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.

China

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)

The total decay widths of heavy mesons can be systematically calculated in terms of an expansion in the two parameters 1/$\textit{m}$ and $\textit{α}$ ($\textit{m}$ ), where $\textit{Q}$ = $\textit{c}$, $\textit{b}$ denotes the heavy quark. The dominant contributions to meson lifetime splittings stem from terms which are suppressed by $$ 1/{m}_Q^3 $$ with respect to the leading universal contribution to the total decay width. We calculate three-loop contributions of order $$ {\alpha}_s^2/{m}_q^3 $$ to the lifetime ratios $$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ , $\textit{τ}$($\textit{D}$ )/$\textit{τ}$($\textit{D}$ ), and $$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ in the limit of exact isospin and V-spin symmetry, respectively. Furthermore, we present new $$ {\alpha}_s/{m}_q^3 $$ corrections to the Cabibbo-suppressed terms in $$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ . Combining our perturbative coefficients with hadronic matrix elements calculated from Heavy Quark Effective Theory sum rules, we find $$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ = 1.072 ± 0.024. Using hadronic matrix elements from a recent lattice QCD calculation we find $\textit{τ}$($\textit{D}$ )/$\textit{τ}$($\textit{D}$ ) = 2.344 ± 0.170 and $$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ = 1.289 ± 0.042. We find good agreement of our predictions with experimental data, which constitutes a successful probe of the calculations of hadronic matrix elements and permits estimates of the unknown $$ 1/{m}_Q^4 $$ contributions as well as the V-spin breaking terms in $$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ .

Germany

Francesco Moretti

Ulrich Nierste

Pascal Reeck

Matthias Steinhauser

Next-to-next-to-leading QCD corrections to the $$ {\mathrm{B}}^{+}-{\mathrm{B}}_{\mathrm{d}}^0 $$ , D+ − D0, and $$ {\mathrm{D}}_{\mathrm{s}}^{+}-{\mathrm{D}}^0 $$ lifetime ratios

We investigate the three-body <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mi>K</mi></math> system with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><msup><mn>0</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> within a coupled-channel framework that incorporates the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mi>K</mi></math>, <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><mi>K</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mi>D</mi><mi>s</mi></msub><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mi>D</mi><mi>s</mi></msub><mi>π</mi></math> channels. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> interactions are described using the one-boson-exchange model constrained by heavy-quark symmetry and fitted to the pole positions of <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>K</mi></math> interaction is from the chiral effective field theory, motivated by the molecular interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math>, and is further constrained by lattice-QCD results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> scattering lengths. The resulting three-body problem is solved using the Gaussian expansion method, while the complex scaling method is employed to search for possible resonant states. We find that coupled-channel effects from <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><mi>K</mi></math> are negligible, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mi>K</mi></math> system supports a deeply bound state across a wide range of parameters. Depending on the long-range behavior of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> interaction, an additional shallow state may emerge near the particle-dimer (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mtext>−</mtext><mi>D</mi><mi>K</mi></mrow></math>) threshold. The deeply bound state exhibits a compact three-body structure, whereas the shallow state displays characteristic features of a three-body halo configuration. Similar results are obtained for 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><mi>K</mi></math> system. We also observe that the coupled-channel effects originating from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mi>D</mi><mi>s</mi></msub><mi>η</mi></math> channel produce only minor corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mi>K</mi></math> bound state and lead to a modest reduction in its binding energy. By contrast, opening the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mi>D</mi><mi>s</mi></msub><mi>π</mi></math> channel substantially alters the nature of the three-body <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mi>K</mi></math> state and transforms the bound state into a resonance. These findings may provide new insight into few-body dynamics in systems involving charmed mesons and kaons.

Hai-Peng Xie

Si-Yi Chen

Ning Li

Wei Chen

Coupled-channel study of the three-body <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mi>D</mi><mi>K</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mi>K</mi></mrow></math>

By performing a fit to the merged BES 2008 and BESIII 2024 <math altimg='si15.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow></math> cross-section data, we find that the <italic>&#968;</italic>(2S) subthreshold pole influences this process markedly. The statistical significance of the <italic>&#968;</italic>(2S) as a subthreshold pole is 8 <italic>&#963;</italic>. A fit assuming it and seven resonances excels with the fit quality characterized by <math altimg='si8.svg'><mrow><msup><mi>&#967;</mi><mn>2</mn></msup><mo linebreak='goodbreak'>/</mo><mtext>DOF</mtext><mo linebreak='goodbreak'>=</mo><mn>240.4</mn><mo linebreak='goodbreak'>/</mo><mn>284</mn></mrow></math>, which means a <italic>p</italic>-value of 97%. The interference of resonances with the continuum provided by the subthreshold pole changes their shapes, positions, and widths.

