Neutralino dark matter
185
and all three pairs from A O , HO, hO.
Analytic expressions for the a tenns for all of these processes are compact
but the b tenns are very involved [22]. Neutralinos are Majorana fermions and
are, therefore, their own antiparticles. This means that, in an s-wave state, the two
neutralinos must have their spins oppositely directed because of Fenni statistics.
Therefore, if the neutralinos annihilate to a fermion (f)-antifermion pair ,
then f and j must also have their spins antiparallel, and this implies that the
amplitude acquires a factor m f to account for the helicity flip. Another way
to see this is to note that the initial s-wave xfxf state has CP = -I, so CPinvariance requires that the final state also has C P = -I. Annihilation into light
fermion pairs will always be kinematically allowed but the previous argument
shows that the s-wave contribution to, and therefore the a term in, the annihilation
cross section is proportional to m}/mi. Thus, annihilation into light quarks and
leptons is negligible compared With annihilation into c, band t-quark pairs: the
latter occurs only when m x > m, and dominates all other channels when it is
open. CP-invariance also affects other amplitudes. For example, annihilation
into Higgs bosons can be important when such channels are open. However, the
s-wave amplitudes for the final states hOh O , HO HO, HOh O , AO A O , H+ H- are
identically zero because of CP-invariance: the same is true of the zO A 0 final
state.
The allowed parameter space is restricted by other data [23] besides the
cosmological bounds (5.22). Specifically, the LEP bound on mh, and b -. sy
data, both force the parameter mI/2 to larger values, while the BNL E821
measurement of the g - 2 factor of the muon [24] favours relatively low values of
mo and m 1/2, at least for IL > O-the actual bounds are dependent on tan {J. There
is also the requirement that the neutralino ;s the LSP and that the parameters allow
radiatively driven electroweak symmetry breaking. The current position seems to
be [25] that the MSSM can simultaneously satisfy all of these constraints. In the
most constrained model, the CMSSM, there is a 'bulk' region in the (m 1/2, mol
plane with relatively low values of mo and m 1/2 in which both the cosmological
and the non-cosmological constraints are satisfied, see figure 6.2 taken from [25].
In this region, supersymmetry is relatively easy to detect at coJliders. The
constraints deriving from the precision WMAP data have substantially reduced
the size of this region. The bulk region is essentially defined by using the
expression (6.54) and, in this region, the neutralino is essentially the Bino (B),
i.e. NIO » Nzo, N30, N4{) in (6.50). In this case the annihilation proceeds mainly
via t-channeI sfermion exchange.
Extending from the bulk region to larger values of m 1/2 is a co-annihilation
'tail', where the neutralino LSP is almost degenerate with the next-to-Iightest
sparticle, usually the stau i. At larger values of mo, close to the region where
radiative electroweak symmetry breaking is no longer possible, there is a 'focuspoint' region in which the neutralino has a larger Higgsino component, i.e. N30 or
N4{) in (6.50) are non-negligible. Lastly, when both mo and m 1/2 are large there
may be a 'funnel' where rapid direct-channel annihilations via the A and H Higgs
185
and all three pairs from A O , HO, hO.
Analytic expressions for the a tenns for all of these processes are compact
but the b tenns are very involved [22]. Neutralinos are Majorana fermions and
are, therefore, their own antiparticles. This means that, in an s-wave state, the two
neutralinos must have their spins oppositely directed because of Fenni statistics.
Therefore, if the neutralinos annihilate to a fermion (f)-antifermion pair ,
then f and j must also have their spins antiparallel, and this implies that the
amplitude acquires a factor m f to account for the helicity flip. Another way
to see this is to note that the initial s-wave xfxf state has CP = -I, so CPinvariance requires that the final state also has C P = -I. Annihilation into light
fermion pairs will always be kinematically allowed but the previous argument
shows that the s-wave contribution to, and therefore the a term in, the annihilation
cross section is proportional to m}/mi. Thus, annihilation into light quarks and
leptons is negligible compared With annihilation into c, band t-quark pairs: the
latter occurs only when m x > m, and dominates all other channels when it is
open. CP-invariance also affects other amplitudes. For example, annihilation
into Higgs bosons can be important when such channels are open. However, the
s-wave amplitudes for the final states hOh O , HO HO, HOh O , AO A O , H+ H- are
identically zero because of CP-invariance: the same is true of the zO A 0 final
state.
The allowed parameter space is restricted by other data [23] besides the
cosmological bounds (5.22). Specifically, the LEP bound on mh, and b -. sy
data, both force the parameter mI/2 to larger values, while the BNL E821
measurement of the g - 2 factor of the muon [24] favours relatively low values of
mo and m 1/2, at least for IL > O-the actual bounds are dependent on tan {J. There
is also the requirement that the neutralino ;s the LSP and that the parameters allow
radiatively driven electroweak symmetry breaking. The current position seems to
be [25] that the MSSM can simultaneously satisfy all of these constraints. In the
most constrained model, the CMSSM, there is a 'bulk' region in the (m 1/2, mol
plane with relatively low values of mo and m 1/2 in which both the cosmological
and the non-cosmological constraints are satisfied, see figure 6.2 taken from [25].
In this region, supersymmetry is relatively easy to detect at coJliders. The
constraints deriving from the precision WMAP data have substantially reduced
the size of this region. The bulk region is essentially defined by using the
expression (6.54) and, in this region, the neutralino is essentially the Bino (B),
i.e. NIO » Nzo, N30, N4{) in (6.50). In this case the annihilation proceeds mainly
via t-channeI sfermion exchange.
Extending from the bulk region to larger values of m 1/2 is a co-annihilation
'tail', where the neutralino LSP is almost degenerate with the next-to-Iightest
sparticle, usually the stau i. At larger values of mo, close to the region where
radiative electroweak symmetry breaking is no longer possible, there is a 'focuspoint' region in which the neutralino has a larger Higgsino component, i.e. N30 or
N4{) in (6.50) are non-negligible. Lastly, when both mo and m 1/2 are large there
may be a 'funnel' where rapid direct-channel annihilations via the A and H Higgs