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a key motivation for tev scale supersymmetry ( susy ) is that it provides a natural dark matter candidate if the lightest neutralino is the lsp .
however the regions of parameter space that yield neutralino dark matter in agreement with wmap look very restricted .
we recently studied the naturalness of dark matter in @xcite .
questions of fine - tuning have long been considered in the case of electroweak symmetry breaking . in many of these studies
the degree of fine - tuning required was quantified through a measure of the sensitivity of @xmath1 to the input parameters of the mssm @xmath2 .
we use a similar measure @xcite to quantify the degree of fine - tuning required of the mssm parameters to produce an lsp that reproduces the observed dark matter relic density : @xmath3 we take the total tuning of a point to be @xmath4 .
the calculation of @xmath5 primarily depends on @xmath2 through their effect on the annihilation cross - section of the lightest neutralino @xmath6 .
this is primarily determined by the mass and composition of @xmath6 .
this in turn is determined by diagonalising the neutralino mass matrix at low energy .
the matrix depends upon @xmath7 , @xmath8 , and @xmath9 .
if one of these is much lighter than the others @xmath6 will be primarily of that form .
this allows us to divide up the mssm parameter space depending on the composition of @xmath6 .
a wino lsp ( @xmath10 ) or higgsino lsp ( @xmath11 ) annihilates very efficiently , resulting in too little dark matter , @xmath12 .
a bino lsp ( @xmath13 ) annihilates primarily via t - channel slepton exchange .
this process is only efficient for light sleptons and so bino lsps generally result in too large a relic @xmath14 .    therefore to fit the observed dark matter density we are required to move to unusual regions of the parameter space .
one possibility is to consider a mixed lsp .
if we have a bino lsp with just enough of either wino or higgsino mixed in , we can fit @xmath15 .
this is the so called `` well - tempered '' neutralino championed in @xcite .
alternatively we can consider a bino lsp in which the annihilation cross - section is enhanced via some means .
this can occur in a few different ways .
firstly , if there are light sfermions , t - channel sfermion is enhanced .
secondly if @xmath16 the neutralinos can annihilate to an on - shell boson .
finally if the nlsp is quasi - degenerate in mass with the lsp , there will be a significant nlsp number density at freeze out and we must factor in annihilations of the nlsp into our calculations of the susy relic density .
all of these effects can enhance annihilation of a bino lsp to the extent that we fit the observed dark matter relic density .
we would expect each region to exhibit a different sensitivity to the mssm input parameters . to study these regions we take 4 different sets of boundary conditions on the mssm input parameters @xmath2 at @xmath17 , beginning with the familiar case of the constrained minimal supersymmetric standard model ( cmssm ) .
the rest of this talk is set out as follows . in section [ cmssm ]
we consider the cmssm , which provides us with a useful reference point against which the subsequent non - universal cases may be compared . in section [ scalar ]
we allow the third family soft sfermion and higgs mass squared to vary independently . in section [ gauge ]
we consider neutralino dark matter with non - universal gaugino masses , but with a universal soft scalar mass . in section [ scalargauge ]
we consider _ both _ the effects of including an independent third family sfermion mass squared _ and _ non - universal soft gaugino masses .
section [ conc ] concludes the talk .
the cmssm has 4 free inputs : @xmath18 @xmath19 is a common scalar mass that sets the soft masses of the sfermion and higgs sectors .
@xmath20 is a common gaugino mass .
@xmath21 sets the soft susy breaking trilinear coupling .
@xmath22 is the ratio of the higgs vevs .
finally the requirement that the model provide radiative electroweak symmetry breaking determines the magnitude of the susy conserving higgs mass @xmath9 but leaves the sign as a free parameter .
the mass and composition of the lightest neutralino is determined by diagonalising a mass matrix that depends upon the parameters @xmath23 at the electroweak scale . in the cmssm @xmath24 at the gut scale . as running effects mean that @xmath25 and @xmath26 , gaugino mass unification sets @xmath27 . therefore ,
unless @xmath28 , the lightest neutralino will be dominantly bino .    in fig .
