A high-energy neutrino signature from supersymmetric relics

Download A high-energy neutrino signature from supersymmetric relics

Post on 31-Aug-2016

214 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

<ul><li><p>Volume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>A H IGH-ENERGY NEUTRINO S IGNATURE FROM SUPERSYMMETRIC REL ICS </p><p>John S. HAGEL IN </p><p>Department of Physics, Maharishi International University, Fairfield, IA 52556, USA </p><p>K.W. NG and Keith A. OL IVE </p><p>School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA </p><p>Received 21 July 1986 </p><p>We compute the energy spectrum of high-energy (0.1-10 GeV) neutrinos produced by the annihilation of supersym- metric (SUSY) cold dark matter trapped in the sun. We compare this spectrum to the spectrum of atmospheric neutrinos and find that in the direction of the sun the solar flux of neutrinos can exceed the atmospheric background for neutrino energies E v &gt;~ 1 GeV, and are as much as a factor ~ 30 above background for energies E v ~ few GeV. We discuss these sig- natures for standard SUSY relics as well as for superstring relics. </p><p>Although observations of the overall mass-density of the universe are consistent [1 ] with ~2 ~- 0.1 (~2 = P/Pc, Pc = 1.88 X 10 -29 h 2 gcm -3 andh 0 =H0/100 km Mpc-1 s -1 ) inflation as well as theoretical prejudice demand that ~2 = 1. This discrepancy is accounted for by postulating the existence of dark matter. By utilizing big-bang nucleosynthesis constraints [2] on the abundances of the light elements, one finds that the cosmological mass density of baryons is limited to ~2 B </p></li><li><p>Volume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>model, the LSP is in general a mixture of four neutral f~ermions [15] : the photino ~; the zino Z (or equivalently the wino ~, and the bino B); and two higgsinos H and ft. The present mass density of the LSP, X, can be deter- mined from the annihilation cross section which is derived from the effective low-energy lagrangian for the inter- action between X and ordinary fermions (quarks or leptons) f: </p><p> = ~ (XT#75X) [fTu(AfP L + BfPR) f ] , (1) f </p><p>where PL,R are the left and right projection operators (1 + 75)/2 and expressions for Af and Bf can be found in ref. [15]. In terms of Af and Bf the annihilation cross section is given by </p><p> = ~ + bx , (2) </p><p>a = ~ O(mx - mr) -- mf /mx) mf(Af - Bf) , (3a) f 27r (1 2 2 1/2 2 2 </p><p>"~ ~jO(m-mf) (1 - 2 2 1/2 2+B2) (4m2 x3 2- ~AfBfm2+7~ -mr /m) ] = mf /mx) [(Af -~-mf )+ 3m2(Af_Bf )2 (1 2 2 -1 f 2rr (3b) </p><p>where (O2el &gt; = 6 Tim x = 6x. The resulting value of ~2 x will of course depend on the squark and slepton masses contained in A f and Bf. </p><p>We are interested in the high energy tail of the neutrino spectrum resulting from "primary" neutrinos XX ~ ff -~ X + v + ~, and in the case where f is a b-quark, from "secondary" neutrinos due to b -~ c ~ X + v. These primary and secondary neutrinos are directly calculable, since the intermediate heavy fermions b, c and r have lifetimes that are short compared to the mean free path in the strongly interacting solar interior. In addition to these primary and secondary neutrinos there are expected to be a significant number of soft neutrinos due to pion and kaon decays, with energy spectra that are more difficult to estimate. These soft neutrinos have been the basis of previous analyses [ 10,11 ] and are not our principle focus here. </p><p>To compute the primary and secondary neutrinos, we first need the annihilation rate of X's in the sun. De- pending on the mass of the LSP, the sun will loose X'S either through evaporation [8] or annihilation. It was found [17] that for m x &gt;~ 6 GeV, annihilation dominates over evaporation. This domain, m &gt;~ 6 GeV, is actually favored by terrestrial and cosmological arguments. For example, an LSP higgsino must be more massive than the