Elastic -vs- Inelastic Collisisons
Elastic Collisions: Conserve P and E
Inelastic : Only Conserve P
Definition of Mission Mass
Definition of Momentum Transfer
4-Momentum vector definition using Ryder convention
- [math]P_{\mu} \equiv \left ( \frac{E}{c} , - \vec p \right )[/math]
- [math]P^{\mu} \equiv \left ( \frac{E}{c} , \vec p \right )[/math]
- [math]P_{\mu} P^{\mu} = \left ( \frac{E}{c}\right )^2 - \vec p^2 = E^2-p^2 = m^2[/math] if you define the speed of light as unity
- Note
- Other conventions used by Perkins
- [math]P_{\mu} \equiv \left ( \vec p, -E \right )[/math]
- [math]P^{\mu} \equiv \left ( \vec p , E\right )[/math]
or Kollen
- [math]P_{\mu} \equiv \left ( \vec p, iE \right )[/math]
- [math]P^{\mu} \equiv \left ( \vec p , iE\right )[/math]
Momentum transfer is defined as
- [math]q_{\mu} \equiv ( \omega, \vec q) = P^i_{\mu} - P^f_{\mu}[/math] : conservation of momentum
- [math]q_{\mu}q^{\mu} = (E_i - E_f)^2 - (\vec {P}_i - \vec{P}_f) \cdot (\vec {P}_i - \vec{P}_f)[/math]
- [math]= m_i^2 +m_f^2 - 2E_iE_f + 2 \left | \vec {P}_i \right | \left | \vec {P}_f \right |[/math]
References
2014 Ph.D thesis of Naomi's student Sylvester Joosten
Semi-inclusive deep inelastic scattering at small transverse momentum
Naomi's SIDIS Hermes talk from 2011 at NNPSS11
TF_SIDIS_Physics