<p>In this article, the vector, axial vector, and tensor form factors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>h</mi><mi>c</mi></msub></math> are analyzed within the framework of three-point QCD sum rules. With the calculated vector and axial vector form factors, we directly study the decay widths and branching ratios of semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mi>l</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>l</mi></msub><mo>,</mo><msub><mi>h</mi><mi>c</mi></msub><mi>l</mi><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>l</mi></msub></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>l</mi><mo>=</mo><mi>e</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>) and analyze the nonleptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><msup><mi>π</mi><mo>−</mo></msup><mo>,</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><msup><mi>K</mi><mo>−</mo></msup><mo>,</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><msup><mi>ρ</mi><mo>−</mo></msup><mo>,</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><msup><mi>K</mi><mrow><mo>*</mo><mo>−</mo></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><msub><mi>h</mi><mi>c</mi></msub><msup><mi>π</mi><mo>−</mo></msup><mo>,</mo><msub><mi>h</mi><mi>c</mi></msub><msup><mi>K</mi><mo>−</mo></msup><mo>,</mo><msub><mi>h</mi><mi>c</mi></msub><msup><mi>ρ</mi><mo>−</mo></msup><mo>,</mo><msub><mi>h</mi><mi>c</mi></msub><msup><mi>K</mi><mrow><mo>*</mo><mo>−</mo></mrow></msup></math> by using the naive factorization approach. These results can provide more information to understand the properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> meson and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmonia and to study the heavy quark dynamics.</p>

China

Jie Lu

Dian-Yong Chen

Guo-Liang Yu

Zhi-Gang Wang

Bin Wu

Systematic analysis of the form factors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmonia and corresponding weak decays

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We investigate the Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>&#965;</mi></mrow><mrow><mi>&#965;</mi></mrow></msubsup></math>. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital <italic>&#8467;</italic>-excitations, for all radial quantum numbers <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>&#8805;</mo><mn>0</mn></math>. Our procedure is shown to be quite handy, in the sense that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

Türkiye

Omar Mustafa

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

In this study, we obtain specific picture of the phase transitions for the 6-dimensional Gauss-Bonnet Anti-de Sitter (AdS) black hole with triple phases, using the generalized free energy we constructed and Kramers escape rate in stochastic motion. There are six possible phase transition processes between the three different stable states (small, medium, and large black hole states). During these phase transitions, there are two key temperatures. One is the temperature at which the medium black hole state emerges, and the other is the temperature at which the small black hole state annihilates. Meanwhile, two dynamic equilibrium processes are formed. One is a dynamic equilibrium of the transition from the medium black hole state to the large black hole state and the transition from the small black hole state to the medium black hole state. The other is a dynamic equilibrium of the transition from the small black hole state to the medium black hole state and the transition from the medium black hole state to the small black hole state.

Chen Ma

Pan-Pan Zhang

Zhen-Ming Xu

The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases

A novel thermodynamic phenomenon has been observed in the quantum Bañados-Teitelboim-Zanelli (qBTZ) black hole, utilizing generalized free energy and Kramers escape rate. This phenomenon also reveals the unique property of the quantum black hole. The stochastic thermal motion of various thermodynamic states within the black hole system induces phase transitions, under the influence of generalized free energy which obtained by extending Maxwell’s construction. Through the analysis of Kramers escape rate, it is discovered that the qBTZ black hole thermodynamic system exhibits a bounce effect. It originates from the non-monotonicity of entropy in black hole thermodynamic systems. Furthermore, the overall thermodynamic picture of the qBTZ black hole has been obtained under different quantum backreactions.

Xing Zhang

Thermodynamic bounce effect in quantum BTZ black hole

The assumption of factorization lies at the core of calculations of medium effects on observables computable in perturbative Quantum Chromodynamics. In this work we examine this assumption, for which we propose a setup to study hard processes and bulk nuclear matter in heavy-ion collisions on the same footing using the Glauber modelling of heavy nuclei. To exemplify this approach, we calculate the leading-order corrections to azimuthal decorrelation in Drell-Yan and boson-jet processes due to cold nuclear matter effects, not considering radiation. At leading order in both the hard momentum scale and the nuclear size, the impact-parameter dependent cross section is found to factorize for both processes. The factorization formula involves a convolution of the hard cross section with the medium-modified parton distributions, and, for boson-jet production, the medium-modified jet function.

