- Email: [email protected]
Fluxes of vμ and ve in the atmosphere: Is there an anomaly?
I| l l [ | I W-q,'| | --L'kq][1~1 :!
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 35 (1994) 209-215 North-Holland
Fluxes of
a n d Ve in t h e a t m o s p h e r e : Is there an a n o m a l y ?
T.K. Gaisser a* aBartol Research Institute, University of Delaware Newark DE 19716 USA There is a persistent discrepancy between the calculated and observed flavor ratio of cosmic ray neutrinos in the atmosphere, particularly in the energy region below 1 GeV. In this talk I review the status of calculations of atmospheric neutrinos and discuss possible interpretations in terms of neutrino oscillations. Limits from neutrinoinduced upward muons are also considered.
interactions of v and ~ is
1. I N T R O D U C T I O N Simple considerations of kinematics lead to the expectation that the ratio ue/u t, in the atmosphere should be approximately one-half for energies low enough so that almost all muons decay. The relevant energy is ,,, 1 GeV. The asymmetry of the two-body decay lr --* p + v~ means that the v~ from pion decay has about the same energy as the vu and the ve from the decay chain a- ~ / ~ ---, e + v~ + re. This simple expectation is borne out by several calculations [1-4], which give
Rel#
--
~'e ut, ++ l['e ½~t, -
0.49 -4- 0.01
(1)
for 0.1 < Ev < 1 GeV [5]. In contrast, the large water Cherenkov detectors find a ratio ve/v~ > 1 from measurement of contained electrons and muons due to charged current interactions of neutrinos and antineutrinos inside the fiducial volume of the detectors [6,7]. Part of the difference between expectation and observation is a consequence of the fact that the acceptance of the detectors spans a larger energy range for electrons than for muons. Even after accounting for flavor-dependence of the acceptance, however, a significant discrepancy remains. Detailed simulations of the detector response, including acceptance effects, lead to the result that the ratio of ratios for charged leptons from *Work supported in part by the U.S. Department of Energy under Grant DE-FG02-91ER40626.
(u/e),,,
0.60 ± 0.06 ± 0.05
(2)
for Kamiokande with 6.2 kT-yrs of data (389 contained, single-ring events) [8]. The corresponding IMB result is (F/e)data (~,le),,,,
-
0.54 + 0.03 + 0.05
(3)
for 7.7 kT-yrs of data (507 contained, single-ring events [7]). The water detectors thus show at least a 4a discrepancy between observation and expectation for the vg/v~ ratio. Measurements with tracking calorimeters give mixed results, and the statistical uncertainties are significantly larger than for the water detectors. NUSEX (0.74 kT-yrs, [9]) and Frejus (1.56 kT-yrs, [10]) are both consistent with expectation. In contrast, Soudan 2 (1.0 kT-yrs, [11]) finds a ratio of ratios similar to Kamiokande. The number of events is relatively low in all three experiments, and the systematic effects are also different. Beam tests of the response of water Cherenkov detectors to electrons and muons will soon be carried out at KEK. This should help to resolve questions about the efficiency for discrimination between neutrino flavors in these detectors. Another possible source of systematic error that has been pointed to is the cross section for charged current interactions of neutrinos in nuclei. The Fermi gas model has been used for calculation of the spectra of the produced charged leptons by both gamiokande [12] and IMB [13]. Recent calculations by Engel et al. [14] include
0920-5632194/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0920-5632(94)00458-8
-
210
T.K. Gaisser /Fluxes o f v ~ and u e in the atmosphere." Is there an anomaly?
several effects that go beyond the Fermi gas model. They find no significant shift in the spectra of electrons relative to muons that would distort the inferred ve/u~ ratio. In addition, there is some direct confirmation of the Fermi gas model for Ev > 400 M e V in data discussed in Ref. [15]. Another experiment [16] which appears to show an anomalous result for the rnuon spectrum in v~, -{- carbon ---, p -{- ... is in any case below the energy range of interest here (p~, > 200 M e V / c for Kamiokande and p~ > 300 M e V / c for IMB). In this talk I take the discrepancy in the ratio of ratios at face value and consider the potential consequences for an interpretation in terms of neutrino oscillations. Section 2 is a detailed comparison of the four calculations of the atmospheric neutrino flux with emphasis on the implications for a neutrino oscillation interpretation. The point is that, although all the calculations give the same value (within 5%) for the v~/v~ ratio, an interpretation in terms of oscillations depends on whether there are too few v~ or too m a n y re. This in turn depends on the magnitude of the calculated fluxes. The conclusion is that vacuum oscillations in the ~ ~ v~ sector could account for the observations. Section 3 is a discussion of the implication for neutrino-induced upward muons. I conclude that the Kamiokande [17] and I M B [18] measurements of upward muons are both consistent with a v~ ~ v~ interpretation of the contained event anomaly. This appears not to be the case with the Baksan [19] data, a point to which I return in the concluding section.
[3] are intermediate. In all cases, 3-flavor oscillation scenarios are allowed. The calculations of Refs. [1,2] are, however, inconsistent with 2-flavor oscillations between v~ and re, and that of Ref. [4] is inconsistent with 2-flavor v~ ~ yr. It has also been suggested [22] that the Bugaev & Naui-nov fluxes [4] are consistent with an interpretation in terms of proton decay, p ---,e + v v. To discriminate among these and other possible interpretations of the atmospheric neutrino anomaly requires a better knowledge of the shape and normalization of the neutrino flux than that shown in Fig. 1. The neutrino flux in the atmosphere depends on the primary cosmic ray spectrum, geomagnetic cutoffs, pion production in the atmosphere, and propagation and decay of muons in the atmosphere. W e [23] have made detailed comparisons of as many of these ingredients as possible in an attempt to understand the source of the differences in the calculated fluxes. W e find [23] that differences in treatment of primary spectrum/composition and geomagnetic cutoffs are relatively small and that the characteristic shape and magnitude of the fluxes of Ref. [4] arise mainly from a difference in the treatment of pion production.
