In this paper, we study the quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> [with <math><mi>P</mi><mo>=</mo><mo>(</mo><mi>π</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>η</mi><mo>,</mo><msup><mi>η</mi><mo>′</mo></msup><mo>)</mo></math>] within framework of perturbative QCD (PQCD) factorization approach. With the help of <math><mi>π</mi><mo>−</mo><mi>π</mi></math> distribution amplitude and scalar form factor <math><msub><mi>F</mi><mrow><mi>π</mi><mi>π</mi></mrow></msub><mo>(</mo><msup><mi>ω</mi><mn>2</mn></msup><mo>)</mo></math>, we calculate the <math><mi>C</mi><mi>P</mi></math> averaged branching fraction and the <math><mi>C</mi><mi>P</mi></math> asymmetry for the quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. Taking the quasi-two-body decay <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> as an explicit example, we present the behavior of differential branching fraction and direct <math><mi>C</mi><mi>P</mi></math> violation versus the <math><mrow><mi>π</mi><mtext>−</mtext><mi>π</mi></mrow></math> invariant mass. The total branching fraction and direct <math><mi>C</mi><mi>P</mi></math> violation are <math><mi>B</mi><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>[</mo><mi>σ</mi><mo>→</mo><mo>]</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mo>(</mo><mn>1.78</mn><mo>±</mo><mn>0.41</mn><mo>±</mo><mn>0.51</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and <math><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>[</mo><mi>σ</mi><mo>→</mo><mo>]</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mo>(</mo><mn>29.8</mn><mo>±</mo><mn>11.1</mn><mo>±</mo><mn>13.0</mn><mo>)</mo><mo>%</mo></math> respectively. Our results could be tested by further experiments.

China

Jia-Wei Zhang

Bo-Yan Cui

Xing-Gang Wu

Hai-Bing Fu

Ya-Hui Chen

Quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> in the perturbative QCD approach

In this work, we investigate the resonant contributions of <math id="M4"><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup><mfenced><mrow><mn>1430</mn></mrow></mfenced></math> and <math id="M5"><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup><mfenced><mrow><mn>1950</mn></mrow></mfenced></math> in the three-body <math id="M6"><msub><mrow><mi>B</mi></mrow><mrow><mfenced><mrow><mi>s</mi></mrow></mfenced></mrow></msub><mo>⟶</mo><msub><mrow><mi>D</mi></mrow><mrow><mfenced><mrow><mi>s</mi></mrow></mfenced></mrow></msub><mi>K</mi><mi>π</mi></math> within the perturbative QCD approach. The form factor <math id="M7"><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi><mi>π</mi></mrow></msub><mfenced><mrow><mi>s</mi></mrow></mfenced></math> is adopted to describe the nonperturbative dynamics of the S-wave <math id="M8"><mi>K</mi><mi>π</mi></math> system. The branching ratios of all concerned decays are calculated and predicted to be in the order of <math id="M9"><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup></math> to <math id="M10"><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. The ratio <math id="M11"><mi>R</mi></math> of branching fractions between <math id="M12"><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>⟶</mo><msup><mrow><mover><mi>D</mi><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo><mn>0</mn></mrow></msubsup><mfenced><mrow><mn>1430</mn></mrow></mfenced><mo>⟶</mo><msup><mrow><mover><mi>D</mi><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math> and <math id="M13"><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>⟶</mo><msup><mrow><mover><mi>D</mi><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mover><mi>K</mi><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo><mn>0</mn></mrow></msubsup><mfenced><mrow><mn>1430</mn></mrow></mfenced><mo>⟶</mo><msup><mrow><mover><mi>D</mi><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math> is predicted to be 0.0552, which implies the discrepancy for the LHCb measurements. We expect that the predictions in this work can be tested by the future experiments, especially, to resolve <math id="M14"><mi>R</mi></math> ratio discrepancy.

Contributions of And in the Charmed Three-Body Meson Decays

Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Japan

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

We study the quasi-two-body decays 
					 by employing the perturbative QCD (PQCD) factorization approach, where the charmonia 
					 represents 
					 and 
					. The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude (DA) 
					, which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor 
					 appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account, which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of 
					 are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for 
					 modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle II experiments.
				

