation fractions are determined to be $\textit{f}$ = 0.534 ± 0.012 ± 0.009 and $\textit{f}$ = 0.211 ± 0.014 ± 0.005, respectively, where the first uncertainty is statistical and the second is systematic. The $\textit{CP}$ asymmetries are measured with 3–7% precision and are found to be consistent with zero. These measurements, along with an updated determination of the branching fraction relative to the $\textit{B}$ → $\textit{J}$/$\textit{ψK}$ decay, are combined with previous LHCb results, providing the most precise values for these observables to date.

R. Aaij

A. Abdelmotteleb

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A. Adefisoye

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

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

Updated measurement of $\textit{CP}$ violation and polarisation in $$ {B}_s^0\to J/\psi {\overline{K}}^{\ast }{(892)}^0 $$ decays

In this paper, we model <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> as a <math altimg='si15.svg'><mrow><mn>4</mn><mi>S</mi></mrow></math>- <math altimg='si16.svg'><mrow><mn>3</mn><mi>D</mi></mrow></math> bottomonium mixture and <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> as a <math altimg='si18.svg'><mrow><mn>5</mn><mi>S</mi></mrow></math>- <math altimg='si19.svg'><mrow><mn>4</mn><mi>D</mi></mrow></math> mixture, and predict the properties of a new bottomonium state, <math altimg='si68.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10950</mn><mo>)</mo></mrow></math>, as the mixing partner of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math>. The mixing angles are derived from dielectron decay widths and mass shifts of these bottomonia. We consider open-bottom meson loops in the decays of the <math altimg='si8.svg'><mi>D</mi></math>-wave bottomonium components, based on a nonrelativistic effective field theory power counting. We show that the <math altimg='si7.svg'><mi>S</mi></math>- <math altimg='si8.svg'><mi>D</mi></math> mixing scheme is consistent with the experimental data of the decays of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math> ( <math altimg='si69.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math>) and <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math> ( <math altimg='si70.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math>). Predictions for the dielectron widths and partial decay widths into <math altimg='si71.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub><mi>&#969;</mi></mrow></math> for <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> and <math altimg='si68.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10950</mn><mo>)</mo></mrow></math> are presented.

Zheng-Li Luo

Yi-Lin Song

Feng-Kun Guo

Decays of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> and <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math>

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> into the light pseudoscalar mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math>. Within a lattice computation we obtain the transition form factors as a function of photon virtuality from the timelike region, accessible experimentally via the “Dalitz” decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msup><mi>η</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></math>, through to the real photon point corresponding to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>η</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></math>. This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> appears as the first excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators, the use of which also improves the purity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> over the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.

Mischa Batelaan

Jozef J. Dudek

Robert G. Edwards

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>η</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> Production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> Radiative Decays from Quantum Chromodynamics

We report on the computation of amplitudes describing the radiative decay processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>η</mi><mo>′</mo></msup></math> from first principles via lattice quantum chromodynamics (QCD). Using lattices with two heavier than physical degenerate flavors of light quark where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>∼</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and a strange quark tuned to approximately the physical value, we compute three-point correlation functions using optimized meson operators with a range of momenta. The use of optimized operators allows access to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math>, even though it appears as an excited state, lying above the ground-state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> in the isoscalar pseudoscalar channel. Statistically precise signals are obtained in this disconnected process by averaging over large numbers of kinematically equivalent correlators. We determine transition form factors as a function of photon virtuality across the timelike region, which describe also the Dalitz processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msup><mi>η</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></math>. Significantly lower magnitudes of transition form factor for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> are found than those extracted from experimental data, and possible explanations for this observation are presented.

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> meson production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> radiative decays from lattice QCD