The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose neutrino experiment under construction in South China. This paper presents an updated estimate of JUNO’s sensitivity to neutrino mass ordering using the reactor antineutrinos emitted from eight nuclear reactor cores in the Taishan and Yangjiang nuclear power plants. This measurement is planned by studying the fine interference pattern caused by quasi-vacuum oscillations in the oscillated antineutrino spectrum at a baseline of 52.5 km and is completely independent of the CP violating phase and neutrino mixing angle θ $_{23}$. The sensitivity is obtained through a joint analysis of JUNO and Taishan Antineutrino Observatory (TAO) detectors utilizing the best available knowledge to date about the location and overburden of the JUNO experimental site, local and global nuclear reactors, JUNO and TAO detector responses, expected event rates and spectra of signals and backgrounds, and systematic uncertainties of analysis inputs. We find that a 3σ median sensitivity to reject the wrong mass ordering hypothesis can be reached with an exposure of about 6.5 years × 26.6 GW thermal power.

Chile

Angel Abusleme

France

Thomas Adam

Pakistan

Shakeel Ahmad

Rizwan Ahmed

Italy

Sebastiano Aiello

Muhammad Akram

Abid Aleem

China

Fengpeng An

Qi An

Giuseppe Andronico

JINR

Nikolay Anfimov

Vito Antonelli

Tatiana Antoshkina

Thailand

Burin Asavapibhop

João Pedro Athayde Marcondes de André

Didier Auguste

Weidong Bai

Nikita Balashov

Wander Baldini

Andrea Barresi

Davide Basilico

Eric Baussan

Marco Bellato

Marco Beretta

Antonio Bergnoli

Germany

Daniel Bick

Lukas Bieger

Svetlana Biktemerova

Thilo Birkenfeld

Iwan Morton-Blake

David Blum

Simon Blyth

Anastasia Bolshakova

Mathieu Bongrand

Taiwan

Clément Bordereau

Dominique Breton

Augusto Brigatti

Riccardo Brugnera

Riccardo Bruno

Antonio Budano

Jose Busto

Anatael Cabrera

Barbara Caccianiga

Hao Cai

Xiao Cai

Yanke Cai

Zhiyan Cai

Stéphane Callier

Antonio Cammi

Agustin Campeny

Chuanya Cao

Guofu Cao

Jun Cao

Rossella Caruso

Cédric Cerna

Vanessa Cerrone

Chi Chan

Jinfan Chang

Yun Chang

Auttakit Chatrabhuti

Chao Chen

Guoming Chen

Pingping Chen

Shaomin Chen

Yixue Chen

Yu Chen

Zhangming Chen

Zhiyuan Chen

Zikang Chen

Jie Cheng

Yaping Cheng

Yu Chin Cheng

Russia

Alexander Chepurnov

Alexey Chetverikov

Davide Chiesa

Brazil

Pietro Chimenti

Yen-Ting Chin

Ziliang Chu

Artem Chukanov

Gérard Claverie

Catia Clementi

Belgium

Barbara Clerbaux

Marta Colomer Molla

Selma Conforti DiLorenzo

Alberto Coppi

Daniele Corti

Simon Csakli

Flavio Dal Corso

United States

Olivia Dalager

Jaydeep Datta

Christophe De La Taille

Zhi Deng

Ziyan Deng

Xiaoyu Ding

Xuefeng Ding

Yayun Ding

Bayu Dirgantara

Carsten Dittrich

Sergey Dmitrievsky

Czechia

Tadeas Dohnal

Potential to identify neutrino mass ordering with reactor antineutrinos at JUNO  

<p>We study the next-to-leading order (NLO) electroweak (EW) corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> process in a Pb-Pb ultraperipheral collision (UPC). We find that the EW correction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><msub><mi>σ</mi><mi>EW</mi></msub></math> decreases the total cross section <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>NLO</mi></mrow></msub><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>LO</mi></mrow></msub><mo>+</mo><mi>δ</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>EW</mi></mrow></msub></mrow></math> by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>−</mo><mn>3</mn><mo>%</mo></mrow></math> at Pb-Pb center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.02</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. The weak correction plays a significant role whose contribution is about–4 times that of QED. The CMS and ATLAS Collaborations use the reaction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> in Pb-Pb and proton-proton UPCs to constrain tau’s anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub></math>. By parametrizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>τ</mi><mi>τ</mi></math> vertex with two form factors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math>, the cross section can be written