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)

We investigate a scale-invariant general two-Higgs-doublet model with explicit <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. Using the Gildener-Weinberg method, we analyze the Higgs mass spectrum and couplings at the one-loop level, focusing on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation originating from both the Higgs potential and the Yukawa sector. We show that, due to the flatness condition, both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-even and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-odd mixings between the 125 GeV Higgs boson and the heavier Higgs states arise only radiatively. As a result, the Higgs couplings to gauge bosons and fermions remain Standard Model-like, in agreement with current LHC constraints. We also find that the magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation from the Higgs potential depends on the new complex Yukawa couplings and heavy Higgs masses, due to the flatness condition. In the case where only an additional top Yukawa coupling (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub></math>) is present, the electron electric dipole moment is directly proportional to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Im</mi><msubsup><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow><mn>2</mn></msubsup></math>. Furthermore, a nontrivial cancellation region can occur for a specific Higgs mass spectrum. We extend our analysis to scenarios with an additional complex electron Yukawa coupling, identifying the conditions under which the electron electric dipole moment is suppressed or vanishes.

Czechia

Dang Bao Nhi Nguyen

Vietnam

Eibun Senaha

Exploring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation and vanishing electric dipole moment of the electron in a scale-invariant general 2HDM

We investigate the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> (with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mo>=</mo><mi>e</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi></mrow></math>) within the framework of perturbative QCD. The six independent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> transition form factors are first calculated in the low-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>k</mi><mi>T</mi></msub></math> factorization approach. These are then extrapolated to the full physical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range via the model-independent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math> expansion, incorporating recent lattice QCD results at high <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math>. Based on the obtained form factors, we compute the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mo>ℓ</mo><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> decays. Our prediction for the lepton flavor universality ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.2</mn><msubsup><mrow><mn>9</mn></mrow><mrow><mo>−</mo><mn>0.11</mn></mrow><mrow><mo>+</mo><mn>0.12</mn></mrow></msubsup></mrow></math>, is slightly larger than the latest experimental measurement. In addition, we analyze several angular observables, including forward-backward asymmetries, lepton-side convexity parameters, and polarization asymmetries. These results offer valuable theoretical input for current and future experimental investigations of semileptonic heavy-to-heavy baryon transitions.

Ying Li

Jie Chen

Ya-Xin Wang

Zhi-Tian Zou

Investigation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><mover accent="true"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></math> decays in the perturbative QCD approach

We study heavy-hadron semileptonic decays proceeding via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi></math> transition, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>τ</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mi>τ</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>. In the heavy-quark limit, where the heavy-quark symmetry holds, we provide a fundamental framework for heavy-quark sum rules among these decays based on the spin decomposition picture. The relation holds directly for the squared amplitudes without requiring phase-space integration. We then apply this relation to reproduce the sum rule among <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>τ</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mi>τ</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub></math>. Furthermore, we derive new sum rules for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ω</mi><mi>c</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transitions and those involving excited states, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mo stretchy="false">{</mo><msubsup><mi>D</mi><mn>0</mn><mo>*</mo></msubsup><mo>,</mo><msubsup><mi>D</mi><mn>1</mn><mo>*</mo></msubsup><mo stretchy="false">}</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mo stretchy="false">{</mo><msub><mi>D</mi><mn>1</mn></msub><mo>,</mo><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">}</mo></math>.

Japan

Motoi Endo

Syuhei Iguro

Satoshi Mishima

Ryoutaro Watanabe

Constructing heavy-quark sum rule for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi></math> meson and baryon decays

Motivated by the recent observation of the open-charm tetraquark $$T_{c\bar{s}0}^{a}(2327)$$ by the LHCb Collaboration, as well as results from Lattice QCD calculations, we consider the $$T_{c\bar{s}0}^{a}(2327)$$ and the $$D_{s0}^{*}(2317)$$ as $\textit{DK}$ molecular states, with $$I(J^{P})$$ equal to $$1(0^{+})$$ and $$0(0^{+})$$ , respectively, and we investigate their strong decay behavior in an effective Lagrangian approach. Within the model parameter range, we can reproduce the $$T_{c\bar{s}0}^{a}(2327)$$ experimental decay width, with the assumption that the $$D_{s}^{+}\pi ^{0}$$ is the dominant decay channel of the $$T_{c\bar{s}0}^{a+}(2327)$$ . In the same parameter range, we can establish a stringent limitation for the decay width of the $$D_{s0}^{*}(2317)$$ , which is $$(63.0-209)~\textrm{keV}$$ being significantly smaller than the PDG upper limit value.

Italy

Zi-Li Yue

Quan-Yun Guo

Dian-Yong Chen

Elena Santopinto

Determining the width of $$D_{s0}^{*}(2317)$$ by using $$T_{c\bar{s}0}^{a}(2327)$$ in a molecular frame

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

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

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)