Cosmic rays and neutrino interactions beyond the standard model

3 Pages·0.09 MB·English

by  Guenter Sigl

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Cosmic rays and neutrino interactions beyond the standard model
Gu¨nter Sigla
a D´epartement d’Astrophysique Relativiste et de Cosmologie,CNRS
Observatoire de Paris, 92195 Meudon Cedex, France
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Some solutions of the hierarchy problem of particle physics can lead to significantly increased neutrino cross
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sections beyond the electroweak scale. We discuss some consequences for and constraints resulting from cosmic
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ray physics.
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n
a
J 1. Introduction The total cross section is dominated by a con-
6 tributionoftheformEq.(1)atenergiesE >∼Eth,
Ithasbeensuggestedthattheneutrino-nucleon where, for M >∼ 1TeV, the threshold energy can
cross section could be enhanced by new physics
1 be approximated by
v beyondtheelectroweakscaleinthecenterofmass
9 frame, or above about a PeV in the nucleon rest M 6.28
4 frame. A specific implementation of this possi- Eth ≃2×1013 (cid:18)TeV(cid:19) eV. (3)
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bility is given in theories with n additional di-
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mensions and a quantum gravity scale M ∼TeV This would be reflected by a linear energy de-
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0 that has recently received much attention in the pendence of the typical column depth of induced
0 literature [1] because it provides an alternative shower development if the optical depth in the
/ solution (i.e., without supersymmetry) to the hi- detection medium is of order unity, or by a flat-
h
p erarchy problem in grand unifications of gauge tening of the differential detection rate by one
- interactions. In such scenarios, the exchange of poweroftheenergyiftheopticaldepthissmaller
p
bulk gravitons (Kaluza-Kleinmodes) can lead to than unity. Comparisonwith observations would
e
h an extra contribution to any two-particle cross eitherrevealsignaturesforthesescenariosorcon-
: section given by [2] straintheminawaycomplementarytoandinde-
v
pendent of many studies on signatures in human
i 4
X σ ≃ 4πs ≃10−27 TeV E cm2, (1) made accelerators [4] or other laboratory experi-
r g M4 (cid:18) M (cid:19) (cid:18)1020eV(cid:19) ments that have recently appeared in the litera-
a
ture.
where the lastexpressionapplies to a neutrino of
energy E hitting a nucleon at rest. Note that
2. A Bound from the “Cosmogenic” Neu-
a neutrino would typically start to interact in
trino Flux
the atmosphere and therefore become a primary
candidate for the highest energy cosmic rays for
Fig. 1 shows neutrino fluxes for the atmo-
σνN >∼10−27cm2, i.e. for E >∼1020eV, assuming spheric background at different zenith angles [5]
M ≃1TeV.
(hatched region marked “atmospheric”), for pro-
The total charged-current neutrino-nucleon
tonblazarsthatarephotonopticallythick tonu-
crosssectionisgivenbythesumofEq.(1)andthe
cleons[6]andwhosefluxwasnormalizedtorecent
cross section within the Standard Model, which
estimates of the blazar contribution to the dif-
can be estimated by [3] fuse γ−ray background[7] (“proton blazar”), for
E 0.363 neutrinos created as secondaries from the decay
σSM(E)≃2.36×10−32 cm2 (2) of charged pions produced by ultra-high energy
νN (cid:18)1019eV(cid:19)
(UHE) nucleons interacting with the cosmic mi-
in the energy range 1016eV<∼E <∼1021eV. crowave background [8] (“cosmogenic”), and for
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the Standard Model cross section Eq. (2). Us-
ing the conservative, lower estimate of the cos-
mogenic flux in Fig. 1 yields
σνN(E =1019eV)<∼2.4×10−29cm2, (4)
as long as σνN(E = 1019eV) <∼ 10−27cm2, such
thatneutrinoswouldgiverisetodeeplypenetrat-
ing air showers. Using Eq. (1) results in
M >∼1.4TeV. (5)
Itisinterestingtonotethattheselimitsdonot
depend on the number n of extra dimensions, in
contrast to some other astrophysical limits such
as from graviton emission from a hot supernova
coreintotheextradimensionswhichdependmore
Figure 1. Predictions for the differential fluxes
explicitly onphasespaceintegrations(see Sect.3
summedoverallneutrinoflavors(solidlines)from
below).
