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arXiv 2017年

作者： He, Daoyin Witt, Ingo Yin, Huicheng Department of Mathematics and IMS Nanjing University Nanjing210093 China Mathematical Institute University of Göttingen Bunsenstr. 3-5 GöttingenD-37073 Germany School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and [9]. For the semilinear Tricomi equation ∂t2u−t∆u = |u|p with initial data (u(0, ·), ∂tu(0, ·)) = (u0, u1), where t ≥ 0, x ∈ Rn (n ≥ 3), p > 1, and ui ∈ C0∞(Rn) (i = 0, 1), we have shown in [8] and [9] that there exists a critical exponent pcrit(n) > 1 such that the solution u, in general, blows up in finite time when 1 crit(n), and there is a global small solution for p > pcrit(n). In the present paper, firstly, we prove that the solution of ∂t2u − t∆u = |u|p will generally blow up for the critical exponent p = pcrit(n) and n ≥ 2, secondly, we establish the global existence of small data solution to ∂t2u − t∆u = |u|p for p > pcrit(n) and n = 2. Thus, we have given a systematic study on the blowup or global existence of small data solution u to the equation ∂t2u − t∆u = |u|p for n ≥ 2.35L70, 35L65, 35L67 Copyright © 2017, The Authors. All rights reserved.

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The Schrödinger equation for general non-hermitian quantum system

arXiv

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arXiv 2017年

作者： Xiong, Ye Tong, Peiqing Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing210023 China National Laboratory of Solid State Microstructures Nanjing University Nanjing210093 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

We derive a new time-dependent Schrödinger equation(TDSE) for quantum models with nonhermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively. The physical quantities are also identical in these two spaces. Based on this TDSE, we show that exchanging two quasi-particles in a non-hermitian model can generate arbitrary geometric phase. The system can also violate the Lieb-Robinson bound in non-relativistic quantum mechanics so that an action in one place will immediately cause a change in the distance. We show that the above two surprising behaviors can also appear in anyonic model, which makes us propose that the non-hermitian single particle model may possess many common features with anyonic model. Copyright © 2017, The Authors. All rights reserved.

关键词： Quantum optics

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Next-to-leading order corrections to B→ρ transition in the kT factorization

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Physical Review D 2019年第1期99卷 016007-016007页

作者： Jun Hua Ya-Lan Zhang Zhen-Jun Xiao Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Department of Faculty of Mathematics and Physics Huaiyin Institute of Technology Huaian Jiangsu 223001 People’s Republic of China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China

In this paper, we investigate the factorization hypothesis step by step for the exclusive process B→ρ at next-to-leading order (NLO), and then we extend our results to the kT factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions of the mesons involved. The full NLO amplitudes can be factorized into two parts: the B meson and the ρ meson NLO wave functions containing the collinear divergence and the finite leading order hard kernels. We give the general expressions of the nonlocal hadron matrix for the NLO B meson and ρ meson wave functions and the analytical results of factorization for the combinations of different twist parts.

关键词： Form factors

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Quasi-two-body decays B(s)→D(ρ(1450), ρ(1700))→Dππ in the perturbative QCD factorization approach

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Physical Review D 2017年第9期96卷 093011-093011页

作者： Ai-Jun Ma Ya Li Wen-Fei Wang Zhen-Jun Xiao Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Institute of Theoretical Physics Shanxi University Taiyuan Shanxi 030006 People’s Republic of China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China

By employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach, we calculate the branching ratios of the decays B(s)→D(ρ(1450), ρ(1700))→Dππ with D=(D(s),D¯(s)). The pion vector form factor Fπ, acquired from a BABAR Collaboration analysis of e+e−→π+π−(γ) data, is involved in the two-pion distribution amplitudes ΦππI=1. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of 10−10–10−4. The PQCD predictions for B(B0→D¯0(ρ0(1450),ρ0(1700))→D¯0π+π−) agree well with the measured values as reported by LHCb if one takes still large theoretical errors into account. Unlike the traditional way of the PQCD approach, one can extract the decay rates for the two-body decays B(s)→D(ρ(1450),ρ(1700)) from the results of the corresponding quasi-two-body decays. The PQCD predictions for B(B(s)→Dρ(1450)) and B(B(s)→Dρ(770)) are similar in magnitude: an interesting relation to be tested by future experimental measurements.

