- Email: [email protected]
Relic density calculations in mSUGRA including all coannihilations
New Astronomy Reviews 49 (2005) 159–162 www.elsevier.com/locate/newastrev
Relic density calculations in mSUGRA including all coannihilations Joakim Edsjo¨ a, Mia Schelke a, Piero Ullio b, Paolo Gondolo
c,*
a
c
Department of Physics, AlbaNova, University of Stockholm, SE-106 91 Stockholm, Sweden b SISSA, via Beirut 4, I-34014, Trieste, Italy Department of Physics, University of Utah, 115 S 1400 E #201, Salt Lake City, UT 84112, USA Available online 26 February 2005
Abstract We have made a very accurate calculation of the relic density of neutralino dark matter in the minimal supergravity framework. This calculation includes all so-called coannihilations and it uses the DarkSUSY package. In agreement with earlier analyses, we find that coannihilations have a huge effect on the density and this extends the interval of neutralino masses which are cosmologically favoured. We quantify the effect of coannihilations and the neutralino mass bounds. 2005 Elsevier B.V. All rights reserved.
In the recent years, the results of different cosmological measurements have been combined to form the concordance model. In this model, about 70% of the energy density of the Universe at present is in a dark energy component with negative pressure, around 30% is non-baryonic cold (i.e., non-relativistic at the time when structures began to form) dark matter, and only a few percent is ordinary baryonic matter. From one of the recent analyses, Tegmark et al. (2003), we have the following numbers for the three components just þ0:080 þ0:020 mentioned: XK ¼ 0:6600:097 ; XCDM h2 ¼ 0:1030:022 ; *
Corresponding author. E-mail addresses: [email protected] (J. Edsjo¨), schelke@ physto.se (M. Schelke), [email protected] (P. Ullio), paolo@ physics.utah.edu (P. Gondolo).
XB h2 ¼ 0:0238þ0:0036 0:0026 and for the total mass/energy density Xtot ¼ 1:056þ0:045 0:045 . The matter/energy density has here been given as the ratio, X, between the mean density and the critical density qc = 1.879 · 1029h2 g cm3, where h is the Hubble constant in þ0:11 units of 100 km s1 Mpc1 and h ¼ 0:550:06 in this analysis. One of the favoured candidates for the cold dark matter is the lightest neutralino which arises in supersymmetric extensions of the Standard Model of particle physics. When it is assumed that the lightest neutralino is the lightest of all the new particles predicted by supersymmetry, and when it is assumed that the so-called R-parity holds, then the lightest neutralino will be stable while the other supersymmetric particles are not.
1387-6473/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.newar.2005.01.010
160
J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
In this paper, which is a summary of our work (Edsjo¨ et al., 2003), we focus on the lightest neutralino as a cold dark matter candidate within the framework of the minimal supergravity model (mSUGRA). (Minimal supergravity was introduced by Barbieri et al., 1982; Chamseddine et al., 1982; Hall et al., 1983; Nath et al., 1983.) The effective model in mSUGRA is described by the Lagrangian of the minimal supersymmetric extension of the Standard Model (MSSM), i.e., a global N = 1 supersymmetric model, plus the soft supersymmetry breaking potential with universality of the parameters at the grand unification scale (GUT). There are then only five free parameters in mSUGRA: m1/2, m0, A0, tan b and sign(l). The parameters m1/2, m0 and A0 are the GUT unification values of the soft supersymmetry breaking fermionic mass parameters, scalar mass parameters and trilinear scalar coupling parameters, respectively. The fourth parameter, tan b, is the ratio, v2/v1, of the vacuum expectation values of the two neutral components of the SU(2) Higgs doublets in the MSSM. The sign of the Higgs superfield parameter, l, is free, while its absolute value follows from electroweak symmetry breaking. (Our convention for the sign of l is that l appears with a minus sign in the superpotential.) Minimal supergravity is also sometimes called constrained MSSM (cMSSM). In the five-dimensional parameter space of mSUGRA there are five regions, where the predicted relic density of the lightest neutralino is in the cosmologically favoured interval. These regions are called: the bulk, the funnel, the stau coannihilation tail, the focus point region and the stop coannihilation region. In the three last mentioned regions the so-called coannihilations have a large effect on the relic density of the lightest neutralino. Coannihilations are particle processes with any two supersymmetric particles in the initial state and Standard Model particles in the final state. Some examples are v01 þ v01 ! sþ þ s ; v01 þ ~s ! c þ s and ~s þ ~eþ ! s þ eþ ; where v01 is the lightest neutralino, ~s is a stau, a supersymmetric partner of the tau lepton and ~e is a selectron, a supersymmetric partner of the electron/positron. Coannihilations include pair-annihilation of the lightest neutralino. Sometimes