1000 ~
Ka.miokande,
n 2. F L U X C A L C U L A T I O N S The biggest difference a m o n g the flux calculations is the low value found by Bugaev & N a u m o v [4] at low energy, as illustrated in Fig. I. Honda et ai. [20] have analysed the ve/u~ anomaly for the different fluxes in a Frampton-Glashow plot [21]. Each set of fluxes (v~ and re), together with the experimental uncertainties, defines an allowed region in the Frampton-Glashow plane of 3-flavor oscillations. The higher fluxes of Refs. [1,2]agree with the observed rate of electron-like events but predict too m a n y v#. Thus they suggest an interpretation in terms of v~ ~ v~. In contrast, the lower fluxes of Ref. [4] predict too few ve and so suggest v~ ~ u~, oscillations. The fluxes of Ref.
L ,5
~
1,5
2
2.5
F-.. GeV
Fig. 1. Fluxes of v~ + ~ (upper set) and v~ + ~ (lower set) at Kamiokande averaged over all directions at solar m i n i m u m from three calculations: Points-[1]; solid lines-[2]; dashed lines-[4].
TK. Gaisser /Fluxes o f L,~ and t,e in the atmosphere: Is there an anomaly?
The inclusive cross sections for production of low energy (< 2 GeV) pions in the parametrizations used by Bugaev & Naumov [4] are lower than those used in the other calculations, as illustrated in distributions used in the four calculations~ for 24 GeV protons interacting in air (A:14.5). These distributions are compared with data from interactions in beryllium of 24 GeV/c [24] and 19 GeV/c [25] protons. The difference is larger for lower interaction energies. Perkins [private communication] has pointed out that the pion distribution of Bugaev & Naumov that is shown in Pig. 2 agrees with pion spectra measured in proton-proton coUisions.[26] The excess events at low pion momentum in the models of Refs. [1,2] are presumably due to the effect of the target nucleus. Whether the nuclear effect is overestimated remains an open question, but it should surely be present. The parametrization of Ref. [4] is almost certainly an underestimate at low interaction energy in view of the fact that it gives a multiplicity of charged pions lower than that in proton-proton collisions [27]. One way to check the caiculations is by comparison to measurements of the muon flux at high altitude [28]. Existing measurements [29-31] have large uncertainties, and the conditions of the experiments (including epoch of the solar cycle) are not fully specified. The calculated muon fluxes at 10 - 20 km differ significantly for E~ ~ 1 GeV, about a factor of 1.5 higher for Ref. [1] than for R.ef. [4]. A precision measurement of the muon energy spectrum in this energy range as a function of altitude (such as that of Ref. [32]) should be able to reduce uncertainties in the magnitude of the
211
a preliminary version of this 3-dimensional calculation [33], a comparison with a corresponding one-dimensional calculation showed that the two were indistinguishable for E~ > 0.2 GeV.
.8 ~-['~ iLl
Hist: TARGET
Dash: Naumov
.6
.2
0
ltl''ll''ll''ll,,ll,, ~-~.]
IS&24 GeV ~
.8 ~-~ I ~,J"~"I X
pBe lr- data
Hist: TARGET Dash: Naumov
.6
.2
0 0
.2
.4
.6
.8
XL
Fig. 2. Inclusive cross sections for production of charged pions by protons on beryllium: Histogram-Ill; Dots-J2]; Dashes-[4]. In the remainder of this talk I will assume that the higher normalization (and steeper low energy spectra) of the atmospheric flux caiculations of Refs. [1,2] are correct and that an explanation of the contained event anomaly (Ev < 1 GeV) in terms of oscillations would be closer to ua *-* u~ than to v, *-* vs. The Kamiokande group [6] indeed found a relatively large allowed region at large mixing angle in the sin 2 28-6m 2 plane for v, *-* v, oscillations. Fogli et aL [34] have recently done a compos-
T.K. Gaisser /Fluxes o f u ~, and u e in the atmosphere: Is there an anomaly?
212
ite analysis of all the measurements of contained neutrino events. They find an allowed region at the 2 a level t h a t is bounded approximately by 6rn s > 10 -~ eV s and sin s 20 > 0.55 for ug ~-* vr two-flavor vacuum oscillations. This region is truncated from above (6m s < 0.3 eV s) by accelerator measurements [35]. Fogli et al. point out that a simultaneous MSW solution [37,36] of the solar neutrino problem is possible with ms "-" 3 x 10 -3 eV. Such a solution would give the "natural" relation, m l < ms < ms. Since m S " ' r n , r < 1 eV, however, the simple see-saw relation [38], =
~ 5000
would not be satisfied. 8. N E U T R I N O - I N D U C E D
UPWARD
MUONS A n explanation of the contained event problem at low energy in terms of v~ 4--,v~. oscillations will have significant implications for the predicted rate of neutrino-induced upward muons. For example, for 6m s = 8 x 10 - s eV s, and L : 104 km (a typical propagation distance for an upward muon that interacts below the detector) the first node of 1 - P~_..,~
:
P~-~v~
-
sins 20 sins ( 1 2 7 6 m
-
(4) _
E-'~-v~vj
is at E -- 65 GeV. This energy is in the middle of the energy range important for generation of neutrino-induced upward muons. Thus, for large mixing angles the upward m u o n flux would be significantly suppressed, approaching the level of 1 - ½sin s 20 for L 6 m S / E > > lr/2. In Ref. [39] we made a detailed comparison with the Kamiokande d a t a [17] on neutrinoinduced upward muons for various values of input parameters for an assumed two flavor v~ ~ v,. mixing. We used the experimental definition of a throughgoing muon in Karniokande [40]. We checked t h a t we reproduced the results of Ref. [40] for several calculations in the absence of neutrino oscillations for a variety of specific assumptions a b o u t neutrino propagation and cross sections.
The signal of neutrino-induced upward muons is given by a convolution of Signal ,,, R~ @ av--.~ @ Pv~-,~ @ Cv.
