We compute various averages over bulk geometries of quantum states prepared by the Chern-Simons path integral, for any level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi></math> and compact simple gauge group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math>. We do so by carefully summing over all topologically distinct bulk geometries which have <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> disjoint boundary tori and a decomposition into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>space</mi><mo>×</mo><mi>time</mi></mrow></math> of fixed spatial topology. We find that to leading order in the complexity of the state, the typical state contains many types of multiparty entanglement, proving a conjecture of Balasubramanian et al. Combined with the fact that periodic link states are Greenberger–Horne–Zeilinger (GHZ)-like, this result implies that a generic fibered link state contains non-GHZ entanglement if and only if its link complement is hyperbolic. Additionally, we compute an averaged wave function which captures the leading order statistics of boundary observables in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> torus Chern-Simons Hilbert space.

United States

Charlie Cummings

Entanglement in typical states of Chern-Simons theory

We discuss the dynamics of the quantum fluctuation around the nonlinear massive wave solution in the Higgs potential. In particular, we analyze the stability and instability of the mode function. Using the stability condition for Hill’s equation, we obtain the instability region of the mode function in the quantum fluctuation as the function of the parameters in the mode equation. We show that the two types of the instabilities of the system in the particle number can be understood by the Floquet’s exponents in the instability parameter region. The analysis will be useful to understand the dynamics of the quantum field theory around the nonlinear massive wave solution when the classical background slightly deviates from the constant background during the middle stage of the phase transition.

Taiwan

Yoshio Kitadono

Japan

Tomohiro Inagaki

Instability of quantum fluctuation around classical nonlinear massive wave solution in Higgs potential and particle creations

We introduce a novel parametrization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mo>ℓ</mo><mi>ν</mi></math> form factors relying on partial-wave decompositions and series expansions in suitable variables. We bound the expansion coefficients through unitarity and include left-hand cut contributions using established dispersive methods. The two-hadron line shapes are treated in a model-independent manner using Omnès functions, thus allowing for a data-driven determination of the expansion parameters. We study the underlying composition of the di-pion system in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mo>ℓ</mo><mi>ν</mi></math> decays through fits to differential spectra of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi></math> measured by the Belle experiment. In contrast to previous works, we are able to study the full phase space and are not limited to certain kinematic regions. As a consequence, we extract branching fractions for the different partial waves of the di-pion system. We find <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mo stretchy="false">)</mo><mi>S</mi></msub><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mn>2.2</mn><mrow><mo>−</mo><mn>1.0</mn></mrow><mrow><mo>+</mo><mn>1.4</mn></mrow></msubsup><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><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mo stretchy="false">)</mo><mi>P</mi></msub><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><msubsup><mn>19.6</mn><mrow><mo>−</mo><mn>2.7</mn></mrow><mrow><mo>+</mo><mn>2.8</mn></mrow></msubsup><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><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mo stretchy="false">)</mo><mi>D</mi></msub><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mn>3.5</mn><mrow><mo>−</mo><mn>1.1</mn></mrow><mrow><mo>+</mo><mn>1.3</mn></mrow></msubsup><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. In addition, we derive predictions for the thus far unobserved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi></math> decay and obtain a sizable branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><mi>ν</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mn>2.9</mn><mrow><mo>−</mo><mn>0.7</mn></mrow><mrow><mo>+</mo><mn>0.9</mn></mrow></msubsup><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>.

Switzerland

Florian Herren

Germany

Bastian Kubis

Raynette van Tonder

Model-independent parametrization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mo>ℓ</mo><mi>ν</mi></math> decays

The pseudorapidity density distributions of charged particles and the transverse-momentum spectra of identified particles in proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math>) collisions at the center-of-mass energies ranging from <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV to 13 TeV have been systematically studied using the newly released parton and cascade model paciae 4.0 based on pythia 8.3. The available experimental data are well reproduced across all analyzed aspects. This theoretical method can be easily extended to anywhere the experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions are currently unavailable. Furthermore, since <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions serve as the baseline for heavy-ion collisions, our results can provide a valuable resource for both experimentalists and theorists.

