We perform a detailed comparison between three formalisms used in recent studies of $\textit{DD}$ scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, $$ {T}_{cc}^{+}(3875) $$ . These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

United States

Sebastian Dawid

Switzerland

Fernando Romero-López

Stephen Sharpe

Comparison of integral equations used to study $$ {T}_{cc}^{+} $$ for a stable $\textit{D}$

The Cabibbo–Kobayashi–Maskawa matrix element $$|V_{\textrm{cb}}|$$ is an important Standard Model parameter, whose value can be determined by using the semi-leptonic decay $$B\rightarrow D^{*}\ell {\bar{\nu }}_\ell $$ . The perturbative QCD (pQCD) corrections to the $$B \rightarrow D^{*}$$ transform form factor $${{\mathcal {F}}}(w)$$ has been known up to the $$\hbox {N}^3$$ LO level, whose magnitude remains sensitive to the choice of renormalization scale $$\mu _r$$ . To improve the precision of $${{\mathcal {F}}}(w)$$ and hence $$|V_{\textrm{cb}}|$$ , we first apply the single-scale approach of Principle of Maximum Conformality (PMC) to eliminate the conventional (Conv.) renormalization scale dependence of the short-distance parameter $$\eta _A$$ and then predict the contribution of its unknown $$\hbox {N}^4$$ LO term via Bayesian analysis. In this paper, we adopt two probabilistic models for Bayesian analysis: the Cacciari–Houdeau model (CH model) and the geometric behavior model (GB model). It is shown that by using the PMC series in combination with Bayesian analysis, one can achieve high degree of reliability in estimating unknown higher-order terms. A more convergent behavior is achieved by applying the PMC, confirmed by the predicted $$\hbox {N}^4$$ LO contributions: for the CH model, $$\eta _A|_{\mathrm{Conv.}}^{\text {N}^{4}\text {LO}}=\{-\,0.0032,+\,0.0052\}$$ and $$\eta _A|_{\textrm{PMC}}^{\text {N}^{4}\text {LO}}=\{-\,0.0004,+\,0.0004\}$$ ; for the GB model, $$\eta _A|_{\mathrm{Conv.}}^{\text {N}^{4}\text {LO}}=\{-\,0.0049,+\,0.0075\}$$ and $$\eta _A|_{\textrm{PMC}}^{\text {N}^{4}\text {LO}}= \{-\,0.0007,+\,0.0007\}$$ . Comparing with the latest experimental measurements, we obtain $$|V_{\textrm{cb}}||_{\textrm{PMC}}=(40.58^{+0.53}_{-0.57})\times 10^{-3}$$ , which is consistent for both CH and GB models and in good agreement with the PDG world average, $$|V_{\textrm{cb}}|_{\textrm{PDG}}=(41.1\pm 1.2)\times 10^{-3}$$ within errors.

China

Wang Li

Xing-Gang Wu

Hua Zhou

Xu-Chang Zheng

Determination of $$|V_{\textrm{cb}}|$$ using Bayesian analysis of the $$B \rightarrow D^{*}\ell {\bar{\nu }}_\ell $$ semileptonic decay width with four-loop QCD corrections

Motivated by the large non-<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> branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, we investigate the light meson decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave charmonia in the present work with the meson loop mechanism. With the parameter range determined by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ϕ</mi><mi>η</mi></mrow></math>, our estimations of the branching fractions of the light meson decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> are consistent with the estimations in the literature. As for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>3823</mn><mo stretchy="false">)</mo></math>, the partial widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> channel is estimated to be around 200 keV, which is the predominant light meson decay channel of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>3823</mn><mo stretchy="false">)</mo></math>. Our estimations also indicate that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>π</mi></math> are the dominant light meson decay modes of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>3842</mn><mo stretchy="false">)</mo></math>, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>3822</mn><mo stretchy="false">)</mo></math> dominantly decays into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>ρ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mi>ω</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>ϕ</mi></math>.

Xiao-Yu Qi

Xing-Dao Guo

Dian-Yong Chen

Light meson decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> wave charmonia

By extending the six-dimensional hybrid formalism for the superstring to include $\textit{d}$ = 6 $$ \mathcal{N} $$ = 1 superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator $\textit{U}$. We demonstrate that the BRST invariance of $\textit{U}$ implies the $\textit{d}$ = 6 $$ \mathcal{N} $$ = 1 SYM equations of motion in superspace. Furthermore, we show that spacetime supersymmetric scattering amplitudes can be computed in a manner analogous to that of the non-minimal pure spinor formalism.

Brazil

Cassiano Daniel

Vertex operators for the superstring with manifest $\textit{d}$ = 6 $$ \mathcal{N} $$ = 1 supersymmetry

In this paper, a systematic investigation is conducted to explore the potential molecular states formed by heavy meson pairs $$D^{(*)}D^{(*)}$$ and $$D^{(*)}{\bar{D}}^{(*)}$$ with the complex scaling method, in the framework of the one-boson-exchange (OBE) model. The exchange interactions are mediated by the pseudoscalar, scalar and vector mesons( $$\pi $$ , $$\sigma $$ , $$\rho $$ , $$\omega $$ ). The interaction potential within the OBE model is derived using the Bonn approximation, followed by the application of the complex scaling method to determine the bound and resonant states. The results demonstrate that the $$D^{(*)}D^{(*)}$$ and $$D^{(*)}{\bar{D}}^{(*)}$$ systems can form not only multiple bound states, but also several P-wave resonant states. In the hadronic molecular state framework, the $\textit{X}$(3872), $$T_{cc}^+$$ , and $$Z_c(3900)$$ states can be consistently explained as bound states, while the $\textit{G}$(3900) can be interpreted as a P-wave resonant state. Furthermore, we also predict other new bound and resonant states, which have the potential to be observed experimentally.