(5)
Here ¢~ is the differential flux of v~ ( ~ ) , and
cr~__.~ is the cross section (differential in Et,) for the charged current interaction of a v~ (D~). For the range calculation (R~) we used the calculation of Lipari & Stanev [41],which gives the probability that a muon of initialenergy E~ survives with energy E~. The results of Ref. [41] are essentially the same as those of Lohmann et al. [42] in the relevant energy range. The m a j o r sources of uncertainty in Eq. 5 are the neutrino flux and, to a lesser extent, the cross section for v~,(f,~,) + N ---* # - ( p + ) + anything. We need values for these quantities up to much higher energies (,,- 1 TeV) than for the contained events. Both IMB [18] and Kamiokande [17] used relatively low values of cross section [43] and neutrino flux [44] as central values for comparison with their data. In Ref. [39], we showed that, with the same input as IMB [18] we reached the same conclusion; namely, that u~ ~-~ v~ oscillations are excluded at 90% c.1. for 6m 2 > 10 -2 eV 2 and sin 2 20 > 0.4. When we used a better representation of the neutrino cross section [45] and a higher neutrino flux [46,47], however, the region excluded by upward, throughgoing muons was much smaller (see Fig. 4 of Ref. [48]). In particular, much of the region "allowed" by the Kamiokande measurement [6] is also allowed by the upward muons in the sense that it is not excluded at the 90% confidence level. The region between ,~ 3 × 10 -4 and ,-, 10 - s eV s excluded by the IMB analysis of stopping to throughgoing muons is more stable because uncertainties tend to cancel in the ratio. 4. S U M M A R Y
The large water Cherenkov detectors have now accumulated nearly i000 single-ring, contained interactions of atmospheric neutrinos, which they have classified as electron-like or muon-like. Taken at face value, comparison between simulations and observations shows a discrepancy of more than four sigma. If the higher neutrino flux calculations [1,2] prove to be correct, the discrepancy would imply a deficit of v~, at the detector,
TK. Gaisser/Fluxes o f t,~ and t,e in the atmosphere: Is there an anomaly?
while the observed number of v~ agrees with expectation. This suggests v~, ~ v~ for an explanation in terms of neutrino oscillations. To explain the magnitude and lack of angular dependence of the contained event anomaly, one would need large mixing angle and large Srn2 (e.g. sin s 20 >_ 0.5 and 6m 2 10 -2 to 10 -1 eV2). The parameters of a vf, ~-* v~- scenario are then such that there should also be a significant deficit of upward v~,-induced muons. We have shown [39] that the Karniokande measurement of throughgoing muons (from all angles below the horizon) is indeed about 15% below the calculated rate when we use the best representation of the cross section [45] and a relatively high neutrino flux, as suggested by two recent calculations [46,47]. This could be nicely accounted for by an oscillation that would also explain the contained event anomaly. We have shown indirectly that the IMB data could also be interpreted in this way. The Baksan experiment has also measured the rate of upward muons. They find, however, that they still exclude most of the Kamiokande Uallowed" region even when they use the highest neutrino flux calculation [46] and a renormalized cross section that is approximately equivalent to that of Ref. [45] as used by Frati et al. [39]. The Baksan limit on v~, ,--* v~ oscillations is based on upward events near the vertical, specifically zenith angles in the interval - 1 < cos 0 < -0.6. Table 1 is a comparison of experiments and calculations in this limited angular region. Table 1. Upward muon fluxes Baksan Experiment: 161 Calculations: - - H i g h v-flux 163 - - L o w v-flux 142
for cos 0 < -0.6. Kamiokande 1.42 =t: 0.18 1.76 (1.34) 1.55
In Table 1 the Baksan column is the number of events with cos 0 < - 0 . 6 obtained in a live time of 7.15 years [19] The Kamiokande column contains the upward flux averaged over the same angular region 3 in units of 10 -13 c m - 2 s - l s r -1. I have avoided comparing the experimental fluxes directly because that would require converting between two different and non-trivial threshold ~The total r e p o r t e d Ksmiokande d a t a sample [17] consists of 252 events from all directions below the horizon.
213
functions. 4 Instead, I compare each data set with a calculation that folds in the detector acceptance in detail. The calculation for Baksan is from Ref. [19] and that for Kamiokande from Ref. [39]. Both calculations use similar assumptions for neutrino cross section and muon propagation. Inspection of Table 1 shows that the calculation with the high neutrino flux [46] and no oscillations agrees with the Baksan data whereas the corresponding calculation is two a higher than the Kamiok~nde data. The number in parentheses (1.34) is the predicted rate for Kamiol~nde with the high neutrino flux [46] assuming vz ~ v~ oscillations with sin 2 26 = 0.5 and 10 -~ < 6m 2 < 10 -1 eV 2. It is consistent with the Kamiokande data. A similar suppression of the corresponding Baksan number would be 3 a below their observation. To the extent that the two calculations contain the same physics, this discrepancy indicates a (modest) difference in the measured rate between Baksan and Kamiokande. The MACRO group reported for the first time at this conference [49] its measurement of upward muon rates together with a comparison to calculations. The MACRO acceptance is mostly in the vertical direction, where there is some indication of a deficit with respect to the expected value based on a high neutrino flux, but there are large st~istical and systematic uncertainties at present. In half year of running with six supermodules there are 27 events in the zenith angle range cos 0 < -0.6. (The data sample also includes two years of data with one supermodule.) At this rate the MACRO experiment will have comparable statistics to Baksan in two more years of running. My conclusion is that the present data on upward muons do r,ot rule out a v~, ~ vr oscillation at a level sufficient to explain the contained event anomaly. A tenfold increase in statistics would help resolve the situation, particularly if the full zenith angle range can be measured accurately. For example, with 6m 2 ~ 0.1 eV 2 the flux would be significantly suppressed near the horizontal as well as for cos 8 < -0.2, but for 6m ~ ,,, 0.01 eV 2 the near horizontal flux would not be suppressed. 4There is an approximate conversion in Rei'. [39] to a commo~ effective threshold of 3 GeV which shows that the experiments are not giving grossly different results.
214
T.K. Gaisser/Fluxes of u~ and ue in the atmosphere: Is there an anomaly?
A C K N O W L E D G M E N T S . I am grateful to Maury Goodman, Paolo Lipari, A.K. Mann, S. Mikheyev, Don Perkins and Todor Stanev for helpful discussions on the subject of atmospheric neutrinos.