[ fig : cmssm ] we consider the @xmath29 plane of the cmssm parameter space with @xmath30 . across this parameter space
@xmath6 is bino .
this generally results in @xmath31 .
however at low @xmath19 the @xmath32 becomes light . in the light ( green ) region @xmath33 and the region
is ruled out as this would result in a charged lsp . along the edge of this region @xmath34 .
this means that at the time of freeze out there would have been a large number density of @xmath32 alongside the @xmath6 , allowing many more annihilation channels than are open for neutralinos alone .
this results in a significant decrease of the neutralino relic density . in the multicoloured strip that lies alongside the @xmath32 lsp region , this coannihilation process results in @xmath35 .
the varying colours of this strip represent the value of @xmath36 , defined by the colour legend on the right .
coannihilation occurs when the lsp and nlsp are close in mass . as a result
, the efficiency of coannihilation processes is highly sensitive to the mass difference @xmath37 .
if these masses are determined by separate parameters we would expect that a large degree of tuning would be required to fit the observed dark matter density . in the coannihilation strip of fig .
[ fig : cmssm ] the nlsp is the stau .
the stau mass is set at the gut scale by @xmath19 and the neutralino mass is set by @xmath20 . as these are independent parameters , we would expect the @xmath38 coannihilation region to exhibit considerable fine - tuning .
the colour coding of the coannihilation strip shows a tuning of @xmath39 , considerably lower than would be expected if @xmath40 and @xmath41 were unrelated .
the smallness of the tuning comes from the fact that along the coannihilation strip @xmath42 .
the running of the right handed slepton masses are strongly dependent on @xmath7 .
when @xmath19 is small , the dominant contribution to the low energy @xmath32 mass is via this running contribution from @xmath7 .
thus in this region of the cmssm @xmath40 depends strongly on @xmath20 , resulting in a correlation of the masses of the neutralino and the stau at low energy .
it is this correlation of the masses that results in the low tuning observed .
though we do not show it here , we have also investigated the other regions of the cmssm that fit @xmath15 . for large @xmath19 @xmath9 becomes small and we have a bino / higgsino lsp .
we find that such regions exhibit a tuning @xmath43 , less natural than the coannihilation strip . for large @xmath22 we can also access a region in which @xmath44 .
this allows for neutralino annihilation via the production of an on - shell pseudoscalar higgs boson .
we find such an annihilation channel to require a tuning @xmath45 . finally at large @xmath22
the running of the @xmath32 mass is no longer dominated by @xmath7 .
this breaks the correlation between @xmath41 and @xmath40 at low energies and results in the coannihilation strip that requires a tuning @xmath46 .
this bears out our expectations that coannihilation should require significant tuning to achieve in normal circumstances .
our first move away from the universality of the cmssm is to relax the universality between the generations of sfermions , setting the soft masses to be : @xmath47    this allows us to vary the 3rd family sfermion and higgs mass squareds separately from the 1st and 2nd families .
this allows us to have light 1st and 2nd family sfermions without violating lep bounds on the lightest higgs .
in such a region we will also have a normal mass hierarchy ( nmh ) in which the 1st family sfermions are the lightest and the 3rd family sfermions are the heaviest , in contrast to the inverted mass hierarchy found in the case of universal soft scalar masses .    in fig .
[ fig : scalar1 ] we display the @xmath29 plane for @xmath48 tev , @xmath49 , @xmath50 . by increasing the soft mass of the higgs bosons to @xmath51
the lep bound has moved down to @xmath52 . as before we have a coannihilation strip but as @xmath53 , the coannihilation here is with selectrons and smuons rather than the stau .    as before the coannihilation strip exhibits a tuning @xmath54 across much of its length .
this drops to @xmath55 for @xmath56 .
this decrease has two causes .
firstly , for @xmath57 we can access @xmath58 . for @xmath59 , the mass of @xmath60 and @xmath61
are almost entirely determined by the running effects from @xmath7 resulting in a strong correlation between @xmath62 and @xmath41 .
