from tf_pwa.tensorflow_wrapper import tf
from .core import Particle, Variable, register_particle
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def cal_monentum(m, ma, mb):
mabp = ma + mb
mabm = ma - mb
s = m * m
p2 = (s - mabp * mabp) * (s - mabm * mabm) / 4 / s
zeros = tf.zeros_like(s)
p_p = tf.complex(tf.sqrt(tf.abs(p2)), zeros)
p_m = tf.complex(zeros, tf.sqrt(tf.abs(p2)))
return tf.where(p2 > 0, p_p, p_m)
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def cal_monentum_sympy(m, ma, mb):
import sympy
mabp = ma + mb
mabm = ma - mb
s = m * m
p2 = (s - mabp * mabp) * (s - mabm * mabm)
return sympy.sqrt(p2) / 2 / m
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@register_particle("Flatte")
class ParticleFlatte(Particle):
"""
Flatte like formula
.. math::
R(m) = \\frac{1}{m_0^2 - m^2 + i m_0 (\\sum_{i} g_i \\frac{q_i}{m})}
.. math::
q_i = \\begin{cases}
\\frac{\\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\\\
\\frac{i\\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\\\
\\end{cases}
.. plot::
>>> import matplotlib.pyplot as plt
>>> plt.clf()
>>> from tf_pwa.utils import plot_particle_model
>>> _ = plot_particle_model("Flatte", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("Flatte", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "mass": 0.7}, {"R_BC_g_0": -0.3,"R_BC_g_1": -0.2})
>>> _ = plt.legend(["$g_i$", "$-g_i$"])
Required input arguments `mass_list: [[m11, m12], [m21, m22]]` for :math:`m_{i,1}, m_{i,2}`.
"""
def __init__(self, *args, mass_list=None, im_sign=1, **kwargs):
super().__init__(*args, **kwargs)
if mass_list is None:
raise ValueError("required mass_list: [[a, b], [mc, md]]")
self.mass_list = mass_list
self.g_value = []
self.float_list = list(kwargs.get("float", []))
self.im_sign = im_sign
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def init_params(self):
self.d = 3.0
if self.mass is None:
self.mass = self.add_var("mass", fix=True)
# print("$$$$$",self.mass)
else:
if not isinstance(self.mass, Variable):
if "m" in self.float_list:
self.mass = self.add_var(
"mass", value=self.mass, fix=False
)
else:
self.mass = self.add_var("mass", value=self.mass, fix=True)
self.g_value = []
for i, mab in enumerate(self.mass_list):
name = f"g_{i}"
if hasattr(self, name):
if name in self.float_list:
self.g_value.append(
self.add_var(
f"g_{i}", value=getattr(self, name), fix=False
)
)
else:
self.g_value.append(
self.add_var(
f"g_{i}", value=getattr(self, name), fix=True
)
)
else:
self.g_value.append(self.add_var(f"g_{i}"))
def __call__(self, m):
return self.get_amp({"m": m})
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def get_width(self, m=None):
if m is None:
m0 = self.get_mass()
m = tf.reshape(m0, (-1,))
amp = self.get_amp({"m": m})
w = tf.math.imag(1 / amp)
return w
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def get_amp(self, *args, **kwargs):
m = args[0]["m"]
mass = self.get_mass()
zeros = tf.zeros_like(m)
delta_s = mass * mass - m * m
m_c = mass / m
rhos = []
for i, mab in enumerate(self.mass_list):
ma, mb = mab
pi = cal_monentum(m, ma, mb)
# print(pi)
m_rho_i = pi * tf.complex(zeros, self.g_value[i]() * m_c)
rhos.append(m_rho_i)
rho = self.im_sign * sum(rhos)
re = delta_s + tf.math.real(rho)
im = tf.math.imag(rho)
d = re * re + im * im
ret = tf.complex(re / d, -im / d)
return ret
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def get_sympy_var(self):
import sympy as sym
gi = [sym.var(f"g_{i}") for i, _ in enumerate(self.mass_list)]
return (*sym.var("m m0"), *gi)
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def get_num_var(self):
mass = self.get_mass()
gi = [self.g_value[i]() for i, _ in enumerate(self.mass_list)]
return (mass, *gi)
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def get_sympy_dom(self, m, m0, *gi, sheet=0):
import sympy as sym
mass = m0
delta_s = mass * mass - m * m
m_c = mass / m
rhos = []
for i, mab in enumerate(self.mass_list):
ma, mb = mab
pi = cal_monentum_sympy(m, ma, mb)
if sheet & 1 == 0:
pi = -pi
sheet = sheet >> 1
# print(pi)
m_rho_i = pi * sym.I * gi[i] * m_c
rhos.append(m_rho_i)
rho = self.im_sign * sum(rhos)
re = delta_s + rho
return re
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@register_particle("FlatteC")
class ParticleFlatteC(ParticleFlatte):
"""
Flatte like formula
.. math::
R(m) = \\frac{1}{m_0^2 - m^2 - i m_0 (\\sum_{i} g_i \\frac{q_i}{m})}
.. math::
q_i = \\begin{cases}
\\frac{\\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\\\
\\frac{i\\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\\\
\\end{cases}
Required input arguments `mass_list: [[m11, m12], [m21, m22]]` for :math:`m_{i,1}, m_{i,2}`.
