The Standard Model prediction for the rare <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> quarks, provided terms falling as the inverse square of the omitted charm quark mass, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msubsup><mi>m</mi><mi>c</mi><mn>2</mn></msubsup></math>, are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancellation, this three-flavor theory contains additional low-energy constants that depend on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub></math>. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math> quark masses that are heavier than physical.

United States

En-Hung Chao

Norman Christ

Ceran Hu

Renormalizing a three-flavor lattice calculation of the two-photon contribution to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>

The recently announced NA62 measurement of the $${K^+ \rightarrow \pi ^+\nu \bar{\nu }}$$ branching ratio, based on 2016–2024 data, is fully consistent with its very accurate Standard Model (SM) prediction. While it is not excluded that the final result based on 2016–2026 data will deviate from the SM prediction, the question arises whether a similar fate awaits the $${K_L \rightarrow \pi ^0\nu \bar{\nu }}$$ decay. This decay is currently being searched for by the KOTO experiment, with the present upper bound roughly two orders of magnitude above its very precise SM prediction. The proposed KOTO II experiment aims to provide the first discovery of the $${K_L \rightarrow \pi ^0\nu \bar{\nu }}$$ decay and measure its branching ratio. Building on the findings of several previous papers we demonstrate that in the presence of suitably chosen large new complex phases and of a small amount of new right-handed $$\bar{s} d$$ couplings, in addition to the left-handed ones, the $${K_L \rightarrow \pi ^0\nu \bar{\nu }}$$ branching ratio can still be enhanced by one order of magnitude with respect to the SM prediction while keeping both $${K^+ \rightarrow \pi ^+\nu \bar{\nu }}$$ and $$\varepsilon _K$$ SM-like. Simultaneously the decays $$K_S\rightarrow \mu ^+\mu ^-$$ , studied by LHCb, and $$K_L\rightarrow \pi ^0\ell ^+\ell ^-$$ , searched for by KOTO II, can be strongly enhanced and the anomaly in the ratio $$\varepsilon '/\varepsilon $$ , as claimed by Dual QCD, removed. We illustrate this with an example of a specific $$Z^\prime $$ scenario.

Germany

Monika Blanke

Andrzej Buras

United Kingdom

Cristina Lazzeroni

Switzerland

Joel Swallow

Prospects for $${K_L \rightarrow \pi ^0\nu \bar{\nu }}$$ , $$K_S\rightarrow \mu ^+\mu ^-$$ , $$K_L\rightarrow \pi ^0 \ell ^+\ell ^-$$ and $$\varepsilon '/\varepsilon $$ after the new $${K^+ \rightarrow \pi ^+\nu \bar{\nu }}$$ result from NA62

New binning schemes for the Dalitz plots of $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ and $$D\to {K}_{\text{S}}^{0}{K}^{+}{K}^{-}$$ decays are presented. These are determined using a new figure of merit for optimisation that better represents the sensitivity to $\textit{γ}$ than previous metrics. Further augmentation comes from including consideration of degeneracy with other physics parameters determined simultaneously and a more accurate treatment of relevant backgrounds. The overall expected improvement in the precision of $\textit{γ}$ measurements using $\textit{B}$ → $\textit{DK}$ decays, followed by $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ , is estimated at around 5%. In addition, the first dedicated optimisation is performed for the observables relevant to charm mixing, $\textit{x}$ and ∆$\textit{x}$, in $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ decays. This procedure accounts for both statistical sensitivity and the migration of events between bins due to detector resolution. The resulting binning scheme leads to an estimated gain of approximately 20% in statistical sensitivity, while maintaining the bias due to bin migration at a level comparable to the currently used scheme.

M. Bovill

N. Jurik

S. Malde

Optimal binning of $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ and $$D\to {K}_{\text{S}}^{0}{K}^{+}{K}^{-}$$ phase space for experimental measurements

Motivated by the observation of numerous charmed-strange hadrons lying close to the $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}D^{(*)}$$ thresholds, we systematically investigate their mass spectra and electromagnetic characteristics, explicitly incorporating the $\textit{S}$-$\textit{D}$ wave mixing and coupled-channel effects. For the mass spectra, we employ the one-boson-exchange model and obtain several promising $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}D^{(*)}$$ molecular candidates awaiting future experimental confirmation. The coupled-channel dynamics is found to play an essential role: it not only enhances binding in existing channels but also generates new loosely bound states that are absent in the single-channel approximation. Regarding the electromagnetic characteristics, we discuss the M1 radiative decay widths and magnetic moments of these charmed-strange molecular tetraquarks based on our obtained mass spectra and spatial wave functions within the constituent quark model. Our results demonstrate that the electromagnetic observables serve as valuable discriminants for clarifying the nature of these hadronic molecules. We encourage experimental collaborations to focus on such predicted charmed-strange molecular tetraquark candidates, especially the genuinely exotic $$K^{(*)}\bar{D}^{(*)}$$ states comprising four different flavors with valence quark content $$\bar{c} \bar{s} u d$$ .

