In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an $\textit{SU}$(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$ . Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$ . In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$ ( $\text{MeV}$ ).

China

Na Li

Ye Xing

Jing-Rui Shi

Analysis of molecular state $\textit{η$_{c}$D}$ $^{*}$ and $\textit{J}$/$\textit{ψD}$ $^{*}$ in the effective Lagrangian approach * Supported by the National Natural Science Foundation of China (NSFC) (12005294)

We report stronger evidence for the $X(7200)$ state and markedly improved measurements of the $X(6900)$ resonance parameters based on a combined analysis of the di- $J/\psi$ mass spectrum using published data from LHCb, ATLAS, and CMS. Through simultaneous fits to the datasets from all three experiments, we observe the $X(6900)$ with overwhelming significance ( $ \gt 12\sigma$ ) and determine its mass and width with improved precision. For the $X(7200)$ , we find consistent signals across multiple interference models, with significances ranging from $3.7\sigma$ to $6.6\sigma$ ; in the best-fit model (the CMS three-resonance scheme), the significance reaches $6.6\sigma$ , providing substantially stronger evidence for this state. Our results underscore the essential role of interference effects in fully charmed tetraquark spectroscopy and offer new constraints on their production mechanisms at the LHC.

Yuan Wang

Ran Li

Bin Zhong

Ya-Qian Wang

Enhanced evidence of $\textit{X}$(7200) and improved measurements of $\textit{X}$(6900) parameters from a combined LHCb-ATLAS-CMS analysis * Supported by the National Natural Science Foundation of China (NSFC) (12475077)

The Kerr/CFT correspondence establishes a correspondence between extremal black holes in higher dimensions and a chiral conformal field theory (CFT) in their near-horizon limit. A generalization of this framework, known as the EVH/CFT correspondence, has been developed for four- and five-dimensional AdS black holes. It was further proposed in [ ${\rm{AdS}}_{D=6,7}$ black holes, a generalized duality between $(D-2)$ -dimensional geometry and $(D-3)$ -dimensional field theory may emerge in a suitably defined extremal vanishing horizon (EVH) limit. In this work, we show that, in the EVH limit, the near-EVH geometries of these ${\rm{AdS}}_{D=6,7}$ black holes reduce to lower-dimensional black holes whose metrics are conformally related to solutions of Einstein-Maxwell-Maxwell-dilaton (EMMD) gravity. This structural resemblance suggests a potential route toward the microscopic counting of non-AdS black hole entropy via higher-dimensional AdS/CFT techniques.

Weichao Bu

Yang Lei

Probing decoupled throats of AdS $\textit{D}$ black holes in $\textit{D}$ = 6, 7 * Supported by National Natural Science Foundation of China (NSFC) (2305081), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the NSFC-Royal Society International Collaboration (W2421035)

We study the Page curve and information paradox for Kerr AdS black hole in light of entanglement entropy by employing the recently proposed island paradigm. By incorporating the island rule, we show that the entanglement entropy of Kerr AdS black hole grows linearly at early times and declines to a constant value at late times in agreement with the well established Page curve. The novelty of this study resides in the investigation of influence of phase transitions on the page curve in two different ensembles. We find that a first order phase transition results in a sharp discontinuity in the Page curve. We study the evaporation process in different scenarios and find that in all the situations, the Page curve doesn’t violate the unitary principle of quantum mechanics.

India

Digen Das

Mozib Awal

Prabwal Phukon

Entanglement islands, Page curves and phase transitions of Kerr-AdS black holes

Perturbative expansions in quantum field theory are typically asymptotic, with large-order growth driven by instantons (factorial proliferation of diagrams) and renormalons (factorial growth from momentum integrations). In this work we compute the large-order behavior and Borel-plane singularity structure for several nontrivial truncations of Schwinger-Dyson equations, including diagram classes whose asymptotics have not, to our knowledge, been previously worked out. We recover the known chain-, rainbow-, and Hopf-series results in $\textit{ϕ}$ theory and extend the analysis to additional truncations, including the two-arm $\textit{ϕ}$ self-energy class in $\textit{d}$ = 6 and several classes in $\textit{ϕ}$ theory in $\textit{d}$ = 4. Our derivations use Schwinger-Dyson equations together with Borel transforms and a direct renormalization-group/leading-log analysis: given the same primitive integral input, this yields the relevant differential/recursion structure and makes the renormalon interpretation of the dominant Borel singularities manifest. Finally, we provide a self-contained, example-driven introduction to the Connes-Kreimer Hopf-algebraic organization of renormalization and its relation to conventional QFT notions, serving as a bridge between the combinatorial-Hopf and perturbative-QFT communities.