the sources discussed in the text. 1 sigma er-
AscanbeseenfromFig.1,withanexperiment
rorbarsarethe combineddatafromthe Haverah
suchasOWL,theupperlimitonthecrosssection
Park[10],theFly’sEye[11],andtheAGASA[12]
Eq. (4) could improve by about 4 orders of mag-
experimentsabove1019eV.Alsoshownarepiece- nitude,andthelowerlimitonM consequentlyby
wise power law fits to the observed charged CR
about a factor 10.
flux (thick solid line). Points with arrows rep-
resent approximate upper limits on the diffuse 3. Comparison with Other Astrophysical
neutrino flux from the Frejus [13], the EAS- and Laboratory Bounds
TOP [15], and the Fly’s Eye [16] experiments, as
indicated. TheprojectedsensitivityforthePierre There are also astrophysical constraints on
Auger project is using the acceptance estimated M which result from limiting the emission of
in Ref. [17], and the one for the OWL concept bulk gravitons into the extra dimensions. The
study is basedonRef. [20],both assuming obser- strongest constraints in this regard come from
vations over a few years period. nucleon-nucleonbremsstrahlungintypeII super-
novae [21]. These contraints read M >∼ 50TeV,
M >∼ 4TeV, and M >∼ 1TeV, for n = 2,3,4,
respectively, and, therefore, n ≥ 4 is required if
amodelwhereUHEcosmicraysareproducedby neutrino primariesare to serve as a primary can-
decay of particles close to the Grand Unification didate for the UHE cosmic ray events observed
Scale (“SLBY98”, see Ref. [9] for details). above 1020eV (note that n = 7 for the super-
Apartfrom the atmospheric neutrino flux only string and n = 22 for the heterotic string). This
the cosmogenic neutrinos are guaranteedto exist assumes that all extra dimensions have the same
due to the known existence of UHE cosmic rays, size given by
at least if these contain nucleons and are not ex-
clusively of galactic origin. r ≃ M−1 MPl 2/n
The non-observation of deeply penetrating air (cid:18) M (cid:19)
sinhotwheersprbeysenthcee oexfptehriismceonstmsoifnedniiccatfleudxincanFing.ow1 ≃ 2×10−17 TeV MPl 2/ncm, (6)
(cid:18) M (cid:19)(cid:18) M (cid:19)
be translated into an upper limit on the total
neutrino-nucleon cross section σνN ≡ σνSNM +σg where MPl denotes the Planck mass. The above
by scaling the diffuse neutrino flux limits from lower bounds on M thus translate into the cor-
3
responding upper bounds r <∼ 3×10−4mm, r <∼ 5 (1996) 215.
4×10−7mm, andr <∼2×10−8mm, respectively. 9. G. Sigl, S. Lee, P. Bhattacharjee, and
UHE cosmic rays and neutrinos together with S. Yoshida, Phys. Rev. D 59 (1999) 043504.
other astrophysical and cosmological constraints 10. See, e.g., M. A. Lawrence,R. J. O.Reid, and
thus provide an interesting testing ground for A. A. Watson, J. Phys. G Nucl. Part. Phys.
theories involving extra dimensions which rep- 17(1991)733,andreferencestherein;seealso
resent one possible kind of physics beyond the http://ast.leeds.ac.uk/haverah/hav-home
Standard Model. In this context, we mention .html.
that in theories with large compact extra dimen- 11. D. J. Bird et al., Phys. Rev. Lett. 71 (1993)
sions mentioned above, Newton’s law of gravity 3401; Astrophys. J. 424 (1994) 491; ibid. 441
is expected to be modified at distances smaller (1995) 144.
