The beyond-the-standard-model scenario presented in this work is motivated by the observations of neutrino masses, the anomalous magnetic moments of the electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all of which are odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams featuring the same fields also explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without conflicting with direct detection constraints, or those from big bang nucleosynthesis or cosmic microwave background observations. Finally, prospective signatures at the LHC are discussed.

India

Vandana Sahdev

Neutrino masses, anomalous magnetic moments and dark matter with vector-like fermions and an inert scalar doublet * V.S. acknowledges the support from research grant no. CRG/2018/004889 of the SERB, India; T.R. Seshadri for providing resources during the initial stages of the work; and Brajesh Choudhary for providing access to computers bought under the aegis of Grant No. SR-MF/PS-0212014-DUB (G) of the DST (India)

We present an investigation of the $ K^*(1680) $ state in its strong decays into two-body final states within the flux-tube model and quark pair creation model. Since charge conjugation parity is not conserved in the strange sector, the conventional $ q\bar{q} $ states with $ J^{P(C)}=1^{-(-)} $ can mix with the lowest hybrid states with $ J^{P(C)}=1^{-(+)} $ . Our analysis of the $ K^*(1680) $ two-body strong decays indicates that the decay pattern of $ K^*(1680) $ cannot be explained by the conventional $ q\bar{q} $ scenario. Moreover, there is strong evidence for the $ q\bar{q} $ -hybrid mixing mechanism in the strange sector. The phenomenological consequences of such mixing are also discussed. Our study can provide guidance for future searches for hybrid multiplets in experiments at BESIII, LHCb, and Belle II.

China

Samee Ullah

Ye Cao

Ming-Xiao Duan

Hai-Bing Fu

Qiang Zhao

Nature of ${K^*(1680)}$ and ${q\bar{q}}$ -hybrid mixing as the $\textit{SU}$(3) partner of ${\eta_{1}(1855)}$ in the strange sector * Supported in part by the National Natural Science Foundation of China (12235018, 12265010, 12505098), and the Project of Guizhou Provincial Department of Science and Technology (MS[2025]219, CXTD[2025]030, ZD[2026]168, QN[2025]178), and the project of Guizhou Normal University (GZNUD[2025]05)

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov–Arnold Network (KAN) to investigate the algebraic structure underlying the baryon octet and decuplet mass spectra. Within a symbolic regression framework and without imposing theoretical priors, KAN recovers a symbolic representation equivalent to the classical Gell-Mann–Okubo mass relations, which can be transformed into the standard form through algebraic rearrangement. Compared with conventional fitting approaches, this method achieves comparable predictive accuracy while providing substantially improved interpretability and analytical transparency. Our results demonstrate the potential of KAN as a powerful tool for symbolic discovery in hadron physics and for bridging data-driven modeling with fundamental physical laws.

Jian-Yao He

Italy

Xun Chen

Xiao-Yan Zhu

Wen Luo

Discovering the Gell-Mann–Okubo formula with Kolmogorov-Arnold networks * Supported by the National Natural Science Foundation of China (NSFC) (12405154) and the European Union – Next Generation EU through research grant (P2022Z4P4B), ''SOPHYA - Sustainable Optimised PHYsics Algorithms: fundamental physics to build an advanced society'', under the PRIN 2022 PNRR program of the Italian Ministero dell'Università e Ricerca (MUR)

The rare exclusive decay of the Higgs boson, $ H \to J/\psi + \gamma $ , is a crucial channel for assessing the Yukawa coupling of the charm quark. In this article, we examine this process up to the next-to-next-to-leading order (NNLO) in QCD utilizing the Principle of Maximum Conformality (PMC). The PMC offers a systematic approach to eliminate renormalization scale uncertainties by resumming non-conformal $\textit{β}$ contributions into the QCD running coupling through the renormalization group equation (RGE). A PMC scale of $ Q_\star = 3.29\ {\rm{GeV}} $ is obtained, which reflects the low virtuality of the underlying QCD dynamics in the $ H \to J/\psi + \gamma $ process. Notably, this is an order of magnitude smaller than the scale estimated using the conventional method, $\textit{i.e.}$, $ \mu_r = m_H/2 $ . By removing the non-conformal $ \{\beta_i\} $ -terms from the perturbative QCD (pQCD) series, we observe that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we calculate the decay width $ \Gamma(H \to J/\psi + \gamma) = $ $ 14.183^{+0.249}_{-0.347} \pm 0.022 $ eV, where the first uncertainty arises from the factorization scale $ \mu_\Lambda \in [1, 2]\ {\rm{GeV}} $ , and the second is due to the estimation of unknown higher-order terms using the Pad $ \acute{e} $ approximant approach. The corresponding branching fraction is $ {\cal{B}}(H \to J/\psi + \gamma) = 3.485_{-0.161}^{+0.152} \times 10^{-6} $ .

