Strangelets in cosmic rays

M.Rybczynskia ∗, Z.W�lodarczyka† and G.Wilkb ‡

aInstitute of Physics, Swietokrzyska Academy, Kielce, Poland

bThe Andrzej Soltan Institute for Nuclear Studies, Nuclear Theory Department, Warsaw, Poland

Recently new data from the Cosmo-LEP project appeared, this time from the DELPHI detector. They essen-tially confirm the findings reported some time ago by ALEPH, namely the appearance of bundles of muons withunexpectedly high multiplicities, which so far cannot be accounted for by present day models. We argue, usingarguments presented by us some time ago, that this phenomenon could be regarded as one more candidate for thepresence in the flux of cosmic rays entering the Earth’s atmosphere from outer space nuggets of Strange QuarkMatter (SQM) in form of so called strangelets.

1. Introduction

Recently new data from the Cosmo-LEP pro-gram, this time from the DELPHI detector, hasbeen reported [1]. Among other things they haveconfirmed the findings reported before by ALEPH[2], namely that one observes bunches of cos-mic ray muons (i.e., muons produced at the topof the Earth’s atmosphere) of unexpected largemultiplicities (up to Nμ = 150). Their origin isso far unexplained and no model used in MonteCarlo (MC) programs simulating cascades of cos-mic rays (CR) in the atmosphere is able to ac-count for this phenomenon. In [1] it was sug-gested that the source of this discrepancy couldpossibly come directly from the elementary inter-action model used in MC. However, in our opin-ion, which we would like to elaborate here in moredetail, the discrepancy could rather come (at leastto a large extent) from the projectile initiatingthe cascade. Namely, as we have already done inmany places on other occasions [3,4], we shall ar-gue that the above mentioned results of both ex-periments can be regarded as yet another signal ofthe presence of nuggets of Strange Quark Matter(SQM), called strangelets, in the CR flux enteringthe Earth’s atmosphere. In this way results of [1]and [2] would just continue a long list of other∗e-mail: mryb@pu.kielce.pl†e-mail: wlod@pu.kielce.pl‡e-mail: wilk@fuw.edu.pl

phenomena explainable in this way like anoma-lous cosmic ray burst from Cygnus X-3, extraordi-nary high luminosity gamma-ray bursts from thesupernova remnant N49 in the Large MagellanicCloud or Centauro (to mention only the most in-teresting and intriguing examples, for more de-tails see [4,5] and references therein). In [6] wehave already proposed a successful explanationfor the ALEPH observations by using strangeletsand assuming their flux to be the same as the oneobtained from the analysis of all previous signalsof strangelets listed in the literature. (Actually,at that time ALEPH results were circulated onlyas conference papers, however, the final resultspresented in [2] turned out to be identical to thoseaddressed in [6]).

It is worth to recall here that the CosmoLEPdata are very important because: (a) the highmultiplicity muon events (muon bundles) are po-tentially a very important source of informationconcerning the composition of primary CR be-cause muons provide essentially undisturbed in-formation on the first interaction of the cosmicray particles in the atmosphere; (b) such eventshave never been studied with such precise detec-tors as provided by the LEP program at CERN,nor have they been studied at such depth as atCERN [7] (ranging between 30 and 140 metersunderground, which corresponds to muon cut-offenergies between 15 and 70 GeV).

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2. Some features of strangelets

For completeness let us remind of the most im-portant features of strangelets (see [3,4] for de-tails). They are hadron-like, being a bag of up,down and strange quarks (essentially in equalproportion) and becoming absolutely stable athigh mass number A (more stable than the mosttightly bound nucleus, iron). However, they be-come unstable below some critical mass number,Acrit = 300−400. Despite the fact that their geo-metrical radii are comparable to those of ordinarynuclei of the corresponding mass number A, R =r0A

1/3, they can still propagate very deep intothe atmosphere. This is because after each col-lision with an atmospheric nucleus, a strangeletof mass number A0 becomes just another new

0 5 10 15

log10 A0

-20

-15

-10

-5

0

log 1

0flu

x(m

-2h-1

sr-1

)

Big BangDark Matterupper exp. limitsAMSour estimations

Figure 1. The estimated flux of strangelets [4]compared with existing upper experimental limits[9] and with other predicted astrophysical limits.

strangelet with mass number approximately equalA0−Aair [3]. This procedure continues unless ei-ther a strangelet reaches the Earth or (most prob-able) disintegrates at some depth h in the atmo-sphere, reaching A(h) = Acrit. Actually, in a firstapproximation (in which Aair << Acrit < A0), at

the total penetration depth of the order of

Λ � 43

λN−air

(A0

Aair

)1/3

(1)

where λN−air is the usual mean free path of thenucleon in the atmosphere.