only the v01 –v01 annihilations are included in the calculation of the relic density of the v01 , but the importance of coannihilations was recognised by Binetruy et al. (1984), and Griest and Seckel (1991). For the calculation of the relic density of the lightest neutralino we should therefore consider all N supersymmetric particles. They were produced in thermal equilibrium in the early Universe, and we therefore have N Boltzmann equations which describe the density evolution of each of the supersymmetric particles. We have assumed that R-parity holds, and as all supersymmetric particles are R-odd, while Standard Model particles are R-even, this means that the lightest supersymmetric particle, here assumed to be the lightest neutralino, will be stable while all other supersymmetric particles will have decayed into it. Consequently, we do not have to solve a system of N coupled Boltzmann equations, but instead we can consider the sum of all N equations. This sum can be written on the following form; see e.g., Griest and Seckel (1991), or Edsjo¨ and Gondolo (1997): dn ¼ 3Hn hreff viðn2 n2eq Þ dt
ð1Þ
with hreff vi ¼
N X N X i¼1
j¼1
hrij vij i
eq neq i nj ; neq neq
ð2Þ
where H is the Hubble parameter, n is the number P density and n ¼ nðv01 Þ ¼ Ni¼1 ni . The index ‘‘eq’’ denotes thermal equlibrium. Finally, Ærijvijæ is the thermal average of the cross-section times relative velocity for the coannihilation process vi + vj ! X + Y, where vi,j denotes the supersymmetric particles and X and Y are Standard Model particles. We see that a given coannihilation process can affect the relic density of the lightest neutralino if it gives a large contribution to Ærijvijæ. There is an inverse correlation between the effect of a given coannihilation and the mass splitting between the lightest neutralino and the supersymmetric particles in the initial state of the coannihilation process. We will show a numerical example of this below, but it can also be inferred from the equation above, as we can approximate
J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
state were introduced in DarkSUSY by Edsjo¨ et al. (2003). All final states and all exchange channels are included and we make the full numerical calculation of the cross-sections. In the work just mentioned, we studied how coannihilations affect the relic density of the lightest neutralino in mSUGRA. The conclusions we found agreed with those of previous analyses by other groups (a list of references can be found in the work on which we report here), but with DarkSUSY we had a higher degree of accuracy in the numerical results. We found that an accuracy on 1% in the density calculations required that we included the coannihilations of all supersymmetric particles with a mass below 1:5mðv01 Þ. Fig. 1 shows one of the figures from our previous work (Edsjo¨ et al., 2003). This figure is from the stau coannihilation tail. As the name indicates, the most dominant coannihilations in this region are those with stauÕs in the initial state. This is because the lightest stau is the next-to-lightest supersymmetric particle in this region. In the left panel of Fig. 1, we see the effect of coannihilations as a function of the neutralino mass. This effect is
3000% 2
Ωh = 0.1
0.15
0.2
mass splitting
∆Ω / Ω
eq the ratio neq by expð½mðv01 Þ mðvi Þ=T Þ, where i =n T is the temperature. (We just use this form of the Boltzmann suppression for illustrative purpose, while we do not use this approximation in the full calculation.) Even though, the other supersymmetric particles will always be heavier than the lightest neutralino they might be more important for Æreffvæ than the v01 –v01 annihilations are. This is because the neutralinos only interact through the weak interaction while many of the other supersymmetric particles have electric charge and some of them even colour. Coannihilations with neutralinos and charginos in the initial state were included in the DarkSUSY package by Edsjo¨ and Gondolo (1997). DarkSUSY (Gondolo et al., 2002) is a publicly-available computer package for neutralino relic density and neutralino signal calculations. The Boltzmann equation is solved numerical and very accurately in DarkSUSY. Coannihilations with two sfermions (the supersymmetric partners of Standard Model fermions) in the initial state and with one sfermion and one neutralino or chargino (supersymmetric partners of gauge and Higgs bosons) in the initial
161
0.3
1000%
30%
tan β = 30, A0 = 0, small m0 µ>0
10%
300% 3%
100%
30%
M χ upper limit if no coann. incl. 2 and Ωh less than:
1%
2
Ωh = 0.3 0.2
0.1
10%
3%
0.15
3‰
tan β = 30, A0 = 0, small m0
0.15
0.2
µ>0
0.3
0.1
1‰
1% 0
100
200
300
400
500
600
700
800
M χ [ GeV ]
0
100
200
300
400
500
600
700
800
M χ [ GeV ]
Fig. 1. The figure shows isolevel curves of Xvh2 in the stau coannihilation tail (i.e., small m0). Three of the free mSUGRA parameters have been fixed: tan b = 30, l > 0 and A0 = 0. In the left-hand panel, we show the importance, DX/X, of including all coannihilations in the density calculation. This is shown as a function of the mass of the lightest neutralino. In the right-hand panel, we show the mass splitting between the lightest neutralino and the lightest stau as a function of the neutralino mass. We also indicate by arrows, where the upper limit on the mass would be if the density was calculated from the neutralino–neutralino annihilations alone. The figure is taken from Edsjo¨ et al. (2003).