Astrophyaics (Takayama, ed. Y. Suzuki & K.
21. 22.
REFERENCES
23.
1. G. Barr, T.K. Galeser & Todor Stanev, Phys. Rev. D39 (1989) 3532. 2. M. Honda, K. Kasahara, K. Hidaka & S. Midorikawa, Physics Letters B 248 (1990) 193. 3. H. Lee & Y.S. Koh, Nuovo Cimento B 105 (1990) 883. 4. E.V. Bugaev & V.A. Naumov, Physics Letters B 232 (1989) 391. 5. T.K. Gaisser Phil. Trans R. Soc. Lond. A (1993). 6. K.S. Hirata et al. (Kamio_~nde Collaboration), Phys. Letters B 280 (1992) 146. 7. R. Becker-Szendy et al. (IMB Collaboration), Phys. Rev. D 46 (1992) 3720. 8. T. Kajita, in Frontiers of Neutrino Astrophysics (Takayarna, ed. Y. Suzuki & K. Nakamura, Universal Academy Press, Tokyo, 1992) p. 293. 9. M. Aglietta et al. (NUSEX) Europhysics Letters 8 (1989) 611. 10. Ch. Berger et al. (Frejus) Physics Letters B 245 (1990) 305. and 227 (1989) 489. 11. M. Goodman in Proc. C~l#a~y Worluhop on A t m o s p h e r i c u ' s 21 July 1993, p. 1. 12. M. Takita, Ph.D. Thesis, Univ. of Tokyo, February 1989, ICR-Report-186-89-3. 13. David W. Casper, Ph.D. Thesis, Univ. of Michigan, 1990. 14. J. Engel, E. Kolbe, K. Langanke & P. Vogel, Phys. Rev. D 48 (1993) 3048. 15. R. Merenyi et al. Phys. Rev. D 45 (1992) 743. 16. D.D. Koetke et al., Phys. Rev. C 46 (1992) 2554. 17. M. Mori et al., Physics Letters B 210 (1991) 89. 18. R. Becker-Ssendy et al., Phys. Rev. Letters 69 (1992) 1010. 19. M.M. Boliev et al.,in Proc. Bed Int. Workahop on Neutrino Telescopes (ed. M. Baldo Ceolin) (1991) 235. 20. M. Honda, K. Kasahara & S. Midorikawa in Frontiers
of
Neutrino
24. 25. 26. 27. 28. 29. 30.
31.
Nakamura, Universal Academy Press, Tokyo, 1992) p. 309. P.H. Frampton & S.L. Glashow, Phya. Rev. D 25 (1982) 1982. W.A. Mann, T. Kafl~ & W. Leeson, Physics Letters B 291 (1992) 200. T.K. Gaisser, Todor Stanev, V. Agrawal, V. Nanmov, M. Honda, K. Kasahara, in preparation (1993). T. Eichten et al., Nucl. Phys. B 44 (1972) 333. J.V. A11aby et al., CERN Yellow Report 70-12 (1970) unpublished. H.J. Mfick et al. Physics Letters 39B (1972) 303. M. Antinucci et al. Lettere al Nuovo Cimento 6 (1973) 121. D.H. Perkins Oxford preprint 85/84 and Nucl. Phys. B 399 (1992) 3. M. Conversi, Phys. Rev. 79 (1950) 749. E.A. Bogomolov et al. as quoted by E.V. Bugaev, G.V. Domogatsky & V.A. Naumov in Proc. Japan-U.S. Seminar on Cosmic Ray Muon and Neutrino Physics/Astrophysics (ed. Y. Ohashi & V.Z. Peterson, 1986) p. 232. L.T. Baradzei et a/. Zh. Eksp. Teor. Fiz. 36
(1959) 1617. 32. M. Circella et al., Proc. 23rd Int. Cosmic Ray Conf. (Calgary) 4 (1993) 503. 33. H. Lee & S.A. Bludman, Phys. Rev. D 37 (1988) 122. 34. G.L. Fogli, E. Lisi & D. Montanino, CERNTH. 6944/93, BARI-TH/146/93, Phys. Rev. D (to be published). 35. C D H S W Collaboration, F. Dydak et al. Physics Letters B 134 (1984) 281. 36. L. Wolfenstein, Phys. Rev. D 17 (1979) 2369. 37. S.P, Mikheyev & A. Yu. Smirnov, Soy. Phys. JETP 64 (1986) 64. 38. M. Gel]-Mann, P. Ramond & R. Slansky in S u p e r ~ / t y (eds. F. Van Nieuwenhuisen & D. Freedman, Amsterdam, North Holland, 1979) p. 315. 39. W. Frati, T.K. Gaisser, A.K. Mann & Todor Stanev, Phys. Rev. D 48 (1993) 1140. 40. Yuichi Oyama, Ph.D. Thesis, Univ. of Tokyo ICR-Report-193-89-10 (1989). 41. Paolo Lipari & Todor Stanev, Phys. Rev. D 44 (1991) 3543. 42. W. Lohmann, R. Kopp & R. Vow, CERN Yel-
TK. Gaisser/Fluxes of v~ and v e in the atmosphere: Is there an anomaly?
low Report No. EP/85-03 (unpublished). 43. E. Eichten, I. Hinchcliffe, K. Lane & C. Quigg, Revs. Mod. Phys. 56 (1984) 579 and E~tum 58 (1986) 1065. 44. L.V. Volkova Soy. J. Nucl. Phys. 31 (1980) 784. 45. J.F. Owens, Physics Letters B 266 (1991) 126. 46. A.V. Butkevich, L.G. Dedenko & I.M. Zheleznykh Soy. J. Nucl. Phys. 50 (1988) 90. 47. V. Agrawal, T.K. Gaisser, P. Lipari & T. Stanev, in preparation (1993). 48. T.K. Gaisser in Frontier8 o f N e u t r i n o Aatroph~sic8 (Takayama, ed. Y. Suzuki & K. Nakamura, Universal Academy Press, Tokyo) (1992) p. 309. 49. D. Michael, talk presented at TAUP93, 21 Sept. 1993.
