Two-Body Scattering Research Articles

Unitarity bounds on the massive spin-2 particle explanation of muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly

Motivated by the long-standing discrepancy between the Standard Model prediction and the experimental measurement of the muon magnetic dipole moment, we have recently proposed to interpret this muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly in terms of the loop effect induced by a new massive spin-2 field G. In the present paper, we investigate the unitarity bounds on this scenario. We calculate the s-wave projected amplitudes for two-body elastic scatterings of charged leptons and photons mediated by G at high energies for all possible initial and final helicity states. By imposing the condition of the perturbative unitarity, we obtain the analytic constraints on the charged-lepton-G and photon-G couplings. We then apply our results to constrain the parameter space relevant to the explanation of the muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly.

Unitarity bounds on extensions of Higgs sector

It is widely believed that extensions of the minimal Higgs sector is one of the promising directions for resolving many puzzles beyond the Standard Model (SM). In this work, we study the unitarity bounds on the models by extending the two-Higgs-doublet model with an additional real or complex Higgs triplet scalar. By noting that the SM gauge symmetries SU(2)L × U(1)Y are recovered at high energies, we can classify the two-body scattering states by decomposing the direct product of two scalar multiplets into their direct sum of irreducible representations of electroweak gauge groups. In such state bases, the s-wave amplitudes of two-body scalar scatterings can be written in the form of block-diagonalized scattering matrices. Then the application of the perturbative unitarity conditions on the eigenvalues of scattering matrices leads to the analytic constraints on the model parameters. Finally, we numerically investigate the complex triplet scalar extension of the two-Higgs-doublet model, finding that the perturbative unitarity places useful stringent bounds on the model parameter space.

Effective two-body scatterings around a massive object

ABSTRACT Two-body scatterings under the potential of a massive object are very common in astrophysics. If the massive body is far enough away that the two small bodies are in their own gravitational sphere of influence, the gravity of the massive body can be temporarily ignored. However, this requires the scattering process to be fast enough that the small objects do not spend too much time at distances near the surface of the sphere of influence. In this paper, we derive the validation criteria for effective two-body scattering and establish a simple analytical solution for this process, which we verify through numerical scattering experiments. We use this solution to study star–black hole scatterings in the discs of active galactic nuclei and planet–planet scatterings in planetary systems, and calculate their one-dimensional cross-section analytically. Our solution will be valuable in reducing computational time when treating two-body scatterings under the potential of a much more massive third body, provided that the problem settings are in the valid parameter space region identified by our study.

The large time asymptotic solutions of nonlinear Schrödinger type equations

We give a short description of the proof of asymptotic-completeness for NLS-type equations with radial data in three dimensions. We also show some aspects of the method by giving a new proof of Asymptotic Completeness for the two-body Quantum Scattering case.

The shear viscosity of parton matter under anisotropic scatterings

The shear viscosity eta of a quark–gluon plasma in equilibrium can be calculated analytically using multiple methods or numerically using the Green–Kubo relation. It has been realized, which we confirm here, that the Chapman–Enskog method agrees well with the Green–Kubo result for both isotropic and anisotropic two-body scatterings. We then apply the Chapman–Enskog method to study the shear viscosity of the parton matter from a multi-phase transport model. In particular, we study the parton matter in the center cell of central and midcentral Au + Au collisions at 200A GeV and Pb + Pb collisions at 2760A GeV, which is assumed to be a plasma in thermal equilibrium but partial chemical equilibrium. As a result of using a constant Debye mass or cross section sigma for parton scatterings, the eta /s ratio increases with time (as the effective temperature decreases), contrary to the trend preferred by Bayesian analysis of the experimental data or pQCD results that use temperature-dependent Debye masses. At sigma =3 mb that enables the transport model to approximately reproduce the elliptic flow data of the bulk matter, the average eta /s of the parton matter in partial equilibrium is found to be very small, between one to two times 1/(4pi ).

Gauged Lμ−Lτ at a muon collider

We investigate the sensitivity of the projected TeV muon collider to the gauged $L^{}_{\mu}$-$L^{}_{\tau}$ model. Two processes are considered: $Z'$-mediated two-body scatterings $\mu^+ \mu^- \to \ell^+ \ell^-$ with $\ell = \mu$ or $\tau$, and scattering with initial state photon emission, $\mu^+ \mu^- \to \gamma Z',~Z' \to \ell \overline{\ell}$, where $\ell$ can be $\mu$, $\tau$ or $\nu_{\mu/\tau}$. We quantitatively study the sensitivities of these two processes by taking into account possible signals and relevant backgrounds in a muon collider experiment with a center-of-mass energy $\sqrt{s} = 3~{\rm TeV}$ and a luminosity $L=1~{\rm ab^{-1}}$. For two-body scattering one can exclude $Z'$ masses $M^{}_{Z'} \lesssim 100~{\rm TeV}$ with $\mathcal{O}(1)$ gauge couplings. When $M^{}_{Z'} \lesssim 1~{\rm TeV} <\sqrt{s}$, one can exclude $g' \gtrsim 2\times 10^{-2}$. The process with photon emission is more powerful than the two-body scattering if $M^{}_{Z'} < \sqrt{s}$. For instance, a sensitivity of $g' \simeq 4 \times 10^{-3}$ can be achieved at $M^{}_{Z'} = 1~{\rm TeV}$. The parameter spaces favored by the $(g-2)^{}_{\mu}$ and $B$ anomalies with $M^{}_{Z'} > 100~{\rm GeV}$ are entirely covered by a muon collider.