There are a number of candidates for strange-lets known in the literature, the common featureis their small ratio of charge Z to mass number A,Z/A. The so called Saito events have Z � 14 andA � 350 and A � 450 [8]. The most spectacularis the Price event [9] with Z � 46 and A > 1000.On the other hand the Exotic Track event (ET)[10] has been produced after the respective pro-jectile has traversed ∼ 200 g/cm2 of atmosphere.Finally, the so called Centauro events [11] hadbeen produced at depth ∼ 600 g/cm2 and con-tains probably ∼ 200 baryons [12]. In Fig. 1we show the resulting flux of strangelets obtainedby considering the above signals [4]. One canadd to them the recently registered AMS detectorevent [13] with a small ratio Z/A and also verysmall A, estimated to be A � 17.5; it could be ametastable strangelet.

3. Results

This is the picture we shall use to estimate theproduction of muon bundles produced as a resultof interactions of strangelets with atmosphericnuclei. We use for this purpose the SHOWERSIM[14] modular software system specifically modi-fied for our present purpose. The Monte Carloprogram describes the interaction of the primaryparticles at the top of the atmosphere and fol-lows the resulting electromagnetic and hadroniccascades through the atmosphere down to the ob-servation level. Registered are muons with ener-gies exceeding 70 GeV for ALEPH and 50 GeV forDELPHI. Primaries initiated showers were sam-pled from the usual power spectrum P (E) ∝ E−γ

with the slope index equal to γ = 2.7 and withenergies above 10 · A TeV.

The integral multiplicity distribution of muonsfrom ALEPH data are compared with our simu-lations in Fig. 2. For completeness DELPHI dataare present also. At first we have used here theso called “normal” chemical composition of pri-

M. Rybczynski et al. / Nuclear Physics B (Proc. Suppl.) 151 (2006) 341–344342

maries with 40 % protons, 20 % helium, 20 % C-N-O mixture, 10 % Ne-S mixture and 10 % Fe. Asone can see in Fig. 2 the simulations can only de-scribe the low multiplicity (Nμ ≤ 20) region of theALEPH data. The small admixture of strangeletswith the mass number A = 400 being just abovethe critical mass estimated at Acrit ∼ 320 in theprimary flux. Thsis corresponds to relative flux ofstrangelets of FS/Ftotal � 2.4 ·10−5 and can fullyaccommodate the ALEPH data. As can be seen,the DELPHI data [1] differ rather substantially inshape from the ALEPH data. They could be de-scribed equally well for Nμ > 40 but only with a5-fold smaller flux of strangelets. However, in thiscase events with small Nμ would fall completelyoutside the fit4.

One should note that the results of both ex-periments differ already at low muon multiplic-ity. It looks like DELPHI prefers a heavy primarycomposition right from the beginning whereasALEPH prefers a lighter (protons). In any case,the excess of muons is clearly visible. We there-fore regard this as a possible additional signal ofstrangelets5.

4. Conclusions

To conclude, we propose to regard the Cosmo-LEP data on CR muons obtained so far as anadditional possible signal of the possible SQMadmixture present in the primary CR flux. Wewould like to add here that such admixture wouldalso contribute to the CR flux at energies greaterthan the GZK cut-off [4,16], explaining thereforethis phenomenon in a quite natural way6. Thismakes strangelets an interesting subject to inves-tigate in the future.

We would like to close with the following re-mark. With the flux of strangelets as estimatedby us and used here (equal to FS/Ftotal = 2.4 ·10−5 in the energy range of tens of GeV) theenergetic spectrum of strangelets should fall like

4In fact nothing better can be done because neitherALEPH nor DELPHI can at the moment provide any ex-planation of the visible discrepancy of their respective re-sults.5There are still data expected from the L3 experiment,however, so far the muonic part is not yet ready [15].6If it will be finally confirmed by experiment [17].

20 40 60 80 100 120 140 160 180 200N

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

P(>

N)

DELPHIALEPH

Figure 2. Our results (dotted line) correspond-ing to the normal composition, compared withALEPH data [2]. Note that there is a big discrep-ancy between the ALEPH and DELPHI data [1],shown here for comparison.

∼ E−2.4, i.e., with spectral index being muchsmaller than for protons. Actually, this resultagrees nicely with an A-dependence of the spec-tral index of CR’s obtained when fitting the worlddata [18].

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