b-quark in order to annihilate efficiently enough to present over-closing the universe [15]. With regard to the photino, experimental searches for anomalous single photons (ASPs) in e+e - annihilations appear to rule out m~ 6 GeV, the annihilation rate at equilibrium will be equal to 1/2 the trapping rate, which is given by [9,11 ] </p><p>F T -~ (6.8 1028 s -1 )ap ,36fEmxl , (4) </p><p>2 hee 1 er ross f r ' son r on d mm 1 where Op,36 = o /10 -36 cm is t last'c scat t ing c section o X p ot s an fE = " [ , 43mpm(m 2 + ~2) -1 ]. In terms ofAu, d and Bu, d (the Af and Bf for the up and down quarks), the elastic scat- tering cross section is [11,20] </p><p>Op = (A d - Bd)2(~j -- )2(3/rr )m2m2(mx + rap) -2 , (5) </p><p>where ~'--- (A u - Bu)/(A d - Bd). One can identify several sources of high energy neutrinos: X)( ~ r+r - followed by r ~ + u r + ~ (with a </p><p>branching ratio of 0.175); XX -+ c~ followed by c ~ s + + u~ (0.126); XX -~bb followed by b ~ c + + 9~ (0.117) </p><p>376 </p></li><li><p>Volume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>and the subsequent c decay; and finally i fx is massive enough XX -+ tt- followed by t ~ b + ~ + v~ (0.11) and the subsequent b decay. The branching ratios for XX ~ tt , bb, c~ or r+r - are obtained from eqs. (2) and (3). The average (in a strong sense, since the spectrum turns out to be very flat) neutrino energy will be E v ~- (1/3)m x. </p><p>The differential flux of neutrinos from the sun is now easily computed: 1 </p><p>d~_~FTBf 1 dI'f </p><p>dE v f (4~rd 2) I'f dE v ' (6) </p><p>where d is 1 au, Ff and Bf are the decay rates and branching ratios for f-+ f ' + + v~. For Ff, we use the standard weak decay matrix element ]M} 2 = 64G2(pf Pv~)(P~" Pf'), which yields the following differential rates: </p><p>2 2 m4,pf dFf GF Ev~ I mf, mf lq 2Efpf(m2_ 2m2,) 4 2 3 4 2 [m2- 2Ev~(Ef + Pf) dEv~---47r3Efpf -3Ev~(3Efpf+Pf) Ev~ 4E2~ ln~m~-- - - -~-~]d ' t .~. ~ .1. (7a) </p><p>for Ev~ </p></li><li><p>Vo lume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>10-2 </p><p>~ 104 0 </p><p>10 .4 </p><p>I : 10-5 </p><p>lO- </p><p>1~.1 o12' o.5 1.o 2:0 lO Eve(GeM) </p><p>1o .2 ~ - - r ~ - ~ r - - ~ - ' r T ~ - - \ </p><p>\ \ c) Photino </p><p>,&gt; \ 10 -3 \ </p><p>O \ \ '7, 6 \ </p><p>E \ \ 0 10 -4 10 </p><p>I~ lO-5 + 20 </p><p>&amp; </p><p>40 </p><p>10-7 ~ 0.1 </p><p>' ' ' ~ . . . . I . . . . . . . . I ~] 102 ~ ~ ~ " k - ~ - \ </p><p>\ \ \ a) Higgsino 1 \ \ b) Higgsino \ (generic) [ ~ \ (closure) </p><p>= 6 \ , '~ 10 -3 </p><p>'E 1o - '~ ~-a~. \ </p><p>L- /"l\ el j10- .o 'I L , ,~ ,1 , , ~ l~, , t x I_1 1 0 - 7 ~ </p><p>5.0 20 0.1 0.2 0.5 1.0 2.0 5.0 10 </p><p>I=ve(GeV) 20 </p><p>10215 ~ " ' ~,' ' ' ' I </p><p>"7, \ </p><p>10_3 \ \ \ </p><p>' I \ \ </p><p>dl 4I \ ~ 10- \ \ \ </p><p>\ </p><p>1&gt;~ 10_s ~E- \ </p><p>e l j lO5L-2,0 ,,o ' I f </p><p>10,~ ~o . . . . . . . , 2:0 </p><p>I I I I ~ i=[ </p><p>d) Superstring </p><p>\ </p><p>\ \ \ </p><p>\ \ 50 </p><p>~o~-~ I I ~ i i i l l </p><p>5.0 10 20 0.2 0.5 1.0 2.0 5.0 10 20 0.1 0.2 0.5 1.0 </p><p>Evo(GeV ) Eve(GeV) </p><p>Fig. 1. The differential flux of v e + ~e from the sun due to the annihilation of cold dark matter as compared to the atmospheric background flux in the direction of the sun (dashed line) for (a) a generic higgsino, X = H or H for rn x = 6, 10, 20 and 40 GeV. In this case, S2 x = 1, 0.37, 0.12 and 0.036 respectively; (b) a symmetric higgsino, x = (~H + o~l) (o 2 + ~2) -1~ with o/-~ adjusted so that S2 x = 1 : u/E = 3, 1.8, 1.4 and 1.2 for the same set of LSP masses as in (a) ; (e) a photino with degenerate squark and slepton masses, m~, adjusted so that $Z x = 1: m~, = 71, 88 ,117 and 166 GeV for the same set of LSP masses as in (a); (d) superstring LSP (photino) with masses 20, 40 and 50 GeV and ffermion masses taken from the relations of refs. [ 20,21 ]. </p><p>(d /dEatm) &gt; 1 when E v t&gt; 3 GeV. At its max imum, R ~- 10 for m~ = 6 GeV at E v TM 3 GeV;R -~ 15 for