Ya Li

Zhou Rui

Zhen-Jun Xiao

P-wave contributions to B(s)→ψKπ decays in perturbative QCD approach Supported by the National Natural Science Foundation of China (11947013, 11605060, 11775117, 11547020); Ya Li is also Supported by the Natural Science Foundation of Jiangsu Province (BK20190508) and the Research Start-up Funding of Nanjing Agricultural University; Zhou Rui is Supported in part by the Natural Science Foundation of Hebei Province (A2019209449)

We analyze the transverse momentum (pT) and rapidity (y) spectra of top quark pairs, hadronic top quarks, and top quarks produced in proton-proton (pp) collisions at center-of-mass energy TeV. For spectra, we use the superposition of the inverse power-law suggested by the QCD (quantum chromodynamics) calculus and the Erlang distribution resulting from a multisource thermal model. For y spectra, we use the two-component Gaussian function resulting from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured at the detector level, in the fiducial phase-space, and in the full phase-space by the ATLAS Collaboration at the Large Hadron Collider (LHC). Based on the parameter values extracted from pT and y spectra, the event patterns in three-dimensional velocity (βx-βy-βz), momentum (px-py-pz), and rapidity (y1-y2-y) spaces are obtained, and the probability distributions of these components are also obtained.

Fu-Hu Liu

United States

Roy A. Lacey

Event patterns extracted from top quark-related spectra in proton-proton collisions at 8 TeVSupported by National Natural Science Foundation of China (11575103, 11747319), the Shanxi Provincial Natural Science Foundation (201701D121005), the Fund for Shanxi “1331 Project” Key Subjects Construction and the US DOE (DE-FG02-87ER40331.A008)

Transverse momentum (<math id="M2"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>) and rapidity (<math id="M3"><mrow><mi>y</mi></mrow></math>) spectra of <math id="M4"><mrow><mi>Z</mi></mrow></math> bosons and quarkonium states (some charmonium <math id="M5"><mi>c</mi><mover><mrow><mi>c</mi></mrow><mo>¯</mo></mover></math> mesons such as <math id="M6"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math id="M7"><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math> and some bottomonium <math id="M8"><mi>b</mi><mover><mrow><mi>b</mi></mrow><mo>¯</mo></mover></math> mesons such as <math id="M9"><mi>Υ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></math>, <math id="M10"><mi>Υ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math>, and <math id="M11"><mi>Υ</mi><mo>(</mo><mn>3</mn><mi>S</mi><mo>)</mo></math>) produced in proton-proton (pp) and lead-lead (Pb-Pb) collisions at the large hadron collider (LHC) are uniformly described by a hybrid model of two-component Erlang distribution for <math id="M12"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> spectrum and two-component Gaussian distribution for <math id="M13"><mrow><mi>y</mi></mrow></math> spectrum. The former distribution results from a multisource thermal model, and the latter one results from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured in pp collisions at center-of-mass energies <math id="M14"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>2.76</mn></math> and 7 TeV and in Pb-Pb collisions at center-of-mass energy per nucleon pair <math id="M15"><msqrt><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>2.76</mn></math> TeV. Based on the parameter values extracted from <math id="M16"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> and <math id="M17"><mrow><mi>y</mi></mrow></math> spectra, the event patterns (particle scatter plots) in two-dimensional <math id="M18"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>-<math id="M19"><mrow><mi>y</mi></mrow></math> space and in three-dimensional velocity space are obtained.

Event Patterns Extracted from Transverse Momentum and Rapidity Spectra of Bosons and Quarkonium States Produced in pp and Pb-Pb Collisions at LHC

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan–Chen background fluid are obtained. We have considered the important case of the model parameter ψ≈1 , which corresponds to the “saturation effect”, and this regime corresponds to an effective form of “asymptotic freedom” for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversablities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius.

Deng Wang

Xin-He Meng

Wormholes supported by phantom energy from Shan–Chen cosmological fluids

The transverse momentum and rapidity distributions of net-baryons (baryons minus antibaryons) produced in central gold-gold (Au-Au) collisions at 62.4 and 200 GeV are analyzed in the framework of a multisource thermal model. Each source in the model is described by the Tsallis statistics to extract the effective temperature and entropy index from the transverse momentum distribution. The two parameters are used as input to describe the rapidity distribution and to extract the rapidity shift and contribution ratio. Then, the four types of parameters are used to structure some scatter plots of the considered particles in some three-dimensional (3D) spaces at the stage of kinetic freeze-out, which are expected to show different characteristics for different particles and processes. The related methodology can be used in the analyses of particle production and event holography, which are useful for us to better understand the interacting mechanisms.

Guo-Xing Zhang

On Productions of Net-Baryons in Central Au-Au Collisions at RHIC Energies

The transverse momentum spectrums of final-state products produced in nucleus-nucleus and proton-proton collisions at different center-of-mass energies are analyzed by using a multicomponent Erlang distribution and the Lévy distribution. The results calculated by the two models are found in most cases to be in agreement with experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The multicomponent Erlang distribution that resulted from a multisource thermal model seems to give a better description as compared with the Lévy distribution. The temperature parameters of interacting system corresponding to different types of final-state products are obtained. Light particles correspond to a low temperature emission, and heavy particles correspond to a high temperature emission. Extracted temperature from central collisions is higher than that from peripheral collisions.