The neutral supersymmetric spectrum

Date: 2015-10-07; view: 458.

Supersymmetric particles that are electrically neutral, and so promising dark matter candidates, are shown with their standard model partners in Fig. 2. In supersymmetric models, two Higgs doublets are required to give mass to all fermions. The two neutral Higgs bosons are H_d and H_u, which give mass to the down-type and up-type fermions, respectively, and each of these has a superpartner. Aside from this subtlety, the superpartner spectrum is exactly as one would expect. It consists of spin 0 sneutrinos, one for each neutrino, the spin 3/2 gravitino, and the spin 1/2 Bino, neutral Wino, and down- and up-type Higgsinos. These states have masses determined (in part) by the corresponding mass parameters listed in the top row of Fig. 2. These parameters are unknown, but are presumably of the order of the weak scale, given the motivations described above.

Fig. 2. Neutral particles in the supersymmetric spectrum. M₁, M₂, μ, , and m_3/2 are unknown weak-scale mass parameters. The Bino, Wino, and down- and up-type Higgsinos mix to form neutralinos.

The gravitino is a mass eigenstate with mass m_3/2. The sneutrinos are also mass eigenstates, assuming flavor and R-parity conservation (see Section 2.4). The spin 1/2 states are differentiated only by their electroweak quantum numbers. After electroweak symmetry breaking, these gauge eigenstates therefore mix to form mass eigenstates. In the basis the mixing matrix is

(7)

where c_W≡cosθ_W, s_W≡sinθ_W, and β is another unknown parameter defined by tanβ≡ H_u / H_d , the ratio of the up-type to down-type Higgs scalar vacuum expectation values (vevs). The mass eigenstates are called neutralinos and denoted χ ≡ χ₁, χ₂, χ₃, χ₄ , in order of increasing mass. If M₁ M₂, |μ|, the lightest neutralino χ has a mass of approximately M₁ and is nearly a pure Bino. However, for M₁ M₂ |μ|, χ is a mixture with significant components of each gauge eigenstate.

Finally, note that neutralinos are Majorana fermions; they are their own anti-particles. This fact has important consequences for neutralino dark matter, as will be discussed below.

2.4. R-Parity

Weak-scale superpartners solve the gauge hierarchy problem through their virtual effects. However, without additional structure, they also mediate baryon and lepton number violation at unacceptable levels. For example, proton decay p → π⁰e⁺ may be mediated by a squark as shown in Fig. 3.

Fig. 3. Proton decay mediated by squark.

An elegant way to forbid this decay is to impose the conservation of R-parity R_p ≡ (−1)^{3(B−L) + 2S}, where B, L, and S are baryon number, lepton number, and spin, respectively. All standard model particles have R_p = 1, and all superpartners have R_p = −1. R-parity conservation implies ΠR_p = 1 at each vertex, and so both vertices in Fig. 3 are forbidden. Proton decay may be eliminated without R-parity conservation, for example, by forbidding B or L violation, but not both. However, in these cases, the non-vanishing R-parity violating couplings are typically subject to stringent constraints from other processes, requiring some alternative explanation.

An immediate consequence of R-parity conservation is that the lightest supersymmetric particle (LSP) cannot decay to standard model particles and is therefore stable. Particle physics constraints therefore naturally suggest a symmetry that provides a new stable particle that may contribute significantly to the present energy density of the universe.