.. plot::
>>> import matplotlib.pyplot as plt
>>> plt.clf()
>>> from tf_pwa.utils import plot_particle_model
>>> _ = plot_particle_model("FlatteC", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
"""
def __init__(self, *args, im_sign=-1, **kwargs):
super().__init__(*args, im_sign=im_sign, **kwargs)
[docs]
@register_particle("FlatteGen")
class ParticleFlateGen(ParticleFlatte):
"""
More General Flatte like formula
.. math::
R(m) = \\frac{1}{m_0^2 - m^2 - i m_0 [\\sum_{i} g_i \\frac{q_i}{m} \\times \\frac{m_0}{|q_{i0}|} \\times \\frac{|q_i|^{2l_i}}{|q_{i0}|^{2l_i}} B_{l_i}'^2(|q_i|,|q_{i0}|,d)]}
.. math::
q_i = \\begin{cases}
\\frac{\\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\\\
\\frac{i\\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\\\
\\end{cases}
Required input arguments `mass_list: [[m11, m12], [m21, m22]]` for :math:`m_{i,1}, m_{i,2}`. And addition arguments `l_list: [l1, l2]` for :math:`l_i`
`has_bprime=False` to remove :math:`B_{l_i}'^2(|q_i|,|q_{i0}|,d)`.
`cut_phsp=True` to set :math:`q_i = 0` when :math:`(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0`
The plot use parameters :math:`m_0=0.7, m_{0,1}=m_{0,2}=0.1, m_{1,1}=m_{1,2}=0.3, g_0=0.3,g_1=0.2,l_0=0,l_1=1`.
.. plot::
>>> import matplotlib.pyplot as plt
>>> plt.clf()
>>> from tf_pwa.utils import plot_particle_model
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7, "has_bprime": False}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7, "cut_phsp": True}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plt.legend(["all l=0", "has_bprime=False", "cut_phsp=True", "normal"])
`no_m0=True` to set :math:`i m_0 => i` in the width part.
`no_q0=True` to remove :math:`\\frac{m_0}{|q_{i0}|}` and set others :math:`q_{i0}=1`.