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J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
shown as a relative difference DX/X ” (Xv, no coann Xv, coann)/Xv, coann, where v in this case denotes the lightest neutralino and ‘‘no coann’’ means that only v01 –v01 annihilations are included while ‘‘coann’’ means that all coannihilations within the 50% mass-cut have been included. The curves have been obtained by varying the m0 and m1/2 parameters and keeping the three other free mSUGRA parameters fixed. We show a curve for four different values of Xvh2 ” Xv, coannh2. In the bulk, to which the tail is connected at low masses, the coannihilations just have a small correctional effect on the density. On the other hand, when we move into the stau coannihilation tail at higher neutralino masses, then the coannihilations will completely control the size of the relic neutralino density. The density can be off by as much as 1000% if only the v01 –v01 annihilations are included in the density calculation. The plot to the right in Fig. 1 shows the same Xvh2 isolevel curves as in the left plot, but here they are plotted as functions of the mass of the lightest neutralino and the relative mass splitting between the lightest stau and the lightest neutralino, ðm~s mv0 Þ=mv0 . We see that each iso1 1 level curve reaches an upper bound in the neutralino mass in the limit where the lightest stau becomes degenerate with the neutralino. In the left corner of the figure, we have inserted for comparison the upper neutralino mass bound in the bulk/ tail for the case where only v01 –v01 annihilations are included. (These mass bounds are not shown as functions of the mass splitting.) These mass bounds are much lower than those obtained by including coannihilations. Finally, let us compare the left and the right panel in Fig. 1. We see that there is a strong correlation between the error in the density and the mass splitting. When the mass splitting between the lightest neutralino and the next-to-lightest supersymmetric particle is very small then there is a very large difference between the neutralino density calculated from neutra-
lino–neutralino annihilations and the true density calculated by including all coannihilations. The conclusions that we found for the stop coannihilation region and the high mass end of the focus point region were similar to those we found above for the stau coannihilation tail: the predictions for the relic density of the lightest neutralino can be completely wrong if coannihilations are not included. A given coannihilation has the largest effect when the supersymmetric particles in the initial state become almost degenerate with the lightest neutralino. The range of neutralino masses with cosmologically interesting density is extended when coannihilations are included in the calculations. In the stau coannihilation tail as well as in the focus point region, the upper mass bound is increased while the lower mass limit on the lightest neutralino is decreased in the stop coannihilation region. The high accuracy of DarkSUSY enables us to find the exact values of these mass bounds.
References Barbieri, R., Ferrara, S., Savoy, C.A., 1982. Phys. Lett. B119, 343. Binetruy, P., Girardi, G., Salati, P., 1984. Nucl. Phys. B237, 285. Chamseddine, A.H., Arnowitt, R., Nath, P., 1982. Phys. Rev. Lett. 49, 970. Edsjo¨, J., Gondolo, P., 1997. Phys. Rev. 56, 1879. Edsjo¨, J., Schelke, M., Ullio, P., Gondolo, P., 2003. JCAP 0304, 001, [hep-ph/0301106]. Gondolo, P., Edsjo¨, J., Ullio, P., Bergstro¨m, L., Schelke, M., Baltz, E.A., 2002. These proceedings and proceedings of idm2002, York, England, September. Available from:; . Griest, K., Seckel, D., 1991. Phys. Rev. D43, 3191. Hall, L.J., Lykken, J., Weinberg, S., 1983. Phys. Rev. D27, 2359. Nath, P., Arnowitt, R., Chamseddine, A.H., 1983. Nucl. Phys. B227, 121. Tegmark, M., et al., 2003. Phys. Rev. D. 69, 103501.