this decreases the tuning required to provide coannihilation . secondly ,
as we move to low @xmath19 and @xmath20 , we decrease the mass of the sleptons themselves , enhancing neutralino annihilation via t - channel slepton exchange . indeed at point s2 t - channel slepton exchange accounts for @xmath63 of the annihilation .
the cross - section for t - channel slepton exchange varies slowly with the mass of the exchanged slepton and is relatively insensitive to other parameters .
therefore it requires little or no tuning to achieve . by maximising annihilation via t - channel slepton exchange
we minimise the required tuning .
we now relax the constraint of universal gaugino masses . by allowing @xmath7 , @xmath8 and @xmath64 to vary
independently we can control the bino / wino mixture of @xmath6 .
@xmath64 also has a strong effect on the running of the higgs masses so by keeping @xmath64 large we can avoid the lep bound on the lightest higgs .    in fig .
[ fig : gauge1 ] we show the @xmath65 plane for @xmath66 , @xmath49 and @xmath50 .
in contrast to previous figures there are a large number of strips that agree with @xmath15 .
the strip running from g2 to g3 is the stau coannihilation strip we have seen before .
the tuning of this strip agrees with our previous findings in the case of the cmssm .
the strip that runs from g3 through g4 corresponds to a well - tempered bino / wino neutralino .
as this strip exhibits a tuning of order 30 we once again find that such `` well - tempered '' regions are less natural than coannihilation strips . at low @xmath7
there are two broken vertical lines .
these correspond to neutralino annihilation via the production of an on - shell @xmath67 or @xmath68 .
the @xmath68 resonance stretches to @xmath69 but is too thin for this plot to resolve .
this channel requires tunings @xmath70 and so can not be considered natural .
finally , the yellow region that incorporates the point g1 represents annihilation solely via t - channel slepton exchange .
this region requires a tuning @xmath71 and represents supernatural dark matter .
finally we relax both the universality of the gaugino masses and the universality between sfermion generations at the same time .
this allows us to test the robustness of our findings in each case against further non - universality .
it also allows us to study a region in which @xmath72 and the lightest neutralino is a `` maximally - tempered '' bino / wino / higgsino .    in fig .
[ fig : scalargauge2 ] we show the @xmath65 plane with @xmath66 , @xmath73 , @xmath49 and @xmath50 . at low @xmath7
we find the @xmath68 and @xmath67 resonances as before .
the new feature is the line at @xmath74 that incorporates the point sg3 . throughout this region @xmath6
is a mix of bino , wino and higgsino . at point
sg3 the wino and higgsino components are roughly equal resulting in a maximally - tempered neutralino .
this region exhibits a low tuning @xmath75 , considerably below that required for either bino / wino or bino / higgsino neutralinos .
we have studied the naturalness of the annihilation channels that allow mssm neutralinos to account for the observed dark matter density . within the four different sets of gut scale boundary conditions considered , these annihilation channels each display characteristic degrees of fine - tuning .
the largest tunings ( @xmath36 up to @xmath76 ) appear for annihilation via on - shell production of higgs bosons .
moderate tunings @xmath77 are required for `` well - tempered '' neutralinos or slepton coannihilation with uncorrelated masses .
the most natural annihilation channel is annihilation via t - channel slepton exchange .
we have also found that certain rge effects can result in surprising drops in the tuning for different channels .
this is clearest in the case of slepton coannihilation for low @xmath19 and @xmath22 . in this case
the mass of both particles is dominated by @xmath7 and the low energy masses are correlated .
this results in almost natural coannihilation , which refutes the conclusions of @xcite .
these results have recently been extended to the case of a type i string inspired model @xcite .
in such a model the input parameters differ from those of the mssm and the characteristic tunings of different annihilation channels can vary .
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in this talk we analyse the claim that supersymmetry ( susy ) naturally accounts for the observed dark matter density . in many cases , it is necessary to tune the parameters of a susy model to fit the wmap data . 
 we provide a quantitative analysis of the degree of tuning required for different annihilation channels . 
 some regions are natural , requiring no tuning at all , whereas others require tuning at the @xmath0 level .