Hydrodynamic Diffusion in Integrable Systems.

We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale nonequilibrium dynamics of integrable systems, and arise due to two-body scatterings among quasiparticles. We give exact expressions for the diffusion coefficients. Our results apply to a large class of integrable models, including quantum and classical, Galilean and relativistic field theories, chains, and gases in one dimension, such as the Lieb-Liniger model describing cold atom gases and the Heisenberg quantum spin chain. We provide numerical evaluations in the Heisenberg XXZ spin chain, both for the spin diffusion constant, and for the diffusive effects during the melting of a small domain wall of spins, finding excellent agreement with time-dependent density matrix renormalization group numerical simulations.

Unitarity bound in the most general two Higgs doublet model

We investigate unitarity bounds in the most general two Higgs doublet model without a discrete Z2 symmetry nor CP conservation. S-wave amplitudes for two-body elastic scatterings of Nambu–Goldstone bosons and physical Higgs bosons are calculated at high energies for all possible initial and final states (14 neutral, 8 singly-charged and 3 doubly-charged states). We obtain analytic formulae for the block-diagonalized scattering matrix by the classification of the two body scattering states using the conserved quantum numbers at high energies. Imposing the condition of perturbative unitarity to the eigenvalues of the scattering matrix, constraints on the model parameters can be obtained. We apply our results to constrain the mass range of the next-to-lightest Higgs state in the model.

Dark matter self-interactions via collisionless shocks in cluster mergers

While dark matter self-interactions may solve several problems with structure formation, so far only the effects of two-body scatterings of dark matter particles have been considered. We show that, if a subdominant component of dark matter is charged under an unbroken U(1) gauge group, collective dark plasma effects need to be taken into account to understand its dynamics. Plasma instabilities can lead to collisionless dark matter shocks in galaxy cluster mergers which might have been already observed in the Abell 3827 and 520 clusters. As a concrete model we propose a thermally produced dark pair plasma of vector-like fermions. In this scenario the interacting dark matter component is expected to be separated from the stars and the non-interacting dark matter halos in cluster collisions. In addition, the missing satellite problem is softened, while constraints from all other astrophysical and cosmological observations are avoided.

Two-Body Scattering in (1 + 1) Dimensions by a Semi-relativistic Formalism and a Hulthén Interaction Potential

Scattering solutions of two-body Spinless Salpeter Equation (SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulthén potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.

Bi-local field in gravitational shockwave background

Particles with almost light velocity are able to be sources of shockwave gravity (SWG). Then, for ultra-high-energy particles, there exist two-body scatterings such that one particle is scattered from the gravitational background produced by another particle. Since the spacetime of SWG is closely related to a pp-wave solution of the AdS-type background, this type of interaction is also interesting in AdS dual gauge theories. From those viewpoints, the scattering of point particles or strings by SWG were studied. In this paper, we study the case of the bi-local models, which are simple relativistic bound systems having a close relation with specific modes of open strings. In particular, we analyze the bound-state effect on the scattering amplitudes, which describe the interaction between this model and SWG.

Electric conductivity from the solution of the relativistic Boltzmann equation

We present numerical results of electric conductivity ${\ensuremath{\sigma}}_{\text{el}}$ of a fluid obtained solving the relativistic transport Boltzmann equation in a box with periodic boundary conditions. We compute ${\ensuremath{\sigma}}_{\text{el}}$ using two methods: the definition itself, i.e., applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in relaxation time approximation (RTA) where the relaxation time for ${\ensuremath{\sigma}}_{\text{el}}$ is determined by the transport cross section ${\ensuremath{\sigma}}_{\text{tr}}$, i.e., the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the two-body scatterings: isotropic and anisotropic cross section as well as massless and massive particles. We find that the RTA underestimates considerably ${\ensuremath{\sigma}}_{\text{el}}$; for example, at screening masses ${m}_{D}\ensuremath{\sim}T$, such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasiparticle model tuned to lattice QCD (lQCD) thermodynamics, as well as the case of a perturbative QCD (pQCD) gas with running coupling. Also, for these cases more directly related to the description of the QGP system, we find that the RTA significantly underestimates the ${\ensuremath{\sigma}}_{\text{el}}$ by about 60%--80%.

