Neutralino

Neutralinos are hypothetical elementary particles that appear in supersymmetric theories of elementary particle physics .

These theories are characterized by the fact that each (quantum) field is assigned a partner field that differs from the original by the amount  1/2 in the spin . Since the starting fields here are bosons (integer spin), the neutralinos themselves must be fermions (half- integer spin). In particular, neutralinos are Majorana fermions ; that is, they have no electrical charge and therefore do not differ from their antiparticles .

Four neutralinos in the MSSM

In the minimal supersymmetrical standard model (MSSM), neutralinos are superimposed states (mixtures, linear combinations ) of superpartners, both electrical and color-neutral calibration and Higgs fields . The former are the Gauginos (Wino, partner of W ⁰ ) and (Bino, partner of B ⁰ ), the latter are the Higgsinos and (partner of the Higgs bosons and ). ${\displaystyle {\tilde {W}}^{0}}$ ${\displaystyle {\tilde {B}}^{0}}$ ${\displaystyle {\tilde {H}}_{a}^{0}}$ ${\displaystyle {\tilde {H}}_{b}^{0}}$ ${\displaystyle H_{a}^{0}}$ ${\displaystyle H_{b}^{0}}$

A direct identification of a neutralino with a partner field of a Eich or Higgs field is generally not possible, as these usually do not have a defined mass. Usually the neutralinos in a model are named in ascending order according to their mass. In the MSSM these are Neutralino 1 to 4, abbreviated with (sometimes also ). ${\displaystyle {\tilde {\chi }}_{1}^{0}\dots {\tilde {\chi }}_{4}^{0}}$ ${\displaystyle {\tilde {N}}_{1}^{0}\dots {\tilde {N}}_{4}^{0}}$

Alternative composition

The postulated neutralinos can also be expressed as a superposition of the uncharged constructs Photino and Zino (instead of Wino and Bino ) with the uncharged Higgsinos. ${\displaystyle {\tilde {\gamma }}}$ ${\displaystyle {\tilde {Z}}^{0}}$ ${\displaystyle {\tilde {W}}^{0}}$ ${\displaystyle {\tilde {B}}^{0}}$

Photino and Zino are themselves already linear combinations ofand, in the same way as according to the standard model photon and Z ⁰ boson , the electricallyneutral gauge bosons of the electroweak interaction , arise from the neutral gauge fields W ⁰ and B ⁰ : ${\displaystyle {\tilde {\gamma }}}$ ${\displaystyle {\tilde {Z}}^{0}}$ ${\displaystyle {\tilde {W}}^{0}}$ ${\displaystyle {\tilde {B}}^{0}}$ ${\displaystyle \gamma }$

${\displaystyle {\Psi _{\gamma } \choose \Psi _{Z^{0}}}={\begin{pmatrix}\cos \theta _{W}&\sin \theta _{W}\\-\sin \theta _{W}&\cos \theta _{W}\end{pmatrix}}{\Psi _{B^{0}} \choose \Psi _{W^{0}}}}$

${\displaystyle \Rightarrow {\Psi _{\tilde {\gamma }} \choose \Psi _{{\tilde {Z}}^{0}}}={\begin{pmatrix}\cos \theta _{W}&\sin \theta _{W}\\-\sin \theta _{W}&\cos \theta _{W}\end{pmatrix}}{\Psi _{{\tilde {B}}^{0}} \choose \Psi _{{\tilde {W}}^{0}}}.}$

Here is the vineyard angle and the wave function . ${\displaystyle \theta _{W}}$ ${\displaystyle \Psi }$

Because of the not yet considered mixing of the fields and with the uncharged Higgsinos, Photino and Zino are generally not candidates for observable particles. ${\displaystyle {\tilde {\gamma }}}$ ${\displaystyle {\tilde {Z}}^{0}}$

