Higgsino and Wino Dark Matter from Q-Ball Decay in Affleck–Dine

17 January 2002

Physics Letters B 525 (2002) 143–149 www.elsevier.com/locate/npe

Higgsino and wino dark matter from Q-ball decay in Afﬂeck–Dine baryogenesis

Masaaki Fujii, K. Hamaguchi

Department of Physics, University of Tokyo, Tokyo 113-0033, Japan Received 11 October 2001; received in revised form 17 November 2001; accepted 20 November 2001 Editor: T. Yanagida

Abstract

We claim that the higgsino-like and wino-like neutralinos can be good dark matter candidates if they are produced by the late time decay of Q-ball, which is generally formed in Afﬂeck–Dine baryogenesis. The late time decays of the Q-balls into these LSP’s and subsequent pair annihilations of the LSP’s naturally lead to the desired mass density of dark matter. Furthermore, these dark matter can be much more easily detected by the dark-matter search experiments than the standard bino-like dark matter.  2002 Elsevier Science B.V. All rights reserved.

Supersymmetry (SUSY) has been widely consid- been much less interests in other candidates, such as ered as an attractive framework for physics beyond the the higgsino-like and wino-like neutralino, since their standard model. It explains the stability of the elec- thermal relic densities are generally too low to be a troweak scale against quadratically divergent radiative significant component of dark matter [1]. corrections. Furthermore, particle contents of the min- In this Letter, we claim that the higgsino-like and imal SUSY standard model (MSSM) lead to a beauti- wino-like neutralinos are good dark matter candidates ful unification of the three gauge coupling constants of in spite of their large annihilation cross sections, if the the standard model. origin of the observed baryon asymmetry lies in the One of the remarkable features in the MSSM is the Affleck–Dine (AD) baryogenesis [2,3]. In AD mech- existence of an ideal dark matter candidate, that is, the anism, a linear combination of squark and/or slepton lightest SUSY particle (LSP). 1 The most extensively fields (φ field) has a large expectation value along studied LSP as a dark matter candidate is the bino-like a flat direction during an inflationary stage, and its neutralino, since its thermal relic abundance naturally subsequent coherent oscillation creates a large net provides a desired amount of the present mass density baryon asymmetry. The coherent oscillation of the φ of the dark matter. On the other hand, there have field is generally unstable with spatial perturbation and it fragments [4–6] into non-topological solitons [7], Q-balls. It has been, in fact, shown in detailed numeri- E-mail address: [email protected] cal calculations [8] that almost all of the initial baryon (K. Hamaguchi). φ 1 asymmetry carried by the field is absorbed into the We assume that the R-parity is exact and hence the LSP is Q-balls. absolutely stable.