Jia-Liang Lu

Mao Song

Peng Wang

Jian-You Guo

Gang Li

Xuan Luo

The bound and resonant states of $$D^{(*)}D^{(*)}$$ and $$D^{(*)}{\bar{D}}^{(*)}$$ with the complex scaling method

We study the Hamiltonian formulation of SU(2) Yang-Mills theory with staggered fermions in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional small lattice system. We construct a gauge-invariant and finite-dimensional Hilbert space for the theory by applying the loop-string-hadron formulation and specifically map the model to a spin system. We classically emulate digital quantum simulation and observe the real-time evolution of the single-site entanglement entropy, the fermion entanglement entropy, and the fermion pair production.

Zhen-Xuan Yang

Hidefumi Matsuda

Xu-Guang Huang

Japan

Kouji Kashiwa

Quantum simulation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>QC</mi></mrow><mn>2</mn></msub><mi mathvariant="normal">D</mi></mrow></math> on a two-dimensional small lattice

We consider supersymmetric solutions of $\textit{D}$ = 4, $$ \mathcal{N} $$ = 2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Such solutions admit an R-symmetry Killing vector, $\textit{ξ}$, constructed as a bilinear in the Killing spinor. The Killing spinor bilinears can also be used to construct polyforms that are equivariantly closed under the action of the equivariant exterior derivative d = d – $\textit{ξ}$⌟ . This allows one to compute various flux integrals and the on-shell action using localization, without solving any supergravity equations, just assuming the supersymmetric solutions exist. The flux integrals allow one to obtain important UV-IR relations, relating fixed point data in the bulk to data on the asymptotic AdS boundary, allowing one to express the gravitational free energy in terms of boundary SCFT data. We illustrate the formalism with a number of examples, including classes of solutions which are unlikely to be ever constructed in closed form.

Pietro Genolini

United Kingdom

Jerome Gauntlett

Yusheng Jiao

Alice Lüscher

James Sparks

Equivariant localization for $\textit{D}$ = 4 gauged supergravity

We report measurements of the ratios of branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mspace linebreak="goodbreak"></mspace><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. These ratios test the universality of the charged-current weak interaction. The results are based on a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> data sample collected with the Belle II detector at the SuperKEKB <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> collider, which operates at a center-of-mass energy corresponding to the <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> resonance, just above the threshold for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> production. Signal candidates are reconstructed by selecting events in which the companion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson from the <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><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> decay is identified in semileptonic modes. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton is reconstructed via its leptonic decays. We obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msubsup><mrow><mn>0.418</mn></mrow><mrow><mo>−</mo><mn>0.073</mn></mrow><mrow><mo>+</mo><mn>0.075</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.056</mn></mrow><mrow><mo>+</mo><mn>0.049</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msubsup><mrow><mn>0.306</mn></mrow><mrow><mo>−</mo><mn>0.033</mn></mrow><mrow><mo>+</mo><mn>0.035</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.018</mn></mrow><mrow><mo>+</mo><mn>0.016</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></math>, which are consistent with world average values. Accounting for the correlation between them, these values differ from the Standard Model expectation by a collective significance of 1.7 standard deviations.

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

S. Bansal

M. Barrett

M. Bartl

J. Baudot

A. Beaubien

F. Becherer

J. Becker

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

A. Bolz

A. Bondar

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

J. Cerasoli

M.C. Chang

P. Chang

R. Cheaib

P. Cheema

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

I. Consigny

L. Corona

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. Dhamija

F. Di Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

M. Dorigo

D. Dossett

S. Dubey

K. Dugic

G. Dujany

P. Ecker

Test of lepton flavor universality with measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> using semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> tagging at the Belle II experiment

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> data taken at the center-of-mass energy of 3.773 GeV with the BESIII detector, corresponding to an integrated luminosity 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>, we report the first measurement of the decay dynamics of the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math>. The amplitude analysis gives the hadronic form factors of the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> transitions into the axial-vector meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>11.2</mn><mo>±</mo><msub><mrow><mn>1.0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>0.9</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>4.3</mn><mo>±</mo><msub><mrow><mn>1.0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>2.5</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. This is the first in the semileptonic decays of heavy mesons into axial-vector mesons. The angular analysis yields an up-down asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>ud</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><mn>0.01</mn><mo>±</mo><mn>0.11</mn></mrow></math>, which is consistent with the standard model prediction. In addition, the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> are determined with improved precision to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2.27</mn><mo>±</mo><mn>0.1</mn><msub><mrow><mn>1</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>7</mn></mrow><mrow><mtext>input</mtext></mrow></msub><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><mo stretchy="false">(</mo><mn>1.02</mn><mo>±</mo><mn>0.0</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>3</mn></mrow><mrow><mtext>input</mtext></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, respectively. No significant signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1400</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1400</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> are observed and their branching fraction upper limits are set as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.4</mn><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"><mn>0.7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> at 90% confidence level, respectively.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

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. Bertani

D. Bettoni

E. Bianco

A. Bortone

I. Boyko

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

G.R. Che

Y.Z. Che

G. Chelkov

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

First Measurement of the Decay Dynamics in the Semileptonic Transition of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mo>+</mo><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup></mrow></math> into the Axial-Vector Meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math>