breit_wigner
This module provides functions to describe the lineshapes of the intermediate particles, namely generalized Breit-Wigner function. Users can also define new lineshape using the function wrapper regist_lineshape().
- BW(m, m0, g0, *args)[source]
Breit-Wigner function
\[BW(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma_0 }\]
- BWR(m, m0, g0, q, q0, L, d)[source]
Relativistic Breit-Wigner function (with running width). It’s also set as the default lineshape.
\[BW(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
- BWR2(m, m0, g0, q2, q02, L, d)[source]
Relativistic Breit-Wigner function (with running width). Allow complex \(\Gamma\).
\[BW(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
- BWR_normal(m, m0, g0, q2, q02, L, d)[source]
Relativistic Breit-Wigner function (with running width) with a normal factor.
\[BW(m) = \frac{\sqrt{m_0 \Gamma(m)}}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
- Bprime(L, q, q0, d)[source]
Blatt-Weisskopf barrier factors. E.g. the first three orders
\(L\)
\(B_L'(q,q_0,d)\)
0
1
1
\(\sqrt{\frac{(q_0d)^2+1}{(qd)^2+1}}\)
2
\(\sqrt{\frac{(q_0d)^4+3*(q_0d)^2+9}{(qd)^4+3*(qd)^2+9}}\)
\(d\) is 3.0 by default.
- Bprime_num(L, q, d)[source]
The numerator (as well as the denominator) inside the square root in the barrier factor
- Bprime_polynomial(l, z)[source]
It stores the Blatt-Weisskopf polynomial up to the fifth order (\(L=5\))
- Parameters:
l – The order
z – The variable in the polynomial
- Returns:
The calculated value
- Gamma(m, gamma0, q, q0, L, m0, d)[source]
Running width in the RBW
\[\Gamma(m) = \Gamma_0 \left(\frac{q}{q_0}\right)^{2L+1}\frac{m_0}{m} B_{L}'^2(q,q_0,d)\]
- Gamma2(m, gamma0, q2, q02, L, m0, d)[source]
Running width in the RBW
\[\Gamma(m) = \Gamma_0 \left(\frac{q}{q_0}\right)^{2L+1}\frac{m_0}{m} B_{L}'^2(q,q_0,d)\]
- barrier_factor(l, q, q0, d=3.0, axis=0)[source]
Barrier factor multiplied with \(q^L\), which is used as a combination in the amplitude expressions. The values are cached for \(L\) ranging from 0 to l.
- get_bprime_coeff(l)[source]
The coefficients of polynomial in Bprime function.
\[|\theta_{l}(jw)|^2 = \sum_{i=0}^{l} c_i w^{2 i}\]
- regist_lineshape(name=None)[source]
It will be used as a wrapper to define various Breit-Wigner functions
- Parameters:
name – String name of the BW function
- Returns:
A function used in a wrapper