United States

Luen Clingerman

Matthew Schwartz

Asymptotic behavior of diagram classes

We study holographic Krylov complexity in the Coulomb branch of 𝒩 = 4 SYM. Adopting the proposal that the time derivative of the Krylov complexity is dual to the proper radial momentum of a massive particle, we investigate two probe geodesics within this geometry. For one of the radial trajectories we obtain exact analytic results, even when additional motion in the internal space is included. In cases where the geodesic avoids the interior curvature singularity, the Krylov complexity exhibits oscillatory behavior, with a frequency governed by the Coulomb scale and an amplitude determined by the UV cutoff, the Coulomb scale, and the angular momentum. This oscillatory pattern is lost, when the radial trajectory is approaching the singularity. Finally, we compare our holographic results with field-theoretic calculations, finding qualitative agreement.

Greece

Dimitrios Zoakos

Holographic Krylov complexity in the Coulomb branch of 𝒩 = 4 SYM

To shed light on the inner structure of the observed single-bottom strange baryons, in this work we systematically study the Okubo-Zweig-Iizuka allowed strong decay properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> baryons within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi><mtext>−</mtext><mi>j</mi></math> coupling scheme in the framework of the quark pair creation model. For a comparison, we also give the predictions of the chiral quark model. The calculations indicate that (i) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> are highly promising candidates for the observed state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6087</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6095</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6100</mn><mo stretchy="false">)</mo></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> are likely candidates for the state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6227</mn><mo stretchy="false">)</mo></math>. Meanwhile, we cannot rule out the possibility that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6227</mn><mo stretchy="false">)</mo></math> could be a candidate of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>ρ</mi></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>ρ</mi></msub></math>. (ii) For the other <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> states and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states, they may be moderate states with a width of several tens of MeV. Their main decay channels are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>. The width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states are slightly broader, approximately several tens to over one hundred MeV, and the dominant decay channels are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>b</mi></msub><mi>K</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Σ</mi><mi>b</mi><mo>*</mo></msubsup><mi>K</mi></math>. (iii) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states are most likely to be relatively narrow state with a width of only a few to around ten MeV, and they mainly decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math>. Meanwhile, the decay process of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states into the final states containing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> baryons should not be overlooked either. We hope that the theoretical results can provide some reference for future experimental investigations.

Yu-Bin Zhang

Yi-Heng Wang

Hui-Hua Zhong

Li-Ye Xiao

Probing the inner structures of the observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> resonances

We investigate the strong decays of the recently observed hidden-charm pentaquarks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4312</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4440</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math>, as well as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math>, within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</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"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math>, and determine the coupling constants via the residues of the scattering <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4312</mn><mo stretchy="false">)</mo></math> to calibrate the cutoff range, we further explore the spin assignments of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4440</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math>. Our calculations favor the assignment where the lower-mass state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4440</mn><mo stretchy="false">)</mo></math> carries higher spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> and the higher-mass state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math> carries lower spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>. In addition, the experimental widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math> can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math> contains contributions from both spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>2</mn></math> and spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><mn>2</mn></math> states.

Jin-Cheng Deng

Yong Ru

Xin-Yue Wan

Tai-Fu Feng

Bo Wang

Strong decays of the hidden-charm molecular pentaquarks

We consider actions that are general functions of the world sheet/world volume metric and the induced metric for extended objects embedded in spacetime as Riemannian manifolds, area-metric manifolds, and volume-metric manifolds. For strings on a Riemannian spacetime, we consider general actions respecting volume-preserving diffeomorphisms (VPD), general diffeomorphisms, and diffeomorphisms with Weyl symmetry, respectivelyn. Well-known Schild, Nambu-Goto, and Polyakov actions are included as special cases. We reach two main conclusions: (1) When actions are functions of both the worldsheet metric and induced metrics, all nontrivial self-consistent actions are classically equivalent. (2) As a physical constraint on the classical action, VPD symmetry is as strong as the full diffeomorphism symmetry. The discussion is then extended to strings in spacetime manifolds equipped with the area or volume metrics. Then, we further consider higher-dimensional extended objects in spacetime defined with area or volume metrics, and show the equivalence between the generalized Schild actions and the generalized Nambu-Goto action. We prove a general theorem on VPD that explains this equivalence. Incidentally, while only the area metric is needed to define the string world sheet action, we show that the Polyakov action with an area-metric perturbation cannot describe critical strings without other interaction terms.

Taiwan

Pei-Ming Ho

Japan

Hikaru Kawai

Henry Liao

General actions of extended objects and volume-preserving diffeomorphism

Based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2.712</mn><mo>±</mo><mn>0.014</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events collected with the BESIII detector, the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) are observed for the first time with statistical significances exceeding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>. The measured branching fractions are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>7.25</mn><mo>±</mo><mn>0.28</mn><mo>±</mo><mn>0.35</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.33</mn><mo>±</mo><mn>0.12</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</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><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.51</mn><mo>±</mo><mn>0.16</mn><mo>±</mo><mn>0.12</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, where the first uncertainties are statistical and the second systematic. In addition, no significant structures are observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> mass spectra.

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.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

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

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

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

Y.T. Feng

M. Fritsch

Observation and branching fraction measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>