def flatte_lineshape(s, m, g1, g2, ma1, mb1, ma2, mb2):
"""
Flatte line shape
s : squared inv. mass
m : resonance mass
g1 : coupling to ma1, mb1
g2 : coupling to ma2, mb2
"""
mab = atfi.sqrt(s)
pab1 = atfk.two_body_momentum(mab, ma1, mb1)
rho1 = 2. * pab1 / mab
pab2 = atfk.complex_two_body_momentum(mab, ma2, mb2)
rho2 = 2. * pab2 / atfi.cast_complex(mab)
gamma = (atfi.cast_complex(g1**2 * rho1) +
atfi.cast_complex(g2**2) * rho2) / atfi.cast_complex(m)
return relativistic_breit_wigner(s, m, gamma)
def nonresonant_lass_lineshape(m2ab, a, r, ma, mb):
"""
LASS line shape, nonresonant part
"""
m = atfi.sqrt(m2ab)
q = atfk.two_body_momentum(m, ma, mb)
cot_deltab = 1. / a / q + 1. / 2. * r * q
ampl = atfi.cast_complex(m) / atfi.complex(q * cot_deltab, -q)
return ampl
def wigner_capital_d(phi, theta, psi, j, m1, m2):
"""Calculate Wigner capital-D function.
phi,
theta,
psi : Rotation angles
j : spin (in units of 1/2, e.g. 1 for spin=1/2)
m1 and m2 : spin projections (in units of 1/2, e.g. 1 for projection 1/2)
:param phi:
:param theta:
:param psi:
:param j2:
:param m2_1:
:param m2_2:
"""
i = atfi.complex(atfi.const(0), atfi.const(1))
return Exp(-i*atfi.cast_complex(m1/2.*phi)) * \
atfi.cast_complex(wigner_small_d(theta, j, m1, m2)) * \
Exp(-i * atfi.cast_complex(m2 / 2. * psi))
def _model(a1r, a1i, a2r, a2i, a3r, a3i, switches=4 * [1]):
a1 = atfi.complex(a1r, a1i)
a2 = atfi.complex(a2r, a2i)
a3 = atfi.complex(a3r, a3i)
ampl = atfi.cast_complex(atfi.ones(m2ab)) * atfi.complex(
atfi.const(0.0), atfi.const(0.0))
if switches[0]:
ampl += a1 * bw1 * hel_ab
if switches[1]:
ampl += a2 * bw2 * hel_bc
if switches[2]:
ampl += a3 * bw3 * hel_ac
if switches[3]:
ampl += atfi.cast_complex(atfi.ones(m2ab)) * atfi.complex(
atfi.const(5.0), atfi.const(0.0))
return atfd.density(ampl)
def relativistic_breit_wigner(m2, mres, wres):
"""
Relativistic Breit-Wigner
"""
if wres.dtype is atfi.ctype():
return tf.math.reciprocal(
atfi.cast_complex(mres * mres - m2) -
atfi.complex(atfi.const(0.), mres) * wres)
if wres.dtype is atfi.fptype():
return tf.math.reciprocal(atfi.complex(mres * mres - m2, -mres * wres))
return None
def resonant_lass_lineshape(m2ab, m0, gamma0, a, r, ma, mb):
"""
LASS line shape, resonant part
"""
m = atfi.sqrt(m2ab)
q0 = atfk.two_body_momentum(m0, ma, mb)
q = atfk.two_body_momentum(m, ma, mb)
cot_deltab = 1. / a / q + 1. / 2. * r * q
phase = atfi.atan(1. / cot_deltab)
width = gamma0 * q / m * m0 / q0
ampl = relativistic_breit_wigner(m2ab, m0, width) * atfi.complex(
atfi.cos(phase), atfi.sin(phase)) * atfi.cast_complex(
m2ab * gamma0 / q0)
return ampl
def dabba_lineshape(m2ab, b, alpha, beta, ma, mb):
"""
Dabba line shape
"""
mSum = ma + mb
m2a = ma**2
m2b = mb**2
sAdler = max(m2a, m2b) - 0.5 * min(m2a, m2b)
mSum2 = mSum * mSum
mDiff = m2ab - mSum2
rho = atfi.sqrt(1. - mSum2 / m2ab)
realPart = 1.0 - beta * mDiff
imagPart = b * atfi.exp(-alpha * mDiff) * (m2ab - sAdler) * rho
denomFactor = realPart * realPart + imagPart * imagPart
ampl = atfi.complex(realPart, imagPart) / atfi.cast_complex(denomFactor)
return ampl
def model(x, mrho, wrho, mkst, wkst, a1r, a1i, a2r, a2i, a3r, a3i, switches):
a1 = atfi.complex(a1r, a1i)
a2 = atfi.complex(a2r, a2i)
a3 = atfi.complex(a3r, a3i)
m2ab = phsp.m2ab(x)
m2bc = phsp.m2bc(x)
m2ac = phsp.m2ac(x)
hel_ab = phsp.cos_helicity_ab(x)
hel_bc = phsp.cos_helicity_bc(x)
hel_ac = phsp.cos_helicity_ac(x)
ampl = atfi.complex(atfi.const(0.0), atfi.const(0.0))
if switches[0]:
ampl += (
a1
* atfd.breit_wigner_lineshape(
m2ab, mkst, wkst, mpi, mk, mpi, md, rd, rr, 1, 1
)
* atfd.helicity_amplitude(hel_ab, 1)
)
if switches[1]:
ampl += (
a2
* atfd.breit_wigner_lineshape(
m2bc, mkst, wkst, mpi, mk, mpi, md, rd, rr, 1, 1
)
* atfd.helicity_amplitude(hel_bc, 1)
)
if switches[2]:
ampl += (
a3
* atfd.breit_wigner_lineshape(
m2ac, mrho, wrho, mpi, mpi, mk, md, rd, rr, 1, 1
)
* atfd.helicity_amplitude(hel_ac, 1)
)
if switches[3]:
ampl += atfi.cast_complex(atfi.ones(m2ab)) * atfi.complex(
atfi.const(5.0), atfi.const(0.0)
)
return atfd.density(ampl)