215
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 35 (1994) 209-215 North-Holland
Fluxes of
a n d Ve in t h e a t m o s p h e r e : Is there an a n o m a l y ?
T.K. Gaisser a* aBartol Research Institute, University of Delaware Newark DE 19716 USA There is a persistent discrepancy between the calculated and observed flavor ratio of cosmic ray neutrinos in the atmosphere, particularly in the energy region below 1 GeV. In this talk I review the status of calculations of atmospheric neutrinos and discuss possible interpretations in terms of neutrino oscillations. Limits from neutrinoinduced upward muons are also considered.
interactions of v and ~ is
1. I N T R O D U C T I O N Simple considerations of kinematics lead to the expectation that the ratio ue/u t, in the atmosphere should be approximately one-half for energies low enough so that almost all muons decay. The relevant energy is ,,, 1 GeV. The asymmetry of the two-body decay lr --* p + v~ means that the v~ from pion decay has about the same energy as the vu and the ve from the decay chain a- ~ / ~ ---, e + v~ + re. This simple expectation is borne out by several calculations [1-4], which give
Rel#
--
~'e ut, ++ l['e ½~t, -
0.49 -4- 0.01
(1)
for 0.1 < Ev < 1 GeV [5]. In contrast, the large water Cherenkov detectors find a ratio ve/v~ > 1 from measurement of contained electrons and muons due to charged current interactions of neutrinos and antineutrinos inside the fiducial volume of the detectors [6,7]. Part of the difference between expectation and observation is a consequence of the fact that the acceptance of the detectors spans a larger energy range for electrons than for muons. Even after accounting for flavor-dependence of the acceptance, however, a significant discrepancy remains. Detailed simulations of the detector response, including acceptance effects, lead to the result that the ratio of ratios for charged leptons from *Work supported in part by the U.S. Department of Energy under Grant DE-FG02-91ER40626.
(u/e),,,
0.60 ± 0.06 ± 0.05
(2)
for Kamiokande with 6.2 kT-yrs of data (389 contained, single-ring events) [8]. The corresponding IMB result is (F/e)data (~,le),,,,
-
0.54 + 0.03 + 0.05
(3)
for 7.7 kT-yrs of data (507 contained, single-ring events [7]). The water detectors thus show at least a 4a discrepancy between observation and expectation for the vg/v~ ratio. Measurements with tracking calorimeters give mixed results, and the statistical uncertainties are significantly larger than for the water detectors. NUSEX (0.74 kT-yrs, [9]) and Frejus (1.56 kT-yrs, [10]) are both consistent with expectation. In contrast, Soudan 2 (1.0 kT-yrs, [11]) finds a ratio of ratios similar to Kamiokande. The number of events is relatively low in all three experiments, and the systematic effects are also different. Beam tests of the response of water Cherenkov detectors to electrons and muons will soon be carried out at KEK. This should help to resolve questions about the efficiency for discrimination between neutrino flavors in these detectors. Another possible source of systematic error that has been pointed to is the cross section for charged current interactions of neutrinos in nuclei. The Fermi gas model has been used for calculation of the spectra of the produced charged leptons by both gamiokande [12] and IMB [13]. Recent calculations by Engel et al. [14] include
0920-5632194/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0920-5632(94)00458-8
-
210
T.K. Gaisser /Fluxes o f v ~ and u e in the atmosphere." Is there an anomaly?
several effects that go beyond the Fermi gas model. They find no significant shift in the spectra of electrons relative to muons that would distort the inferred ve/u~ ratio. In addition, there is some direct confirmation of the Fermi gas model for Ev > 400 M e V in data discussed in Ref. [15]. Another experiment [16] which appears to show an anomalous result for the rnuon spectrum in v~, -{- carbon ---, p -{- ... is in any case below the energy range of interest here (p~, > 200 M e V / c for Kamiokande and p~ > 300 M e V / c for IMB). In this talk I take the discrepancy in the ratio of ratios at face value and consider the potential consequences for an interpretation in terms of neutrino oscillations. Section 2 is a detailed comparison of the four calculations of the atmospheric neutrino flux with emphasis on the implications for a neutrino oscillation interpretation. The point is that, although all the calculations give the same value (within 5%) for the v~/v~ ratio, an interpretation in terms of oscillations depends on whether there are too few v~ or too m a n y re. This in turn depends on the magnitude of the calculated fluxes. The conclusion is that vacuum oscillations in the ~ ~ v~ sector could account for the observations. Section 3 is a discussion of the implication for neutrino-induced upward muons. I conclude that the Kamiokande [17] and I M B [18] measurements of upward muons are both consistent with a v~ ~ v~ interpretation of the contained event anomaly. This appears not to be the case with the Baksan [19] data, a point to which I return in the concluding section.
[3] are intermediate. In all cases, 3-flavor oscillation scenarios are allowed. The calculations of Refs. [1,2] are, however, inconsistent with 2-flavor oscillations between v~ and re, and that of Ref. [4] is inconsistent with 2-flavor v~ ~ yr. It has also been suggested [22] that the Bugaev & Naui-nov fluxes [4] are consistent with an interpretation in terms of proton decay, p ---,e + v v. To discriminate among these and other possible interpretations of the atmospheric neutrino anomaly requires a better knowledge of the shape and normalization of the neutrino flux than that shown in Fig. 1. The neutrino flux in the atmosphere depends on the primary cosmic ray spectrum, geomagnetic cutoffs, pion production in the atmosphere, and propagation and decay of muons in the atmosphere. W e [23] have made detailed comparisons of as many of these ingredients as possible in an attempt to understand the source of the differences in the calculated fluxes. W e find [23] that differences in treatment of primary spectrum/composition and geomagnetic cutoffs are relatively small and that the characteristic shape and magnitude of the fluxes of Ref. [4] arise mainly from a difference in the treatment of pion production.
