In this work, we present different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. Using a toy model for scattering amplitude, we study the sensitivity of solution of KT equation to the left hand cut of this toy model and to the different approximate methods. At last, we briefly discuss Watson's theorem when three particles in final states are involved.
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on the Mandelstam representation of the amplitude and iterations of unitarity. The input for the iterative procedure is given by the multi-particle double spectral density, the S-wave inelasticity, and the value of the amplitude at the crossing-symmetric point. The output, obtained at the fixed point of the iteration of unitarity, is a nonperturbative scattering…
A dispersive representation based on unitarity and analyticity is used to study the low energy $γN \to πN\ \text{and}\ γ^* N \to πN$ partial wave amplitudes. Final state interactions of the $πN$ system are critical to this analysis. The left-hand cut contribution is estimated by invoking baryon chiral perturbation theory results, while the right-hand cut contribution responsible for final state interaction effects is taken into account via an Omnès formalism with elastic phase shifts as input. It is found that a good numerical fit can be achieved with only one subtraction parameter, and the ex…
Simultaneous Dalitz-plot decomposition of the $e^+ e^- \to J/ψ\, π\, π\, (K \bar{K})$ processes in the 4.13-4.36 GeV region using dispersive final-state interactions
Institut für Kernphysik & PRISMA ++ Cluster of Excellence, Johannes Gutenberg Universität（核物理研究所与PRISMA++卓越集群，约翰内斯·古腾堡大学）
In this paper, we present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final state interaction. For the $s$-wave, we use a coupled-channel $ππ,\, K\bar{K}$ analysis which allows a simultaneous description of both $f_0(500)$ and $f_{0}(980)$ resonances. For higher energies, $f_2(1270)$ shows up as a dominant structure which we approximate by a single channel $ππ$ rescattering in the $d$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel ve…
Composite dark matter (DM) comprised of electrically charged constituents can interact with the electromagnetic field via the particle's dipole moment. This interaction results in a dispersive optical index of refraction for the DM medium. We compute this refractive index for atomic dark matter and more strongly bound systems, modeled via a harmonic oscillator potential. The dispersive nature of the index will result in a time lag between high and low energy photons simultaneously emitted from a distant astrophysical observable. This time lag, due to matter dispersion, could confound potential…
We perform an analysis of $Λ_b\toΛ(1520)$ local form factors. We use dispersive techniques to provide a model-independent parametrisation of the form factors that can be used in the whole kinematic region. We use lattice QCD data to constrain the free parameters in the form factors expansion, which is further constrained by endpoint relations, dispersive bounds, and SCET relations. We analyse different scenarios, where we expand the form factors up to different orders, and their viability. Finally, we use our results to obtain predictions for some observables in $Λ_b\toΛ(1520)\ell^+\ell^-$ dec…
Studies of strong field particle physics processes in electron/laser interactions and lepton collider interaction points are reviewed. These processes are defined by the high intensity of the electromagnetic fields involved and the need to take them into account as fully as possible. The main theoretical framework considered is the Furry picture. In this framework, the influence of a background electromagnetic field in the Lagrangian is calculated non perturbatively, involving exact solutions for quantised charged particles in the background field. These "dressed" particles go on to interact p…
We present a dispersion relation formalism to calculate a massive scalar two-loop vertex function. Such calculation is of direct relevance in the evaluation of the hadronic light-by-light contribution to the muon's anomalous magnetic moment due to meson poles. The discontinuity of the two-loop diagram is obtained by a sum of two- and three-particle cut contributions, which involve a phase space integration over the physical intermediate states. The real part of the vertex function is subsequently reconstructed through evaluation of a dispersion integral. We explicitly demonstrate that the disp…
Scattering off the edge of a composite particle or finite-range interaction can precede that off its center. An effective theory treatment with pointlike particles and contact interactions must find that the scattered experimental wave is slightly advanced, in violation of causality (the fundamental underlying theory being causal). In practice, partial-wave or other projections of multivariate amplitudes exponentially grow with imaginary E, so that upper complex-plane analyticity is not sufficient to obtain a dispersion relation for them, but only for a slightly modified function (the modified…
CP violation (CPV) in $D^0-\overline{D^0}$ mixing is described in terms of the dispersive and absorptive `weak phases' $ϕ_f^M$ and $ϕ_f^Γ$. They parametrize CPV originating from the interference of $D^0$ decays with and without dispersive mixing, and with and without absorptive mixing, respectively, for CP conjugate hadronic final states $f$, $\bar f$. These are distinct and separately measurable effects. For CP eigenstate final states, indirect CPV only depends on $ϕ_f^M$ (dispersive CPV), whereas $ϕ_f^Γ$ (absorptive CPV) can only be probed with non-CP eigenstate final states. Measurements of…
We use a dispersion representation based on unitarity and analyticity to study the low energy $γ^* N\rightarrow πN$ process in the $S_{11}$ channel. Final state interactions among the $πN$ system are critical to this analysis. The left-hand part of the partial wave amplitude is imported from $\mathcal{O}(p^2)$ chiral perturbation theory result. On the right-hand part, the final state interaction is calculated through Omnès formula in $S$ wave. It is found that a good numerical fit can be achieved with only one subtraction parameter, and the eletroproduction experimental data of multipole ampli…
Understanding large localized CP violation in $B^\pm\to K^\pmπ^+π^-$ using dispersive methods
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学赫尔姆霍兹射线与核物理研究所及贝特理论物理中心）；Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid（马德里康普顿斯大学理论物理系及IPARCOS）；Institute for Advanced Simulation (IAS-4), Forschungszentrum Jülich（于利希研究中心高级模拟研究所（IAS-4））；Departamento de Raios Cósmicos e Cronologia, Universidade Estadual de Campinas（坎皮纳斯州立大学宇宙射线与年代学系）；Center of Particle Physics (CPPS), Theoretische Physik 1, Universität Siegen（锡根大学理论物理一系粒子物理中心）
We present a dispersive representation of the $γN\rightarrow πN$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $πN$ final-state-interaction effect are taken into account via an Omnés formalism with elastic $πN$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data…
Dispersive representation of the K pi vector form factor and fits to tau -> K pi nu(tau) and Ke3 data
最近，我们介绍了几个分散表示的矢量$Kπ$形状因子，并将它们拟合到贝尔频谱的$τ\to K πν_τ$。在这里，我们简要介绍了模型，并讨论了最佳拟合所产生的$F_+(s)$的斜率和曲率的结果。此外，我们比较了从我们的模型计算的带电$K^*(892)$的极点位置与文献中的其他结果。最后，我们讨论了同时拟合$τ\to K πν_τ$和$K_{e3}$光谱的前景。
A dispersive method to study CP asymmetries in hadronic multi-body $B$ decays
Universität Bonn（波恩大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Forschungszentrum Jülich（于利希研究中心）；Universidade Estadual de Campinas（坎皮纳斯州立大学）；Universität Siegen（锡根大学）
Amplitude structure of $3\to 3$ scattering in a Mandelstam variable representation
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