.. plot::
>>> import matplotlib.pyplot as plt
>>> plt.clf()
>>> from tf_pwa.utils import plot_particle_model
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7, "no_q0": True}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7, "no_m0": True}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plot_particle_model("FlatteGen", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 1], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
>>> _ = plt.legend(["no_q0=True", "no_m0=True", "normal"])
"""
def __init__(
self,
*args,
im_sign=-1,
l_list=None,
has_bprime=True,
no_m0=False,
no_q0=False,
cut_phsp=False,
**kwargs,
):
super().__init__(*args, im_sign=im_sign, **kwargs)
if l_list is None:
l_list = [0] * len(self.mass_list)
self.l_list = l_list
self.has_bprime = has_bprime
self.no_m0 = no_m0
self.no_q0 = no_q0
self.cut_phsp = cut_phsp
[docs]
def get_coeff(self):
return [i() for i in self.g_value]
[docs]
def get_num_var(self):
mass = self.get_mass()
gi = self.get_coeff()
return (mass, *gi)
[docs]
def get_amp(self, *args, **kwargs):
m = args[0]["m"]
mass = self.get_mass()
zeros = tf.zeros_like(m)
delta_s = mass * mass - m * m
if self.no_m0:
m_c = 1 / m
else:
m_c = mass / m
rhos = []
gi = self.get_coeff()
for i, (mab, l) in enumerate(zip(self.mass_list, self.l_list)):
ma, mb = mab
pi = cal_monentum(m, ma, mb)
pi0 = cal_monentum(mass, ma, mb)
m_rho_i = pi * tf.complex(zeros, gi[i] * m_c)
if self.no_q0:
pi0 = tf.ones_like(pi0)
else:
m_rho_i = m_rho_i * tf.complex(
mass / tf.abs(pi0), tf.zeros_like(mass)
)
if l != 0:
m_rho_i = m_rho_i * tf.complex(
tf.abs(pi / pi0) ** (2 * l), zeros
)
if self.has_bprime:
from tf_pwa.breit_wigner import Bprime_q2
bf = (
Bprime_q2(l, tf.abs(pi) ** 2, tf.abs(pi0) ** 2, self.d)
** 2
)
m_rho_i = m_rho_i * tf.complex(bf, zeros)
if self.cut_phsp:
m_rho_i = tf.where(
m < ma + mb, tf.zeros_like(m_rho_i), m_rho_i
)
rhos.append(m_rho_i)
rho = self.im_sign * sum(rhos)
re = delta_s + tf.math.real(rho)
im = tf.math.imag(rho)
d = re * re + im * im
ret = tf.complex(re / d, -im / d)
return ret
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def get_sympy_dom(self, m, m0, *gi, sheet=0):
import sympy as sym
mass = m0
delta_s = mass * mass - m * m
if self.no_m0:
m_c = 1 / m
else:
m_c = mass / m
rhos = []
for i, (mab, l) in enumerate(zip(self.mass_list, self.l_list)):
ma, mb = mab
pi = cal_monentum_sympy(m, ma, mb)
pi0 = cal_monentum_sympy(mass, ma, mb)
if sheet & 1 == 0:
pi = -pi
sheet = sheet >> 1
# print(pi)
m_rho_i = pi * sym.I * gi[i] * m_c
if self.no_q0:
pi0 = 1
else:
m_rho_i = m_rho_i * mass / abs(pi0)
if l != 0:
m_rho_i = m_rho_i * abs(pi / pi0) ** (2 * l)
if self.has_bprime:
from tf_pwa.formula import Bprime_polynomial
bf = Bprime_polynomial(
l, abs(pi0 * self.d) ** 2
) / Bprime_polynomial(l, abs(pi * self.d) ** 2)
m_rho_i = m_rho_i * bf
if self.cut_phsp:
m_rho_i * sym.Heaviside(m - ma - mb)
rhos.append(m_rho_i)
rho = self.im_sign * sum(rhos)
re = delta_s + rho
return re
[docs]
@register_particle("Flatte2")
class ParticleFlate2(ParticleFlateGen):
"""
General Flatte like formula.
.. math::
R(m) = \\frac{1}{m_0^2 - m^2 - i m_0 [\\sum_{i} \\color{red}{g_i^2}\\color{black} \\frac{q_i}{m} \\times \\frac{m_0}{|q_{i0}|} \\times \\frac{|q_i|^{2l_i}}{|q_{i0}|^{2l_i}} B_{l_i}'^2(|q_i|,|q_{i0}|,d)]}
.. math::
q_i = \\begin{cases}
\\frac{\\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\\\
\\frac{i\\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\\\
\\end{cases}
It has the same options as `FlatteGen`.
.. plot::
>>> import matplotlib.pyplot as plt
>>> plt.clf()
>>> from tf_pwa.utils import plot_particle_model
>>> _ = plot_particle_model("Flatte2", {"mass_list": [[0.1, 0.1], [0.3,0.3]], "l_list": [0, 0], "mass": 0.7}, {"R_BC_g_0": 0.3,"R_BC_g_1": 0.2})
"""
[docs]
def get_coeff(self):
return [i() ** 2 for i in self.g_value]