than the length scale given by Eq. (6). Indeed, 12. N. Hayashida et al., Phys. Rev. Lett.
therearelaboratoryexperimentsmeasuringgrav- 73 (1994) 3491; S. Yoshida et al., As-
itational interaction at small distances (for a re- tropart. Phys. 3 (1995) 105; M. Takeda et
cent review of such experiments see Ref. [22]), al., Phys. Rev. Lett. 81 (1998) 1163; see also
which also probe these theories. Thus, future http://icrsun.icrr.u-tokyo.ac.jp/as/project
UHE cosmic ray experiments and gravitational /agasa.html.
experiments in the laboratory together have the 13. W. Rhode et al., Astropart. Phys. 4 (1996)
potentialofprovidingratherstrongtests ofthese 217.
theories. Thesetests wouldbe complementaryto 14. Proc. 24th International Cosmic Ray Con-
constraints from collider experiments [4]. ference (Istituto Nazionale Fisica Nucleare,
Rome, Italy, 1995)
15. M. Aglietta et al. (EAS-TOP collaboration),
REFERENCES
in [14], Vol. 1, 638.
1. N. Arkani-Hamed, S. Dimopoulos, and 16. R. M. Baltrusaitis et al., Astrophys. J. 281
G. Dvali, Phys. Lett. B 429 (1998) 263; (1984) L9; Phys. Rev. D 31 (1985) 2192.
I.Antoniadis,N.Arkani-Hamed,S.Dimopou- 17. J. J. Blanco-Pillado, R. A. Va´zquez, and
los, and G. Dvali, Phys. Lett. B 436 (1998) E. Zas, Phys. Rev. Lett. 78 (1997) 3614;
257; N. Arkani-Hamed, S. Dimopoulos, and K. S. Capelle, J. W. Cronin, G. Parente,and
G. Dvali, Phys. Rev. D 59 (1999) 086004. E. Zas, Astropart. Phys. 8 (1998) 321.
2. S. Nussinov and R. Shrock, Phys. Rev. D 59 18. Proc.25thInternationalCosmic RayConfer-
(1999) 105002. ence, eds.: M. S. Potgieter et al. (Durban,
3. R. Gandhi, C. Quigg, M. H. Reno, and 1997).
I. Sarcevic, Astropart. Phys. 5 (1996) 81; 19. Proc. of International Symposium on Ex-
Phys. Rev. D 58 (1998) 093009. tremely High Energy Cosmic Rays: As-
4. see, e.g., T. G. Rizzo and J. D. Wells, trophysics and Future Observatories, ed.
Phys. Rev. D 61 (2000) 016007, and refer- M. Nagano (Institute for Cosmic Ray Re-
ences therein. search, Tokyo, 1996).
5. P. Lipari, Astropart. Phys. 1 (1993) 195. 20. J. F. Ormes et al., in [18], Vol. 5, 273;
6. R. Protheroe, in Accretion Phenomena and Y. Takahashi et al., in [19], p. 310; see also
Related Outflows, Vol. 163 of IAU Collo- http://lheawww.gsfc.nasa.gov/docs/gamcosray
quium, eds. D. Wickramasinghe,G. Bicknell, /hecr/OWL/.
and L. Ferrario (Astron. Soc. of the Pacific, 21. S.Cullen andM.Perelstein,Phys.Rev.Lett.
1997), p. 585. 83 (1999) 268; V. Barger, T. Han, C. Kao,
7. R. Mukherjee and J. Chiang, and R.-J. Zhang, Phys. Lett. B 461 (1999)
Astropart. Phys. 11 (1999) 213. 34.
8. R. J. Protheroe and P. A. Johnson, As- 22. J. C. Long, H. W. Chan, and J. C. Price,
tropart.Phys.4(1996)253,anderratumibid. Nucl. Phys. B 539 (1999) 23.