Spain

Néstor Armesto

Florian Cougoulic

Cold nuclear matter effects on azimuthal decorrelation in heavy-ion collisions

The form factors of <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> are analyzed in the framework of three-point QCD sum rules. In the calculations, the contributions of the vacuum condensate terms <math><mo>〈</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>G</mi><mi>G</mi><mo>〉</mo></math> and <math><mo>〈</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mi>G</mi><mi>G</mi><mi>G</mi><mi>f</mi><mo>〉</mo></math> are considered. In addition, the decay widths and branching ratios of several decay channels are predicted by using the calculated form factors. These decay processes include the nonleptonic decays <math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup></math>, and the semileptonic decays <math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mi>l</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>l</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>. These results about the form factors and decay properties of <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math> meson provide useful information for us to study the heavy-quark dynamics and find new physics beyond Standard Model.

Systematic analysis of the form factors of → , / And Corresponding Weak Decays

Inspired by the great progress in the observations of charmonium-like states in recent years, we perform a systematic analysis about the ground states and the first radially excited states of  $$qc\bar{q}\bar{c}$$  <math> <mrow> <mi>q</mi> <mi>c</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   (q = u/d and s) tetraquark systems. Their mass spectra, root mean square (r.m.s.) radii and radial density distributions are predicted within the framework of relativized quark model. By comparing with experimental data, some potential candidates for hidden-charm tetraquark states are suggested. For  $$qc\bar{q}\bar{c}$$  <math> <mrow> <mi>q</mi> <mi>c</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   (q = u/d) system, if  $$Z_{c}(3900)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   is supposed to be a compact tetraquark state with  $$J^{PC}=1^{+-}$$  <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>1</mn> <mrow> <mo>+</mo> <mo>-</mo> </mrow> </msup> </mrow> </math>  , Z(4430) can be interpreted as the first radially excited states of  $$Z_{c}(3900)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>  . Another broad structure  $$Z_{c}(4200)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4200</mn> <mo>)</mo> </mrow> </mrow> </math>   can also be explained as a partner of  $$Z_{c}(3900)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>  , and it arise from a higher state with  $$J^{PC}=1^{+-}$$  <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>1</mn> <mrow> <mo>+</mo> <mo>-</mo> </mrow> </msup> </mrow> </math>  . In addition, theoretical predictions indicate that the possible assignments for X(3930), X(4050) and X(4250) are low lying  $$0^{++}$$  <math> <msup> <mn>0</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math>   tetraquark states. As for the  $$sc\bar{s}\bar{c}$$  <math> <mrow> <mi>s</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   system, X(4140) and X(4274) structures can be interpreted as this type of tetraquark states with  $$J^{PC}=1^{++}$$  <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>1</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </mrow> </math>  , and X(4350) can be described as a  $$sc\bar{s}\bar{c}$$  <math> <mrow> <mi>s</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   tetraquark with  $$J^{PC}=0^{++}$$  <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>0</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </mrow> </math>  . With regard to  $$qc\bar{s}\bar{c}$$  <math> <mrow> <mi>q</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   (q = u/d) system, we find two potential candidates for this type of tetraquark, which are  $$Z_{cs}(4000)$$  <math> <mrow> <msub> <mi>Z</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4000</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$Z_{cs}(4220)$$  <math> <mrow> <msub> <mi>Z</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4220</mn> <mo>)</mo> </mrow> </mrow> </math>   structures. The measured masses of these two structures are in agreement with theoretical predictions for the  $$1^{+}$$  <math> <msup> <mn>1</mn> <mo>+</mo> </msup> </math>   state.

Zhen-Yu Li

Ze Zhou

The ground states of hidden-charm tetraquarks and their radial excitations

Thermal properties of quantum fields at finite temperature are crucial to understanding strongly interacting matter and recent development in quantum computing has provided an alternative and promising avenue of study. In this work, we study thermal field theories involving only fermions using quantum algorithms. We first delve into the presentations of fermion fields via qubits on digital quantum computers alongside the quantum algorithms such as quantum imaginary time evolutions employed to evaluate thermal properties of generic quantum field theories. Specifically, we show numerical results such as the thermal distribution and the energy density of thermal field theories for Majorana fermions in 1+1 dimensions using quantum simulators. In addition to free field theory, we also study the effects of interactions resulting from coupling with a spatially homogeneous Majorana field. In both cases, we show analytically that thermal properties of the system can be described using phase-space distributions, and the quantum simulation results agree with analytical and semiclassical expectations. Our work is an important step to understand thermal fixed points, preparing for quantum simulation of thermalization in real time.

Wenyang Qian

Quantum computation in fermionic thermal field theories

We investigate thermalization of gluons in spatially homogeneous systems using the Boltzmann equation in diffusion approximation. A complete picture on thermalization is obtained for both initially under- and over-populated systems. In an initially under-populated system, we find that its soft sector undergoes three stages: overheating, cooling/overcooling and reheating before full thermalization is achieved. In an initially over-populated system, we find that its soft sector only undergoes two stages towards full thermalization: overheating and cooling. The cooling stage is consistently driven by momentum broadening due to multiple elastic collisions, manifest as a non-thermal scaling solution.