Czechia

Peter Lichard

The <italic>&#968;</italic>(2S) state as a subthreshold pole in electron-positron annihilation into <math altimg='si14.svg'><mrow><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow></math> final states

We construct asymptotically AdS black brane solutions in a theory of gravity with an infinite series of curvature corrections. The action is based on an $\textit{O}$($\textit{d}$, $\textit{d}$) symmetric ansatz which has been argued to describe the classical NSNS sector of string theories. We find that, for this general class of theories, the singularity behind the horizon is not resolved by the curvature corrections. The approach to the singularity is however generically modified, being characterized by different Kasner exponents. We also show that, in the presence of a non-trivial dilaton, a slight generalization of these types of curvature corrections can generate dynamically a negative cosmological constant in the region of small coupling. This provides a mechanism through which asymptotic freedom could emerge in the hypothetical string dual of QCD.

Netherlands

Pedro Marto

Edwan Préau

$\textit{O}$($\textit{d, d}$) symmetric gravity and finite coupling holography

There exist only four known string theories with minimal supersymmetry in eight dimensions, whose low energy effective descriptions are given by minimal supergravity coupled to $\textit{l}$ = 18, 10, or 2 vector multiplets. It has been argued that these numbers are uniquely fixed by consistency conditions of the effective theory. In this work, we investigate the protected couplings of minimal supergravity coupled to two vector multiplets under the assumption that the theory admits a duality symmetry of the form Γ ($\textit{N}$) × Γ ($\textit{N}$) ⊂ SL(2, $\textit{ℤ}$) × SL(2, $\textit{ℤ}$) for some positive integer $\textit{N}$. We show that consistency with anomaly cancellation, higher-dimensional uplifts, and gauge enhancement loci strongly constrains the allowed couplings and isolates a unique consistent theory in the BPS sector. In particular, we find that the Bianchi identity for the three-form flux cannot have gravitational contributions.

France

Guillaume Bossard

United States

Bingxin Lao

Ruben Minasian

Uniqueness of D=8 minimal supergravity with two vector multiplets

We introduce a new method for the determination of the ratio of production fractions $$ {R}^{\pm 0}=\mathcal{B}\left(\mathrm{Y}(4S)\to {B}^{+}{B}^{-}\right)/\mathcal{B}\left(\mathrm{Y}(4S)\to {B}^0{\overline{B}}^0\right) $$ based on $$ \overline{B}\to {D}^{\left(\ast \right)}\ell \overline{\nu} $$ decays. Given the importance of these modes, we perform a comprehensive analysis of the available data, extracting the information on their branching fractions and $\textit{R}$ in parallel and providing their correlations in order to avoid double-use of this information in phenomenological analyses. We obtain the most precise value for $\textit{R}$ from a single channel so far, about 2$\textit{σ}$ from unity. The combination with previously available determinations from other channels yields $\textit{R}$ = 1.062(19), constituting evidence for isospin violation in Υ(4$\textit{S}$) decays. This demonstrates the necessity to take this effect into account in experimental and phenomenological analyses. The results for the $$ \overline{B}\to {D}^{\left(\ast \right)}\ell \overline{\nu} $$ branching fractions are up to 1$\textit{.}$6$\textit{σ}$ larger compared to averages available in the literature, owing to the removal of overlooked inconsistencies in the treatment of older analyses and correcting for d’Agostini bias where possible, thereby reducing the $\textit{V}$ puzzle.

Italy

Martin Jung

United Kingdom

Stefan Schacht

$$ \overline{B}\to {D}^{\left(\ast \right)}\ell \overline{\nu} $$ branching ratios and evidence for isospin breaking in Υ(4$\textit{S}$) decays

The branching fraction of the electromagnetic Dalitz decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> is measured with an <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 sample collected by the BESIII experiment at center-of-mass energies between 4.128 and 4.226 GeV, corresponding to a total 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>. The measurement yields the branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>7.28</mn><mo>±</mo><msub><mrow><mn>0.61</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>0.31</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>. The result is consistent with the previous one, with a 2.5-fold improvement in precision. This provides an important input for constraining the parameters of theoretical models and for determining the absolute branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi>γ</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math>, measured with a relative method that assumes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> decays only via channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi>γ</mi><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

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

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

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Measurement of the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math>

We study near-threshold <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> scattering in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other channel that is kinematically open is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mi>η</mi></math>. Using lattice QCD we compute, as a function of varying light-quark mass, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-matrix for coupled-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mi>η</mi><mo>−</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> state and the <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> threshold.

David J. Wilson

Jozef J. Dudek

Robert G. Edwards

Christopher E. Thomas

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> interactions are weak near threshold in QCD

We investigate the lineshape of the <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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> cross section in the vicinity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> threshold, where the “so-called” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> is observed in the <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><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> channel. To take into account the possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> open channel effects or possible contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, we include the intermediate meson loop transitions in <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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. We present predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum and our results clarify the different manifestations of the kinematic effects and genuine resonances. In particular, we show that resonance structures arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <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> scatterings or hidden charm tetraquark state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> can be identified by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant mass spectrum. It can provide a theoretical guidance for future experimental searches for these exotic candidates.

Jun Wang

Qiang Zhao

Study of the <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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> lineshape near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi fontstyle="italic" mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></mrow></math> threshold and possible signals for exotic hidden charm states