m~ = 10 GeV at E v -~ 4 GeV;R ~- 40 for m~ = 20 GeV at E v -~ 7 GeV andR ~- 120 for mfi = 40 GeV at E v = 20 GeV. </p><p>In a SUSY theory , it is possible to arrange for a decoup l ing o f the LSP higgsino f rom the Z 0 , wh ich occurs </p><p>378 </p></li><li><p>Volume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>when the LSP higgsino is of the form ~0 _+ ~0. This happens in a theor~ when the ratio of VEVs o/~ (= (01HI0)/ (01ill0)) -~ 1 in which case the LSP higgsino is of the form S = (-Off + off) (02 + ~2)-1/2. In fig. lb, we plot the neutrino fluxes resulting from such an LSP S, adjusting the ratio 0/-6 so that ~2 = 1 (for h 0 = 1/2). Thus for m~- = 6, 10, 20 and 40 GeV we choose o/-6 = 3, 1.8, 1.4 and 1.2 respectively. The curves in fig. lb are independent of the choice of rn~ for scalar masses &gt;~ 20 GeV; both scattering and annihilations are controlled by Z exchange. Although for mff = 6 GeV, the spectrum is quite similar to that in the generic higgsino case, for larger masses, the fluxes decrease quite rapidly. This is because for larger values ofmff we have chosen v~ ~- 1 in order to maintain ~2 = 1. This results in a partial decoupling from the Z 0 which boosts the cosmological relic density of the S but also suppresses the trapping rate. We nonetheless find that R &gt; 1 for E v &lt; 10 GeV provided mff &lt; 40 GeV. Also R ~ 5 for mff = 6 GeV at E v = 3 GeV. For both higgsino cases (figs. 1 a, b) secondary neutrinos from b ~ c ~ x + v are important since XX ~ bb is the dominant annihilation channel. </p><p>The photino [14,15] is perhaps the most plausible LSP candidate in many models and is the most frequently discussed SUSY dark matter candidate. The relic photino density can be maintained at ~2 = 1 by adjusting the squark and slepton masses. For now we will assume that these are all degenerate. As in the symmetric higgsino case, S, demanding ~2 = 1 results in reduced neutrino fluxes as m~ is increased (fig. lc). For m~ = 6, 10, 20 and 40 GeV we have taken mi~ "- 71,88, 117 and 166 GeV to ensure ~2 = 1. The flux falls off with increasing m x be- cause the elastic scattering cross section depends on m?, and because PT also depends on mx l . Quantitatively, the photino results are similar to the symmetric higgsino results. </p><p>For completeness, we note that other gaugino LSPs (a W, B or Z) would produce fluxes comparable to the cases, though none of these other gauginos represent favored dark matter candidates in most SUSY models. For any type of gaugino, the neutrino fluxes are reduced if m ff &gt; m fi-: heavy squarks suppress the XP elastic cross sec- tion, Op, while fight sleptons maintain an acceptably low relic mass density as is the case in the superstring candi- dates we are about to discuss. </p><p>The t~mal dark matter candidate we wish to discuss is the LSP found [20] in a minimal phenomenological model [21] inspired by the superstring [22]. In these models E 6 can be broken by Wilson loops via the Hosotani mechanism [23] to one of several low-energy gauge groups [24] the smallest being SU(3)o X SU(2)L U(1)y U(1)E. The matter fields are contained in a 27 of E 6 and have the following SU(10) and SU(5) decompositions: 27 = 16 + 10 + 1 = (10 + 5 + 1) + (5 + 5) + 1. The most general superpotential one can write down is invariant under R-parity with the assignments to the fermion partners R(16) = + 1, R (10) = -1 and R( I ) = -1 . Thus in ad- dition to the gauginos ~ and Z there is at least one extra ZE due to the U(1)E factor, and in addition to the ~I and H (contained in the 10) there is an SO(10) singlet N which must be included. The LSP may now be a linear combination of these six fields [20]. Even in this general case, depending on the scale of supersymmetry breaking m 1/2, the LSP is still predominantly a ~ with some admixture of S. </p><p>One of the features of the minimal model of ref. [21 ] is that the squark and slepton masses