Constraints on Neutralino masses and mixings from Cosmology and Collider Physics

Abstract

Bounds on cross section measurements of chargino pair production at LEP yield a bound on the chargino mass. If the GUT relation $M_1 = 5/3 \tw[2] M_2$ is assumed, then the lightest neutralino must be heavier than $\approx 45 -50\GeV$. If $M_1$ is considered as a free parameter independent of $M_2$ there is no bound on the mass of the lightest neutralino. In this thesis, I examine consequences of light, even massless neutralinos in cosmology and particle physics.<br /> In Chapter 2, I discuss mass bounds on the lightest neutralino from relic density measurements. The relic density can be calculated by solving the Boltzmann equation. If the relic density is considered as a function of the particle mass then there are two mass regions where the relic density takes on realistic values. In the first region the neutralino is relativistic and its mass must be lower than $0.7\,\mathrm{eV}$, in the second region the neutralino is nonrelativistic and must be heavier than $\approx 13\GeV$. I compare the Cowsig-McClelland bound, the approximate solution of a relativistic particle for the Boltzmann equation, and the Lee-Weinberg bound, the non-relativistic approximation, with the full solution and I find that the approximation and the full solution agree quite well.<br /> In Chapter 3, I derive bounds on the selectron mass from the observed limits on the cross section of the reaction $e^+e^-\rightarrow \x{1}\x{2}$ at LEP, if the lightest neutralino is massless. If \mbox{$M_2,\mu < 200\GeV$}, the selectron must be heavier than $350\GeV$.<br /> In Chapter 4, I study radiative neutralino production $e^+e^- \to \tilde\chi^0_1 \tilde\chi^0_1\gamma$ at the linear collider with longitudinally polarised beams. I consider the Standard Model background from radiative neutrino production $e^+e^- \to \nu \bar\nu \gamma$, and the supersymmetric radiative production of sneutrinos $e^+e^- \to \tilde\nu \tilde\nu^\ast \gamma$, which can be a background for invisible sneutrino decays. I give the complete tree-level formulas for the amplitudes and matrix elements squared. In the Minimal Supersymmetric Standard Model, I study the dependence of the cross sections on the beam polarisations, on the parameters of the neutralino sector, and on the selectron masses. I show that for bino-like neutralinos longitudinal polarised beams enhance the signal and simultaneously reduce the background, such that search sensitivity is significantly enhanced. I point out that there are parameter regions where radiative neutralino production is the {\it only} channel to study SUSY particles at the ILC, since heavier neutralinos, charginos and sleptons are too heavy to be pair-produced in the first stage of the linear collider with $\sqrt{s} =500\GeV$.<br /> % I analyze the impact of electron and positron beam polarization on % radiative neutralino production at the International Linear Collider % (ILC). <br /> In Section 4.4, I focus on three different mSUGRA scenarios in turn at the Higgs strahlung threshold, the top pair production threshold, and at $\sqrt{s} =500\GeV$. In these scenarios at the corresponding $\sqrt{s}$, radiative neutralino production is the only supersymmetric production mechanism which is kinematically allowed. The heavier neutralinos, and charginos as well as the sleptons, squarks and gluinos are too heavy to be pair produced. I calculate the signal cross section and also the Standard Model background from radiative neutrino production. For my scenarios, I obtain significances larger than $10$ and signal to background ratios between $2\%$ and $5\%$, if I have electron beam polarization $P_{e^-} = 0.0- 0.8$ and positron beam polarization $P_{e^+} = 0.0 - 0.3$. If I have electron beam polarization of $P_{e^-} = 0.9$, then the signal is observable with $P_{e^+} = 0.0$ but both the significance and the signal to background ratio are significantly improved for $P_{e^+} = 0.3$.<br /> In Chapter 5, I present a method to determine neutralino couplings to right and left handed selectrons and $Z$ bosons from cross section measurements of radiative neutralino production and neutralino pair production $e^+ e^- \rightarrow \x{1}\x{2/3/4}$, $e^+ e^- \rightarrow \x{2}\x{2}$ at the ILC. The error on the couplings is of order $\mathcal{O}(0.001 -0.01)$. From the neutralino couplings the neutralino diagonalisation matrix can be calculated. If all neutralino masses are known, $M_1$, $M_2$, and $\mu$ can be calculated with an error of the order $\mathcal{O}(1\GeV)$. If also the cross sections of the reactions $e^+ e^- \rightarrow \x{2}\x{3/4}$ can be measured the error of $M_1$, $M_2$, and $\mu$ reduces to $\mathcal{O}(1\GeV)$.