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December 1997

DETECTIONRELIC PARTICLES a RATES OF SUPERSYMMETRIC

N. Fornengo

Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino Via P. Giuria 1, 10125 Torino, Italy

fornengo@to.infn.it http://www.to.infn.it/~fornengo/index.html

Abstract

Calculations of direct and indirect detection rates of relic neutralinos are presented in the framework of the Minimal Supersymmetric Standard Model and compared with the most recent experimental upper bounds. The properties of neutralino under the hypothesis that some preliminary experimental results of the DAMA/NaI Collaboration may be indicative of a yearly modulation e ect are examined.

Talk presented by Nicolao Fornengo at \Physics Beyond the Standard Model: from theory to experiment (Valencia97)", Valencia, Spain, 13{17 October 1997

a Report on the work done in collaboration with

A. Bottino, F. Donato and S. Scopel.

DETECTION RATES OF SUPERSYMMETRIC RELIC PARTICLES b

Nicolao FORNENGO Dipartimento di Fisica Teorica, Universita di Torino and INFN - Sezione di Torino, via P. Giuria 1, 10125 Torino, Italy E-mail: fornengo@to.infn.it

Calculations of direct and indirect detection rates of relic neutralinos are presented in the framework of the Minimal Supersymmetric Standard Model and compared with the most recent experimental upper bounds. The properties of neutralino under the hypothesisthat some preliminaryexperimentalresults of the DAMA/NaI Collaboration may be indicative of a yearly modulation e ect are examined.

Supersymmetric models with R{parity conservation have the interesting feature of containing stable particles which are natural candidates for dark matter. Among the di erent supersymmetric candidates, the most promising is certainly the neutralino, which arises as the lightest supersymmetric particle in a large number of gravity mediated supersymmetric models. The neutralino ~ is de ned as the lowest mass linear superposition of photino (~), zino (Z) and ~ ~ ~ + a3 H1 + a4H2 . ~ 1 , H2 ), i.e. ~ the two higgsino elds (H a 1 ~ + a2 Z The aim of this paper is at providing the latest results on the calculation of di erent kinds of detection rates of relic neutralinos, in the framework of the Minimal Supersymmetric extension of the Standard Model (MSSM), constrained by the most recent experimental data coming from accelerator physics. We do not discuss here the details of the model, for which we refer to Refs. 1;2 and to the references quoted therein. We only recall the standard assumptions employed here: i) all trilinear parameters are set to zero except those of the third family, which are uni ed to a common value A; ii) all squarks and sleptons soft{mass parameters are taken as degenerate: m~ = mq m0 ; iii) the gaugino masses are assumed to unify at MGUT , and ~ l this implies M1 = (5=3) tan2 W M2 at the electroweak scale. After these conditions are applied, the free parameters are: M2 ; ; tan ; mA ; m0; A. The parameters are varied in the following ranges: 10 GeV M2 500 GeV; 10 GeV j j 500 GeV; 65 GeV mA 500 GeV; 100 GeV m0 500 GeV; ?3 A +3; 1:01 tan 50. In our analysis the supersymmetric parameter space is constrained by all the experimental limits obtained from accelerators on supersymmetric and

i i

1 Introduction

b Report on the work done in collaboration with A.

Bottino, F. Donato and S. Scopel.

1

(nucleon) Figure 1: The scalar neutralino{nucleon cross section scalar , multiplied by the scaling factor , is plotted versus the neutralino mass m . The open curve denotes the 90% C.L. upper bound obtained from the total counting rates of Ref.6 . The scatter plot represents the theoretical predictions calculated within the MSSM scheme ( > 0 only). The closed contour delimits the region singled out at 90% C.L. when the data of Ref.12 are interpreted in terms of a modulation signal.

2 Direct detection

Higgs searches. In particular, the latest data from LEP on Higgs, neutralino, chargino and sfermion masses are used 3 . Moreover, the constraints due to the b ! s + process 3 are satis ed. In addition to the experimental limits, we require that the neutralino is the lightest supersymmetric particle. Finally, the regions of the parameter space where the neutralino relic abundance exceeds the cosmological bound, i.e. h2 > 1, are also excluded.