China

Zhen Xie

An-Ke Lei

Hua Zheng

Wenchao Zhang

Dai-Mei Zhou

Zhi-Lei She

Yu-Liang Yan

Ben-Hao Sa

Pseudorapidity density distributions of charged particles and transverse-momentum spectra of identified particles in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions in the PACIAE 4.0 model

Since the LHCb collaboration successively reported the hidden-charm exotic states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>, these exotic states have rightfully attracted significant attention from theoretical perspectives. Motivated by these exotic states, this study systematically investigates the hidden-charm double-strange pentaquark system with the quark configuration <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mi>s</mi><mi>s</mi><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> using the resonating group method within the framework of the quark delocalization color screening model. The dynamical estimations, incorporating channel coupling, identify five resonance states in the hidden-charm double-strange systems, denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ω</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, through scattering phase shifts processes of various channels. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, with mass range and decay widths of (4684 MeV–4688 MeV, 6.4 MeV–24.2 MeV) and (4751 MeV–4756 MeV, 3.2 MeV–18.7 MeV), can be derived from the scattering processes of channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><msub><mi>η</mi><mi>c</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math>, it should be noted that resonance state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, in addition to the channels mentioned above, can also be observed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mo>*</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>. For the quantum number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ω</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> can be identified in channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mo>*</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mo>*</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, respectively, the estimated masses and decay widths of these resonance states range from approximately (4749 MeV–4755 MeV, 16.4 MeV) and (4771 MeV-4772 MeV, 18.8 MeV). However, the residual resonance state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math>, for which the estimated mass and decay width are about 4600 MeV and 21.7 MeV, is expected to be found only in channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>. Given the current theoretical estimations, experiments are anticipated to further explore hidden-charm double-strange pentaquark states through the possible decay channels, thereby offering a strong theoretical foundation for their experimental investigation.

Xuejie Liu

Yue Tan

Xiaoyun Chen

Dianyong Chen

Hongxia Huang

Jialun Ping

Study on the properties of hidden-charm pentaquarks with double strangeness

We holographically study the far-from-equilibrium isotropization dynamics of the strongly coupled $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills plasma. The dual gravitational background is driven to be out of equilibrium and anisotropic by a time-dependent change in boundary conditions. At late times, the system relaxes and asymptotically approaches a static configuration. The large initial energy densities accelerate the isotropization significantly compared to the initial geometry corresponding to the supersymmetric Yang-Mills vacuum. We analyze shear transport during isotropization by directly computing the time-dependent stress tensor, which is now a nonlinear function of the shear rate. The shear viscosity far from equilibrium displays much richer dynamics than its near-equilibrium counterpart. Moreover, we uncover that the equilibrium viscosity-to-entropy ratio at late times depends on the details of the quench function and the initial data, which could be due to a resummation of the hydrodynamic description. In particular, this ratio can be parametrically smaller than the Kovtun-Son-Starinets bound calculated from linear response theory.

Shoucheng Wang

Song He

Li Li

Shear transport in far-from-equilibrium isotropization of supersymmetric Yang-Mills plasma

Among the three known types of static solutions proposed within the Hamiltonian constraint approach to effective quantum gravity (EQG), the first two have been extensively investigated, whereas the third type-which preserves general covariance, is free of Cauchy horizons, and was only recently obtained-remains relatively unexplored. This solution can describe a black hole with an event horizon for certain parameter ranges, or a horizonless compact object beyond those ranges. In this paper, we focus on the third type and show that its light rings feature both stable and unstable branches, and that the black hole shadow size grows with the quantum parameter-unlike in the first two types. However, when we account for both the shadow and the lensing ring, the overall behavior closely resembles that of the second type, in which an increasing quantum parameter leads to a larger portion of the lensing ring being occupied by the shadow. This feature can serve as a hallmark of black holes in EQG, offering a potential way to distinguish them from their GR counterparts. Remarkably, the parameter ranges under which the solution remains a black hole are highly consistent with the current observational constraints on black hole shadows, lending strong support to the classification of the third type of compact object in EQG as a black hole endowed with an event horizon.

