First steps

Try the following inside a python script (or interactive session) to produce a plot of the Omnes function of the Madrid p-wave:

import numpy as np
import matplotlib.pyplot as plt

from khuri import madrid_global, phases, omnes


THRESHOLD = (2.0 * madrid_global.PION_MASS)**2


@phases.asymptotic1(matching_point=1.12**2)
def phase(s):
    return madrid_global.p_wave_phase(s)


omnes_function = omnes.generate_omnes(phase, threshold=THRESHOLD,
                                      constant=np.pi, cut=1e10)

energies = np.linspace(0, 1.2, 200)
omnes_values = omnes_function(energies**2)

plt.title('The Omnes function of the Madrid p-wave')
plt.plot(energies, np.real(omnes_values), label='Re')
plt.plot(energies, np.imag(omnes_values), label='Im')
plt.xlabel('E/GeV')
plt.legend()
plt.show()