and is related to the strange quark scalar density in the nucleon.The largest source of uncertainty in fro stems from the determination of this quantity,for which the current data implies EN =(64+8)MeV [10],which translates into a variation of a factor 4 in frs.Notice that in general the WIMP interaction with strange quarks would be the leading contribution to the SI cross section,due to its larger Yukawa coupling.In this case,oo is roughly proportional to frs2 and the above uncertainty in the strange quark content leads to a variation of more than one order of magnitude in the resulting SI cross section [7;9]). Similarly,for the SD cross section the uncertainties in the strange spin contribution As are the dominant contribution to the error in 0o.However,in the case of the neutralino, this can imply a correction of as much as a factor 2 in the resulting cross section [9],being therefore much smaller than the above uncertainty for the SI cross section.It should be emphasized,however,that uncertainties in the determination of the spin form factors S(g) would also affect the theoretical predictions for the dark matter detection rate. 3 Astrophysics input 3.1 Local DM density The differential event rate is directly proportional to the local WIMP density,po =p(r= Ro)where Ro =(8.0+0.5)kpc [11]is the solar radius.Any observational uncertainty in Po therefore translates directly into in an uncertainty in the event rate and the inferred constraints on,or measurements of,the scattering cross-sections. Exclusion limits are traditionally calculated assuming a canonical local WIMP density, Po =0.3GeVcm-3.The local WIMP density is calculated by applying observational con- straints (including measurements of the rotation curve)to models of the Milky Way and the values obtained can vary by a factor or order 2 depending on the models used [12-15]. A recent study [16],using spherical halo models with a cusp (p o r(r)-as r-0)finds p0=(0.30±0.05)GeV cm-3 3.2 Speed distribution The standard halo model,conventionally used in calculations of exclusion limits and signals, has an isotropic,Gaussian velocity distribution (often referred to as Maxwellian) 1 f()= v/2 -exp √2m石 2a2 (25) The speed dispersion is related to the local circular speed by a =v3/2vc and ve=(220+ 20)kms-1 [17](see Sec.3.3)so that o270kms-1.This velocity distribution corresponds to an isotropic singular isothermal sphere with density profile p(r)r-2.The isothermal sphere is simple,and not unreasonable as a first approximation,however it is unlikely to be an accurate model of the actual density and velocity distribution of the Milky Way.Observations and numerical simulations(see chapter 1)indicate that dark matter halos do not have a 1/r2 density profile and are (to some extent at least)triaxial and anisotropic. If the velocity distribution is isotropic there is a one to one relation between f(v)and the the spherically symmetric density profile given by Eddington's formula [18],see Refs.[19;20]. In general the steady state phase-space distribution of a collection of collisionless particles 6and is related to the strange quark scalar density in the nucleon. The largest source of uncertainty in f p T q stems from the determination of this quantity, for which the current data implies ΣπN = (64 ± 8) MeV [10], which translates into a variation of a factor 4 in fT s. Notice that in general the WIMP interaction with strange quarks would be the leading contribution to the SI cross section, due to its larger Yukawa coupling. In this case, σ0 is roughly proportional to fT s 2 and the above uncertainty in the strange quark content leads to a variation of more than one order of magnitude in the resulting SI cross section [7; 9]). Similarly, for the SD cross section the uncertainties in the strange spin contribution ∆s are the dominant contribution to the error in σ0. However, in the case of the neutralino, this can imply a correction of as much as a factor 2 in the resulting cross section [9], being therefore much smaller than the above uncertainty for the SI cross section. It should be emphasized, however, that uncertainties in the determination of the spin form factors S(q) would also affect the theoretical predictions for the dark matter detection rate. 3 Astrophysics input 3.1 Local DM density The differential event rate is directly proportional to the local WIMP density, ρ0 ≡ ρ(r = R0) where R0 = (8.0 ± 0.5) kpc [11] is the solar radius. Any observational uncertainty in ρ0 therefore translates directly into in an uncertainty in the event rate and the inferred constraints on, or measurements of, the scattering cross-sections. Exclusion limits are traditionally calculated assuming a canonical local WIMP density, ρ0 = 0.3 GeV cm−3 . The local WIMP density is calculated by applying observational con￾straints (including measurements of the rotation curve) to models of the Milky Way and the values obtained can vary by a factor or order 2 depending on the models used [12–15]. A recent study [16], using spherical halo models with a cusp (ρ ∝ r(r) −α as r → 0) finds ρ0 = (0.30 ± 0.05) GeV cm−3 . 3.2 Speed distribution The standard halo model, conventionally used in calculations of exclusion limits and signals, has an isotropic, Gaussian velocity distribution (often referred to as Maxwellian) f(v) = 1 √ 2πσ exp − |v| 2 2σ 2 ! . (25) The speed dispersion is related to the local circular speed by σ = p 3/2vc and vc = (220 ± 20) km s−1 [17] (see Sec.3.3) so that σ ≈ 270 km s−1 . This velocity distribution corresponds to an isotropic singular isothermal sphere with density profile ρ(r) ∝ r −2 . The isothermal sphere is simple, and not unreasonable as a first approximation, however it is unlikely to be an accurate model of the actual density and velocity distribution of the Milky Way. Observations and numerical simulations (see chapter 1) indicate that dark matter halos do not have a 1/r2 density profile and are (to some extent at least) triaxial and anisotropic. If the velocity distribution is isotropic there is a one to one relation between f(v) and the the spherically symmetric density profile given by Eddington’s formula [18], see Refs. [19; 20]. In general the steady state phase-space distribution of a collection of collisionless particles 6