arXiv subjects

Qing-hai Wang

Publications and source records attributed to Qing-hai Wang.

At least 19 recordsLinked to original sources

arXiv2026

Scalar Casimir Effect on a Two-Dimensional Sphere with a Wu--Yang Magnetic Monopole

We investigate the Casimir effect of a complex scalar field on a two-dimensional sphere threaded by a fixed Wu--Yang magnetic monopole at the center. In this background the charged scalar field is a section of a nontrivial complex line bundle over $S^2$, reflecting the monopole's nontrivial topology. We solve the Klein--Gordon equation analytically and compute the Casimir energy using a generalized Abel--Plana formula for multivalued functions. We find that the monopole can reverse the sign of the Casimir pressure, turning an attractive force into a repulsive one when the monopole strength is sufficiently large. This behavior persists across a broad range of curvature couplings and suggests that Wu--Yang monopoles may provide a source of repulsive vacuum stress, with possible implications for gravitational and cosmological settings.

hep-th↗

arXiv2026

Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$

For the two-loop next-to-leading-order electroweak (NLO EW) corrections to $gg \rightarrow ZH$, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform an analytic computation of the master integrals (MIs) associated with the four planar topologies. Canonical bases are constructed using the Magnus-expansion method, and the resulting alphabets consist of algebraic symbol letters involving nontrivial radicals. We develop a systematic framework for identifying the radical structures of the canonical MIs, enabling their organization into suitable subsystems and, whenever possible, their representation in terms of Goncharov polylogarithms (GPLs) up to $\mathcal{O}(ε^4)$. Only a few MIs at $\mathcal{O}(ε^3)$ and $\mathcal{O}(ε^4)$ are instead represented as one-fold integrals over GPLs, due to the presence of nested square roots that obstruct the simultaneous rationalization of all radicals.

hep-ph↗

arXiv2026

Why Barriola--Vilenkin Global Monopoles Cannot Rotate?

The Barriola--Vilenkin global monopoles are topological defects predicted by certain grand unified theories and have been extensively studied for their astrophysical and cosmological implications, including their distinctive spacetime geometry and characteristic gravitational lensing effects. Despite this interest, an exact solution for a global monopole remains elusive, with research largely confined to approximations of the static, spherically symmetric case. This paper addresses the fundamental question of whether a rotating global monopole can exist as a solution to the coupled Einstein-scalar field equations. We first prove that metrics generated by applying the Newman-Janis algorithm to the static monopole are inconsistent with the scalar field's equation of motion. Furthermore, we perform an asymptotic analysis for general static, axially symmetric spacetimes and establish that the only such solution that is regular at large distances is the spherically symmetric one. These results lead to the conclusion that the Barriola--Vilenkin global monopoles are incompatible with rotating spacetime within the framework of Einstein's general relativity.

gr-qc↗

arXiv2026

Doubly charged Higgs production within the Higgs triplet model at future electron-positron colliders

We investigate in detail the discovery potential of the doubly charged Higgs boson at the Compact Linear Collider in $e^-e^-$, $e^-γ$, $γγ$, and $e^+e^-$ collision modes, within the Higgs triplet model at two extreme benchmark points as representatives of the Yukawa-like and gauge-like regions. In the Yukawa-like region, the most promising production mechanism is the single production via $e^-e^-$ and $e^-γ$ collisions. Given the subsequent decay of the doubly charged Higgs into a same-sign lepton pair, CLIC can achieve statistical significance well beyond the discovery threshold, within the parameter space permitted by experimental constraints. In the gauge-like region, with the $\ell^{\pm}\ell^{\pm} + \geq 3j$ final state, CLIC exhibits robust discovery potential for the doubly charged Higgs boson, up to a mass of approximately $1.2~\mathrm{TeV}$. We also investigate the search for doubly charged Higgs at the HL-LHC. Our results demonstrate that CLIC possesses greater advantages and offers superior discovery potential for the doubly charged Higgs boson, compared to the HL-LHC.

hep-ph↗

arXiv2025

Finite-Distance Gravitational Lensing of a Global Monopole in a Schwarzschild-de Sitter Spacetime

