Draft

Helicity formalism

Warning

These pages are under development.

WarningTo do
  • Lorentz-invariance of helicity operator
  • Types
    • Two-body decay amplitude
    • Sequential two-body decay amplitude
  • Definition of angles
    • Production angle
    • Helicity angle
    • Treiman-Yang angle
    • Overview of kinematic variables
  • Dynamics:
    • Wigner-D functions
    • Clebsch-Gordan coefficients
  • Kinematic variables
  • An example

[1]

Canonical formulation

[2]

Alignment problem

Recommended literature:

  • General introductions to helicity angles:
    [3; 4]
  • Suggested solutions:
    [5–8]
  • LHCb study that led to these solution papers:
    [9]

References

[1]
M. Jacob and G. C. Wick, “On the general theory of collisions for particles with spin,” Annals of Physics, vol. 7, no. 4, pp. 404–428, Aug. 1959, 10.1016/0003-4916(59)90051-X.
[2]
X.-Y. Li, X.-K. Dong, and H.-J. Jing, “Spin-orbit amplitudes for decays with arbitrary spin,” Nuclear Physics A, vol. 1040, p. 122761, Dec. 2023, 10.1016/j.nuclphysa.2023.122761.
[3]
R. Kutschke, “An Angular Distribution Cookbook.” Jan. 1996. https://home.fnal.gov/~kutschke/Angdist/angdist.ps
[4]
J. D. Richman, “An Experimenter’s Guide to the Helicity Formalism.” Jun. 1984. https://inspirehep.net/literature/202987
[5]
H. Chen and R.-G. Ping, “Coherent helicity amplitude for sequential decays,” Physical Review D, vol. 95, no. 7, p. 076010, Apr. 2017, 10.1103/PhysRevD.95.076010.
[6]
D. Marangotto, “Helicity Amplitudes for Generic Multibody Particle Decays Featuring Multiple Decay Chains,” Advances in High Energy Physics, vol. 2020, pp. 1–15, Dec. 2020, 10.1155/2020/6674595.
[7]
M. Wang, Y. Jiang, Y. Liu, W. Qian, X.-R. Lyu, and L. Zhang, “A novel method to test particle ordering and final state alignment in helicity formalism,” Chinese Physics C, vol. 45, no. 6, p. 063103, Jun. 2021, 10.1088/1674-1137/abf139.
[8]
M. Mikhasenko et al., “Dalitz-plot decomposition for three-body decays,” Physical Review D: Particles and Fields, vol. 101, no. 3, p. 034033, Feb. 2020, 10.1103/PhysRevD.101.034033.
[9]
R. Aaij et al., “Observation of 𝐽/𝜓 𝑝 Resonances Consistent with Pentaquark States in 𝛬𝑏⁰ → 𝐽/𝜓𝐾⁻𝑝 Decays,” Physical Review Letters, vol. 115, no. 7, p. 072001, Aug. 2015, 10.1103/PhysRevLett.115.072001.