Neutralinos interact with matter both through coherent e ects and spin dependent interactions 1;4. We con ne here to the coherent e ects, since these are the ones which are currently accessible to direct detection. The relevant quantity, dependent on the supersymmetric parameters, which enters in the event rate of direct detection as well as in the indirect signals (nucleon) (nucleon) is the {nucleon scalar considered in Sect.3, is scalar , where scalar (nucleon) cross{section and is the neutralino local density. The expression of scalar 2

and its relation to the di erential event rate for elastic neutralino{nucleus scattering may be found in Ref. 4. The local density is factorized as = l , i.e. in terms of the (total) local dark matter density l . Here is calculated as = min(1; h2=( h2 )min ), where h2 is calculated as a function of the supersymmetric parameters 1;5 and ( h2 )min is a minimal value compatible with observational data and with large{scale structure calculations 2 . In the following we use l = 0:5 GeV cm?3 and ( h2)min = 0:03 1. We are now in the position to compare our calculations with the most stringent experimental data for neutralino direct searches, given by the DAMA/NaI experiment 6 . The comparison is shown in Fig.1, where our results are provided in the form of a scatter plot, obtained by varying the parameters of the supersymmetric model in the intervals quoted above (only > 0 is displayed). We see that the scatter plot of the theoretical predictions reaches abundantly the curve of the 90% C.L. upper bound. This shows that the sensitivity of the direct detection experiment is adequate for a signi cant exploration of the neutralino parameter space. This result applies to the above mentioned choice of the astrophysical parameters l and ( h2 )min . Di erent choices of these parameters inside their allowed ranges 1;4 can lower the theoretical predictions by at most one order of magnitude. Pair annihilations of neutralinos captured in the Earth and in the Sun produce a ux of 's which can be detected as up{going muons in a neutrino telescope. The values of the calculated uxes of up{going muons 7;8 Earth and Sun are displayed in Figs.2,3 together with the experimental 90% C.L. upper bounds of Ref. 9 (solid line) and Ref. 10 (dashed line). From Figs.2,3 it turns out that many supersymmetric con gurations give muon uxes exceeding the present experimental upper bounds. Also in this case the variation of the astrophysical parameters may lower the calculated uxes by at most one order of magnitude. During the orbital motion of the Earth around the Sun, the direction of the velocity of the relic particles with respect to the detector changes as a function of time, and this induces a time dependence in the di erential detection rate, i.e. 11;12 S(E; t) = S0 (E) + Sm (E) cos !(t ? t0 )], where ! = 2 =365 days and t0 = 153 days (June 2nd ). S0 (E) is the average (unmodulated) di erential rate and Sm (E) is the modulation amplitude of the rate. The relative importance of Sm (E) with respect to S0 (E) for a given detector, depends both on the mass of the dark matter particle and on the value of the recoil energy where the e ect is looked at. Typical values of Sm (E)=S0 (E) for a NaI detector are 3

3 Indirect detection at neutrino telescopes

4 Direct detection: yearly modulation of the signal

Figure 2: Flux of up-going muons Earth as a function of m , calculated within the MSSM scheme ( > 0 only). The solid (dashed) line represents the experimental 90% C.L. upper bound of Ref.9 (10 ).

in the range from a few percent up to roughly 15%, for neutralino masses of the order of 20{80 GeV and recoil energies below 8{10 KeV. The DAMA/NaI Collaboration reported on an analysis of a collection of data over an exposure of 4549 Kg days, obtained with an experimental setup consisting of nine 9.70 Kg NaI(Tl) detectors 12 . The extraction of a possible signal is obtained by employing a maximumlikelihood method applied to a binning in the recoil energy of the daily counts per detector. When interpreted in terms of a modulation signal due to a WIMP of mass m and elastic cross (nucleon) section scalar , the data of Ref. 12 single out (at 90% C.L.) the region of Fig. 1 which is delimited by a closed contour (hereafter de ned as region Rm ). The occurrence of region Rm as a domain relevant for a possible modulation e ect will necessarily require further investigation with much higher statistics. This point has clearly been stressed in Ref. 12. Meanwhile, it is very interesting to analyze the possible implications that can be inferred from this preliminary result. Speci cally, a number of questions deserve to be answered: a) what would be the features of a neutralino to satisfy the prerequisites of region Rm ; b) would any other experimental search for relic neutralinos be able to inves4