Relic density calculations in mSUGRA including all coannihilations Joakim Edsjo¨ a, Mia Schelke a, Piero Ullio b, Paolo Gondolo
c,*
a
c
Department of Physics, AlbaNova, University of Stockholm, SE-106 91 Stockholm, Sweden b SISSA, via Beirut 4, I-34014, Trieste, Italy Department of Physics, University of Utah, 115 S 1400 E #201, Salt Lake City, UT 84112, USA Available online 26 February 2005
Abstract We have made a very accurate calculation of the relic density of neutralino dark matter in the minimal supergravity framework. This calculation includes all so-called coannihilations and it uses the DarkSUSY package. In agreement with earlier analyses, we find that coannihilations have a huge effect on the density and this extends the interval of neutralino masses which are cosmologically favoured. We quantify the effect of coannihilations and the neutralino mass bounds. 2005 Elsevier B.V. All rights reserved.
In the recent years, the results of different cosmological measurements have been combined to form the concordance model. In this model, about 70% of the energy density of the Universe at present is in a dark energy component with negative pressure, around 30% is non-baryonic cold (i.e., non-relativistic at the time when structures began to form) dark matter, and only a few percent is ordinary baryonic matter. From one of the recent analyses, Tegmark et al. (2003), we have the following numbers for the three components just þ0:080 þ0:020 mentioned: XK ¼ 0:6600:097 ; XCDM h2 ¼ 0:1030:022 ; *
Corresponding author. E-mail addresses: [email protected] (J. Edsjo¨), schelke@ physto.se (M. Schelke), [email protected] (P. Ullio), paolo@ physics.utah.edu (P. Gondolo).
XB h2 ¼ 0:0238þ0:0036 0:0026 and for the total mass/energy density Xtot ¼ 1:056þ0:045 0:045 . The matter/energy density has here been given as the ratio, X, between the mean density and the critical density qc = 1.879 · 1029h2 g cm3, where h is the Hubble constant in þ0:11 units of 100 km s1 Mpc1 and h ¼ 0:550:06 in this analysis. One of the favoured candidates for the cold dark matter is the lightest neutralino which arises in supersymmetric extensions of the Standard Model of particle physics. When it is assumed that the lightest neutralino is the lightest of all the new particles predicted by supersymmetry, and when it is assumed that the so-called R-parity holds, then the lightest neutralino will be stable while the other supersymmetric particles are not.
1387-6473/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.newar.2005.01.010
160
J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
In this paper, which is a summary of our work (Edsjo¨ et al., 2003), we focus on the lightest neutralino as a cold dark matter candidate within the framework of the minimal supergravity model (mSUGRA). (Minimal supergravity was introduced by Barbieri et al., 1982; Chamseddine et al., 1982; Hall et al., 1983; Nath et al., 1983.) The effective model in mSUGRA is described by the Lagrangian of the minimal supersymmetric extension of the Standard Model (MSSM), i.e., a global N = 1 supersymmetric model, plus the soft supersymmetry breaking potential with universality of the parameters at the grand unification scale (GUT). There are then only five free parameters in mSUGRA: m1/2, m0, A0, tan b and sign(l). The parameters m1/2, m0 and A0 are the GUT unification values of the soft supersymmetry breaking fermionic mass parameters, scalar mass parameters and trilinear scalar coupling parameters, respectively. The fourth parameter, tan b, is the ratio, v2/v1, of the vacuum expectation values of the two neutral components of the SU(2) Higgs doublets in the MSSM. The sign of the Higgs superfield parameter, l, is free, while its absolute value follows from electroweak symmetry breaking. (Our convention for the sign of l is that l appears with a minus sign in the superpotential.) Minimal supergravity is also sometimes called constrained MSSM (cMSSM). In the five-dimensional parameter space of mSUGRA there are five regions, where the predicted relic density of the lightest neutralino is in the cosmologically favoured interval. These regions are called: the bulk, the funnel, the stau coannihilation tail, the focus point region and the stop coannihilation region. In the three last mentioned regions the so-called coannihilations have a large effect on the relic density of the lightest neutralino. Coannihilations are particle processes with any two supersymmetric particles in the initial state and Standard Model particles in the final state. Some examples are v01 þ v01 ! sþ þ s ; v01 þ ~s ! c þ s and ~s þ ~eþ ! s þ eþ ; where v01 is the lightest neutralino, ~s is a stau, a supersymmetric partner of the tau lepton and ~e is a selectron, a supersymmetric partner of the electron/positron. Coannihilations include pair-annihilation of the lightest neutralino. Sometimes