Wentao Liu

Di Wu

Jieci Wang

Light rings and shadows of static black holes in effective quantum gravity II: A new solution without Cauchy horizons

Using data samples of 102 million <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> events and 158 million <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> events collected by the Belle detector at the KEKB asymmetric-energy <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, we search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>u</mi><mi>d</mi><mi>s</mi><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">]</mo></math> pentaquark states decaying to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>. Using the first observations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> inclusive decays to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>, we find evidence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> state with a local significance of 3.3 standard deviations, including statistical and systematic uncertainties. We measure the mass and width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>4471.7</mn><mo>±</mo><mn>4.8</mn><mo>±</mo><mn>0.6</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>22</mn><mo>±</mo><mn>13</mn><mo>±</mo><mn>3</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, respectively. The branching fractions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> production are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>/</mo><msub><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3.5</mn><mo>±</mo><mn>2.0</mn><mo>±</mo><mn>0.2</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>/</mo><mspace linebreak="goodbreak"></mspace><msub><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.9</mn><mo>±</mo><mn>1.7</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>. The inclusive branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>36.9</mn><mo>±</mo><mn>5.3</mn><mo>±</mo><mn>2.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</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><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>22.3</mn><mo>±</mo><mn>5.7</mn><mo>±</mo><mn>3.1</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>. We measure the visible cross section <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>σ</mi><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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>90</mn><mo>±</mo><mn>14</mn><mo>±</mo><mn>6</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mrow><mi>fb</mi></mrow></mrow></math> for the continuum production at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10.52</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. In all cases, the first uncertainties are statistical and the second are systematic.

I. Adachi

L. Aggarwal

H. Ahmed

J.K. Ahn

H. Aihara

N. Akopov

M. Alhakami

A. Aloisio

N. Althubiti

D.M. Asner

H. Atmacan

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. Baur

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

D. Biswas

D. Bodrov

A. Bolz

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

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

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

X. Dong

D. Dossett

K. Dugic

G. Dujany

P. Ecker

J. Eppelt

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

B.G. Fulsom

A. Gabrielli

E. Ganiev

M. Garcia-Hernandez

G. Gaudino

Search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4338</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> Inclusive Decays at Belle

We measure the time-integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <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><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays reconstructed 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><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></math> events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>428</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, respectively. To infer the flavor of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> meson, we exploit the correlation between the flavor of the reconstructed decay and the electric charges of particles reconstructed in the rest of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></mrow><mo stretchy="false">→</mo><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></math> event. This results in a sample which is independent from any other previously used at Belle or Belle II. The result, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.3</mn><mo>±</mo><mn>2.0</mn><mo>±</mo><mn>0.2</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, where the first uncertainty is statistical and the second systematic, is consistent with previous determinations and with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry.

Y. Ahn

S. Alghamdi

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

T. Aushev

T. Bilka

A. Bobrov

A. Bondar

J. Borah

J. Chin

I. Consigny

G. de Marino

A. Di Canto

M. Dorigo

D. Epifanov

R. Farkas

A. Fodor

A. Gale

R. Garg

V. Gaur

Measurement of the time-integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <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><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays using opposite-side flavor tagging at Belle and Belle II

The recent observation of a diphoton excess around 95 GeV by the CMS and ATLAS Collaborations, along with the <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> excess reported by the LEP Collaboration in the same mass region, has drawn significant interest in the possibility of new physics beyond the Standard Model (SM). The Georgi-Machacek (GM) model, which extends the Higgs sector of the SM by introducing additional triplet scalars while preserving custodial symmetry at tree level, provides a compelling framework to explain both excesses simultaneously via a light custodial singlet Higgs. In this work, we investigate whether the GM model can still accommodate these excesses when taking into account newly proposed vacuum stability constraints, particularly the positive definiteness conditions. Our numerical analysis not only confirms the existence of a viable parameter space capable of explaining the 95 GeV excesses, but also demonstrates that, compared to traditional tree-level constraints at the electroweak scale, the positive definiteness conditions further expand the allowed parameter space, thereby enhancing the viability of the GM model. Furthermore, we emphasize that future collider experiments will play a crucial role in testing this interpretation by refining Higgs coupling measurements and searching for additional Higgs bosons.

Xiaokang Du

Huiling Liu

Qin Chang

Interpretation of 95 GeV excess within the Georgi-Machacek model in light of positive definiteness constraints