Production of hyperon resonances induced by kaons on a deuteron target

The $K^- d \to \pi YN$reaction is theoretically studied so as to investigate the $K^{-}$-induced production of the hyperon resonances $\Sigma (1385)$ and $\Lambda (1405)$. For this purpose we take into account the p-wave amplitudes for the meson-baryon two-body scatterings as well as the s-wave amplitudes. Due to the fact that the hyperon resonances are selectively produced from the $\bar{K} N$ channel in this reaction, the $\Lambda (1405)$ peak appears at 1420 MeV, which implies that $\Lambda (1405)$ and $\Sigma (1385)$ could be separately seen in the missing mass spectrum of the emitted nucleon in the $K^{-} d \to n X$ reaction. The $\pi Y$ invariant mass spectrum in this study is consistent with experimental data both for $\Sigma (1385)$ and $\Lambda (1405)$. The pion exchange contributions are also included and are found to give smooth background without distorting the peak structure of the hyperon resonances.

Construction of energy-independent potentials above inelastic thresholds in quantum field theories

We construct energy independent but non-local potentials above inelastic thresholds, in terms of Nambu-Bethe-Salpeter wave functions defined in quantum field theories such as QCD. As an explicit example, we consider NN --> NN + n pi scattering processes for n=0,1,2,.... We show an existence of energy-independent coupled channel potentials with a non-relativistic approximation, where momenta of all particles are small compared with their own masses. In the case of two-body inelastic scatterings such as Lambda Lambda --> Lambda Lambda, N Xi, Sigma Sigma, on the other hand, we show that energy-independent potentials can be constructed without relying on non-relativistic approximations. We also propose a method to extract these potentials using time-dependence of general correlation functions.

Quantum Bose and Fermi gases with large negative scattering length in the two-bodyS-matrix approximation

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.

Bistability in Feshbach resonance

A coupled atom–molecule condensate with an intraspecies Feshbach resonance is employed to explore matter wave bistability both in the presence and in the absence of a unidirectional optical ring cavity. In particular, a set of conditions are derived that allow the threshold for bistability, due both to two-body s-wave scatterings and to cavity-mediated two-body interactions, to be determined analytically. The latter bistability is found to support, not only transitions between a mixed (atom–molecule) state and a pure molecular state as in the former bistability, but also transitions between two distinct mixed states.

Faddeev calculation of the pentaquarkΘ+in the Nambu–Jona-Lasinio model-based diquark picture

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $$\Theta^+$$ in the diquark picture of Jaffe and Wilczek in which $$\Theta^+$$ is a diquark-diquark-$${\bar s}$$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of $${\bar s}D$$ and $D D$. With the use of coupling constants determined from the meson sector, we find that $${\bar s}D$$ interaction is attractive in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $$ \frac 12^+$$ pentaquark state. Instead, a bound pentaquark $$\Theta^+$$ with $$ \frac 12^-$$ is obtained with a unphysically strong vector mesonic coupling constants.

A Faddeev Calculation for Pentaquark Θ+in Diquark Picture with Nambu-Jona-Lasinio Type Interaction

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark Θ+ in the diquark picture of Jaffe and Wilczek in which Θ+ is a diquark-diquark-\bars three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of \barsD and DD. With the use of coupling constants determined from the meson sector, we find that \barsD interaction is attractive while DD interaction is repulsive. However, we cannot find a bound ½+ pentaquark state. Instead, a bound pentaquark Θ+ in ½- channel is obtained with unphysically strong vector mesonic coupling constants.

Quantum Spin Nematic States in Bose–Einstein Condensates

We review some recent results on discrete symmetries and topological order in spinor Bose–Einstein condensates (BECs) of 23Na. For spin one bosons with two-body scatterings dominated by a total spin equal to two channel, the BECs are in quantum spin nematic states at a low density limit. We study spin correlations in condensates at different limits and analyze hidden symmetries using a non-perturbative approach developed recently. Furthermore we investigate the influence of hidden Z2 symmetries and U(1) quantum orders in symmetry partially restored states, particularly the effects on topological excitations.

Three-body coupling in electron-hydrogen ionizing collisions

In this work a method is established for isolating effects due to single or successive two-body scatterings from those arising from three-body coupling in a three-particle Coulomb system above the complete breakup threshold. It is shown that three-body interactions decide the weighting of individual scattering amplitudes, and hence, determined the interference pattern of these amplitudes. In addition, the method is applied to the analysis of low-energy, electron-impact ionization of atomic hydrogen in the coplanar asymmetric energy-sharing kinematic. The ionization dynamic leading to the measured cross section is unraveled. It is demonstrated that, unlike the situation at higher energies, at low incident energies the cross section is largely decided by interferences indicating a strong three-body coupling. {copyright} {ital 1997} {ital The American Physical Society}