关键词： Electroweak interaction Form factors Particle decays Particle phenomena

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Perturbative QCD factorization of ργ⋆→ρ

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Physical Review D 2016年第3期93卷 036002-036002页

作者： Ya-lan Zhang Shan Cheng Jun Hua Zhen-Jun Xiao Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Theoretische Elementarteilchenphysik Naturwissenschaftlich Technische Fakultät Universiät Siegen 57068 Siegen Germany Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China

In this paper we first demonstrate step by step that the factorization hypothesis is valid at the next-to-leading order (NLO) for the exclusive process ργ⋆→ρ by employing the collinear factorization approach, and then extend this proof to the case of the kT factorization by taking into account the transversal momentum of the light external quark (antiquark) lines in the ρ meson. At the NLO level, we then show that the soft divergences from different subdiagrams will cancel each other in the quark level, while the remaining collinear divergences can be absorbed into the NLO meson wave functions. The full NLO amplitudes can therefore be factorized as the convolution of the NLO wave functions Φρ(1) and the infrared-finite leading order (LO) hard kernels GX,IJ,kl0 in the kT factorization. We also write down the polarized NLO ρ meson wave functions in the form of nonlocal hadron matrix elements with the gauge factor integral path deviating from the light cone. These NLO ρ meson wave functions can be used to calculate the NLO hard corrections to some relevant exclusive processes, such as B→ρ transition.

关键词： Perturbative QCD Scattering amplitudes Mesons

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ργ*→π(ρ) transition form factors in the perturbative QCD factorization approach

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Physical Review D 2015年第9期92卷 094031-094031页

作者： Ya-Lan Zhang Shan Cheng Jun Hua Zhen-Jun Xiao Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Theoretische Elementarteilchenphysik Naturwissenschaftlich Technische Fakultät Universiät Siegen 57068 Siegen Germany Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China

In this paper, we studied the ργ*→π and ργ*→ρ transition processes and made the calculations for the ρπ transition form factor Q4Fρπ(Q2) and the ρ-meson electromagnetic form factors, FLL,LT,TT(Q2) and F1,2,3(Q2), by employing the perturbative QCD (PQCD) factorization approach. For the ργ*→π transition, we found that the contribution to form factor Q4Fρπ(Q2) from the term proportional to the distribution amplitude combination ϕρT(x1)ϕπP(x2) is absolutely dominant, and the PQCD predictions for both the size and the Q2-dependence of this form factor Q4Fρπ(Q2) agree well with those from the extended anti-de Sitter/QCD models or the light-cone QCD sum rule. For the ργ*→ρ transition and in the region of Q2≥3 GeV2, furthermore, we found that the PQCD predictions for the magnitude and their Q2-dependence of the F1(Q2) and F2(Q2) form factors agree well with those from the QCD sum rule, while the PQCD prediction for F3(Q2) is much larger than the one from the QCD sum rule.

关键词： Perturbative quantum chromodynamics Wave functions Factorization method (Quantum theory)

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B¯s0→Kπ,KK decays and effects of the next-to-leading order contributions

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Physical Review D 2014年第7期89卷 074046-074046页

作者： Jing-Jing Wang Dong-Ting Lin Wen Sun Zhong-Jian Ji Shan Cheng Zhen-Jun Xiao Department of Physics Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China

By employing the perturbative QCD (pQCD) factorization approach, we calculate the branching ratios and charge parity (CP)-violating asymmetries of the four B¯s0→Kπ and KK decays, with the inclusion of all known next-to-leading order (NLO) contributions. We find numerically that (a) the NLO contribution can interfere with the leading order (LO) part constructively or destructively for different decay modes; (b) the NLO contribution leads to a 22% decrease for the central values of the LO pQCD prediction for Br(B¯s0→K+π−), but ∼50% enhancement to the other three considered B¯s decays, the agreement between the central values of the pQCD predictions and the data are therefore improved effectively after the inclusion of the NLO contributions; (c) for both B¯s0→K+π− and B¯s0→K+K− decays, the NLO pQCD predictions for the direct and mixing induced CP-violating asymmetries agree well with the measured values in both the sign and the magnitude; and (d) the theoretical errors of the pQCD predictions for decay rates are about 35% of the cental values and larger than that of the relevant data.

