Available Resonances Model¶

"default", "BWR" (Particle)

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
"x" (ParticleX)

simple particle model for mass, (used in expr)

\[R(m) = m\]

"BWR2" (ParticleBWR2)

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
"BWR_normal" (ParticleBWR_normal)

\[R(m) = \frac{\sqrt{m_0 \Gamma(m)}}{m_0^2 - m^2 - i m_0 \Gamma(m)}\]
"GS_rho" (ParticleGS)

Gounaris G.J., Sakurai J.J., Phys. Rev. Lett., 21 (1968), pp. 244-247

c_daug2Mass: mass for daughter particle 2 (\(\pi^{+}\)) 0.13957039

c_daug3Mass: mass for daughter particle 3 (\(\pi^{0}\)) 0.1349768

\[R(m) = \frac{1 + D \Gamma_0 / m_0}{(m_0^2 -m^2) + f(m) - i m_0 \Gamma(m)}\]

\[f(m) = \Gamma_0 \frac{m_0 ^2 }{q_0^3} \left[q^2 [h(m)-h(m_0)] + (m_0^2 - m^2) q_0^2 \frac{d h}{d m}|_{m0} \right]\]

\[h(m) = \frac{2}{\pi} \frac{q}{m} \ln \left(\frac{m+q}{2m_{\pi}} \right)\]

\[\frac{d h}{d m}|_{m0} = h(m_0) [(8q_0^2)^{-1} - (2m_0^2)^{-1}] + (2\pi m_0^2)^{-1}\]

\[D = \frac{f(0)}{\Gamma_0 m_0} = \frac{3}{\pi}\frac{m_\pi^2}{q_0^2} \ln \left(\frac{m_0 + 2q_0}{2 m_\pi }\right) + \frac{m_0}{2\pi q_0} - \frac{m_\pi^2 m_0}{\pi q_0^3}\]
"BW" (ParticleBW)

\[R(m) = \frac{1}{m_0^2 - m^2 - i m_0 \Gamma_0}\]
"LASS" (ParticleLass)

\[R(m) = \frac{m}{q cot \delta_B - i q} + e^{2i \delta_B}\frac{m_0 \Gamma_0 \frac{m_0}{q_0}} {(m_0^2 - m^2) - i m_0\Gamma_0 \frac{q}{m}\frac{m_0}{q_0}}\]

\[cot \delta_B = \frac{1}{a q} + \frac{1}{2} r q\]

\[e^{2i\delta_B} = \cos 2 \delta_B + i \sin 2\delta_B = \frac{2 cot \delta_B }{cot^2 \delta_B +1 } + i \frac{cot^2\delta_B -1 }{cot^2 \delta_B +1}\]
"one" (ParticleOne)

\[R(m) = 1\]
"exp" (ParticleExp)

\[R(m) = e^{-|a| m}\]
"exp_com" (ParticleExp)

\[R(m) = e^{-|a+ib| m^2}\]
"interp" (Interp)