Symmetry studies represent one of the most promising frontiers in particle physics research. This investigation focuses on exploring P and $\rm CP $ symmetries in the charm system through the measurement of asymmetry decay parameters in the three-body decay of $ \Xi_c^{+} $ . By incorporating electron and positron beam polarization effects and utilizing the helicity formalism, we characterize the decay of $ \Xi_c^{+} $ and its secondary hyperons through asymmetry decay parameters. The complete angular distribution formula for these decays is systematically derived. Our study evaluates the sensitivity of the asymmetry parameters for the $ \Xi_c^{+} \to \Xi^{-}\pi^{+}\pi^{+} $ decay channel under various data sample sizes and beam polarization scenarios. The findings establish a robust theoretical framework for future experimental studies at the Super Tau-Charm Facility, providing valuable insights for symmetry investigations in the charm sector.

China

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Ronggang Ping

Study of P and CP symmetries in ${ \boldsymbol\Xi^{\bf +}_{\boldsymbol c}\rightarrow \boldsymbol\Xi^-\boldsymbol\pi^+\boldsymbol\pi^+ }$ at electron-positron collider

An $\textit{SU}$(3) flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude within the framework of the $1/N_c$ expansion of quantum chromodynamics (QCD), where $N_c$ represents the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects from the first-order perturbative $\textit{SU}$(3) flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by explicitly accounting for the effects of the decuplet-octet baryon mass difference. At order ${\cal{O}}(1/N_c^2)$ , a large number of unknown operator coefficients appear, and therefore, there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is sufficiently general that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi\to N\pi$ scattering processes are explicitly considered.

Víctor Miguel Banda Guzmán

Rubén Flores-Mendieta

Johann Hernández

Use of $\textit{SU}$(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/ N$_{c}$ expansion * The authors are grateful to Consejo Nacional de Humanidades, Ciencias y Tecnologías (Mexico) for support through the $\textit{Ciencia de Frontera}$ project CF-2023-I-162

In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Jun Wang

Qiang Zhao

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)

Searches are presented for <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><mi>D</mi><msup><mi>h</mi><mo>+</mo></msup><msup><mi>h</mi><mo>−</mo></msup></math> decays, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> is a charmed meson and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mo>±</mo></msup></math> is a charged pion or kaon, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collision data collected by the LHCb experiment 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 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><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</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><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, and <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><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> are observed for the first time. Their branching fractions, expressed as ratios relative to that of 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><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decay, are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.96</mn><mo>±</mo><mn>0.23</mn><mo>±</mo><mn>0.08</mn><mo>±</mo><mn>0.10</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>3.67</mn><mo>±</mo><mn>0.55</mn><mo>±</mo><mn>0.24</mn><mo>±</mo><mn>0.20</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.61</mn><mo>±</mo><mn>0.35</mn><mo>±</mo><mn>0.13</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, where the first uncertainty is statistical, the second is systematic, and the third is due to the limited precision on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-meson branching fractions. The decay channels proceed primarily through excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> resonances or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> mesons, and open a new avenue for studies of charge-parity violation in beauty mesons.

Netherlands

R. Aaij

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

R. Aleksiejunas

CERN

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

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

O. Bezshyyko

J. Bhom

M.S. Bieker

N.V. Biesuz

P. Billoir

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

Observation 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><mi>D</mi><msup><mi>h</mi><mo>+</mo></msup><msup><mi>h</mi><mo>−</mo></msup></math> Decays

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

Z Areg

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

In this work, we investigate the dipion transition processes <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><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>0</mn></mrow></math>, 1, 2) within the framework of heavy hadron chiral perturbation theory, treating <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 molecular state composed of <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><mo>+</mo><mi mathvariant="normal">H</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math> components. By analyzing the box and triangle loop diagrams with the nonrelativistic effective field theory power-counting rule, we demonstrate that box diagrams dominate these dipion transition processes. Branching ratios are calculated as functions of the mixing angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>, which parametrizes the neutral and charged meson compositions 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>. Our results indicate that the branching fractions for <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><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <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><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, and <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><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> are of the orders of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, respectively. We also predict the ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">]</mo></mrow><mo>/</mo><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">]</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">]</mo></mrow><mo>/</mo><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><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><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">]</mo></mrow></math>. The latter deviates from isospin-symmetry expectations, revealing various degrees of isospin violation. By studying 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><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> invariant mass spectra, we find a double-bump structure in 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> invariant mass distributions of the process <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><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math> invariant mass distribution of the process <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><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, which could be tested by future experimental measurements.