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Study of Bs→K(*)ℓ+ℓ− decays in the PQCD factorization approach with lattice QCD input

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Physical Review D 2020年第1期102卷 013001-013001页

作者： Su-Ping Jin Xue-Qing Hu Zhen-Jun Xiao Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu 210023 People’s Republic of China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China

In this paper, we studied systematically the semileptonic decays B¯s→K(*)ℓ+ℓ− with l−=(e−,μ−,τ−) by using the perturbative QCD (PQCD) and the “PQCD+Lattice” factorization approach, respectively. We first evaluated all relevant form factors Fi(q2) in the low-q2 region using the PQCD approach, and we also took the available lattice QCD results at the end point qmax2 as additional inputs to improve the extrapolation of the form factors to the high-q2 region. We calculated the branching ratios and twelve other kinds of physical observables. From our studies, we find the following points: (a) for B¯s→Kl+l− decays, the PQCD and PQCD+Lattice predictions for branching ratios B(B¯s→Kl+l−), the ratios of the branching ratios RKeμ and RKμτ, and the longitudinal polarization asymmetry of the leptons PL agree well within errors; (b) the PQCD and PQCD+Lattice predictions for the CP-averaged branching ratio B(B¯s→K*μ+μ−) are (3.17−0.78+0.95)×10−8 and (2.48−0.50+0.56)×10−8 respectively, which agree well with the LHCb measured value (2.9±1.1)×10−8 and the light-cone sum rule prediction; (c) for the ratios RK*eμ and RK*μτ, the PQCD and PQCD+Lattice predictions agree well with each other and have a small error less than 10%; (d) for the direct CP asymmetries ACP of all considered decay modes, they are always very small as expected: less than 5% in magnitude; (e) for the angular observables P1,2,3 and P4,5,6,8′, our theoretical predictions for each kind of lepton are consistent within errors; (f) the theoretical predictions of the angular observables P3 and P6′ are less than 10−2 in size, but the magnitude of P1,2 and P4,5′ are larger than 0.2; and (g) the PQCD and PQCD+Lattice predictions of the binned values of all considered observables in the two q2 bins [0.1–0.98] GeV2 and [1.1–6] GeV2 generally agree with each other and are also consistent with the light-cone sum rule results within errors. We believe that above predictions could be tested by future LHCb and Belle-II experiment

关键词： Electroweak interaction Flavor changing neutral currents Form factors Particle interactions Particle phenomena

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Supplementary Variable Method for Developing Structure-Preserving numerical Approximations to Thermodynamically Consistent Partial Differential Equations

arXiv

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arXiv 2020年

作者： Gong, Yuezheng Hong, Qi Wang, Qi College of Science Nanjing University of Aeronautics and Astronautics Nanjing210016 China Beijing Computational Science Research Center Beijing100193 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Department of Mathematics University of South Carolina ColumbiaSC29208 United States

We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The central idea behind it is to introduce a supplementary variable to the thermodynamically consistent model to make the over-determined equation system, consisting of the thermodynamically consistent PDE system, the energy definition and the energy dissipation equation, structurally stable. The supplementary variable allows one to retain the consistency between the energy dissipation equation and the PDE system after the temporal discretization. We illustrate the method using a dissipative gradient flow model. Among virtually infinite many possibilities, we present two ways to add the supplementary variable in the gradient flow model to develop energy-dissipation-rate preserving algorithms. Spatial discretizations are carried out using the pseudo-spectral method. We then compare the two new schemes with the energy stable SAV scheme and the fully implicit Crank-Nicolson scheme. The results favor the new schemes in the overall performance. This new numerical paradigm can be applied to any thermodynamically consistent models. Copyright © 2020, The Authors. All rights reserved.

关键词： Partial differential equations

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Fully charm and bottom pentaquarks in a lattice-QCD inspired quark model

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Physical Review D 2022年第1期106卷 014005-014005页

作者： Gang Yang Jialun Ping Jorge Segovia Department of Physics Zhejiang Normal University Jinhua 321004 China Department of Physics and Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 China Departamento de Sistemas Físicos Químicos y Naturales Universidad Pablo de Olavide E-41013 Sevilla Spain

The fully charm and bottom pentaquarks, i.e., ccccc¯ and bbbbb¯, with spin-parity quantum numbers JP=12−, 32−, and 52−, are investigated within a lattice-QCD inspired quark model, which has already successfully described the recently announced fully charm tetraquark candidate X(6900) and has also predicted several other fully heavy tetraquarks. A powerful computational technique, based on the Gaussian expansion method combined with a complex-scaling range approach, is employed to predict, and distinguish, bound, resonance, and scattering states of the mentioned five-body system. Both baryon-meson and diquark-diquark-antiquark configurations, along with all of their possible color channels are comprehensively considered. Narrow resonances are obtained in each spin-parity channel for the fully charm and bottom systems. Moreover, most of them seem to be compact multiquarks whose wave functions are dominated by either hidden-color baryon-meson or diquark-diquark-antiquark structure or by the coupling between them.

关键词： Quark model Strong interaction

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