Scattering Amplitude

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Stephen R Sharpe - One of the best experts on this subject based on the ideXlab platform.

  • i 3 three pion Scattering Amplitude from lattice qcd
    Physical Review Letters, 2020
    Co-Authors: Tyler D Blanton, Fernando Romerolopez, Stephen R Sharpe
    Abstract:

    We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass M≈200  MeV in Horz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.142002]. Using the relativistic three-particle quantization condition, we find ∼2σ evidence for a nonzero value for the contact part of the 3π^{+} (I=3) Scattering Amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold and some tension in the energy dependent part of the 3π^{+} Scattering Amplitude. We also find that the 2π^{+} (I=2) spectrum is fit well by an s-wave phase shift that incorporates the expected Adler zero.

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    Physical Review D, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)] derived a relation between the Scattering Amplitude of three identical bosons, ${\mathcal{M}}_{3}$, and a real function referred to as the divergence-free $K$ matrix and denoted ${\mathcal{K}}_{\mathrm{df},3}$. The result arose in the context of a relation between finite-volume energies and ${\mathcal{K}}_{\mathrm{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between ${\mathcal{K}}_{\mathrm{df},3}$ and ${\mathcal{M}}_{3}$. We show that, for any real choice of ${\mathcal{K}}_{\mathrm{df},3}$, ${\mathcal{M}}_{3}$ satisfies the three-particle unitarity constraint to all orders. Given that ${\mathcal{K}}_{\mathrm{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    arXiv: High Energy Physics - Lattice, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    In a previous publication, two of us derived a relation between the Scattering Amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

  • expressing the three particle finite volume spectrum in terms of the three to three Scattering Amplitude
    Physical Review D, 2015
    Co-Authors: Maxwell T Hansen, Stephen R Sharpe
    Abstract:

    In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three Scattering Amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the spectrum to a non-standard infinite-volume quantity, denoted ${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\cal M}_3$ from the finite-volume energy spectrum.

  • expressing the three particle finite volume spectrum in terms of the three to three Scattering Amplitude
    Physical Review D, 2015
    Co-Authors: Maxwell T Hansen, Stephen R Sharpe
    Abstract:

    In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three Scattering Amplitude, ${\mathcal{M}}_{3}$. In previous work [Phys. Rev. D 90, 116003 (2014)], we found a quantization condition relating the spectrum to a nonstandard infinite-volume quantity, denoted ${\mathcal{K}}_{\mathrm{df},3}$. Here we present the relation between ${\mathcal{K}}_{\mathrm{df},3}$ and ${\mathcal{M}}_{3}$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\mathcal{M}}_{3}$ from the finite-volume energy spectrum.

Takeshi Yamazaki - One of the best experts on this subject based on the ideXlab platform.

  • Scattering Amplitude from bethe salpeter wave function inside the interaction range
    Physical Review D, 2018
    Co-Authors: Y Namekawa, Takeshi Yamazaki
    Abstract:

    We propose a method to calculate Scattering Amplitudes using the Bethe-Salpeter wave function inside the interaction range on the lattice. For an exploratory study of this method, we evaluate a Scattering length of $I=2$ S-wave two pions by the use of the on-shell Scattering Amplitude. Our result is confirmed to be consistent with the value obtained from the conventional finite volume method. The half-off-shell Scattering Amplitude is also evaluated.

  • relation between Scattering Amplitude and bethe salpeter wave function in quantum field theory
    Physical Review D, 2017
    Co-Authors: Takeshi Yamazaki, Y Kuramashi
    Abstract:

    We reexamine the relations between the Bethe-Salpeter (BS) wave function of two particles, the on-shell Scattering Amplitude, and the effective potential in quantum filed theory. It is emphasized that there is an exact relation between the BS wave function inside the interaction range and the Scattering Amplitude, and the reduced BS wave function, which is defined in this article, plays an essential role in this relation. Based on the exact relation, we show that the solution of Schr\"odinger equation with the effective potential gives us a correct on-shell Scattering Amplitude only at the momentum where the effective potential is calculated, while wrong results are obtained from the Schr\"odinger equation at general momenta. We also discuss about a momentum expansion of the reduced BS wave function and an uncertainty of the Scattering Amplitude stemming from the choice of the interpolating operator in the BS wave function. The theoretical conclusion obtained in this article could give hints to understand the inconsistency observed in lattice QCD calculation of the two-nucleon channels with different approaches.

