a high-energy neutrino signature from supersymmetric relics

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  • Volume 180, number 4 PHYSICS LETTERS B 20 November 1986

    A H IGH-ENERGY NEUTRINO S IGNATURE FROM SUPERSYMMETRIC REL ICS

    John S. HAGEL IN

    Department of Physics, Maharishi International University, Fairfield, IA 52556, USA

    K.W. NG and Keith A. OL IVE

    School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

    Received 21 July 1986

    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 >~ 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.

    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

  • Volume 180, number 4 PHYSICS LETTERS B 20 November 1986

    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:

    = ~ (XT#75X) [fTu(AfP L + BfPR) f ] , (1) f

    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

    = ~ + bx , (2)

    a = ~ O(mx - mr) -- mf /mx) mf(Af - Bf) , (3a) f 27r (1 2 2 1/2 2 2

    "~ ~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)

    where (O2el > = 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.

    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.

    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 >~ 6 GeV, annihilation dominates over evaporation. This domain, m >~ 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 ]

    F T -~ (6.8 1028 s -1 )ap ,36fEmxl , (4)

    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]

    Op = (A d - Bd)2(~j -- )2(3/rr )m2m2(mx + rap) -2 , (5)

    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

    branching ratio of 0.175); XX -+ c~ followed by c ~ s + + u~ (0.126); XX -~bb followed by b ~ c + + 9~ (0.117)

    376

  • Volume 180, number 4 PHYSICS LETTERS B 20 November 1986

    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.

    The differential flux of neutrinos from the sun is now easily computed: 1

    d~_~FTBf 1 dI'f

    dE v f (4~rd 2) I'f dE v ' (6)

    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:

    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)

    for Ev~

  • Vo lume 180, number 4 PHYSICS LETTERS B 20 November 1986

    10-2

    ~ 104 0

    10 .4

    I : 10-5

    lO-

    1~.1 o12' o.5 1.o 2:0 lO Eve(GeM)

    1o .2 ~ - - r ~ - ~ r - - ~ - ' r T ~ - - \

    \ \ c) Photino

    ,> \ 10 -3 \

    O \ \ '7, 6 \

    E \ \ 0 10 -4 10

    I~ lO-5 + 20

    &

    40

    10-7 ~ 0.1

    ' ' ' ~ . . . . I . . . . . . . . I ~] 102 ~ ~ ~ " k - ~ - \

    \ \ \ a) Higgsino 1 \ \ b) Higgsino \ (generic) [ ~ \ (closure)

    = 6 \ , '~ 10 -3

    'E 1o - '~ ~-a~. \

    L- /"l\ el j10- .o 'I L , ,~ ,1 , , ~ l~, , t x I_1 1 0 - 7 ~

    5.0 20 0.1 0.2 0.5 1.0 2.0 5.0 10

    I=ve(GeV) 20

    10215 ~ " ' ~,' ' ' ' I

    "7, \

    10_3 \ \ \

    ' I \ \

    dl 4I \ ~ 10- \ \ \

    \

    1>~ 10_s ~E- \

    e l j lO5L-2,0 ,,o ' I f

    10,~ ~o . . . . . . . , 2:0

    I I I I ~ i=[

    d) Superstring

    \

    \ \ \

    \ \ 50

    ~o~-~ I I ~ i i i l l

    5.0 10 20 0.2 0.5 1.0 2.0 5.0 10 20 0.1 0.2 0.5 1.0

    Evo(GeV ) Eve(GeV)

    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 ].

    (d /dEatm) > 1 when E v t> 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.

    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

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  • Volume 180, number 4 PHYSICS LETTERS B 20 November 1986

    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 >~ 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 > 1 for E v < 10 GeV provided mff < 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.

    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 . Quantitativ