Wen-Yuan Li

Ting Sun

Sheng-Quan Wang

Jian-Ming Shen

Hua Zhou

Xing-Gang Wu

Leonardo Di Giustino

Analysis of $\textit{H}$ → $\textit{J}$/$\textit{ψ}$ + $\textit{γ}$ up to Next-to-Next-to-Leading order QCD corrections * Supported in part by the Natural Science Foundation of China (12265011, 12175025, 12347101); the Project of Guizhou Provincial Department of Science and Technology (YQK[2023]016, ZK[2023]141, CXTD[2025]030); the Hunan Provincial Natural Science Foundation (2024JJ3004); the YueLuShan Center for Industrial Innovation (2024YCII0118), and the Natural Science Foundation of Sichuan Province (2024NSFSC1367)

This work presents a comprehensive analysis of polarization transfer in the decays of $\chi_{cJ}$ ( $J=0,1,2$ ) into octet baryon-antibaryon pairs in polarized electron-positron collisions. Using the spin density matrix formalism, we trace the polarization from the initial beams through the production chain $e^+e^- \to \psi(2S) \to \gamma \chi_{cJ}$ to the final-state baryon-antibaryon system. The helicity amplitude analysis for $\chi_{c1} \to B\bar{B}$ confirms the universal angular distribution parameter $\alpha = -1/3$ , as dictated by the charge-conjugation helicity selection rule. For $\chi_{c2}$ decays, $\textit{α}$ and the transverse polarization depend on two independent amplitudes, and our quark-model calculations agree with existing data. We demonstrate that the longitudinal beam polarization $P_z$ modifies the spin observables for $\chi_{c1}$ and $\chi_{c2}$ . This offers new experimental handles at future polarized facilities, such as the Super $\textit{τ}$-Charm Facility (STCF), to test decay mechanisms and explore baryonic spin entanglement as a quantum information resource.

Cai-Ying Pang

Rong-Gang Ping

Dai-Hui Wei

Polarization analysis of χ$_{cJ}$ decay into octet baryonic pairs * Supported by the National Natural Science Foundation of China (NSFC) (12575112, 12465015)

The triangle singularity interpretation of the $a_1(1420)$ observed by the COMPASS Collaboration has been widely accepted. In this work, we investigate the triangle mechanism in the decay $B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)$ , where the $a_0(980)$ is treated as a dynamically generated state. The $\bar{K}^{*0}$ - $K^+$ - $K^-$ triangle loop originates from the decay $B^0 \to D^- K^+ \bar{K}^{*0}$ , which has been observed by the Belle Collaboration, followed by the subsequent decay $\bar{K}^{*0} \to K^- \pi^+$ . The triangle amplitude develops a pronounced peak around 1420 MeV, which is reflected in the invariant mass spectrum of the $\pi a_0(980)$ system. The differential decay width is calculated and exhibits a narrow peak around $980~\mathrm{MeV}$ in the $\pi^0 \eta$ invariant mass distribution. Furthermore, the invariant mass distribution of the $\pi^+ \pi^0 \eta$ system shows a clear peak around $1420~\mathrm{MeV}$ , which further confirms the triangle singularity explanation of the $a_1(1420)$ . We expect that the proposed $B^0$ decay mode could provide a potential platform for further exploring the triangle-singularity nature of the $a_1(1420)$ and could be tested in future experiments such as LHCb, BESIII, and Belle II.

Wei Wang

Dazhuang He

Xuan Luo

The role of triangle singularity in the $ {B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)}$ decay * Dazhuang He is supported by the Heze University doctoral fund project (010008002039037). Xuan Luo is supported by the National Natural Science Foundation of China (12205002)

<p>We report the first observation of the decays <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><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mo>−</mo></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mn>0</mn></mrow></msubsup></mrow></math>, with significances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.4</mn><mi>σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.3</mn><mi>σ</mi></math>, respectively, including systematic uncertainties. This analysis is based on data samples containing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>771.6</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> decays collected with the Belle detector at the KEKB collider and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>520.6</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> decays collected with the Belle II detector at the SuperKEKB collider. The branching fractions are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mo>−</mo></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.69</mn><mo>±</mo><mn>0.31</mn><mo>±</mo><mn>0.1</mn><msubsup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>0.56</mn></mrow><mrow><mo>+</mo><mn>1.39</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mn>0</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.28</mn><mo>±</mo><mn>0.32</mn><mo>±</mo><mn>0.1</mn><msubsup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>0.22</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, where the first and second uncertainties are statistical and systematic, respectively, and the third arises from the uncertainties in the absolute branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mn>0</mn></msubsup></math> decays. This result represents the first observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays into a pair of charmed baryon-antibaryon states belonging to the same <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor sextet.</p>

M. Abumusabh

A. Aggarwal

H. Ahmed

J.K. Ahn

Y. Ahn

M. Akdag

N. Akopov

S. Alghamdi

M. Alhakami

N. Althubiti

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

K. Arai

H. Atmacan

T. Aushev

V. Aushev

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Beaubien

F. Becherer

J. Becker

G.F. Benfratello

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

M. Carminati

G. Casarosa

C. Cecchi

P. Cheema

L. Chen

B.G. Cheon

C. Cheshta

H. Chetri

K. Chilikin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

S. Chutia

J. Cochran

J.A. Colorado-Caicedo

I. Consigny

L. Corona

S. Cuccuini

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

R. Dhayal

A. Di Canto

J. Dingfelder

Z. Doležal

X. Dong

M. Dorigo

G. Dujany

P. Ecker

D. Epifanov

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

Observation of the decays <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><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mo>−</mo></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mn>0</mn></mrow></msubsup></mrow></math>

<p>By analyzing <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> collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.33</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected with the BESIII detector at center-of-mass energies ranging from 4.128 to 4.226 GeV, we report the observations of the hadronic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>. Their decay branching fractions are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>4.08</mn><mo>±</mo><mn>0.4</mn><msub><mn>6</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.4</mn><msub><mn>5</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><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"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>3.32</mn><mo>±</mo><mn>0.6</mn><msub><mn>4</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.3</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>3</mn></mrow></msup></math>, where the first uncertainties are statistical and the second are systematic.</p>

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

E. Bianco

A. Bortone

I. Boyko

United States

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

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

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J.C. Cheng

L.N. Cheng

South Korea

X. Chu

Measurement of branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>