Figure 3: Flux of up-going muons Sun as a function of m , calculated within the MSSM scheme ( > 0 only). The solid (dashed) line represents the experimental 90% C.L. upper bound of Ref.9 (10 ).

tigate the region Rm ; c) are neutralino con gurations of region Rm accessible to accelerator searches in the near future; d) what are the cosmological and astrophysical implications of relic neutralinos whose scalar elastic cross section is compatible with region Rm ? We start our analysis by comparing the result of Ref. 12 with our calculation within the MSSM scheme. This comparison is shown in Fig.1, where we (nucleon) observe that many supersymmetric con gurations provide a value of scalar compatible with the region Rm (we will call hereafter set S the supersymmetric con gurations compatible with region Rm ). As it was shown in Ref. 1, many of these con gurations provide sizeable muon uxes from the Earth and the Sun, reachable by the foreseeable improvements in neutrino telescopes. This result is interesting since it suggests the possibility to have an independent tool of exploration of the same con gurations of set S. In the case of the indirect signal from the Earth, it is already possible to exclude part of the con gurations of set S since they provide muon uxes exceeding the Baksan and Macro Collaborations limits 1. We therefore include in our following considerations only con gurations which are not in con ict with indirect searches at neutrino 5

Figure 4: The con gurations compatible with the closed region of Fig. 1 are plotted in the m {tan plane, within the gray area. Con gurations which provide muon uxes from the Earth and from the Sun which exceed the limits of Refs.9;10 have been dropped. The dark region on the left side is excluded by current LEP data3. The region on the left of the vertical solid line will be accessible to LEP23 . The region on the left of the vertical dashed line will be explorable at TeV333 . In the region delimited by the closed dashed line, the neutralino relic abundance h2 may exceed the value 0.1.

telescopes (we de ne this subset as set T). Let us now consider the features of the supersymmetric con gurations of set T. Fig.4 shows, within the gray area, the neutralino mass ranges compatible with set T, for di erent values of tan . The dark area on the left side of the gure is excluded by current LEP data 3. The region on the left of the vertical solid line around m ' 50 GeV is the region explorable by LEP2 3 . We notice that, as far as the neutralino sector is concerned, LEP will be able to investigate only marginally the region of parameter space singled out by set T. A better chance to explore the neutralino mass range compatible with set T is given by the future upgrades at the Tevatron and by LHC. As an example, the region which extends up to the vertical dashed line is the mass region which will be possibly explored by TeV33 3 . Fig.5 shows the properties of the con gurations of set T with respect to the lightest Higgs mass mh , a parameter which is crucial in establishing the size of 6

Figure 5: The same con gurations of Fig. 4 are displayed in the mh {tan plane, within the gray area. The dark regions are excluded by current LEP searches3 or by theoretical arguments. Con gurations which provide h2 > 0:1 fall within the region delimited by the closed dashed line. The region on the left of the solid line will be accessible to LEP23 .

both direct and indirect detection signals. The gray area in Fig.5 corresponds to values of mh and tan compatible with set T. The dark regions are excluded by current LEP searches 3 (on the left of the plot) or by theoretical arguments (on the right side). In Fig.5 it is also reported the region which will be accessible to LEP2 3 . A large portion of the region compatible with the modulation analysis will be covered by the LEP analysis. In particular, all the region for tan < 3 will be analyzed. In Ref. 1 it was shown that a large number of con gurations belonging to set T provide a large value of the neutralino relic abundance. These con gurations are very appealing from the point of view of dark matter, and they are shown in Fig.4,5 where the closed dashed line contains the portion of the parameter space where h2 may exceed the value 0.1. In order to investigate the cosmological and astrophysical properties of the con gurations of set T, we present an analysis which is meant to obtain from the experimental data the relevant cosmological implications for relic neutralinos in the most direct way. We adopt the following procedure 2 : 1) we 7

(nucleon) Figure 6: The neutralino local density , calculated for scalar ]expt = 1 10?9 nbarn and l = 0:5 GeV cm?3 , is plotted versus the neutralino relic abundance h2 . For the (nucleon) value of scalar ]expt employed here, the neutralino mass is restricted to the range 40 GeV < m < 85 GeV, as obtained from the closed contour in Fig. 1. The two horizontal lines denote the physical range for the local density of non{baryonic dark matter. The two solid vertical lines denote the physical band for h2 , and the two dashed lines give the preferred band for the cold dark matter contribution to . The two tilted dot{dashed lines denote the band where linear rescaling procedure for the local density is usually applied.