1000 ~
Ka.miokande,
n 2. F L U X C A L C U L A T I O N S The biggest difference a m o n g the flux calculations is the low value found by Bugaev & N a u m o v [4] at low energy, as illustrated in Fig. I. Honda et ai. [20] have analysed the ve/u~ anomaly for the different fluxes in a Frampton-Glashow plot [21]. Each set of fluxes (v~ and re), together with the experimental uncertainties, defines an allowed region in the Frampton-Glashow plane of 3-flavor oscillations. The higher fluxes of Refs. [1,2]agree with the observed rate of electron-like events but predict too m a n y v#. Thus they suggest an interpretation in terms of v~ ~ v~. In contrast, the lower fluxes of Ref. [4] predict too few ve and so suggest v~ ~ u~, oscillations. The fluxes of Ref.
L ,5
~
1,5
2
2.5
F-.. GeV
Fig. 1. Fluxes of v~ + ~ (upper set) and v~ + ~ (lower set) at Kamiokande averaged over all directions at solar m i n i m u m from three calculations: Points-[1]; solid lines-[2]; dashed lines-[4].
TK. Gaisser /Fluxes o f L,~ and t,e in the atmosphere: Is there an anomaly?
The inclusive cross sections for production of low energy (< 2 GeV) pions in the parametrizations used by Bugaev & Naumov [4] are lower than those used in the other calculations, as illustrated in distributions used in the four calculations~ for 24 GeV protons interacting in air (A:14.5). These distributions are compared with data from interactions in beryllium of 24 GeV/c [24] and 19 GeV/c [25] protons. The difference is larger for lower interaction energies. Perkins [private communication] has pointed out that the pion distribution of Bugaev & Naumov that is shown in Pig. 2 agrees with pion spectra measured in proton-proton coUisions.[26] The excess events at low pion momentum in the models of Refs. [1,2] are presumably due to the effect of the target nucleus. Whether the nuclear effect is overestimated remains an open question, but it should surely be present. The parametrization of Ref. [4] is almost certainly an underestimate at low interaction energy in view of the fact that it gives a multiplicity of charged pions lower than that in proton-proton collisions [27]. One way to check the caiculations is by comparison to measurements of the muon flux at high altitude [28]. Existing measurements [29-31] have large uncertainties, and the conditions of the experiments (including epoch of the solar cycle) are not fully specified. The calculated muon fluxes at 10 - 20 km differ significantly for E~ ~ 1 GeV, about a factor of 1.5 higher for Ref. [1] than for R.ef. [4]. A precision measurement of the muon energy spectrum in this energy range as a function of altitude (such as that of Ref. [32]) should be able to reduce uncertainties in the magnitude of the
211
a preliminary version of this 3-dimensional calculation [33], a comparison with a corresponding one-dimensional calculation showed that the two were indistinguishable for E~ > 0.2 GeV.
.8 ~-['~ iLl
Hist: TARGET
Dash: Naumov
.6
.2
0
ltl''ll''ll''ll,,ll,, ~-~.]
IS&24 GeV ~
.8 ~-~ I ~,J"~"I X
pBe lr- data
Hist: TARGET Dash: Naumov
.6
.2
0 0
.2
.4
.6
.8
XL
Fig. 2. Inclusive cross sections for production of charged pions by protons on beryllium: Histogram-Ill; Dots-J2]; Dashes-[4]. In the remainder of this talk I will assume that the higher normalization (and steeper low energy spectra) of the atmospheric flux caiculations of Refs. [1,2] are correct and that an explanation of the contained event anomaly (Ev < 1 GeV) in terms of oscillations would be closer to ua *-* u~ than to v, *-* vs. The Kamiokande group [6] indeed found a relatively large allowed region at large mixing angle in the sin 2 28-6m 2 plane for v, *-* v, oscillations. Fogli et aL [34] have recently done a compos-
T.K. Gaisser /Fluxes o f u ~, and u e in the atmosphere: Is there an anomaly?
212
ite analysis of all the measurements of contained neutrino events. They find an allowed region at the 2 a level t h a t is bounded approximately by 6rn s > 10 -~ eV s and sin s 20 > 0.55 for ug ~-* vr two-flavor vacuum oscillations. This region is truncated from above (6m s < 0.3 eV s) by accelerator measurements [35]. Fogli et al. point out that a simultaneous MSW solution [37,36] of the solar neutrino problem is possible with ms "-" 3 x 10 -3 eV. Such a solution would give the "natural" relation, m l < ms < ms. Since m S " ' r n , r < 1 eV, however, the simple see-saw relation [38], =
~ 5000
would not be satisfied. 8. N E U T R I N O - I N D U C E D
UPWARD
MUONS A n explanation of the contained event problem at low energy in terms of v~ 4--,v~. oscillations will have significant implications for the predicted rate of neutrino-induced upward muons. For example, for 6m s = 8 x 10 - s eV s, and L : 104 km (a typical propagation distance for an upward muon that interacts below the detector) the first node of 1 - P~_..,~
:
P~-~v~
-
sins 20 sins ( 1 2 7 6 m
-
(4) _
E-'~-v~vj
is at E -- 65 GeV. This energy is in the middle of the energy range important for generation of neutrino-induced upward muons. Thus, for large mixing angles the upward m u o n flux would be significantly suppressed, approaching the level of 1 - ½sin s 20 for L 6 m S / E > > lr/2. In Ref. [39] we made a detailed comparison with the Kamiokande d a t a [17] on neutrinoinduced upward muons for various values of input parameters for an assumed two flavor v~ ~ v,. mixing. We used the experimental definition of a throughgoing muon in Karniokande [40]. We checked t h a t we reproduced the results of Ref. [40] for several calculations in the absence of neutrino oscillations for a variety of specific assumptions a b o u t neutrino propagation and cross sections.
The signal of neutrino-induced upward muons is given by a convolution of Signal ,,, R~ @ av--.~ @ Pv~-,~ @ Cv.