We investigate the gravitational lensing of a Schwarzschild-de Sitter black hole with a global monopole at finite distances. In this asymptotically nonflat spacetime, the deflection angle of light is decomposed into two parts: the first derives from the orbit differential equation, and the second originates from the metric itself. By absorbing the cosmological constant into the effective impact parameter, we derive an analytical expression for the first part using elliptic integrals. Combined with the second part, we obtain a complete exact solution for the deflection angle in this context. Additionally, considering that the distances from the source to the observer are large, we derive expressions for the light deflection angle in both the weak and strong field limits. In both cases, we find that the deflection is enhanced by the presence of the global monopole, further supporting its potential role as an alternative to elusive dark matter.

gr-qc↗

arXiv2024

Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders

The discrepancy between the CDF measurement and the Standard Model theoretical prediction for the $W$-boson mass underscores the importance of conducting high-precision studies on the $W$ boson, which is one of the predominant objectives of proposed future $e^+e^-$ colliders. We investigate in detail the production of $W$-boson pairs at $e^+e^-$ colliders, and compute the next-to-next-to-leading order mixed QCD-EW corrections to both the integrated cross section and various kinematic distributions. By employing the method of differential equations, we analytically calculate the two-loop master integrals for the mixed QCD-EW virtual corrections to $e^+e^- \rightarrow W^+W^-$. Utilizing the Magnus transformation, we derive a set of canonical master integrals for each integral family. This canonical basis satisfies a system of differential equations in which the dependence on the dimensional regulator is linearly factorized from the kinematics. We then express all these canonical master integrals as Taylor series in $ε$ up to $ε^4$, with coefficients articulated in terms of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis of $W$-pair production, we observe that the $\mathcal{O}(αα_s)$ corrections are significantly impactful in the $α(0)$ scheme, particularly in certain phase-space regions. However, these mixed QCD-EW corrections can be heavily suppressed by adopting the $G_μ$ scheme.

hep-ph↗

arXiv2024

Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation

The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for $W$-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling $27$, $45$ and $15$, respectively. These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator $ε$. For the first two family branches, the differential systems can be successfully transformed into canonical form by adopting appropriate bases of MIs. This enables the MIs of these family branches to be expressed either as Goncharov polylogarithms (GPLs) or as one-fold integrals over GPLs, up to $\mathcal{O}(ε^4)$. In contrast, the differential system for the third family branch can only be cast into a form linear in $ε$ due to the presence of elliptic integrals. The solution to this linear-form differential system is expressed in an iterated form owing to the strictly lower-triangular structure of the coefficient matrices at $ε= 0$. Our analytic expressions for these MIs are verified with high accuracy against the numerical results from the \texttt{AMFlow} package.

hep-ph↗

arXiv2024

Next-to-next-to-leading order $\text{QCD} \otimes \text{EW}$ corrections to $Z$-boson pair production at electron-positron colliders

We present a comprehensive analytic calculation of the next-to-next-to-leading order $\text{QCD} \otimes \text{EW}$ corrections to $Z$-boson pair production at electron-positron colliders. The two-loop master integrals essential to this calculation are evaluated using the differential equation method. In this work, we detail the formulation and solution of the canonical differential equations for the two-loop three-point master integrals with two on-shell $Z$-boson external legs and a massive internal quark in the loops. These canonical master integrals are systematically expanded as Taylor series in the dimensional regulator, $ε= (4-d)/2$, up to the order of $ε^4$, with coefficients expressed in terms of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis of $Z$-pair production, we observe that the $\mathcal{O}(αα_s)$ corrections manifest at a level of approximately one percent compared to the leading-order predictions, underscoring their significance for comparisons with future high-precision experimental data.

hep-ph↗

arXiv2023

Mixed $\text{QCD} \otimes \text{EW}$ corrections to charged Higgs pair production in THDM at electron-positron colliders

