7.2. DPD angles#
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from ampform_dpd.angles import (
formulate_scattering_angle,
formulate_theta_hat_angle,
formulate_zeta_angle,
)
from polarimetry.io import display_latex
Equation (A1) from [2]:
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angles = [
formulate_scattering_angle(1, 2),
formulate_scattering_angle(2, 3),
formulate_scattering_angle(3, 1),
]
display_latex(dict(angles))
for i in [1, 2, 3]:
_, θii = formulate_theta_hat_angle(i, i)
assert θii == 0
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angles = [
formulate_theta_hat_angle(3, 1),
formulate_theta_hat_angle(1, 2),
formulate_theta_hat_angle(2, 3),
]
display_latex(dict(angles))
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θ31hat = formulate_theta_hat_angle(3, 1)[1]
θ13hat = formulate_theta_hat_angle(1, 3)[1]
θ12hat = formulate_theta_hat_angle(1, 2)[1]
θ21hat = formulate_theta_hat_angle(2, 1)[1]
θ23hat = formulate_theta_hat_angle(2, 3)[1]
θ32hat = formulate_theta_hat_angle(3, 2)[1]
assert θ31hat == -θ13hat
assert θ12hat == -θ21hat
assert θ23hat == -θ32hat
for i in [1, 2, 3]:
for k in [1, 2, 3]:
_, ζi_k0 = formulate_zeta_angle(i, k, 0)
_, ζi_ki = formulate_zeta_angle(i, k, i)
_, ζi_kk = formulate_zeta_angle(i, k, k)
assert ζi_ki == ζi_k0
assert ζi_kk == 0
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angles = [
formulate_zeta_angle(1, 1, 3),
formulate_zeta_angle(1, 2, 1),
formulate_zeta_angle(2, 2, 1),
formulate_zeta_angle(2, 3, 2),
formulate_zeta_angle(3, 3, 2),
formulate_zeta_angle(3, 1, 3),
]
display_latex(dict(angles))
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ζ1_12 = formulate_zeta_angle(1, 1, 2)[1]
ζ1_21 = formulate_zeta_angle(1, 2, 1)[1]
ζ2_23 = formulate_zeta_angle(2, 2, 3)[1]
ζ2_32 = formulate_zeta_angle(2, 3, 2)[1]
ζ3_31 = formulate_zeta_angle(3, 3, 1)[1]
ζ3_13 = formulate_zeta_angle(3, 1, 3)[1]
assert ζ1_12 == -ζ1_21
assert ζ2_23 == -ζ2_32
assert ζ3_31 == -ζ3_13
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angles = [
formulate_zeta_angle(1, 2, 3),
formulate_zeta_angle(2, 3, 1),
formulate_zeta_angle(3, 1, 2),
]
display_latex(dict(angles))
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ζ1_32 = formulate_zeta_angle(1, 3, 2)[1]
ζ1_23 = formulate_zeta_angle(1, 2, 3)[1]
ζ2_13 = formulate_zeta_angle(2, 1, 3)[1]
ζ2_31 = formulate_zeta_angle(2, 3, 1)[1]
ζ3_21 = formulate_zeta_angle(3, 2, 1)[1]
ζ3_12 = formulate_zeta_angle(3, 1, 2)[1]
assert ζ1_32 == -ζ1_23
assert ζ2_13 == -ζ2_31
assert ζ3_21 == -ζ3_12