(5)
Here ¢~ is the differential flux of v~ ( ~ ) , and
cr~__.~ is the cross section (differential in Et,) for the charged current interaction of a v~ (D~). For the range calculation (R~) we used the calculation of Lipari & Stanev [41],which gives the probability that a muon of initialenergy E~ survives with energy E~. The results of Ref. [41] are essentially the same as those of Lohmann et al. [42] in the relevant energy range. The m a j o r sources of uncertainty in Eq. 5 are the neutrino flux and, to a lesser extent, the cross section for v~,(f,~,) + N ---* # - ( p + ) + anything. We need values for these quantities up to much higher energies (,,- 1 TeV) than for the contained events. Both IMB [18] and Kamiokande [17] used relatively low values of cross section [43] and neutrino flux [44] as central values for comparison with their data. In Ref. [39], we showed that, with the same input as IMB [18] we reached the same conclusion; namely, that u~ ~-~ v~ oscillations are excluded at 90% c.1. for 6m 2 > 10 -2 eV 2 and sin 2 20 > 0.4. When we used a better representation of the neutrino cross section [45] and a higher neutrino flux [46,47], however, the region excluded by upward, throughgoing muons was much smaller (see Fig. 4 of Ref. [48]). In particular, much of the region "allowed" by the Kamiokande measurement [6] is also allowed by the upward muons in the sense that it is not excluded at the 90% confidence level. The region between ,~ 3 × 10 -4 and ,-, 10 - s eV s excluded by the IMB analysis of stopping to throughgoing muons is more stable because uncertainties tend to cancel in the ratio. 4. S U M M A R Y
The large water Cherenkov detectors have now accumulated nearly i000 single-ring, contained interactions of atmospheric neutrinos, which they have classified as electron-like or muon-like. Taken at face value, comparison between simulations and observations shows a discrepancy of more than four sigma. If the higher neutrino flux calculations [1,2] prove to be correct, the discrepancy would imply a deficit of v~, at the detector,
TK. Gaisser/Fluxes o f t,~ and t,e in the atmosphere: Is there an anomaly?
while the observed number of v~ agrees with expectation. This suggests v~, ~ v~ for an explanation in terms of neutrino oscillations. To explain the magnitude and lack of angular dependence of the contained event anomaly, one would need large mixing angle and large Srn2 (e.g. sin s 20 >_ 0.5 and 6m 2 10 -2 to 10 -1 eV2). The parameters of a vf, ~-* v~- scenario are then such that there should also be a significant deficit of upward v~,-induced muons. We have shown [39] that the Karniokande measurement of throughgoing muons (from all angles below the horizon) is indeed about 15% below the calculated rate when we use the best representation of the cross section [45] and a relatively high neutrino flux, as suggested by two recent calculations [46,47]. This could be nicely accounted for by an oscillation that would also explain the contained event anomaly. We have shown indirectly that the IMB data could also be interpreted in this way. The Baksan experiment has also measured the rate of upward muons. They find, however, that they still exclude most of the Kamiokande Uallowed" region even when they use the highest neutrino flux calculation [46] and a renormalized cross section that is approximately equivalent to that of Ref. [45] as used by Frati et al. [39]. The Baksan limit on v~, ,--* v~ oscillations is based on upward events near the vertical, specifically zenith angles in the interval - 1 < cos 0 < -0.6. Table 1 is a comparison of experiments and calculations in this limited angular region. Table 1. Upward muon fluxes Baksan Experiment: 161 Calculations: - - H i g h v-flux 163 - - L o w v-flux 142
for cos 0 < -0.6. Kamiokande 1.42 =t: 0.18 1.76 (1.34) 1.55
In Table 1 the Baksan column is the number of events with cos 0 < - 0 . 6 obtained in a live time of 7.15 years [19] The Kamiokande column contains the upward flux averaged over the same angular region 3 in units of 10 -13 c m - 2 s - l s r -1. I have avoided comparing the experimental fluxes directly because that would require converting between two different and non-trivial threshold ~The total r e p o r t e d Ksmiokande d a t a sample [17] consists of 252 events from all directions below the horizon.
213
functions. 4 Instead, I compare each data set with a calculation that folds in the detector acceptance in detail. The calculation for Baksan is from Ref. [19] and that for Kamiokande from Ref. [39]. Both calculations use similar assumptions for neutrino cross section and muon propagation. Inspection of Table 1 shows that the calculation with the high neutrino flux [46] and no oscillations agrees with the Baksan data whereas the corresponding calculation is two a higher than the Kamiok~nde data. The number in parentheses (1.34) is the predicted rate for Kamiol~nde with the high neutrino flux [46] assuming vz ~ v~ oscillations with sin 2 26 = 0.5 and 10 -~ < 6m 2 < 10 -1 eV 2. It is consistent with the Kamiokande data. A similar suppression of the corresponding Baksan number would be 3 a below their observation. To the extent that the two calculations contain the same physics, this discrepancy indicates a (modest) difference in the measured rate between Baksan and Kamiokande. The MACRO group reported for the first time at this conference [49] its measurement of upward muon rates together with a comparison to calculations. The MACRO acceptance is mostly in the vertical direction, where there is some indication of a deficit with respect to the expected value based on a high neutrino flux, but there are large st~istical and systematic uncertainties at present. In half year of running with six supermodules there are 27 events in the zenith angle range cos 0 < -0.6. (The data sample also includes two years of data with one supermodule.) At this rate the MACRO experiment will have comparable statistics to Baksan in two more years of running. My conclusion is that the present data on upward muons do r,ot rule out a v~, ~ vr oscillation at a level sufficient to explain the contained event anomaly. A tenfold increase in statistics would help resolve the situation, particularly if the full zenith angle range can be measured accurately. For example, with 6m 2 ~ 0.1 eV 2 the flux would be significantly suppressed near the horizontal as well as for cos 8 < -0.2, but for 6m ~ ,,, 0.01 eV 2 the near horizontal flux would not be suppressed. 4There is an approximate conversion in Rei'. [39] to a commo~ effective threshold of 3 GeV which shows that the experiments are not giving grossly different results.
214
T.K. Gaisser/Fluxes of u~ and ue in the atmosphere: Is there an anomaly?
A C K N O W L E D G M E N T S . I am grateful to Maury Goodman, Paolo Lipari, A.K. Mann, S. Mikheyev, Don Perkins and Todor Stanev for helpful discussions on the subject of atmospheric neutrinos.