only the v01 –v01 annihilations are included in the calculation of the relic density of the v01 , but the importance of coannihilations was recognised by Binetruy et al. (1984), and Griest and Seckel (1991). For the calculation of the relic density of the lightest neutralino we should therefore consider all N supersymmetric particles. They were produced in thermal equilibrium in the early Universe, and we therefore have N Boltzmann equations which describe the density evolution of each of the supersymmetric particles. We have assumed that R-parity holds, and as all supersymmetric particles are R-odd, while Standard Model particles are R-even, this means that the lightest supersymmetric particle, here assumed to be the lightest neutralino, will be stable while all other supersymmetric particles will have decayed into it. Consequently, we do not have to solve a system of N coupled Boltzmann equations, but instead we can consider the sum of all N equations. This sum can be written on the following form; see e.g., Griest and Seckel (1991), or Edsjo¨ and Gondolo (1997): dn ¼ 3Hn hreff viðn2 n2eq Þ dt
ð1Þ
with hreff vi ¼
N X N X i¼1
j¼1
hrij vij i
eq neq i nj ; neq neq
ð2Þ
where H is the Hubble parameter, n is the number P density and n ¼ nðv01 Þ ¼ Ni¼1 ni . The index ‘‘eq’’ denotes thermal equlibrium. Finally, Ærijvijæ is the thermal average of the cross-section times relative velocity for the coannihilation process vi + vj ! X + Y, where vi,j denotes the supersymmetric particles and X and Y are Standard Model particles. We see that a given coannihilation process can affect the relic density of the lightest neutralino if it gives a large contribution to Ærijvijæ. There is an inverse correlation between the effect of a given coannihilation and the mass splitting between the lightest neutralino and the supersymmetric particles in the initial state of the coannihilation process. We will show a numerical example of this below, but it can also be inferred from the equation above, as we can approximate
J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
state were introduced in DarkSUSY by Edsjo¨ et al. (2003). All final states and all exchange channels are included and we make the full numerical calculation of the cross-sections. In the work just mentioned, we studied how coannihilations affect the relic density of the lightest neutralino in mSUGRA. The conclusions we found agreed with those of previous analyses by other groups (a list of references can be found in the work on which we report here), but with DarkSUSY we had a higher degree of accuracy in the numerical results. We found that an accuracy on 1% in the density calculations required that we included the coannihilations of all supersymmetric particles with a mass below 1:5mðv01 Þ. Fig. 1 shows one of the figures from our previous work (Edsjo¨ et al., 2003). This figure is from the stau coannihilation tail. As the name indicates, the most dominant coannihilations in this region are those with stauÕs in the initial state. This is because the lightest stau is the next-to-lightest supersymmetric particle in this region. In the left panel of Fig. 1, we see the effect of coannihilations as a function of the neutralino mass. This effect is
3000% 2
Ωh = 0.1
0.15
0.2
mass splitting
∆Ω / Ω
eq the ratio neq by expð½mðv01 Þ mðvi Þ=T Þ, where i =n T is the temperature. (We just use this form of the Boltzmann suppression for illustrative purpose, while we do not use this approximation in the full calculation.) Even though, the other supersymmetric particles will always be heavier than the lightest neutralino they might be more important for Æreffvæ than the v01 –v01 annihilations are. This is because the neutralinos only interact through the weak interaction while many of the other supersymmetric particles have electric charge and some of them even colour. Coannihilations with neutralinos and charginos in the initial state were included in the DarkSUSY package by Edsjo¨ and Gondolo (1997). DarkSUSY (Gondolo et al., 2002) is a publicly-available computer package for neutralino relic density and neutralino signal calculations. The Boltzmann equation is solved numerical and very accurately in DarkSUSY. Coannihilations with two sfermions (the supersymmetric partners of Standard Model fermions) in the initial state and with one sfermion and one neutralino or chargino (supersymmetric partners of gauge and Higgs bosons) in the initial
161
0.3
1000%
30%
tan β = 30, A0 = 0, small m0 µ>0
10%
300% 3%
100%
30%
M χ upper limit if no coann. incl. 2 and Ωh less than:
1%
2
Ωh = 0.3 0.2
0.1
10%
3%
0.15
3‰
tan β = 30, A0 = 0, small m0
0.15
0.2
µ>0
0.3
0.1
1‰
1% 0
100
200
300
400
500
600
700
800
M χ [ GeV ]
0
100
200
300
400
500
600
700
800
M χ [ GeV ]
Fig. 1. The figure shows isolevel curves of Xvh2 in the stau coannihilation tail (i.e., small m0). Three of the free mSUGRA parameters have been fixed: tan b = 30, l > 0 and A0 = 0. In the left-hand panel, we show the importance, DX/X, of including all coannihilations in the density calculation. This is shown as a function of the mass of the lightest neutralino. In the right-hand panel, we show the mass splitting between the lightest neutralino and the lightest stau as a function of the neutralino mass. We also indicate by arrows, where the upper limit on the mass would be if the density was calculated from the neutralino–neutralino annihilations alone. The figure is taken from Edsjo¨ et al. (2003).