Scenarios for the two light neutralinos

Moortgat-Pick and Fraas have for two lighter Neutralinos and examined three different scenarios. The strengths of the proportions Photino , Zino and Higgsinos and the mixture differ, which suggests or makes it impossible to identify the two Neutralinos with individual proportions: ${\displaystyle {\tilde {N}}_{1}^{0}}$ ${\displaystyle {\tilde {N}}_{2}^{0}}$ ${\displaystyle {\tilde {\gamma }}}$ ${\displaystyle {\tilde {Z}}^{0}}$ ${\displaystyle {\tilde {H}}_{a}^{0}}$ ${\displaystyle {\tilde {H}}_{b}^{0}}$

Neutralino	${\displaystyle {\tilde {N}}_{1}^{0}}$				${\displaystyle {\tilde {N}}_{2}^{0}}$
mixing share	${\displaystyle {\tilde {\gamma }}}$	${\displaystyle {\tilde {Z}}^{0}}$	${\displaystyle {\tilde {H}}_{a}^{0}}$	${\displaystyle {\tilde {H}}_{b}^{0}}$	${\displaystyle {\tilde {\gamma }}}$	${\displaystyle {\tilde {Z}}^{0}}$	${\displaystyle {\tilde {H}}_{a}^{0}}$	${\displaystyle {\tilde {H}}_{b}^{0}}$
Scenario A	+0.94	−0.32	−0.08	−0.07	+0.34	−0.90	−0.16	−0.23
Scenario B	+0.67	−0.63	−0.13	−0.09	+0.65	-0.75	−0.18	−0.10
Scenario C	+0.10	−0.17	−0.19	−0.96	+0.06	−0.31	−0.92	−0.24

(A) In the lightest Neutralino , the Photino component predominates and in the second lightest the Zino component, the Higgsinos only play a minor role. In this case one could equate the two lightest neutralinos with the photino and the zino (roughly). ${\displaystyle {\tilde {N}}_{1}^{0}}$ ${\displaystyle {\tilde {N}}_{2}^{0}}$

(B) and are both composed of approximately equal parts of photino and zino components, the Higgsinos also only play a subordinate role. An assignment is not possible, but the electroweak Gauginos (largely) remain among themselves. ${\displaystyle {\tilde {N}}_{1}^{0}}$ ${\displaystyle {\tilde {N}}_{2}^{0}}$

(C) With the two light Neutralinos and there are only small proportions of Photino and Zino, but strong components of the Higgsinos or . This suggests a corresponding equation of the two light neutralinos with the neutral highsinos. ${\displaystyle {\tilde {N}}_{1}^{0}}$ ${\displaystyle {\tilde {N}}_{2}^{0}}$ ${\displaystyle {\tilde {H}}_{a}^{0}}$ ${\displaystyle {\tilde {H}}_{b}^{0}}$

Easiest neutral as a WIMP candidate

The lightest neutralino is of particular importance. In many models it is stable, has a mass of a few hundred GeV / c² (proton mass for comparison: 0.94 GeV / c²) and, due to its lack of electrical charge, it has little interaction with light. As the lightest supersymmetric particle (LSP) , it would therefore be a very promising candidate for dark matter , a so-called WIMP . The Particle Data Group gave 2006 as the experimental lower limit for the neutral mass 46 GeV / c².

See also

• Chargino : Mixtures of the charged Winos and or and (partner of the electrically charged W bosons ) and the charged Higgsinos and ${\displaystyle {\tilde {W}}^{1}}$ ${\displaystyle {\tilde {W}}^{2}}$ ${\displaystyle {\tilde {W}}^{+}}$ ${\displaystyle {\tilde {W}}^{-}}$ ${\displaystyle {\tilde {H}}^{+}}$ ${\displaystyle {\tilde {H}}^{-}}$

Footnotes and individual references

1. ↑ Only the neutral calibration fields of the electroweak interaction contribute.
2. ^ G. Moortgat-Pick & H. Fraas (both Univ. Würzburg): Angular and Energy Distribution in Neutralino Production and Decay With Complete Spin Correlations . In: Acta Physica B Polonia . 28, No. 11, 1997, pp. 2395-2400 , arxiv : hep-ph / 9712354 .
3. ↑ PDG, see PDF file Searches (Supersymmetry, Compositeness) ; the Joint LEP2 Supersymmetry Working Group, Aleph, Delphi, L3 and Opal Experiments gives 47 GeV / c².