(nucleon) evaluate scalar and h2 by varying the supersymmetric parameters; 2) for (nucleon) (nucleon) any value of scalar ]expt = l scalar ]expt compatible with the exper(nucleon) (nucleon) and restrict imental region Rm we calculate = scalar ]expt = scalar the values of m to stay inside the region Rm . 3) The results are displayed in a scatter plot in the plane vs. h2 . (nucleon) One example of our results is given in Fig.6 for scalar ]expt = 1 10?9 ?3 is used). The two horizontal lines denote the nbarn ( l = 0:5 GeV cm physical range 0.1 GeV cm?3 < l < 0.7 GeV cm?3 for the local density of non{baryonic dark matter 2 . The solid vertical lines denote the physical band for h2: 0:03 < h2 < 1, and the two dashed lines give the favored band for the cold dark matter contribution to : 0:1 < ( h2)CDM < 0:3 2 . The two tilted dot{dashed lines denote the band where linear rescaling procedure for 8

the local density is usually applied. With the aid of this kind of plot we can classify the supersymmetric con gurations belonging to region Rm into various categories. Con gurations whose representative points fall above the maximum value = 0:7 GeV cm?3 have to be excluded (those providing an h2 > 1 are already disregarded in the plot). Among the allowed con gurations, those falling in the region inside both the horizontal and solid vertical lines are very appealing, since they would represent situations where the neutralino could have the role of a dominant cold dark matter component; even more so, if the representative points fall in the subregion inside the vertical band delimited by dashed lines. Con gurations which fall inside the band delimited by the tilted dot{dashed lines denotes situations where the neutralino can only provide a fraction of the cold dark matter both at the level of local density and at the level of the average . Con gurations above the upper dot{dashed line and below the upper solid horizontal line would imply an unlikely special clustering of neutralinos in our halo as compared to their average distribution in the Universe.

References

1. A. Bottino, F. Donato, N. Fornengo and S. Scopel, report DFTT 49/97, hep{ph/9709292, submitted to Phys. Lett. B. 2. A. Bottino, F. Donato, N. Fornengo and S. Scopel, report DFTT 61/97, hep{ph/9710295. 3. For a complete list of references, see Ref. 1 and Ref. 2. 4. A. Bottino, F. Donato, G. Mignola, S. Scopel, P. Belli and A. Incicchitti, Phys. Lett. B 402, 113 (1997); for other recent references, see Ref. 1. 5. A. Bottino, V. de Alfaro, N. Fornengo, G. Mignola and M. Pignone, Astropart. Phys. 2, 67 (1994); for other recent references, see Ref. 1 . 6. R. Bernabei et al., Phys. Lett. B 389, (1996) 757. 7. V. Berezinsky, A. Bottino, J. Ellis, N. Fornengo, G. Mignola and S.Scopel, Astropart. Phys. 5, 333 (1996). 8. A. Bottino, N. Fornengo, G. Mignola and L. Moscoso, Astropart. Phys. 3, 65 (1995); for other recent references, see Ref. 1. 9. O. Suvorova, Baksan Collab., Proc. 4th Int. Neutrino Conference, Heidelberg, April 1997. 10. T. Montaruli, Macro Collab., talk at TAUP97,Laboratori Nazionali del Gran Sasso, September 1997. 11. K. Freese, J. Frieman and A. Gould, Phys. Rev. D37, 3388 (1988). 12. R. Bernabei et al., ROM2F/97/33, September 1997; P. Belli, talk at TAUP97, Laboratori Nazionali del Gran Sasso, September 1997; P. Belli, talk at COSMO97, Ambleside, England, September 1997. 9

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