as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><msub><mi>a</mi><mi>τ</mi></msub></msub><mo>=</mo><msub><mi>σ</mi><mi>LO</mi></msub><mo>+</mo><mi>δ</mi><msub><mi>σ</mi><msub><mi>a</mi><mi>τ</mi></msub></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><msub><mi>σ</mi><msub><mi>a</mi><mi>τ</mi></msub></msub></math> is proportional to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub></math>. The impact of NLO EW corrections on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub></math> bounds in a Pb-Pb UPC is limited, as the current experimental bounds are loose. We also find that various differential distributions of the two ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">d</mi><msub><mi>σ</mi><mi>NLO</mi></msub><mo>/</mo><mi mathvariant="normal">d</mi><msub><mi>σ</mi><mi>LO</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">d</mi><msub><mi>σ</mi><msub><mi>a</mi><mi>τ</mi></msub></msub><mo>/</mo><mi mathvariant="normal">d</mi><msub><mi>σ</mi><mi>LO</mi></msub></math> have different line shapes. This work is significant to precisely study the interaction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>τ</mi><mi>τ</mi></math> via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> process.</p>

Jun Jiang

Peng-Cheng Lu

Zong-Guo Si

Han Zhang

Xin-Yi Zhang

NLO EW corrections to tau pair production via photon fusion in Pb-Pb ultraperipheral collisions

The measurements in $$b\rightarrow s$$ penguin-dominated decays are widely recognized as a powerful test for searching for New Physics by studying the deviation from theoretical estimations within the Standard Model. We examine the final-state rescattering effects on the decay $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$ and provide estimations of the branching ratio and longitudinal polarization of $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$ , which is consistent with experimental observations. Our conclusion is that both short- and long-distance interactions contribute significantly in this decay. The small longitudinal polarization in $$B\rightarrow VV$$ modes may not be a signal for New Physics.

Yao Yu

Hai-Bing Fu

Bai-Cian Ke

A phenomenological estimate of rescattering effects in $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$

Motivated by the near-threshold enhancement and the dip structure around 1 GeV in the <math><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> invariant mass distribution of the process <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> observed by the CLEO Collaboration, we have investigated this process by taking into account the contribution from the <math><mi>S</mi></math>-wave pseudoscalar meson–pseudoscalar meson interactions within the chiral unitary approach, and also the one from the intermediate resonance <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><mo>)</mo></math>. Our results are in good agreement with the CLEO measurements, which implies that the near-threshold enhancement near the <math><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> threshold is mainly due to the contributions from the scalar meson <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math> and the intermediate <math><mrow><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math>, and the cusp structure around 1 GeV in the <math><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> invariant mass distribution should be associated with the scalar meson <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>.

Xiao-Hui Zhang

Li-Juan Liu

De-Min Li

En Wang

Roles of the scalar <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>500</mn><mo>)</mo></mrow></math> and <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> in the process <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math>

Our main objective is to derive the decay rate for the semileptonic decays <math><mi>D</mi><mo>→</mo><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math>, where <math><mi>V</mi></math> represents a vector particle. In these decays, the vector particle <math><mi>V</mi></math> decays into three pseudoscalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the <math><mi>D</mi><mo>→</mo><mi>ω</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math><mi>ω</mi></math> subsequently decays into <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of <math><mi>D</mi><mo>→</mo><mi>ω</mi></math> form factors. These measurements can be performed using data obtained from BESIII.