Qi Wu

Zhong-Quan Sun

Dian-Yong Chen

Shi-Dong Liu

Gang Li

Dipion transitions from <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> to <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> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>0</mn></mrow></math>, 1, 2)

We analyze the potential of rare charm decays as probes of new physics at a high-luminosity flavor facility operating at the $\textit{Z}$ pole, such as the FCC-ee or CEPC. In particular, we identify clean null-test observables in $$D^0 \rightarrow \pi ^+ \pi ^- \nu \bar{\nu }$$ and in polarized $$\varLambda _c^+ \rightarrow p \ell ^+ \ell ^-$$ decays with $$\ell =e, \mu $$ . Complementarity with the LHC and HL-LHC flavor programs arises from the characteristic features of a Tera-$\textit{Z}$ environment: the capability to study missing-energy modes and charm production with significant polarization. We improve the theoretical description of $$D^0 \rightarrow \pi ^+ \pi ^- \nu \bar{\nu }$$ decays and work out the phenomenology of polarization-induced null-test observables in $$\varLambda _c^+ \rightarrow p \ell ^+ \ell ^-$$ decays. In regions of dilepton mass near the $$\phi $$ resonance, polarization asymmetries can reach $$O(5 \%)$$ for muons and $$O(14 \%)$$ for electrons times the $$\varLambda _c^+$$ polarization. We also point out synergies between the dineutrino and the dilepton modes using the SMEFT framework of heavy new physics. Using the IDEA detector concept at FCC-ee, we find in simulation studies that dineutrino branching fractions as low as $$\sim 2 \times 10^{-7}$$ can be probed, which reaches well into the parameter space of new physics, and also allows for discrimination of lepton flavor structures. Furthermore, the measurement of asymmetries in $$\varLambda _c^+ \rightarrow p \mu ^+ \mu ^-$$ at $$O(1 \%)$$ will be possible. Similar sensitivities are expected for dielectron final states, although robust predictions will require further dedicated studies.

Angelo Di Canto

Tabea Hacheney

Gudrun Hiller

Dominik Mitzel

Stéphane Monteil

Lars Röhrig

Dominik Suelmann

New opportunities for rare charm from $$Z\rightarrow c\bar{c}$$ decays

Utilizing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mtext> </mtext><mtext> </mtext><mi>million</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events accumulated by the BESIII experiment, we perform a partial wave analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> decay (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> decay is determined for the first time to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mn>0.575</mn><mo>±</mo><mn>0.048</mn><mo>±</mo><mn>0.018</mn></math>, with a relative phase angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi mathvariant="normal">Φ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mn>0.37</mn><mo>±</mo><mn>0.15</mn><mo>±</mo><mn>0.05</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></math>. The parameters of the angular distribution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mo>−</mo><mn>0.211</mn><mo>±</mo><mn>0.100</mn><mo>±</mo><mn>0.050</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>β</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mo>−</mo><mn>0.039</mn><mo>±</mo><mn>0.089</mn><mo>±</mo><mn>0.033</mn></math>, based on the distribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>N</mi><mo>/</mo><mi>d</mi><mi>cos</mi><mi>θ</mi><mo>=</mo><mn>1</mn><mo>+</mo><msub><mi>α</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><msup><mi>cos</mi><mn>2</mn></msup><mi>θ</mi><mo>+</mo><msub><mi>β</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><msup><mi>cos</mi><mn>4</mn></msup><mi>θ</mi></math>. The width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>12.31</mn><mo>±</mo><mn>0.26</mn><mo>±</mo><mn>0.12</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Additionally, the branching fractions for <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><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.662</mn><mo>±</mo><mn>0.048</mn><mo>±</mo><mn>0.111</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.182</mn><mo>±</mo><mn>0.026</mn><mo>±</mo><mn>0.042</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.704</mn><mo>±</mo><mn>0.035</mn><mo>±</mo><mn>0.057</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>, respectively, where the first uncertainty is statistical and the second systematic.

M. Ablikim

Russia

M.N. Achasov

Sweden

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

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

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Helicity amplitude and branching fraction measurement 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><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math>