We calculate the two-loop mixed QCD$\otimes$EW corrections for the charged Higgs boson pair production within the framework of four types of Two Higgs Doublet Models (THDMs) with the $Z_2$ symmetry. We analyze in detail the dependences of our results on physical parameters, including the charged Higgs mass, $\tanβ$, the scattering angle, and the colliding energy. It is noticeable that the mixed QCD$\otimes$EW relative correction is independent of the scattering angle due to the topology of Feynman diagrams at $O(αα_s)$. Numerical results in most allowed regions of four types of THDMs are provided in the density plots on the $m_{H^{\pm}}$-$\tanβ$ plane. For type-I and type-X, the mixed QCD$\otimes$EW relative correction varies slightly near $1\%$ except in the vicinity of resonance. For type-II and type-Y, the corrections increase consistently in large $\tanβ$ region and reach up to $11.5\%$ at $\tanβ= 50$. We also compute the $O(α)$ corrections to obtain the corrected cross section up to $O(αα_s)$. The numerical results show that the corrected cross section can be larger than $80\ \mathrm{fb}$ in some parameter space region for type-I and type-X THDMs.

hep-ph↗

arXiv2023

Connection problem of the first Painlevé transcendent between poles and negative infinity

We consider a connection problem of the first Painlevé equation ($\mathrm{P_I}$), trying to connect the local behavior (Laurent series) near poles and the asymptotic behavior as the variable $t$ tends to negative infinity for real $\mathrm{P_I}$ functions. We get a classification of the real $\mathrm{P_I}$ functions in terms of $(p,H)$ so that they behave differently at the negative infinity, where $p$ is the location of a pole and $H$ is the free parameter in the Laurent series. Some limiting-form connection formulas of $\mathrm{P_I}$ functions are obtained for large $H$. Specifically, for the real tritronquée solution, the large-$n$ asymptotic formulas of $p_n$ and $H_n$ are obtained, where $p_n$ is the $n$-th pole on the real line in the ascending order and $H_n$ is the associated free parameter. Our approach is based on the complex WKB method (also known as the method of uniform asymptotics) introduced by Bassom, Clarkson, Law and McLeod in their study on the connection problem of the second Painlevé transcendent [Arch. Rational Mech. Anal., 1998, pp. 241-271]. Several numerical simulations are carried out to verify our main results. Meanwhile, we obtain the phase diagram of \PI~solutions in the $(p,H)$ plane, which somewhat resembles the Brillouin zones in solid-state physics. The asymptotic and numerical results obtained in this paper partially answer Clarkson's open question on the connection problem of the first Painlevé transcendent.

math.CA↗

arXiv2022

On the quantization of AB phase in nonlinear systems

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of $π$ at the critical nonlinearity at which the Dirac cone appears or disappears, whereas for all other powers of nonlinearity the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

quant-ph↗

arXiv2022

Floquet band engineering with Bloch oscillations

This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-André-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands or Floquet bands with large Chern numbers due to the interplay between the periodic driving and Bloch oscillations can be obtained, with the band structure and topology extensively tunable by adjusting the ratio of two competing frequencies. To confirm our finding, we further execute the Thouless pumping of one and two interacting bosons in such a lattice system and establish its connection with the topological properties of single- and two-particle Floquet bands.

quant-ph↗

arXiv2022

Solvable dilation model of $\cal PT$-symmetric systems

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.

quant-ph↗

arXiv2021

Cliophysics: A scientific analysis of recurrent historical events

Named after Clio, the Greek goddess of history, cliophysics is a daughter (and in a sense an extension) of econophysics. Like econophysics it relies on the methodology of experimental physics. Its purpose is to conduct a scientific analysis of historical events. Such events can be of sociological, political or economic nature. In this last case cliophysics would coincide with econophysics. The main difference between cliophysics and econophysics is that the description of historical events may be qualitative as well as quantitative. For the handling of qualitative accounts cliophysics has developed an approach based on the identification of patterns. To detect a pattern the main challenge is to break the "noise barrier". The very existence of patterns is what makes cliophysics possible and ensures its success. Briefly stated, once a pattern is detected, it allows predictions to be made. As the capacity to make successful predictions is the hallmark of any science, it becomes easy to decide whether or not the claim made in the title of the paper is indeed fulfilled. A number of examples of clusters of similar events will be given which should convince readers that historical events can be simplified almost at will very much as in physics. One should not forget that physical effects are also subject to the environment. For instance, if tried at the equator, the experiment of the Foucault pendulum will fail. In the last part of the paper, we describe cliophysical investigations conducted over the past decades; they make us confident that cliophysics can be a valuable tool for decision makers.