China

Jia-Ning Cui

Fu-Lai Wang

Mass spectra and electromagnetic characteristics of the $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}{D}^{(*)}$$ molecular tetraquarks from the coupled-channel dynamics

We present a momentum-space framework for the consistent treatment of Coulomb interactions in femtoscopic correlation functions based on a modified Vincent–Phatak method that is more amenable to numerical implementation. The formalism provides a practical approach to incorporating Coulomb effects at the short distances relevant for femtoscopy within the Lippmann–Schwinger equation, while preserving a unified treatment of the strong interaction. As an application, we study the <math altimg='si9.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>4</mn></mrow></math> pseudoscalar&#8211;baryon decuplet interaction in the <math altimg='si1.svg'><mrow><mspace width='0.16em' /><mover><mrow><mspace width='-0.16em' /><mi>K</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle></mrow></math> system and present predictions for the singly and doubly negatively charged channels, <math altimg='si5.svg'><mrow><mspace width='0.16em' /><mover><mrow><mspace width='-0.16em' /><mi>K</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><msup><mrow /><mn>0</mn></msup><msup><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math> and <math altimg='si6.svg'><mrow><msup><mi>K</mi><mo>&#8722;</mo></msup><msup><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>. As an additional validation of the formalism, we have also applied it to the well-studied <italic>pp</italic> system. We further assess the limitations of the asymptotic wave-function approximation and quantify corrections accounting for the short-distance structure of the interaction potential. We introduce a phenomenological parameter that effectively absorbs contributions from both the finite source size and the off-shell structure of the interaction, the latter being one of the main obstacles to extracting detailed information on hadron&#8211;hadron interactions from femtoscopic measurements in a model-independent way.

Spain

Pablo Encarnación

Amador García-Lorenzo

Miguel Albaladejo

Albert Feijoo

Juan Nieves

Italy

Isaac Vidaña

Coulomb effects in momentum-space femtoscopy: A case study of the <math altimg='si1.svg'><mrow><mspace width='0.16em' /><mover><mrow><mspace width='-0.16em' /><mi>K</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle></mrow></math> system

We perform a theoretical study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math>, <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>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup></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><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> reactions by looking at the production mechanisms, with special emphasis in the final state interaction of the charmed mesons, which gives rise to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3930</mn><mo stretchy="false">)</mo></math>, coupling strongly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math>, and another state that we call <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math>, coupling strongly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> that qualifies as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> bound state. The combined study of all these reactions shows that the final state interaction responsible for the production of these resonances is more important in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> reaction than in the <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><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> one. We have taken this into account and shown that normalizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> mass distributions to the same value at the peak of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> production, the two mass distributions are quite different in a range of 10 MeV above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> threshold, with a value about an order of magnitude bigger for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> reaction than for the <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><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> one. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> mass distribution by itself also shows an enhancement of about one order of magnitude in the presence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math> with respect to a calculation where this resonance is absent. We make a call to measure these magnitudes in the coming LHCb upgrades, which would bring great support to the existence of the bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> state.

Xiu-Lei Ren

Hai-Peng Li

Wei-Hong Liang

Chu-Wen Xiao

Eulogio Oset

Search for signals of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> bound state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math> from study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math>, <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>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup></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><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> reactions

We study CP violation induced by neutral kaon mixing in $\textit{a}$ ($\textit{D}$ → $\textit{K}$ $\textit{K}$ ). We show that the contribution from neutral kaon mixing arises only in connection with second-order weak interactions in $\textit{D}$ decays. We estimate this effect to be at the 10 level, and thus negligible compared to current experimental sensitivity and to the expected contribution from CP violation in the charm sector. Similar reasoning can be applied to other systems.

Yuval Grossman

Guglielmo Papiri

Stefan Schacht

$\textit{CP}$ violation in neutral kaon mixing in $\textit{D}$ 0 → $\textit{K}$ $\textit{S}$ $\textit{K}$ $\textit{S}$

By analyzing a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <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> annihilation data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we have made a first measurement of the absolute branching fractions of the radiative decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><mi>ϕ</mi></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.81</mn><mo>±</mo><mn>0.1</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.2</mn><msub><mn>0</mn><mrow><mi>syst</mi></mrow></msub><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>2.51</mn><mo>±</mo><mn>0.4</mn><msub><mn>4</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.1</mn><msub><mn>1</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, respectively. The statistical significances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><mi>ϕ</mi></math> are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>26.8</mn><mi>σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.9</mn><mi>σ</mi></math>, respectively. The obtained branching fractions are consistent with the corresponding world average values. In addition, the measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>0.7</mn><mo>±</mo><msub><mn>5.0</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mn>4.1</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math> is consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> conservation.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

