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Generation of arbitrarily polarized muon pairs via polarized e−e+ collision

Zhi-Wei Lu, Qian Zhao, Feng Wan, Bo-Chao Liu, Yong-Sheng Huang, Zhong-Feng Xu, and Jian-Xing Li
Phys. Rev. D 105, 113002 – Published 14 June 2022
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  • INTRODUCTION
  • METHODS OF THEORY AND NUMERICAL…
  • SIMULATION RESULTS AND DISCUSSIONS
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Generation of arbitrarily spin polarized muon pairs is investigated via polarized e−e+ collision. We calculate the completely polarized cross section dσe−e+→μ−μ+ and construct the fully spin-resolved Monte Carlo simulation method to explicitly describe the production of polarized muon pairs. We find that, due to the flip of mixed helicities along the scattering angle, arbitrarily polarized muon pairs with both of the longitudinal and transverse spin components can be produced. Moreover, we also find that the transverse polarization of the muon pairs depends on the directions of transverse spins of initial electrons and positrons. The collision of tightly collimated electron and positron beams with highly longitudinal polarization and nanocoulomb charge can generate about 40% muon pairs with longitudinal polarization and about 60% muon pairs with transverse polarization. The compact high-flux e−e+→μ−μ+ muon source could be implemented through the next-generation laser-plasma linear collider and would be essential to facilitate the investigation of fundamental physics and the measurement technology in broad areas.

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    • Received 26 January 2022
    • Revised 19 May 2022
    • Accepted 20 May 2022

    DOI:https://doi.org/10.1103/PhysRevD.105.113002

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Laser driven electron accelerationLaser wakefield accelerationParticle interactionsQuantum electrodynamics
    1. Physical Systems
    ElectronsMuonsPositrons
    1. Properties
    PolarizationSpin
    1. Techniques
    Monte Carlo methodsQuantum Monte Carlo
    Plasma PhysicsParticles & Fields

    Authors & Affiliations

    Zhi-Wei Lu1, Qian Zhao1,*, Feng Wan1, Bo-Chao Liu1, Yong-Sheng Huang2,3, Zhong-Feng Xu1, and Jian-Xing Li1,†

    • 1Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, China
    • 2School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, People’s Republic of China
    • 3Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

    • *zhaoq2019@xjtu.edu.cn
    • †jianxing@xjtu.edu.cn

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    Vol. 105, Iss. 11 — 1 June 2022

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    Images

    • Figure 1
      Figure 1

      Interaction scenario for generating ASP muon pairs via polarized e−e+ collision. (a) Schematic helicity configuration in the center of mass frame. The black and helical arrows denote the particle momentum direction and mixed helicity, respectively, n^p and n^p′ denote the momentum directions of e− and μ−, respectively, and θs is the scattering angle. (b) Helicity distribution of μ+ (μ− has an opposite distribution) in the plane of center of mass energy Ecm and cosθs. In our simulation, the electron and positron beams are initialized symmetrically with a transverse Gaussian and longitudinal uniform distribution, divergence angle θb=1  mrad and uniform energy distribution between 110 and 360 MeV in the laboratory frame.

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    • Figure 2
      Figure 2

      Coordinate system of the muon pair production in the c.m. frame. θ and ϕ are the polar and azimuth angles of the electron momentum p, respectively, and (n^p,θ^p,ϕ^p) are the spherical coordinates of electron momentum p. p⊥ in the θ^p−ϕ^p plane is perpendicular to p, and p′ in the p−p⊥ plane is the momentum of μ−.

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    • Figure 3
      Figure 3

      (a) The total cross sections of three processes in the e−e+ interaction. (b) σ¯tot vs Ecm calculated from Eq. (13) with four initial spin states: nonpolarized σ¯non, LSP σ¯∥,2 with ζ−,2ζ+,2=−1, and TSP σ¯⊥,1 and σ¯⊥,2 with ζ−,1ζ+,1=1 and ζ−,1ζ+,1=−1, respectively. (c),(d) The differential cross sections vs θs at the peak energies Ep and 2Ep, respectively. The line types in (c) and (d) have the same meanings as those in (b) but for dσ¯non/dθs, dσ¯∥,2/dθs, dσ¯⊥,1/dθs, and dσ¯⊥,2/dθs calculated from Eq. (12). The unit of the cross section here and below is rμ2 with rμ=re/m.

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    • Figure 4
      Figure 4

      Distributions of differential cross section in the plane of θs and Ecm: (a) with summarized final spins dσ¯+−/dθs [calculated via Eq. (12)], and (b)–(d) with different helicity channels [calculated via Eq. (16a)].

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    • Figure 5
      Figure 5

      Polarization distributions in the plane of θs and Ecm are produced by eR−eL+ collision with helicity eigenstates: (a)–(c) corresponding to ζ′, ζ∥′, and ζ⊥′, respectively, calculated by Eq. (15) or Eq. (22); (d)–(f) corresponding to corresponding to Ptot(μ), P∥(μ), and P⊥(μ), respectively, calculated by Eq. (24) via MC simulations. The simulation parameters are the same as those in Fig. 1.

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    • Figure 6
      Figure 6

      (a)–(c) Polarization of muons vs P∥(e) for all the muons, the muons beamed into 0<θ<0.2π and 0.3π<θ<0.7π, respectively. The filled marks denote the results produced from the collisions with antiparallel transverse polarization ζ+,⊥=−ζ−,⊥, and the hollow marks in (c) denote the results produced from the collisions with parallel transverse polarization ζ+,⊥=ζ−,⊥. Other parameters are the same as those in Fig. 1 but having an exponential energy distribution with an average energy Eav=125  MeV in the laboratory frame.

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    • Figure 7
      Figure 7

      (a) Reaction rates of three different processes in the collision of e− and e+ beams. (b) Pθ=σ¯θ/σ¯tot vs θs for nonpolarized (non), LSP (∥). and TSP (⊥) e±, calculated from Eqs. (13) and (20), where the line types have the same meanings as Fig. 3. The thin and thick lines correspond to Ecm=125  MeV and 1 GeV, respectively.

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    • Figure 8
      Figure 8

      Polarization distributions of (a),(d),(g) Ptot(μ), (b),(e),(h) P∥(μ), and (c),(f),(i) P⊥(μ), produced by colliding electron and positron beams with (a)–(c) P∥(e)=0.8, (d)–(f) P∥(e)=0.6, and (g)–(i) P∥(e)=0.4, respectively. There is no transverse polarization of initial beams.

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    • Figure 9
      Figure 9

      Distributions of simulated polarization. (a) P∥(μ) and (b) P⊥(μ), produced from eR−eL+ collisions with P∥(e)=0.6 and parallel transverse polarization ζ+,⊥=ζ−,⊥, together with the corresponding differential cross sections with final helicity states: (c) |+−⟩ and (d) |±±⟩. (e)–(h) are similar to (a)–(d) but for eR−eL+ collisions with antiparallel transverse polarization ζ+,⊥=−ζ−,⊥.

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