C. Physics Measurements at the NLC

The most obvious (and easiest) measurements to make on the supersymmetric particles is the masses; but there is much more information to be gained by performing a complete set of measurements. Here is a list of measurements that can be made in order to verify that nature is supersymmetric, and to make precision measurements of the supersymmetric parameters:

• Search for the NLSP (next-to-lightest supersymmetric particle); if this is the chargino, then look for $\chionepm \to \chionez q \overline{q}$; from the endpoint method, determine both $\MSS{\chi_1^\pm}$ and $\MSS{\chi_1^0}$. Since the chargino is a spin-$\frac12$ particle, the chargino mass is related to the mSUGRA parameter $m_{1/2}$.

• Measure the production cross section (basically, count the number of events) of chargino pairs at different electron polarizations, and determine $\sigma_L(\epem\to\chionep\chionem)$ and $\sigma_R(\epem\to\chionep\chionem)$ (the cross sections for 100% left- and right-handed polarized electrons). The size of the change in cross section indicates whether the $\chionepm$ is a partner of a wino ($\winopm$) or a higgsino ($\Higgsinopm$).

• Measure the differential cross section (i.e. the number of events as a function of angle), $d\sigma(\epem\to\chionep\chionem)/d\cos\theta$; from the angular distribution, one can measure the spin of the chargino (it should be spin-$\frac12$).

• Measure the branching ratios of $\winop\to \chionez \ell^+\nu_\ell$ and $\winop\to \chionez q \overline{q}$ and compare to $W^+\to \ell^+\nu_\ell$ and $W^+\to q \overline{q}$; supersymmetry requires that the couplings be the same for $W^+$ and $\winop$.

• Find the $\chitwopm$; the relationship between $\MSS{\chi_1^\pm}$ and $\MSS{\chi_2^\pm}$ can either test the mSUGRA model, or determine the SUSY parameters assuming the mSUGRA model, since:
  $$\begin{eqnarray*} \MSS{\chi_1^\pm}^2 + \MSS{\chi_2^\pm}^2 &=& M_2^2 + 2M_W^2 + ... ...1^\pm} \cdot \MSS{\chi_2^\pm} &=& \mu M_2 - M_W^2\sin2\beta \\ \end{eqnarray*}$$
  
  
  
  
  

• Find the massive neutralinos. In the MSSM with GUT unification, $M_1 = \frac12 M_2$, so
  $$\begin{eqnarray*} \MSS{\chi_1^0} \approx \min(\vert\mu\vert,{\textstyle\frac12}... ...2} M_2) \\ \MSS{\chi_4^0} \approx \max(\vert\mu\vert,M_2) \\ \end{eqnarray*}$$
  
  
  
  
  
  Also, the neutralinos are some combination of the $\binoz$, $\winoz$, $\higgsinoz$, and $\Higgsinoz$ (or $\photino$, $\zino$, $\higgsino$, and $\Higgsino$). Measuring the masses, cross sections and branching ratios (such as $B(\chiiz\to b\sbottom)$ compared to $B(\chiiz\to q\squark)$) will help determine the amount of mixing between these states.

• Find the Higgs particles. Supersymmetry predicts that there will be more than one of them. Even though they are not themselves supersymmetric, they can be used to estimate the supersymmetry parameters, assuming the MSSM model. For example,
  
  $$M_{H^0,h^0}^2 = \frac{1}{2} \left[M_A^2 + M_Z^2 \pm \sqrt... ... 4M_A^2M_Z^2\left(\sin^2\beta - \cos^2\beta\right)} \right]$$
  
  
  and
  
  $$M_{H^\pm}^2 = M_W^2 + M_A^2$$
  
  

• Find the selectron and measure its mass. Since the selectron is a spin-$0$ particle, its mass is related to the mSUGRA parameter $m_{0}$.

• Find the smuon and measure its mass. If the mass is the same as the selectron's, this may be an indication that the supersymmetry model has a universal slepton mass.

• Measure the differential cross section $d\sigma(\epem\to\murp\murm)/d\cos\theta$; from the angular distribution, one can measure the spin of the smuon (it should be spin-$0$).

• Find the sneutrino and measure its mass. A test of the MSSM model is to verify that $M_{\tilde{\ell}_L}^2 = M_{\tilde{\nu}}^2 - M_W^2 \cos2\beta$.

• Find the $\stau$; depending on the model, the $\taur$ and $\taul$ can mix to form a light $\tauone$ state and a heavy $\tautwo$ state. By measuring the masses and cross sections, one can determine the mixing angle $\theta_\tau$.

• Find the squarks and measure their masses. Similarly to the $\stau$, the $\stop$'s may also mix to form a light $\topone$ and heavy $\toptwo$. If $\tan\beta \gg 1$ then the $\bottomr$ and $\bottoml$ should also mix to form the $\bottomone$ and $\bottomtwo$.