physics.soc-ph↗

arXiv2020

Exactly solvable nonlinear eigenvalue problems

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental equation can be integrated once to a first order nonlinear equation, e.g., the Ricatti equation. It is shown that the nonlinear eigenvalue problems of these semi-transcendental equations are equivalent to linear eigenvalue problems. They share the exactly same eigenvalues. The eigensolutions in the two problems are closely related. The nonlinear eigenvalue problem equivalent to the (half) harmonic oscillator in quantum mechanics is solved exactly. This is the first solvable nonlinear eigenvalue problem. The nonlinear eigenvalue problems of some extended equations are also studied.

math-ph↗

arXiv2019

Time-dependent $\mathcal{PT}$-symmetric quantum mechanics in generic non-Hermitian systems

$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This line of research was made possible by the introduction of a time-independent metric operator to redefine the inner product of a Hilbert space. To treat the dynamics of generic non-Hermitian systems under equal footing, we advocate in this work the use of a time-dependent metric operator for the inner-product between time-evolving states. This treatment makes it possible to always interpret the dynamics of arbitrary (finite-dimensional) non-Hermitian systems in the framework of time-dependent $\mathcal{PT}$-symmetric quantum mechanics, with unitary time evolution, real eigenvalues of an energy observable, and quantum measurement postulate all restored. Our work sheds new lights on generic non-Hermitian systems and spontaneous $\mathcal{PT}$-symmetry breaking in particular. We also illustrate possible applications of our formulation with well-known examples in quantum thermodynamics.

quant-ph↗

arXiv2019

Nonlinear eigenvalue problems for generalized Painlevé equations

Eigenvalue problems for linear differential equations, such as time-independent Schrödinger equations, can be generalized to eigenvalue problems for nonlinear differential equations. In the nonlinear context a separatrix plays the role of an eigenfunction and the initial conditions that give rise to the separatrix play the role of eigenvalues. Previously studied examples of nonlinear differential equations that possess discrete eigenvalue spectra are the first-order equation $y'(x)=\cos[πxy(x)]$ and the first, second, and fourth Painlevé transcendents. It is shown here that the differential equations for the first and second Painlevé transcendents can be generalized to large classes of nonlinear differential equations, all of which have discrete eigenvalue spectra. The large-eigenvalue behavior is studied in detail, both analytically and numerically, and remarkable new features, such as hyperfine splitting of eigenvalues, are described quantitatively.

math-ph↗

arXiv2019

The future of US-China relations: a scientific investigation

In earlier centuries kings and governments employed astrologists to help them take the best decisions. Present-day governments no longer employ astrologists but still have no clear analytical tool to replace them. Over the past two decades we have developed a methodology for the scientific investigation of recurrent historical events. It consists in two steps. (i) Identification and comparison of historical episodes driven by a common mechanism. (ii) Under the reasonable assumption that what has happened several times in the past is likely to happen again, one then derives testable predictions. This of course is nothing other than the protocol used in experimental science when exploring new phenomena. We believe such a tool can give decision makers much better insight. In the present paper we illustrate this analysis by considering challenges, that span more than a century, to US hegemony in the Pacific. The outcomes suggest that it is only through the sidelining of one of the contenders that the confrontation will end. At the time of writing (late 2018) early evidence of this confrontation is already visible at three levels. (i) Growing US concerns for domestic security that are leading to a new form of McCarthyism. (ii) Political instability due to China-US polarization in several Asian countries as well as in the countries participating in the Belt and Road Initiative. (iii) Tension and sanctions in procurement and trade.

physics.hist-ph↗