[FR] `(phi,theta,-phi)` convention

mmikhasenko commented 4 months ago

The convention on argument of Wigner D functions D(phi, theta, 0) is related to the transition between frames is done. Normally we go between frames B^{-1} R^{-1}, where R = Rz(phi) Ry(theta).

Extra Rz(-phi) added to both transformation gives extra phase to the helicity state, it does not change the value of the helicity. But also, it impacts the Wigner rotations since all transformations get modified.

It's a curiosity question that I have since long:

Are Wigner rotations simpler when using (phi,theta,-phi) conventions?

Implementations:

Two new methods:

helicity_angles_minus_phi_convention
wigner_rotations_minus_phi_convention

Test case

(3b) Lc2pKpi, single spacial point, report values of the angles and Wigner rotations
(4b) single spacial point, report values of the angles and Wigner rotations

Reference

the convention is popular: mentioned in Martin-Spearman, "Elementary Particle Theory" https://www.amazon.com/Elementary-particle-theory-Alan-Martin/dp/0720401577

Richman, An Experimenter's Guide to the Helicity Formalism https://inspirehep.net/literature/202987

KaiHabermann commented 4 months ago

I would prefer convention flag. Thus we can cover this case and the other FR with the existing interface

mmikhasenko commented 4 months ago

Can well be a flag, indeed!

Important to not mixing up conventions since the angles are closely linked to the wigner_rotations.

KaiHabermann commented 4 months ago

I would have all functions returning angles have a flag called convention. This will then get checked against the available ones.

KaiHabermann commented 4 months ago

Lets say we have three conventions: "minus_phi", "canonical", "normal". What would be the best name for normal here?

mmikhasenko commented 4 months ago

Sound good! Perhaps helicity instead of normal

mmikhasenko commented 3 months ago

From Martin Spearman Page 120

KaiHabermann / decayangle