Astrophyaics (Takayama, ed. Y. Suzuki & K.
21. 22.
REFERENCES
23.
1. G. Barr, T.K. Galeser & Todor Stanev, Phys. Rev. D39 (1989) 3532. 2. M. Honda, K. Kasahara, K. Hidaka & S. Midorikawa, Physics Letters B 248 (1990) 193. 3. H. Lee & Y.S. Koh, Nuovo Cimento B 105 (1990) 883. 4. E.V. Bugaev & V.A. Naumov, Physics Letters B 232 (1989) 391. 5. T.K. Gaisser Phil. Trans R. Soc. Lond. A (1993). 6. K.S. Hirata et al. (Kamio_~nde Collaboration), Phys. Letters B 280 (1992) 146. 7. R. Becker-Szendy et al. (IMB Collaboration), Phys. Rev. D 46 (1992) 3720. 8. T. Kajita, in Frontiers of Neutrino Astrophysics (Takayarna, ed. Y. Suzuki & K. Nakamura, Universal Academy Press, Tokyo, 1992) p. 293. 9. M. Aglietta et al. (NUSEX) Europhysics Letters 8 (1989) 611. 10. Ch. Berger et al. (Frejus) Physics Letters B 245 (1990) 305. and 227 (1989) 489. 11. M. Goodman in Proc. C~l#a~y Worluhop on A t m o s p h e r i c u ' s 21 July 1993, p. 1. 12. M. Takita, Ph.D. Thesis, Univ. of Tokyo, February 1989, ICR-Report-186-89-3. 13. David W. Casper, Ph.D. Thesis, Univ. of Michigan, 1990. 14. J. Engel, E. Kolbe, K. Langanke & P. Vogel, Phys. Rev. D 48 (1993) 3048. 15. R. Merenyi et al. Phys. Rev. D 45 (1992) 743. 16. D.D. Koetke et al., Phys. Rev. C 46 (1992) 2554. 17. M. Mori et al., Physics Letters B 210 (1991) 89. 18. R. Becker-Ssendy et al., Phys. Rev. Letters 69 (1992) 1010. 19. M.M. Boliev et al.,in Proc. Bed Int. Workahop on Neutrino Telescopes (ed. M. Baldo Ceolin) (1991) 235. 20. M. Honda, K. Kasahara & S. Midorikawa in Frontiers
of
Neutrino
24. 25. 26. 27. 28. 29. 30.
31.
Nakamura, Universal Academy Press, Tokyo, 1992) p. 309. P.H. Frampton & S.L. Glashow, Phya. Rev. D 25 (1982) 1982. W.A. Mann, T. Kafl~ & W. Leeson, Physics Letters B 291 (1992) 200. T.K. Gaisser, Todor Stanev, V. Agrawal, V. Nanmov, M. Honda, K. Kasahara, in preparation (1993). T. Eichten et al., Nucl. Phys. B 44 (1972) 333. J.V. A11aby et al., CERN Yellow Report 70-12 (1970) unpublished. H.J. Mfick et al. Physics Letters 39B (1972) 303. M. Antinucci et al. Lettere al Nuovo Cimento 6 (1973) 121. D.H. Perkins Oxford preprint 85/84 and Nucl. Phys. B 399 (1992) 3. M. Conversi, Phys. Rev. 79 (1950) 749. E.A. Bogomolov et al. as quoted by E.V. Bugaev, G.V. Domogatsky & V.A. Naumov in Proc. Japan-U.S. Seminar on Cosmic Ray Muon and Neutrino Physics/Astrophysics (ed. Y. Ohashi & V.Z. Peterson, 1986) p. 232. L.T. Baradzei et a/. Zh. Eksp. Teor. Fiz. 36
(1959) 1617. 32. M. Circella et al., Proc. 23rd Int. Cosmic Ray Conf. (Calgary) 4 (1993) 503. 33. H. Lee & S.A. Bludman, Phys. Rev. D 37 (1988) 122. 34. G.L. Fogli, E. Lisi & D. Montanino, CERNTH. 6944/93, BARI-TH/146/93, Phys. Rev. D (to be published). 35. C D H S W Collaboration, F. Dydak et al. Physics Letters B 134 (1984) 281. 36. L. Wolfenstein, Phys. Rev. D 17 (1979) 2369. 37. S.P, Mikheyev & A. Yu. Smirnov, Soy. Phys. JETP 64 (1986) 64. 38. M. Gel]-Mann, P. Ramond & R. Slansky in S u p e r ~ / t y (eds. F. Van Nieuwenhuisen & D. Freedman, Amsterdam, North Holland, 1979) p. 315. 39. W. Frati, T.K. Gaisser, A.K. Mann & Todor Stanev, Phys. Rev. D 48 (1993) 1140. 40. Yuichi Oyama, Ph.D. Thesis, Univ. of Tokyo ICR-Report-193-89-10 (1989). 41. Paolo Lipari & Todor Stanev, Phys. Rev. D 44 (1991) 3543. 42. W. Lohmann, R. Kopp & R. Vow, CERN Yel-
TK. Gaisser/Fluxes of v~ and v e in the atmosphere: Is there an anomaly?
low Report No. EP/85-03 (unpublished). 43. E. Eichten, I. Hinchcliffe, K. Lane & C. Quigg, Revs. Mod. Phys. 56 (1984) 579 and E~tum 58 (1986) 1065. 44. L.V. Volkova Soy. J. Nucl. Phys. 31 (1980) 784. 45. J.F. Owens, Physics Letters B 266 (1991) 126. 46. A.V. Butkevich, L.G. Dedenko & I.M. Zheleznykh Soy. J. Nucl. Phys. 50 (1988) 90. 47. V. Agrawal, T.K. Gaisser, P. Lipari & T. Stanev, in preparation (1993). 48. T.K. Gaisser in Frontier8 o f N e u t r i n o Aatroph~sic8 (Takayama, ed. Y. Suzuki & K. Nakamura, Universal Academy Press, Tokyo) (1992) p. 309. 49. D. Michael, talk presented at TAUP93, 21 Sept. 1993.
215