Cross check with the LHCb code

[mmikhasenko]

Julia implementation based on the paper draft does not match the experimental spectra.
There must be a bug either in the Julia code, or in the paper equations, or in the LHCb code.

The proposal is to cross check an expression for the amplitude for a fixed 4vector input,

p_p = [0.06475391038067438, -0.02003073178471546, -0.6755517109688479]
p_pi = [0.26214307092579037, 0.03249315364199268, 0.17050500919548295]
p_K = [-0.3268969813064646, -0.012462421857277209, 0.5050467017733649]

the three-vectors are given in the Lc rest frame. Particle masses are fixed to be

mLc = 2.28646
mp  = 0.938272046
mK  = 0.493677
mPi = 0.13957018

For the full expression, use the couplings of the chains and lineshape parameters from the default model.
Then

A = [A_{++} A_{+-}
     A_{-+} A_{--}] = ??

In details:

phi_p = ?
theta_p = ?
chi = ?

For the dalitz plot function,

the angles are equal to

# K**
theta_K = ??

# Lambda**
theta_Lambda = ??
theta_p^Lambda = ??
wigner_rot^Lambda = ??

# Delta**
theta_Delta = ??
theta_p^Delta = ??
wigner_rot^Delta = ??

Lastly, the full expression for the individual chains.
The amplitude is a linear function of 26 couplings. The chain-by-chain implementation can be checked by printing
the amplitude matrix for the set up where all couplings but one are set to zero

A = [A_{++} A_{+-}
     A_{-+} A_{--}]

for H = {0,0,0,H,0,0,0,...}.

The LHCb implementation is a fork of the TensorFlowAnalysis
It is stored in the LHCb internal page