Candidates for Dark Matter Particles

§ 1

§ 2

Supersymmetric Candidate Particles

Problems 10.4.1 – 10.4.2

Supersymmetry on weak scale ($\sim 100 {\rm GeV}$, it is the scale which lies in the center of the candidate particles search) represents the most motivated basis for new Particle Physics. It naturally provides the dark matter candidates with approximately correct relic density. This fact gives strongly fundamental and absolutely independent motivation for the supersymmetric theories. That is whay application of supersymmetry to cosmology and vice versa deserves the most attentive consideration. An indirect result of the dark matter research is to transfer the results of the supersymmetry theory into applicative domain where its predictions can be chacked in the nearest future.

10.4.1

Problem 10.4.1

Why accelerator energies just exceeding the WIMP rest mass are insufficient to observe the WIMPs?

solution

Energy of $p-p$ interaction cannot be completely transformed into the creation of the supersymmetric particles. Gluino and s-quarks are produced in interaction between quarks and gluons, which carry not more than $10\%$ of total energy of the proton. That is why the events of creation of WIMPs with masses of order $100$ GeV are expected to be observed on LHC for energies higher than 2 TeV.

10.4.2

Problem 10.4.2

What consequences follow from the $R$-parity conservation?

solution

The most important prediction of the supersymmetry is the fact that every particle has a super-partner with the spin which differs on $1/2$. Without special caution, the appearance of the super-partners may lead to violation of baryon and lepton quantum numbers on an inadmissible level. For example, the proton decay $p \to \pi ^0+ e^+ $ can be realized with help of the $s$-quark (it is the super-partner for the usual one). An elegant way to prohibit the decay is to impose the $R$-parity conservation condition $R_p = ( - 1)^{3(B - L) + 2S},$ where $B,L,S$ are baryon number, leptonnumber and spin respectively (recall that baryons are hadrons with semi-integral spin). All the Standard Model particles have $R_p = 1,$ and all the super-partners have $R_p = - 1.$ Conservation of the $R$-parity implies that $\prod {R_p = 1}$ holds in every vertex. The proton decay can be forbidden without the notion of the $R$-parity conservation. For example it can be done by forbidding of the $B$ or $L$ violation, but not both of them. However it leads to even more difficulties. Direct consequences of the $R$-parity conservation are the following:
1) The lightest supersymmetric particle (LSP) cannot decay on the Standard Model particles and therefore it is stable.
2) The supersymmetric particles are created in pairs only.
3) Supersymmetric particles can decay only on odd number of supersymmetric particles.