H.R. Bao

X.L. Bao

M. Barbagiovanni

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

D. Cabiati

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. 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.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

E. Di Fiore

X.X. Ding

Y. Ding

Y.X. Ding

Yi. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

Z.J. Dong

M.C. Du

S.X. Du

Shaoxu Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

Jin Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

Measurements of the absolute branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><mi>ϕ</mi></math>

Based on $ (10087\pm44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, the $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ J/\psi\rightarrow \gamma \pi^{0}\pi^{0}\eta $ processes are studied. The $ X(2370) $ is observed in both the $ K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ \pi^{0}\pi^{0}\eta $ invariant mass spectra, with statistical significances greater than $ 14\sigma $ and $ 20\sigma $ , respectively. By combining measurements from these processes with those from the previously reported $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\eta^{\prime} $ process, the mass and width of the $ X(2370) $ are determined to be $ 2359^{+13}_{-14}\; \text{MeV}/c^{2} $ and $ 170^{+44}_{-29}\; \text{MeV} $ , respectively. In addition, the decay $ X(2370)\to a_{0}(980)^{0}\pi^{0} $ with $ a_{0}(980)^{0}\to \pi^{0}\eta $ is observed with a statistical significance exceeding $ 9\sigma $ . The properties of the $ X(2370) $ —decay pattern similarities to that of $ \eta_{c} $ , are consistent with those of a pseudoscalar glueball.

M.S. Anderson

R. Briere

C. Chen

Observation of the ${\boldsymbol X(2370)}$ in ${{\boldsymbol J}/\boldsymbol\psi\rightarrow\gamma K^{0}_{S}K^{0}_{S}\pi^{0}}$ and ${J/\psi\rightarrow\gamma \pi^{0}\pi^{0}\eta}$ * This work is supported in part by the National Key R&D Program of China under Contracts Nos. 2025YFA1613900, 2023YFA1606000, 2023YFA1606704; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12342502, 12361141819, 12535005; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the Strategic Priority Research Program of Chinese Academy of Sciences under Contract No. XDA0480600; CAS under Contract No. YSBR-101; 100 Talents Program of CAS; China Postdoctoral Science Foundation under Contracts Nos. GZC20252256, 2025M773423; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile under Contract No. ANID CCTVal CIA250027; ERC under Contract No. 758462; German Research Foundation DFG under Contract No. FOR5327; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation under Contracts Nos. 2021.0174, 2021.0299, 2023.0315; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; Polish National Science Centre under Contract No. 2024/53/B/ST2/00975; STFC (United Kingdom); Swedish Research Council under Contract No. 2019.04595; U. S. Department of Energy under Contract No. DE-FG02-05ER41374

We report a study of the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> (where <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>) based on a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <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> annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider. Based on an investigation of the decay dynamics in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">D</mi></mrow></math>-wave component of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> is observed for the first time with a statistical significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>8.0</mn><mi>σ</mi></math>, in addition to the dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">S</mi></mrow></math>-wave components. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">D</mi></mrow></math>-wave component is determined to account for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>0.092</mn><mo>±</mo><mn>0.02</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>8</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math> of the total decay rate. The branching fractions of the dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> components are measured as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.043</mn><mo>±</mo><mn>0.01</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>2</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.964</mn><mo>±</mo><mn>0.01</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>2</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>, which are the most precise measurements to date and represent significant improvements over the previous world averages. The hadronic form-factor parameters are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>r</mi><mi>V</mi></msub><mo>=</mo><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1.444</mn><mo>±</mo><mn>0.02</mn><msub><mn>6</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>0</mn><mrow><mi>syst</mi></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>r</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.752</mn><mo>±</mo><mn>0.02</mn><msub><mn>0</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mn>4</mn><mrow><mi>syst</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.618</mn><mo>±</mo><mn>0.00</mn><msub><mn>2</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mn>4</mn><mrow><mi>syst</mi></mrow></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math> is the vector form factor and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math> are the axial-vector form factors evaluated at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math>. This is the most precise determination of the form-factor parameters to date measured in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></math> transition. In addition, we report the first model-independent measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">S</mi></mrow></math>-wave phase shift in the hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup></math> system. We also measure the relative ratio between branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">R</mi><mrow><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></mrow><mrow><mi>μ</mi><mo>/</mo><mi>e</mi></mrow></msubsup><mo>=</mo><mn>0.961</mn><mo>±</mo><mn>0.01</mn><msub><mn>2</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mn>5</mn><mrow><mi>syst</mi></mrow></msub></math>, and no violation of lepton flavor universality is found.

Y. Ban

J.C. Cheng

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

Precise measurement of the form factors in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>