Yechun Yu

Zhuang Xiong

Jia-Wei Zhang

Xue-Wen Chen

Five-body <math><mi>D</mi><mo>→</mo><mi>V</mi></math> semileptonic decays

We study the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math> exotic states in the decays of <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub></math> baryons through a molecular scenario. In the final state interaction, the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> decays are followed by the <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> to <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math> rescatterings via exchange of a <math><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math> meson. We predict a branching fraction of <math><mo>(</mo><msubsup><mrow><mn>3.1</mn></mrow><mrow><mo>−</mo><mn>2.6</mn></mrow><mrow><mo>+</mo><mn>1.4</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math>, which can be measured in the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msup><mi>p</mi></math> decay. This study proposes a new approach to test the molecular model, and guides future experimental searches for the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math>.

Dong-Ze He

Rui-Yu Zhou

Investigating (3985) and (4000) Exotic States in Decays

An analysis of the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>η</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math> decay by the BESIII collaboration claims the observation of an exotic state <math><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> with <math><msup><mrow><mi>I</mi></mrow><mrow><mi>G</mi></mrow></msup><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>. To establish its C-parity partner <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo></math> in the picture of the <math><mi>K</mi><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math> molecular state, we propose that <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> receives the main contributions from the final state interaction of <math><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>(<math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>, and <math><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>). Specifically, K and <math><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> in <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> decays transform as <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math>, by exchanging a <math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math>. We predict <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><mi>η</mi><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.3</mn></mrow><mrow><mo>−</mo><mn>3.5</mn></mrow><mrow><mo>+</mo><mn>12.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, and <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.5</mn></mrow><mrow><mo>−</mo><mn>4.6</mn></mrow><mrow><mo>+</mo><mn>6.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, which can be studied in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> decays.

Yi Teng

Qing-Shan Liu

Investigating the Exotic State in the Decays

We derive a parameterization formula for the partial wave analyses of charmed meson semi-leptonic decays while considering the effects of lepton mass. Because the proposed super-tau-charm factory will reach a significantly enhanced luminosity and BESIII is collecting new   $ \psi(3770)\to D\bar{D} $   data, our results will help improve the measurement precision of future partial wave analyses of charmed meson semi-muonic decays.

Lepton mass correction in partial wave analyses of charmed meson semi-leptonic decays  

Because the lowest   $ \Sigma^{*} $   state with quantum numbers spin-parity   $ \Sigma^{*} $   is far from being established experimentally and theoretically, we perform a theoretical study on the   $ \Sigma^{*} $   photo-production within the Regge-effective Lagrangian approach. Considering that   $ \Sigma^{*} $   couples to the   $ \Sigma^{*} $   channel, we study the contributions from the t-channel K exchange diagram. Moreover, the contributions from the t-channel   $ \Sigma^{*} $   exchange, s-channel nucleon pole, u-channel Σ exchange, and contact term are considered. The differential and total cross sections of the process   $ \Sigma^{*} $   are predicted with our model parameters. The results should help in experimentally searching for the   $ \Sigma^{*} $   state in the future.

Yun-He Lyu

Neng-Chang Wei

Ju-Jun Xie

Photo-production of lowest state within the Regge-effective Lagrangian approach  

Based on BESIII measurements of the reaction   $ D_s^+\to \pi^+\pi^0\pi^0 $  , we investigate this process by considering the S-wave pseudoscalar-pseudoscalar interaction within the unitary chiral approach and the contributions from the intermediate resonances   $ D_s^+\to \pi^+\pi^0\pi^0 $   and   $ D_s^+\to \pi^+\pi^0\pi^0 $  . Our calculation can reasonably reproduce the experimental data, and our results imply that   $ D_s^+\to \pi^+\pi^0\pi^0 $  , which is dynamically generated from the S-wave pseudoscalar-pseudoscalar interaction, plays an important role in this process, and the contributions from the intermediate resonances   $ D_s^+\to \pi^+\pi^0\pi^0 $   and   $ D_s^+\to \pi^+\pi^0\pi^0 $   are also necessary. More precise measurements of this process in future can shed light on the nature of   $ D_s^+\to \pi^+\pi^0\pi^0 $   and   $ D_s^+\to \pi^+\pi^0\pi^0 $  .

Role of the scalar In the Process   