The Q-ball has a long lifetime 2 and its decay tem- tion later in the case of Q-ball decay.) Then, we ob- perature is likely to be well below the freeze-out tem- tain 4 perature of the LSP, which leads to the non-thermal 3 dY 2 ∗ ∗ production of the dark matter [6]. We show that χ = 8π g + T dg 2 1 σv MplYχ , (2) in the case of the higgsino-like or wino-like LSP dT 45 3g∗ dT the late-time Q-ball decay and subsequent pair an- = × 18 nihilations of the LSP’s naturally give rise to a de- where Mpl 2.4 10 GeV is the reduced Planck sired dark-matter energy density. It is very encour- scale. This equation can be analytically solved by aging that such candidates are much more easily de- using approximations g∗(T ) g∗(Td ) const and tected than the standard bino-like neutralino. As we σv (T ) const, which results in  will see later, the detection rate is in fact more than ten times larger compared with the case of bino-like  1 Yχ (T ) LSP [13]. Yχ (Td ) Let us first estimate the present energy density of  −1 the non-thermally produced LSP. Suppose that there 2 8π g∗(Td )  is a non-thermal production of LSP at temperature + σvM (Td − T) . 45 pl T = Td ,whereTd is below the freeze-out temperature Tf of the LSP. (Tf is typically given by Tf ∼ (3) mχ /20, where mχ is the mass of the LSP.) The sub- Therefore, for sufficiently large initial abundance sequent evolution of the number density nχ of the Yχ (Td ), the final abundance Yχ0 for T Td is given LSP is described by the following Boltzmann equa- by tion:   −1 2 2 ∗ n˙χ + 3Hnχ =−σvn , (1)  8π g (Td )  χ Yχ σvM Td . (4) 0 45 pl where the overdot denotes a derivative with time, H is the Hubble parameter of the expanding uni- Notice that the final abundance Yχ0 is determined only verse, and σv is the thermally averaged annihila- by the temperature Td and the cross section σv,in- tion cross section of the LSP. Here, we have neglected dependently of the initial value Yχ (Td ) as long as the effect of the pair production of LSP’s, which is Y (T ) Y . From the above formula, we obtain − χ d χ0 suppressed by a Boltzmann factor exp( mχ /T) for the relic mass density of the LSP in the present uni- Tparticles, and form a The decay rate of a single Q-ball is given by [14]: Gaussian distribution around the decaying Q-ball. The central region of this distribution has a radius r¯ dQ ω3A √ Γ ≡− , (7) ντ ,whereν−1 G2m T 4 [6]. (G is the Fermi Q 2 d F χ d F dt 192π coupling constant.) Meanwhile, we can see that the where ω mφ, mφ is the soft scalar mass of the φ number of Q-balls within this radius is much larger field, and A is the surface area of the√Q-ball. (The ra- ¯3 ∼ 10 × − than one, roughly given by (4π/3) r nQ 10 | |−1/2 1 − − − dius of the Q-ball is given by RQ 2 K mφ , (T /1GeV) 6(Q /1020) 1(m /100 GeV) 3/2.Hen- | | d i χ where K 0.01–0.1 [5,6,15].) Then, we obtain the ce, the assumption of the uniform distribution is ≡ lifetime of the Q-ball τd Qi/ΓQ, or equivalently the justified. decay temperature Td of the Q-ball: We should also note that the energy density of the 1/2 m 1/2 20 1/2 Q-balls ρQ is much smaller than that of the radiation 0.01 φ 10 Td 2GeV . (8) ρrad for T Td : |K| 1TeV Qi m n Q Actually, the formed Q-ball has a large charge and ρQ φ Q i typically decays at Td 1 GeV [6], in particular when ρrad ρrad the φ field is lifted by a non-renormalizable dimension m = 3 φ nB six operator in the superpotential with a cutoff scale f 4T s 0 ∼ Mpl. Hereafter, we will take Td 10 MeV–1 GeV. − mφ 10 MeV From above equations, the production rate of the LSP ∼ 10 5f × 1, (11) per time per volume is given by 1TeV T fn where we have used the fact that the energy of the Q- = B − Nχ ΓQnQ Nχ ΓQ θ(Qi ΓQt) ball per charge is roughly given by mφ . Therefore, no Qi significant entropy production takes place during the θ(τd − t) = N fn × , (9) Q-ball decay. χ B τ d We have numerically solved the Boltzmann equa- where Nχ is the number of LSP’s produced per baryon tion (10) for higgsino-like and wino-like neutralino number, which is at least 3. Thus, the evolution of the and calculated the relic abundance Ωχ ,wherewe −10 number density of the LSP is obtained by solving the have taken Nχ = 3, f = 1, (nB/s)0 = 0.7 × 10 , following equation: and h = 0.7. In our calculation, we included final + − n θ(τ − t) states; W W , ZZ, tt¯, h0A0, H 0A0, Zh0, ZH0,and ˙ + = B × d − 2 ± ∓ nχ 3Hnχ Nχ f s σv nχ , W H . 5 (We took the cross sections from Ref. [16].) s 0 τd (10) where we have normalized the baryon number density 5 Here, we included only s-wave annihilation cross sections, by the entropy density and subscript 0 denotes the which is a reasonable approximation for higgsino-like and wino-like present value. neutralino and for T mχ . 146 M. Fujii, K. Hamaguchi / Physics Letters B 525 (2002) 143–149