  • relation between Scattering Amplitude and bethe salpeter wave function in quantum field theory
    Physical Review D, 2017
    Co-Authors: Takeshi Yamazaki, Y Kuramashi
    Abstract:

    We discuss an exact relation between the two-particle Scattering Amplitude and the Bethe-Salpeter (BS) wave function inside the interaction range in quantum field theory. In the relation the reduced BS wave function defined by the BS wave function plays an essential role. Through the relation the on-shell and half off-shell Amplitudes can be calculated. We also show that the solution of Schrodinger equation with the effective potential determined from the BS wave function gives a correct on-shell Scattering Amplitude only at the momentum where the effective potential is determined. Furthermore we discuss a derivative expansion of the reduced BS wave function and a condition to obtain results independent of the interpolating operators in the time-dependent HALQCD method.

Adam P Szczepaniak - One of the best experts on this subject based on the ideXlab platform.

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    Physical Review D, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)] derived a relation between the Scattering Amplitude of three identical bosons, ${\mathcal{M}}_{3}$, and a real function referred to as the divergence-free $K$ matrix and denoted ${\mathcal{K}}_{\mathrm{df},3}$. The result arose in the context of a relation between finite-volume energies and ${\mathcal{K}}_{\mathrm{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between ${\mathcal{K}}_{\mathrm{df},3}$ and ${\mathcal{M}}_{3}$. We show that, for any real choice of ${\mathcal{K}}_{\mathrm{df},3}$, ${\mathcal{M}}_{3}$ satisfies the three-particle unitarity constraint to all orders. Given that ${\mathcal{K}}_{\mathrm{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    arXiv: High Energy Physics - Lattice, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    In a previous publication, two of us derived a relation between the Scattering Amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

Maxwell T Hansen - One of the best experts on this subject based on the ideXlab platform.

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    Physical Review D, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)] derived a relation between the Scattering Amplitude of three identical bosons, ${\mathcal{M}}_{3}$, and a real function referred to as the divergence-free $K$ matrix and denoted ${\mathcal{K}}_{\mathrm{df},3}$. The result arose in the context of a relation between finite-volume energies and ${\mathcal{K}}_{\mathrm{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between ${\mathcal{K}}_{\mathrm{df},3}$ and ${\mathcal{M}}_{3}$. We show that, for any real choice of ${\mathcal{K}}_{\mathrm{df},3}$, ${\mathcal{M}}_{3}$ satisfies the three-particle unitarity constraint to all orders. Given that ${\mathcal{K}}_{\mathrm{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

  • unitarity of the infinite volume three particle Scattering Amplitude arising from a finite volume formalism
    arXiv: High Energy Physics - Lattice, 2019
    Co-Authors: Stephen R Sharpe, Maxwell T Hansen, Raul A Briceno, Adam P Szczepaniak
    Abstract:

    In a previous publication, two of us derived a relation between the Scattering Amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body Scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

  • expressing the three particle finite volume spectrum in terms of the three to three Scattering Amplitude
    Physical Review D, 2015
    Co-Authors: Maxwell T Hansen, Stephen R Sharpe
    Abstract:

    In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three Scattering Amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the spectrum to a non-standard infinite-volume quantity, denoted ${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\cal M}_3$ from the finite-volume energy spectrum.

  • expressing the three particle finite volume spectrum in terms of the three to three Scattering Amplitude
    Physical Review D, 2015
    Co-Authors: Maxwell T Hansen, Stephen R Sharpe
    Abstract:

    In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three Scattering Amplitude, ${\mathcal{M}}_{3}$. In previous work [Phys. Rev. D 90, 116003 (2014)], we found a quantization condition relating the spectrum to a nonstandard infinite-volume quantity, denoted ${\mathcal{K}}_{\mathrm{df},3}$. Here we present the relation between ${\mathcal{K}}_{\mathrm{df},3}$ and ${\mathcal{M}}_{3}$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\mathcal{M}}_{3}$ from the finite-volume energy spectrum.

X Chen - One of the best experts on this subject based on the ideXlab platform.

  • analytical solution of balitsky kovchegov equation with homogeneous balance method
    Physical Review D, 2021
    Co-Authors: Xiaopeng Wang, Yirui Yang, Wei Kou, R G Wang, X Chen
    Abstract:

    Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken ${x}_{\mathrm{B}}$, as they are supposed to restore an upper bound of unitarity for the cross section of high-energy Scattering. In this paper, we present an analytical solution of the Balitsky-Kovchegov equation using the homogeneous balance method. The obtained analytical solution is similar to the solution of a traveling wave. By matching the gluon distribution in the dilute region which is determined from the global analysis of experimental data (CT14 analysis), we get a definitive solution of the dipole-proton forward Scattering Amplitude in the momentum space. Based on the acquired Scattering Amplitude and the behavior of geometric scaling, we present also a new estimated saturation scale ${Q}_{s}^{2}(x)$.