flatte

class ParticleFlate2(*args, im_sign=-1, l_list=None, has_bprime=True, no_m0=False, no_q0=False, cut_phsp=False, **kwargs)

Bases: ParticleFlateGen

General Flatte like formula.

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 [\sum_{i} \color{red}{g_i^2}\color{black} \frac{q_i}{m} \times \frac{m_0}{|q_{i0}|} \times \frac{|q_i|^{2l_i}}{|q_{i0}|^{2l_i}} B_{l_i}'^2(|q_i|,|q_{i0}|,d)]}\]

\[\begin{split}q_i = \begin{cases} \frac{\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\ \frac{i\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\ \end{cases}\end{split}\]

It has the same options as FlatteGen.

(Source code, png, hires.png, pdf)

get_coeff()

model_name = 'Flatte2'

class ParticleFlateGen(*args, im_sign=-1, l_list=None, has_bprime=True, no_m0=False, no_q0=False, cut_phsp=False, **kwargs)

Bases: ParticleFlatte

More General Flatte like formula

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 [\sum_{i} g_i \frac{q_i}{m} \times \frac{m_0}{|q_{i0}|} \times \frac{|q_i|^{2l_i}}{|q_{i0}|^{2l_i}} B_{l_i}'^2(|q_i|,|q_{i0}|,d)]}\]

\[\begin{split}q_i = \begin{cases} \frac{\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\ \frac{i\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\ \end{cases}\end{split}\]

Required input arguments mass_list: [[m11, m12], [m21, m22]] for \(m_{i,1}, m_{i,2}\). And addition arguments l_list: [l1, l2] for \(l_i\)

has_bprime=False to remove \(B_{l_i}'^2(|q_i|,|q_{i0}|,d)\).

cut_phsp=True to set \(q_i = 0\) when \((m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0\)

The plot use parameters \(m_0=0.7, m_{0,1}=m_{0,2}=0.1, m_{1,1}=m_{1,2}=0.3, g_0=0.3,g_1=0.2,l_0=0,l_1=1\).

(Source code, png, hires.png, pdf)

no_m0=True to set \(i m_0 => i\) in the width part.

no_q0=True to remove \(\frac{m_0}{|q_{i0}|}\) and set others \(q_{i0}=1\).

(Source code, png, hires.png, pdf)

get_amp(*args, **kwargs)

get_coeff()

get_num_var()

get_sympy_dom(m, m0, *gi, sheet=0)

model_name = 'FlatteGen'

class ParticleFlatte(*args, mass_list=None, im_sign=1, **kwargs)

Bases: Particle

Flatte like formula

\[R(m) = \frac{1}{m_0^2 - m^2 + i m_0 (\sum_{i} g_i \frac{q_i}{m})}\]

\[\begin{split}q_i = \begin{cases} \frac{\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\ \frac{i\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\ \end{cases}\end{split}\]

(Source code, png, hires.png, pdf)

Required input arguments mass_list: [[m11, m12], [m21, m22]] for \(m_{i,1}, m_{i,2}\).

get_amp(*args, **kwargs)

get_num_var()

get_sympy_dom(m, m0, *gi, sheet=0)

get_sympy_var()

get_width(m=None)

init_params()

model_name = 'Flatte'

class ParticleFlatteC(*args, im_sign=-1, **kwargs)

Bases: ParticleFlatte

Flatte like formula

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 (\sum_{i} g_i \frac{q_i}{m})}\]

\[\begin{split}q_i = \begin{cases} \frac{\sqrt{(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) >= 0 \\ \frac{i\sqrt{|(m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2)|}}{2m} & (m^2-(m_{i,1}+m_{i,2})^2)(m^2-(m_{i,1}-m_{i,2})^2) < 0 \\ \end{cases}\end{split}\]

Required input arguments mass_list: [[m11, m12], [m21, m22]] for \(m_{i,1}, m_{i,2}\).

(Source code, png, hires.png, pdf)

model_name = 'FlatteC'

cal_monentum(m, ma, mb)

cal_monentum_sympy(m, ma, mb)