Fig. 1. The contour plots of the relic abundance Ωχ of the Fig. 2. The contour plots of the relic abundance Ωχ of the higgsino-like neutralino LSP in the mχ –Td plane. We have taken higgsino-like neutralino LSP in the mχ –Td plane. The parameters h = 0.7, M1 = (3/2)µ, M2 = 3µ,tanβ = 5, m 0 = 300 GeV, A are the same as Fig. 1 except m = 330 GeV. The three shaded a = 0, and m0 = 1 TeV. The three shaded regions correspond to 0 regions correspond to the range of Ωχ < 0.1, 0.1 <Ωχ < 1, the range of Ωχ < 0.1, 0.1 <Ωχ < 1, 1 <Ωχ ,fromthetoptothe bottom, respectively. 1 <Ωχ , from the top to the bottom, respectively.

The results are shown in Figs. 1–3 in the mχ –Td plane. Figs. 1 and 2 correspond to the higgsino-like LSP, where we took M1 = (3/2)µ and M2 = 3µ, while Fig. 3 corresponds to the wino-like LSP, where we took M1 = (3/2)µ and M2 = (1/2)µ.(M1 and M2 are the soft gaugino masses for the SU(2)L and U(1)Y gauge groups, respectively, and µ denotes the SUSY contribution to the Higgs-boson (higgsino) masses.) = = As for the other parameters, we used tan β 5, mA0 300 GeV and all trilinear scalar couplings a = 0, in all ﬁgures. For sfermions we assumed universal = = soft masses mfi˜ m0.Weusedm0 1TeVin Figs.1and3,andm0 = 330GeVinFig.2.We used the g∗(T ) given in Ref. [17] for 100 MeV T 1 GeV, adopting the QCD phase transition near 150 MeV. Fig. 3. The contour plots of the relic abundance Ω of the wino-like It is found from these ﬁgures that both of the the χ neutralino LSP in the mχ –Td plane. We took M1 = (3/2)µ and mass densities of the higgsino-like and wino-like LSP M2 = (1/2)µ. Other parameters are the same as Fig. 1. The three in fact fall in the desired region Ωχ 0.1–1 in a shaded regions correspond to the range of Ωχ < 0.1, 0.1 <Ωχ < 1, wide range of LSP mass, for Q-ball decay temper- 1 <Ωχ , from the top to the bottom, respectively. M. Fujii, K. Hamaguchi / Physics Letters B 525 (2002) 143–149 147

6 atures Td 10 MeV–1 GeV. (Wehavealsocon- ﬁrmed that these results are well reproduced by the analytic calculation given in Eq. (5).) It is remarkable that the higgsino-like and the wino-like LSP’s can be excellent dark matter candidates even in the relatively small mass region, where the thermal production would give rise to too small relic abundance. (See discussion below Eq. (5).) As we will see later, these regions are also advantageous for dark matter search experiments. Here, we should note that the Q-ball decay would produce too large amount of dark matter density if there were no pair annihilation of the LSP’s. This can be easily seen by integrating the Eq. (10) with σv=0: N m = χ χ Ωχ no ann 3 f ΩB 3 mn 2 Nχ mχ 0.7 2.6 f × , 3 100 GeV h Fig. 4. Contours of the detection rate for the higgsino-like dark 76 (12) matter in Ge detector. The four shaded regions correspond to the ranges of the detection rate R>0.1, 0.1 R>0.03, −1 where mn 1 GeV is the nucleon mass, and we 0.03 R>0.01, 0.01 R(events (kg day) ) from left to right, have used the bound on the present baryon density respectively. The parameters used in this calculation are the same as 2 in Fig. 1 except tan β. ΩBh 0.004 [18]. Therefore, in the case of the bino-like LSP, the Q-ball formation is a serious ob- halo stacle for the AD baryogenesis. (Detailed discussion where ρχ and vχ is the mass density and the on this problem and possible solutions are given in average speed of the neutralinos in the galactic halo, Ref. [11].) respectively. MN is the mass of the target nucleus, and As we have seen, higgsino-like and wino-like LSP Fξ is the nuclear form factor. By using typical values, are promising candidates for cold dark matter if the this scattering rate is written as AD baryogenesis is responsible for generating the ob- σFξ served baryon asymmetry in the present universe. En- R = 1.8 × 1011 GeV4 mχ MN couragingly enough, if this is the case, the direct de- tecting possibility for these dark matter is enormously ρhalo v events × χ χ . enhanced compared with the case of bino-like dark 0.3 GeV cm−3 320 km s−1 kgday matter [13,19]. The relevant quantity for direct search experiments (14) is the elastic neutralino–nucleon scattering rate [20]: The list of relevant coupling constants are given in Ref. [20]. For the numerical calculations in this work, halo we have neglected the squark and Z-boson exchange σρχ vχ Fξ R = , (13) contributions, since they are subdominant components m M χ N in most of the parameter space [13], and we have taken Fξ = 1 for simplicity.

6 In Figs. 4 and 5, we show the scattering rates for In Fig. 2, the annihilation cross section of the higgsino is 76 dominated by the decay mode into tt¯ because of the light stop when the higgsino-like and wino-like dark matter in Ge mχ >mt . This is why the resultant relic abundance of the LSP detector, respectively. In these calculations, we have seems almost constant contrary to the naive expectation. taken the same parameter sets as in Figs. 1 and 3 148 M. Fujii, K. Hamaguchi / Physics Letters B 525 (2002) 143–149

Fig. 5. Contours of the detection rate for the wino-like dark matter Fig. 6. Contours for the detection rate for the bino-like dark in 76Ge detector. The four shaded regions correspond to the ranges matter in 76Ge detector. The four shaded regions correspond to the of the detection rate R>0.1, 0.1 R>0.03, 0.03 R>0.01, ranges of the detection rate 0.03 R>0.01, 0.01 R>0.003, − − 0.01 R(events (kg day) 1) from left to right, respectively. The 0.003 R>0.001, 0.001 R(events (kg day) 1) from left parameters used in this calculation are the same as in Fig. 3 except to right, respectively. Here we have taken M1 = (1/3)µ and tan β. M2 = (2/3)µ. Other parameters are the same as in Figs. 4 and 5. except tan β. From these figures, we see that the we showed that the relic abundances of these LSP’s detection rates for the higgsino-like and wino-like can naturally explain the observed dark matter density dark matter are R 0.01 events(kg day)−1 in very with natural Q-ball decay temperatures, even in the wide range of parameter space, and they even reach relatively light neutralino mass region, which is much R 0.1events(kg day)−1 in the large tan β region. advantageous for the direct dark matter searches [21]. We should stress that such a parameter region where The novel thermal history of the universe pro- R 0.01 events(kg day)−1 is within the reach of the posed in this Letter may have important implications on-going cold dark matter searches [21]. on general SUSY breaking models, which include For comparison, we also show the scattering rate mSUGRA, no-scale type models with non-universal in 76Ge detector for the case of bino-like dark matter gaugino masses [22], anomaly mediated SUSY break- in Fig. 6. Here, we have taken M1 = (1/3)µ, M2 = ing model [23], and so on. Detailed analysis on spe- (2/3)µ, and other parameters are the same as in Figs. 4 cific models will be given elsewhere [24]. and 5. As we noted, the scattering rate for the bino-like In the context of the anomaly-mediated SUSY dark matter is much smaller than higgsino-like and breaking (AMSB) [23], non-thermal production of the wino-like dark matter, and the direct detection in the wino dark matter from the late time decay of moduli dark matter search experiments is much more difficult. and gravitino was investigated in Ref. [19]. In the case To summarize, we pointed out in this Letter that of moduli decay, however, there exists large entropy the higgsino-like and wino-like LSP’s can be excellent production which substantially dilutes the primordial dark matter candidates if the Affleck–Dine baryogen- baryon asymmetry. The authors suggested that the AD esis is responsible for the generation of the observed baryogenesis can produce enough baryon asymmetry baryon asymmetry in the present universe. Actually, even in this case. Although the AD mechanism in M. Fujii, K. Hamaguchi / Physics Letters B 525 (2002) 143–149 149

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