are fixed by m 1/2, with the ratios m~ : ml/2 :m~L : m~R = 1.95 : 1 : 0.7 : 0.4. Thus the LSP mass and relic density are given solely in terms of ml/2. For ml[ 2 ~ I00 -1000 GeV, it was found [20] that m ~ 20-100 GeV and </p><p>~2x(h0/0.5)2 ~- 202 . (10) </p><p>In fig. ld, we plot the differential flux of v e + ~e for such superstring relics with masses 20, 40 and 50 GeV (we have arbitrarily chosen m t = 40 GeV). For m x = 20 GeV, the LSP is almost a pure photino while for m x = 40 and 50 GeV there is a significant higgsino admixture. Because phot ino-proton elastic scattering takes place exclusively via squark exchange, the large squark masses ( " 200 GeV) in the m x = 20 GeV case greatly suppresses the solar trapping and hence the neutrino flux. At the larger LSP masses, the higgsino admixture allows for a scattering via Z 0 exchange and so the flux in this case is qualitatively similar to previous higgsino examples. This issimilar to the results found in ref. [20], i.e., that as m x is increased the neutrino flux rises due to the enhanced scattering contribution from Z 0 exchange. As one can see however, the flux only rises above the atmospheric background fo re /&gt; 10 GeV. </p><p>l) </p><p>Finally, we would like to stress that in order to test these supersymmetric dark matter candidates, we are really </p><p>379 </p></li><li><p>Volume 180, number 4 PHYSICS LETTERS B 20 November 1986 </p><p>only interested in neutrino events (in underground detectors) withenergies in excess of I GeV. In addition, be- cause the atmospheric neutrino flux ratio [25] between v e +~e and vu +vu is ~-0.3 fo re v "" 1 -2 GeV and the solar flux ratio is unity, one is experimentally much more sensitive to v e + ~e" To see how close we are to existing data, we compare our predictions with neutrino observations by the IMB detector when correlated to the direc- tion of the sun [26]. Data with sufficient information (energy and direction) is available for E v ~- 400 MeV-2 GeV. When the portion of the data between 1 and 2 GeV is examined a neutrino excess (o fv e +re + vn +~) is limited [26] byR '= (d~/dEv)l o dEv/(dcb/dEv) lam a dEv&lt; 1.3, where (dcb/dEv)lat m is the atmospheric background in the direction of the sun as in the figures but with v, + ~u included, R ' calculated from the figures must be cor- rected (to include v, + ~u) by a factor 2/(1 + vu/Ve) ~ 0.46 for E v ~- 1 -2 GeV. Taking m x = 6 GeV, in figs. la, b, c we find R ' = 0.9,0.5 and 0.3 respectively, all within a factor of ~-4 of the present experimental upper limit. Clearly this limit can be improved if more data were available which included higher energies (E v &gt; 2 GeV) and/ or could distinguish between v e and vu. </p><p>In conclusion, we have calculated the differential flux of high energy neutrinos due to the annihilation of supersymmetric relics trapped in the sun. The fluxes can easily exceed the atmospheric neutrino background flux for E v &gt;~ O(1) GeV. Present experimental data comes close to probing the supersymmetric dark matter candidates but is not yet in a position to rule them out. </p><p>We would like to thank D. Burke, S. Gasiorowicz, J. LoSecco, M. Srednicki and S. Rudaz for valuable discus- sions. The work of K.-W.N. and K.A.O. was supported in part by DOE grant DE-AC02-83ER-40105. </p><p>References </p><p>[ 1] See, e.g., M. Davis and P.J.E. Peebles, Astrophys. J. 267 (1983) 465. [2] J. Yang, M.S. Turner, G. Steigman, D.N. Sehramm and K.A. Olive, Astrophys. J. 281 (1984) 493. [3] J.P. Ostriker and PJ.E. Peebles, Astrophys. J. 186 (1973) 467. [4] V.C. Rubin, W.K. Ford and N. Thonnard, Astrophys. J. 255 (1978) L107; </p><p>D. Burstein and V.C. Rubin, Astrophys. J. 297 (1985) 423. [5] S.M. Faber and J.S. Gallagher, Ann. Rev. Astron. Astrophys. 17 (1979) 135. [6] DJ. Hegyi and K.A. Olive, Phys. Lett. B 126 (1983) 28; Astrophys. J. 303 (1986) 56. [7] J. Primack, SLAC preprint 3387 (1984). [...</p></li></ul>