162
J. Edsjo¨ et al. / New Astronomy Reviews 49 (2005) 159–162
shown as a relative difference DX/X ” (Xv, no coann Xv, coann)/Xv, coann, where v in this case denotes the lightest neutralino and ‘‘no coann’’ means that only v01 –v01 annihilations are included while ‘‘coann’’ means that all coannihilations within the 50% mass-cut have been included. The curves have been obtained by varying the m0 and m1/2 parameters and keeping the three other free mSUGRA parameters fixed. We show a curve for four different values of Xvh2 ” Xv, coannh2. In the bulk, to which the tail is connected at low masses, the coannihilations just have a small correctional effect on the density. On the other hand, when we move into the stau coannihilation tail at higher neutralino masses, then the coannihilations will completely control the size of the relic neutralino density. The density can be off by as much as 1000% if only the v01 –v01 annihilations are included in the density calculation. The plot to the right in Fig. 1 shows the same Xvh2 isolevel curves as in the left plot, but here they are plotted as functions of the mass of the lightest neutralino and the relative mass splitting between the lightest stau and the lightest neutralino, ðm~s mv0 Þ=mv0 . We see that each iso1 1 level curve reaches an upper bound in the neutralino mass in the limit where the lightest stau becomes degenerate with the neutralino. In the left corner of the figure, we have inserted for comparison the upper neutralino mass bound in the bulk/ tail for the case where only v01 –v01 annihilations are included. (These mass bounds are not shown as functions of the mass splitting.) These mass bounds are much lower than those obtained by including coannihilations. Finally, let us compare the left and the right panel in Fig. 1. We see that there is a strong correlation between the error in the density and the mass splitting. When the mass splitting between the lightest neutralino and the next-to-lightest supersymmetric particle is very small then there is a very large difference between the neutralino density calculated from neutra-
lino–neutralino annihilations and the true density calculated by including all coannihilations. The conclusions that we found for the stop coannihilation region and the high mass end of the focus point region were similar to those we found above for the stau coannihilation tail: the predictions for the relic density of the lightest neutralino can be completely wrong if coannihilations are not included. A given coannihilation has the largest effect when the supersymmetric particles in the initial state become almost degenerate with the lightest neutralino. The range of neutralino masses with cosmologically interesting density is extended when coannihilations are included in the calculations. In the stau coannihilation tail as well as in the focus point region, the upper mass bound is increased while the lower mass limit on the lightest neutralino is decreased in the stop coannihilation region. The high accuracy of DarkSUSY enables us to find the exact values of these mass bounds.
References Barbieri, R., Ferrara, S., Savoy, C.A., 1982. Phys. Lett. B119, 343. Binetruy, P., Girardi, G., Salati, P., 1984. Nucl. Phys. B237, 285. Chamseddine, A.H., Arnowitt, R., Nath, P., 1982. Phys. Rev. Lett. 49, 970. Edsjo¨, J., Gondolo, P., 1997. Phys. Rev. 56, 1879. Edsjo¨, J., Schelke, M., Ullio, P., Gondolo, P., 2003. JCAP 0304, 001, [hep-ph/0301106]. Gondolo, P., Edsjo¨, J., Ullio, P., Bergstro¨m, L., Schelke, M., Baltz, E.A., 2002. These proceedings and proceedings of idm2002, York, England, September. Available from: