- Email: [email protected]
Indirect search for neutralino dark matter with high energy neutrinos
SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 124 (2003) 253-257
www.clscvicr.com/lociltelnpc
Indirect Search for Neutralino Dark Matter with High Energy Neutrinos Chung Kaoa* “Department of Physics and Astronomy, Norman, Oklahoma 73019, USA
University
of Oklahoma,
We investigate the prospects of indirect searches for the supersymmetric neutralino dark matter with high energy neutrinos produced from neutralino annihilations in the Sun. Muon neutrinos of this origin can be seen in large detectors like the AMANDA, the IceCube, and the ANTARES. We make realistic estimates for the indirect detection rates including effects of the muon detection threshold, quark hadronization, and solar absorption. In the minimal supersymmetric model and supergravity unified models, we find good prospects for detection of neutralinos with mass above 200 GeV.
1. INTRODUCTION In this article we present a brief summary of our results for the prospects of observing muon neutrinos produced by supersymmetric neutralino annihilation in the Sun [l]. We discuss the indirect detection rate for the neutralino dark matter within the framework of the minimal supersymmetric model (MSSM), the minimal supergravity model (mSUGRA), and supergravity unified models with non-universal Higgs boson masses at the grand unified scale. Average matter and energy densities in the Universe (pi) are commonly described in terms of density parameters (& = pi/pc), where
cleosynthesis is Rbh2 N 0.020 f 0.002 [5]. The luminous matter in the Universe has a very small relative density fir, pv 2 x 10b3. The most attractive cold dark matter candidates are stable weakly interacting mass particles (WIMPS) produced in the early Universe. In our analysis, we take R, = RM --Qb to be the WIMP density and conservatively consider 0.055 R,h2 50.3.
(2)
is the critical density to close the Universe, h = Ho/(100 km set- i Mpc-l), Hs is the Hubble constant, and GN is Newton’s gravitational constant. Recent measurements of the Hubble constant are converging to h N 0.6 - 0.7. Studies of clusters of galaxies and large scale structure indicate that the matter density should be at least fl M 2 0.2. The matter density inferred from observations of cluster X-ray [2], supernovae [3], and the cosmic microwave background radiation (CMB) anisotropy data [4] is RM ‘v 0.3-0.4. The baryon density inferred from Big-Bang Nu-
as the cosmologically interesting region for the cold dark matter density. In supersymmetric (SUSY) theories with a conserved R-parity2, the lightest SUSY particle (LSP) is stable and is thus an attractive WIMP candidate [6,7]. Most commonly, the LSP is the lightest neutralino which is a superposition of the supersymmetric partners of the photon, the 2 boson and the neutral Higgs bosons. WIMPS in the halo of our galaxy lose energy when they pass through the Sun and scatter from nuclei. When their velocities fall below the escape velocity from the Sun, they become gravitationally trapped and accumulate. Annihilations of these WIMPS are a potential source of high energy neutrinos that can be detected via Cerenkov light by large under-ice or under-water photomultiplier arrays in neutrino telescopes, such as AMANDA [8], IceCube [9] and ANTARES [lo].
*This research was supported in part by the U.S. Department of Energ under Grant No. DEFG03-98ER41066.
‘R = +1 for Standard Model particles as well as Higgs bosons, and R = -1 for their superpartners.
pc = 3@/(8rG~)
N 1.88 x 10-2gh2 g/cm3,
(1)
0920~5632/03/$ - see front matter 0 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(03)02117-O
254
2. THE MINIMAL MODEL
C. Kuo/Nuclear Physics B (Proc. Supph) 124 (2003) 253-257
SUPERSYMMETRIC
The indirect search for SUSY neutralino dark matter with high energy neutrinos is a promising approach to detect the annihilations of neutralino dark matter accumulated in the Sun. Many previous studies discussed the indirect detection rate for the neutralino dark matter in the minimal supersymmetric model [ll]. These analyses either neglected the threshold effect or assumed a muon detection threshold of at most 1 GeV. Higher muon energy thresholds were considered in Rx&. [12,13]. The impacts of solar absorption and hadronization of quarks were studied in Refs. [14] and [15], respectively. To obtain realistic rate estimates, we consider the muon detection threshold, quark hadronization, and solar absorption. 2.1. The Muon Energy Threshold For neutrinos from XX -t W+W- -+ p+v,+X the average energy of the muon is about m,/4; it is about m,/6 for neutrinos from Xx + QQ --t ~+Y~Q + X. The detection energy threshold for muons makes a significant impact on the indirect detection rate. We note that the higgsino-like neutralino has a substantially higher rate with a higher average muon energy than a gauginolike neutralino. In addition, a higher detector energy threshold effectively reduces the indirect detection rate for background and the signal with rn,: 5 200 GeV. For rn,: 2 500 GeV, the indirect detection rate is not very sensitive to the muon energy threshold. 2.2. Quark Hadronization and Solar Absorption There are uncertainties in the signal rate calculation form hadronization of quarks and from solar absorption that we now discuss. For a gaugino-like neutralino, the dominant annihilation modes are b5 or r7 for m, < rnw* and bb for m, > mw*. For a higgsino-like neutralino, the dominant modes are 22 or W+W- for m, < mt and tffor m, > mt [15]. The effects of hadronization of heavy quarks into heavy mesons or heavy baryons reduces the energy of the neutrinos from the semileptonic decays[ 151. Moreover, neutrinos produced in the Sun may
be absorbed before they escape the solar medium. We use the Ritz and Seckel parameterization up to energies around 1 TeV for all neutrino producing annihilation modes [14] to estimate the neutrino absorption losses. Above the TeV scale, extra corrections are treated in a manner similar to work by Edsjo [12]. High energy neutrino detectors generally have neutrino energy thresholds of at least a few tens of GeV. We have chosen 25 GeV for the muon energy threshold in our analysis which corresponds to a neutrino energy of about 50 GeV. 2.3. Indirect Detection Rate For large tan/3 with heavy SUSY particles, the neutralino annihilation cross section is enhanced by the s-channel diagrams involving broad resonance poles of Higgs bosons, x:x: -+ A”, Ho + bg, 77, where A0 is the CP odd pseudoscalar, and Ho is the heavier CP even scalar. Consequently, the neutralino relic density lies within the cosmologically interesting region in much of the parameter space in SUSY models [16]. Figure 1 shows regions in the parameter plane of (Mz, cl) that may yield an indirect detection rate in events/km2/year: (i) d&D > 100 (dark shading), (ii) 100 > dNID > 10 (intermediate) (iii) d& < 10 (light shading). Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 5 fix: 5 0.3) for the neutralino dark matter. The indirect detection rate can be significant (> 10 events/km2/year) in large regions of the parameter space with 10 5 tanp 5 50: (i) in the neighborhood of MS N 500 GeV and fi N 500 GeV, (ii) in the neighborhood of M2 - 4000 GeV and p N 1200 GeV, (iii) in a narrow band with MS 2 1200 GeV and M2 N 2~, and (iv) in a narrow band with Mz N 400 GeV and p 2 1200 GeV for tanp N 50. 3. THE MINIMAL MODEL
SUPERGRAVITY
In the minimal supergravity (mSUGRA) model [17] it is assumed that supersymmetry is broken in a hidden sector with SUSY breaking communicated to the observable sector through grav-
C. Kao/Nuciear Physics B (Pnx. Suppl.) 124 (2003) 253-257 M S S Y Indirect
Solar
Rate
(eventa/kmg/yr)
Figure 1. Regions of indirect detection rate for the MSSM neutralino dark matter in the (Ms,p) plane with Msusy = MAX(300 GeV, 1.5mxy) for (a) tan/3 = 10 and (b) tanp = 50. The shaded regions have dN1~/dA > 100 (event/km2/year) (dark), 100 > dNm/dA > 10 ( event/km2/year) (intermediate), and dN1~/dA < 10 (event/km2/year) (light). The blank regions do not have a cosmologically interesting relic density (0.05 5 C,,: 5 0.3) for the neutralino dark matter.
itational interactions and there are universalities at the GUT scale (M~ur N 2 x 1016 GeV) which lead to a common scalar mass (ms), a common gaugino mass (m&, a common trilinear coupling (Ao), and a bilinear coupling (Bs). Through minimization of the Higgs potential, the B parameter and magnitude of the superpotential Higgs mixing parameter p are related to tan ,0 and Mz. The SUSY particle masses and couplings at n/iz can be predicted by the evolution of renormalization group equations (RGEs) from MGuT. The mass matrix of the charginos in the basis of the weak eigenstates (I@*, I?*) has the following form
.
(3)
The sign of the p term in Eq. (3) establishes our sign convention. Analyses of b -+ sy decay
255
strongly favor p > 0. We shall only consider /J > 0 and A0 = 0, and impose the following theoretical requirements on the RGE evolution: (i) radiative electroweak symmetry breaking (EWSB) is achieved, (ii) the correct vacuum for EWSB is obtained (tachyon free), and (iii) the lightest SUSY particle is the lightest neutralino. Figure 2 shows regions in the parameter plane of (ml/z, ms) that may yield an indirect detection rate in events/km2/year with: (i) 10 > dN1~/dA > 1 (intermediate shading) and (ii) dN1~/dA < 1 (light shading). There is no region that has dNID/dA > 10. Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 < C$,, < 0.3) for the neutralino dark matter. For tanp = 50, the relic density is suppressed below the cosmologically interesting value when 2m,y = mH, mA. That leads to a blank narrow band in Fig. 2(b).
mSUGRA Indirect Solar la) tad = 10
Rate
(eventa/km*/~rr) = 60
Figure 2. Regions of indirect detection rate of the mSUGRA neutralino dark matter in the (m1,2,mo) plane with p > 0 and A0 = 0 for The (a) tanp = 10 and (b) tan0 = 50. shaded regions have dNID/dA < 1 (light); and 10 > dNID/dA > 1 (event/km2/year) (intermediate). Also shown are the parts of the parameter space (i) excluded by theoretical requirements, or (ii) excluded by the chargino search at LEP 2.
256
C. Kuo/Nuclear PhJvics B (Proc. Suppl.) 124 (2003) 253-257
4. SUPERGRAVITY NONUNIVERSAL MASSES
MODELS WITH HIGGS-BOSON
Regions of dNJdA, (4 tang = 10
6, = -0.5, 6, = 0 (b) tan@ = SO
We next consider high energy neutrinos from neutralino annihilation in a supergravity (SUGRA) unified model with non-universal boundary conditions for the Higgs bosons at the unified scale (m~ur) [18]. We parameterize the GUT-scale Higgs masses as mH,(GuT)
= (1 + &)mO = pimo, i = 1,2
(4
where & = -1 and 2 correspond to pi = 0 and 2 The universal mSUGRA model has 61 = Sz = 0, while 6i = -1 and & = 2 correspond to mH,(GUT) = 0 and mH,(GUT) = 2me. The nonuniversality of Higgs-boson masses at mGuT can significantly affect the values of Higgs masses and couplings at the weak scale. Figures 3 shows regions in the parameter plane of (mi,s,ms) that may yield an indirect detection rate in events/km2/year, (i) dlVrp > 10 (dark shading), (ii) 10 > dNro > 1 (intermediate shading) (iii) dNro < 1 (light shading). Three cases are considered: (a) 61 = -0.5 and 62 = 0 (Fig. IS), Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 5 QX; 5 0.3) for the neutralino dark matter. For tan/I N 50, non-universality can significantly enhance the indirect detection rate for the neutralino dark matter. For tan/3 N 10, the predicted indirect detection rate is interesting only in a very small band near the theoretically excluded region with ml/s 2 600 GeV and ms N 3mi/s. For tan/?’ N 50, the indirect detection rate is significant in a large region of parameter space with m112 ,$lOOO GeV and mo ,S 800 GeV. 5. CONCLUSIONS High energy muons produced by neutrinos from relic neutralino annihilation in the Sun can lead to promising signals in the ice and the water detectors of high energy neutrinos. We find that: (i) The effects hadronization
of detector threshold, and solar absorption can
Figure 3. The same as in Fig. 2, except the Higgs masses have non-universal boundary conditions 61 = -0.5 and 62 = 0 in a non-universal SUGRA model. The shaded regions have dAb/dA > 10 (dark); ~NID/~A < 1 (event/km2/year) (light); and 10 > cilV~~/dA > 1 (event/km2/year) (intermediate).
be essential in the evaluation of indirect detection rates, especially for neutralinos with mass below a few hundred GeV. (ii) In large portions of the MSSM parameter space with tan/3 2 10, the indirect detection rate is predicted to be greater than ten events/km2/year. (iii) The indirect search for the mSUGRA neutralino dark matter will be challenging. Only several years of observation with a square kilometer detector will likely lead to a discovery. SUGRA models with non-universal boundary conditions and tanp 2 35 give more interesting rates. (iv) For large values of tan/3 the neutralino annihilation cross section and the indirect detection rate are enhanced by the s-channel diagrams involving Higgs bosons, x:x? + A”, Ho -+ bb,TT, where A0 is the CP odd pseudoscalar, and Ho is the heavier CP
C. Kuo/Nucleur Physics B (Proc. Suppl.) 124 (2003) 253-257
even scalar, and high energy neutrinos produced in the b and r decays.
(4
are
SUSY neutralino dark matter with a mass larger than about 200 GeV offers great promise for indirect detection experiments. Together with direct detection experiments of neutralino dark matter and accelerator experiments at the upgraded Tevatron and the CERN Large Hadron Collider, highenergy neutrino telescopes will be able to survey large regions of parameter space beyond present experiments.
We have made significant improvements over previous studies. Most previous analysis for the muon flux from neutralino annihilation in supergravity unified models did not consider the muon detection threshold effect [18-201. The realistic studies in R&s. (12,131 present scatter plots without detailed information about SUSY parameters. The utility of our study is that we have carried out a realistic analysis with the effects of detector threshold, hadronization and solar absorption, and we have determined the cosmologically interesting regions for the MSSM and SUGRA parameters. Our study of indirect searches for neutralinos is complementary to direct neutralino searches and collider searches for SUSY particles. REFERENCES 1. V. D. Barger, F. Halzen, D. Hooper and C. Kao, Phys. Rev. D 65 (2002) 075022. 2. J. J. Mohr, B. Mathiesen and A.E. Evrard, Astrophys. J. 517, 627 (1999). 3. S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 517, 565 (1999). 4. The BOOMERANG collaboration: P. de Bernardis et al., Nature 404, 955 (2000); C. B. Netterfield et al. Astrophys. J. 571 (2002) 604; The MAXIMA collaboration: A. Balbi et aZ., Astrophys. J. 545, Ll (2000); The DASI collaboration: C. Pryke et al., Astrophys. J. 568 (2002) 46. 5. S. Burles, K. M. Nollett and M. S. Turner, Phys. Rev. Lett. 82, 4176 (1999); Phys. Rev. D 63, 063512 (2001).
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6. H. Goldberg, Phys. Rev. Lett. 50, 1419 (1983); J. Ellis, J. S. Hagelin, D. V. Nanopoulos, K. Olive and M. Srednicki, Nucl. Phys. B 238, 453 (1984). 7. G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267, 195 (1996). 8. The AMANDA Collaboration, E. Andres et al., Nature 410, 441 (2001). 9. The IceCube, http://pheno.physics.wisc.edu/ icecube/. 10. The ANTARES Collaboration, E. Aslanides et al., astro-ph/9907432 (1999). 11. H.P. Nilles, Phys. Rep. 110, 1 (1984); H. Haber and G. Kane, Phys. Rep. 117, 75 (1985). 12. J. Edsjo, Nucl. Phys. Proc. Suppl. 43, 265 (1995); Ph.D. Thesis, Uppsala University (1993). Bergstrom, J. Edsjo and 13. L. M. Kamionkowski, Astropart. Phys. 7, 147 (1997); L. Bergstrom, J. Edsjo and P. Gondolo, Phys. Rev. D 58, 103519 (1998). 14. S. Ritz and D. Seckel, Nucl. Phys. B 304, 877 (1988). 15. G. Jungman and M. Kamionkowski, Phys. Rev. D 51, 328 (1995). 16. H. Baer and M. Brhlik, Phys. Rev. D 53, 597 (1996); H. Baer, C. Balazs and A. Belyaev, JHEP 0203 (2002) 042; V. D. Barger and C. Kao, Phys. Rev. D 57 (1998) 3131; Phys. Lett. B 518 (2001) 117; L. Roszkowski, R. Ruiz de Austri and T. Nihei, JHEP 0108 (2001) 024; T. Nihei, L. Roszkowski and R. Ruiz de Austri, JHEP 0207 (2002) 024. 17. A. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49 (1982) 970; L. Ibafiez and G. Ross, Phys. Lett. BllO (1982) 215; R. Barbieri, S. Ferrara and C. Savoy, Phys. Lett. B119 (1982) 343; L.J. Hall, J. Lykken and S. Weinberg, Phys. Rev. D27 (1983) 2359. 18. V. Berezinsky, A. Bottino, J. Ellis, N. Fornengo, G. Mignola and S. Scope& Astropart. Phys. 5 (1996) 333. 19. A. Corsetti and P. Nath, Int. J. Mod. Phys. A 15, 905 (2000). 20. J. L. Feng, K. T. Matchev and F. Wilczek, Phys. Rev. D 63, 045024 (2001).
Nuclear Physics B (Proc. Suppl.) 124 (2003) 253-257
www.clscvicr.com/lociltelnpc
Indirect Search for Neutralino Dark Matter with High Energy Neutrinos Chung Kaoa* “Department of Physics and Astronomy, Norman, Oklahoma 73019, USA
University
of Oklahoma,
We investigate the prospects of indirect searches for the supersymmetric neutralino dark matter with high energy neutrinos produced from neutralino annihilations in the Sun. Muon neutrinos of this origin can be seen in large detectors like the AMANDA, the IceCube, and the ANTARES. We make realistic estimates for the indirect detection rates including effects of the muon detection threshold, quark hadronization, and solar absorption. In the minimal supersymmetric model and supergravity unified models, we find good prospects for detection of neutralinos with mass above 200 GeV.
1. INTRODUCTION In this article we present a brief summary of our results for the prospects of observing muon neutrinos produced by supersymmetric neutralino annihilation in the Sun [l]. We discuss the indirect detection rate for the neutralino dark matter within the framework of the minimal supersymmetric model (MSSM), the minimal supergravity model (mSUGRA), and supergravity unified models with non-universal Higgs boson masses at the grand unified scale. Average matter and energy densities in the Universe (pi) are commonly described in terms of density parameters (& = pi/pc), where
cleosynthesis is Rbh2 N 0.020 f 0.002 [5]. The luminous matter in the Universe has a very small relative density fir, pv 2 x 10b3. The most attractive cold dark matter candidates are stable weakly interacting mass particles (WIMPS) produced in the early Universe. In our analysis, we take R, = RM --Qb to be the WIMP density and conservatively consider 0.055 R,h2 50.3.
(2)
is the critical density to close the Universe, h = Ho/(100 km set- i Mpc-l), Hs is the Hubble constant, and GN is Newton’s gravitational constant. Recent measurements of the Hubble constant are converging to h N 0.6 - 0.7. Studies of clusters of galaxies and large scale structure indicate that the matter density should be at least fl M 2 0.2. The matter density inferred from observations of cluster X-ray [2], supernovae [3], and the cosmic microwave background radiation (CMB) anisotropy data [4] is RM ‘v 0.3-0.4. The baryon density inferred from Big-Bang Nu-
as the cosmologically interesting region for the cold dark matter density. In supersymmetric (SUSY) theories with a conserved R-parity2, the lightest SUSY particle (LSP) is stable and is thus an attractive WIMP candidate [6,7]. Most commonly, the LSP is the lightest neutralino which is a superposition of the supersymmetric partners of the photon, the 2 boson and the neutral Higgs bosons. WIMPS in the halo of our galaxy lose energy when they pass through the Sun and scatter from nuclei. When their velocities fall below the escape velocity from the Sun, they become gravitationally trapped and accumulate. Annihilations of these WIMPS are a potential source of high energy neutrinos that can be detected via Cerenkov light by large under-ice or under-water photomultiplier arrays in neutrino telescopes, such as AMANDA [8], IceCube [9] and ANTARES [lo].
*This research was supported in part by the U.S. Department of Energ under Grant No. DEFG03-98ER41066.
‘R = +1 for Standard Model particles as well as Higgs bosons, and R = -1 for their superpartners.
pc = 3@/(8rG~)
N 1.88 x 10-2gh2 g/cm3,
(1)
0920~5632/03/$ - see front matter 0 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(03)02117-O
254
2. THE MINIMAL MODEL
C. Kuo/Nuclear Physics B (Proc. Supph) 124 (2003) 253-257
SUPERSYMMETRIC
The indirect search for SUSY neutralino dark matter with high energy neutrinos is a promising approach to detect the annihilations of neutralino dark matter accumulated in the Sun. Many previous studies discussed the indirect detection rate for the neutralino dark matter in the minimal supersymmetric model [ll]. These analyses either neglected the threshold effect or assumed a muon detection threshold of at most 1 GeV. Higher muon energy thresholds were considered in Rx&. [12,13]. The impacts of solar absorption and hadronization of quarks were studied in Refs. [14] and [15], respectively. To obtain realistic rate estimates, we consider the muon detection threshold, quark hadronization, and solar absorption. 2.1. The Muon Energy Threshold For neutrinos from XX -t W+W- -+ p+v,+X the average energy of the muon is about m,/4; it is about m,/6 for neutrinos from Xx + QQ --t ~+Y~Q + X. The detection energy threshold for muons makes a significant impact on the indirect detection rate. We note that the higgsino-like neutralino has a substantially higher rate with a higher average muon energy than a gauginolike neutralino. In addition, a higher detector energy threshold effectively reduces the indirect detection rate for background and the signal with rn,: 5 200 GeV. For rn,: 2 500 GeV, the indirect detection rate is not very sensitive to the muon energy threshold. 2.2. Quark Hadronization and Solar Absorption There are uncertainties in the signal rate calculation form hadronization of quarks and from solar absorption that we now discuss. For a gaugino-like neutralino, the dominant annihilation modes are b5 or r7 for m, < rnw* and bb for m, > mw*. For a higgsino-like neutralino, the dominant modes are 22 or W+W- for m, < mt and tffor m, > mt [15]. The effects of hadronization of heavy quarks into heavy mesons or heavy baryons reduces the energy of the neutrinos from the semileptonic decays[ 151. Moreover, neutrinos produced in the Sun may
be absorbed before they escape the solar medium. We use the Ritz and Seckel parameterization up to energies around 1 TeV for all neutrino producing annihilation modes [14] to estimate the neutrino absorption losses. Above the TeV scale, extra corrections are treated in a manner similar to work by Edsjo [12]. High energy neutrino detectors generally have neutrino energy thresholds of at least a few tens of GeV. We have chosen 25 GeV for the muon energy threshold in our analysis which corresponds to a neutrino energy of about 50 GeV. 2.3. Indirect Detection Rate For large tan/3 with heavy SUSY particles, the neutralino annihilation cross section is enhanced by the s-channel diagrams involving broad resonance poles of Higgs bosons, x:x: -+ A”, Ho + bg, 77, where A0 is the CP odd pseudoscalar, and Ho is the heavier CP even scalar. Consequently, the neutralino relic density lies within the cosmologically interesting region in much of the parameter space in SUSY models [16]. Figure 1 shows regions in the parameter plane of (Mz, cl) that may yield an indirect detection rate in events/km2/year: (i) d&D > 100 (dark shading), (ii) 100 > dNID > 10 (intermediate) (iii) d& < 10 (light shading). Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 5 fix: 5 0.3) for the neutralino dark matter. The indirect detection rate can be significant (> 10 events/km2/year) in large regions of the parameter space with 10 5 tanp 5 50: (i) in the neighborhood of MS N 500 GeV and fi N 500 GeV, (ii) in the neighborhood of M2 - 4000 GeV and p N 1200 GeV, (iii) in a narrow band with MS 2 1200 GeV and M2 N 2~, and (iv) in a narrow band with Mz N 400 GeV and p 2 1200 GeV for tanp N 50. 3. THE MINIMAL MODEL
SUPERGRAVITY
In the minimal supergravity (mSUGRA) model [17] it is assumed that supersymmetry is broken in a hidden sector with SUSY breaking communicated to the observable sector through grav-
C. Kao/Nuciear Physics B (Pnx. Suppl.) 124 (2003) 253-257 M S S Y Indirect
Solar
Rate
(eventa/kmg/yr)
Figure 1. Regions of indirect detection rate for the MSSM neutralino dark matter in the (Ms,p) plane with Msusy = MAX(300 GeV, 1.5mxy) for (a) tan/3 = 10 and (b) tanp = 50. The shaded regions have dN1~/dA > 100 (event/km2/year) (dark), 100 > dNm/dA > 10 ( event/km2/year) (intermediate), and dN1~/dA < 10 (event/km2/year) (light). The blank regions do not have a cosmologically interesting relic density (0.05 5 C,,: 5 0.3) for the neutralino dark matter.
itational interactions and there are universalities at the GUT scale (M~ur N 2 x 1016 GeV) which lead to a common scalar mass (ms), a common gaugino mass (m&, a common trilinear coupling (Ao), and a bilinear coupling (Bs). Through minimization of the Higgs potential, the B parameter and magnitude of the superpotential Higgs mixing parameter p are related to tan ,0 and Mz. The SUSY particle masses and couplings at n/iz can be predicted by the evolution of renormalization group equations (RGEs) from MGuT. The mass matrix of the charginos in the basis of the weak eigenstates (I@*, I?*) has the following form
.
(3)
The sign of the p term in Eq. (3) establishes our sign convention. Analyses of b -+ sy decay
255
strongly favor p > 0. We shall only consider /J > 0 and A0 = 0, and impose the following theoretical requirements on the RGE evolution: (i) radiative electroweak symmetry breaking (EWSB) is achieved, (ii) the correct vacuum for EWSB is obtained (tachyon free), and (iii) the lightest SUSY particle is the lightest neutralino. Figure 2 shows regions in the parameter plane of (ml/z, ms) that may yield an indirect detection rate in events/km2/year with: (i) 10 > dN1~/dA > 1 (intermediate shading) and (ii) dN1~/dA < 1 (light shading). There is no region that has dNID/dA > 10. Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 < C$,, < 0.3) for the neutralino dark matter. For tanp = 50, the relic density is suppressed below the cosmologically interesting value when 2m,y = mH, mA. That leads to a blank narrow band in Fig. 2(b).
mSUGRA Indirect Solar la) tad = 10
Rate
(eventa/km*/~rr) = 60
Figure 2. Regions of indirect detection rate of the mSUGRA neutralino dark matter in the (m1,2,mo) plane with p > 0 and A0 = 0 for The (a) tanp = 10 and (b) tan0 = 50. shaded regions have dNID/dA < 1 (light); and 10 > dNID/dA > 1 (event/km2/year) (intermediate). Also shown are the parts of the parameter space (i) excluded by theoretical requirements, or (ii) excluded by the chargino search at LEP 2.
256
C. Kuo/Nuclear PhJvics B (Proc. Suppl.) 124 (2003) 253-257
4. SUPERGRAVITY NONUNIVERSAL MASSES
MODELS WITH HIGGS-BOSON
Regions of dNJdA, (4 tang = 10
6, = -0.5, 6, = 0 (b) tan@ = SO
We next consider high energy neutrinos from neutralino annihilation in a supergravity (SUGRA) unified model with non-universal boundary conditions for the Higgs bosons at the unified scale (m~ur) [18]. We parameterize the GUT-scale Higgs masses as mH,(GuT)
= (1 + &)mO = pimo, i = 1,2
(4
where & = -1 and 2 correspond to pi = 0 and 2 The universal mSUGRA model has 61 = Sz = 0, while 6i = -1 and & = 2 correspond to mH,(GUT) = 0 and mH,(GUT) = 2me. The nonuniversality of Higgs-boson masses at mGuT can significantly affect the values of Higgs masses and couplings at the weak scale. Figures 3 shows regions in the parameter plane of (mi,s,ms) that may yield an indirect detection rate in events/km2/year, (i) dlVrp > 10 (dark shading), (ii) 10 > dNro > 1 (intermediate shading) (iii) dNro < 1 (light shading). Three cases are considered: (a) 61 = -0.5 and 62 = 0 (Fig. IS), Parameters in the blank regions do not generate a cosmologically interesting relic density (0.05 5 QX; 5 0.3) for the neutralino dark matter. For tan/I N 50, non-universality can significantly enhance the indirect detection rate for the neutralino dark matter. For tan/3 N 10, the predicted indirect detection rate is interesting only in a very small band near the theoretically excluded region with ml/s 2 600 GeV and ms N 3mi/s. For tan/?’ N 50, the indirect detection rate is significant in a large region of parameter space with m112 ,$lOOO GeV and mo ,S 800 GeV. 5. CONCLUSIONS High energy muons produced by neutrinos from relic neutralino annihilation in the Sun can lead to promising signals in the ice and the water detectors of high energy neutrinos. We find that: (i) The effects hadronization
of detector threshold, and solar absorption can
Figure 3. The same as in Fig. 2, except the Higgs masses have non-universal boundary conditions 61 = -0.5 and 62 = 0 in a non-universal SUGRA model. The shaded regions have dAb/dA > 10 (dark); ~NID/~A < 1 (event/km2/year) (light); and 10 > cilV~~/dA > 1 (event/km2/year) (intermediate).
be essential in the evaluation of indirect detection rates, especially for neutralinos with mass below a few hundred GeV. (ii) In large portions of the MSSM parameter space with tan/3 2 10, the indirect detection rate is predicted to be greater than ten events/km2/year. (iii) The indirect search for the mSUGRA neutralino dark matter will be challenging. Only several years of observation with a square kilometer detector will likely lead to a discovery. SUGRA models with non-universal boundary conditions and tanp 2 35 give more interesting rates. (iv) For large values of tan/3 the neutralino annihilation cross section and the indirect detection rate are enhanced by the s-channel diagrams involving Higgs bosons, x:x? + A”, Ho -+ bb,TT, where A0 is the CP odd pseudoscalar, and Ho is the heavier CP
C. Kuo/Nucleur Physics B (Proc. Suppl.) 124 (2003) 253-257
even scalar, and high energy neutrinos produced in the b and r decays.
(4
are
SUSY neutralino dark matter with a mass larger than about 200 GeV offers great promise for indirect detection experiments. Together with direct detection experiments of neutralino dark matter and accelerator experiments at the upgraded Tevatron and the CERN Large Hadron Collider, highenergy neutrino telescopes will be able to survey large regions of parameter space beyond present experiments.
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