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Atmospheric Neutrino Fluxes
Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95 www.elsevierphysics.com
Atmospheric Neutrino Fluxes Giles Barra a
University of Oxford, Department of Physics, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, United Kingdom Introduction Atmospheric neutrinos, originally considered a background to nucleon decay searches have become an exciting study in their own right — the Earth, it turns out, is just about the most convenient size to see neutrino oscillations [1,2]. With the large statistics sample now available from Super Kamiokande, it is important to push the accuracy of the predictions of neutrino fluxes as far as possible. This paper discusses the progress which has been made since the previous neutrino conference in the neutrino flux calculations, with emphasis on three dimensional calculations which have received considerable interest recently. Cosmic rays which are composed mainly of protons, but with a significant (25%) component of fully ionised heavier nuclei interact hadronically with the air molecules in the upper atmosphere of the Earth. Neutrinos are produced in the decay of muons, pions and kaons in the resulting cascades. The Earth’s magnetic field is important in determining the flux of cosmic rays in the vicinity above the Earth’s atmosphere and in the propagation of the cascade, particularly the muons through the atmosphere. The solar wind, which represents a potential barrier to the cosmic rays as they enter the solar system, varies through the 11 year solar cycle and must be taken into account when computing neutrino fluxes. Figure 1 displays a pictograph of various important features in the production of neutrinos as a function of energy. Firstly, the energy ranges for the different types of events observed underground are indicated. Events where the vertex and all the secondary particles in the neutrino interaction are contained in the detector correspond to neutrino energies from a few hundred 0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.01.092
Pions interact Kaons interact Vertical muons reach Earth’s surface Through going muons Partially C Contained
Energy (GeV) 0.1
1
10
100
1000
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Osc Max Down
Osc Max Horizontal
Osc Max Up
Figure 1. Features of important effects related to atmospheric neutrino fluxes displayed on an energy chart.
MeV to a few GeV depending on the granularity and size of the detector respectively. Through going muons (observable only in the upward direction due to the background of high energy muons in the downward direction1 are induced by neutrinos from about 10 GeV to almost 1 TeV. An intermediate class of “partially contained” events is also observable. The primary cosmic ray energies involved are generally about 2 orders of magnitude higher in energy than the neutrinos [4]. The energies at which the first oscillation maximum assuming ∆m2 ∼ 2.4 × 10−3eV2 are shown 1 SNO, which is deep underground is able to see atmospheric neutrinos induced muons from near but above the horizon.[3]
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on figure 1 for propagation lengths L corresponding to vertically downward (L ∼ 20km), horizontal (L ∼ 500km) and vertically upward (L ∼ 13000km) directions. At an energy of about 3 GeV, vertical muons in the cosmic ray shower have enough energy to penetrate to the ground. This effect causes an important feature of the neutrino fluxes as a function of energy and zenith angle. Another important consideration is the competition between decay and interaction for charged mesons, low energy mesons always decay, whereas above 100 GeV, interaction becomes dominant for π ± . Due to the shorter lifetime of the K± , the point at which kaon interactions dominate does not occur until higher energies. This fact, coupled with the small centre-of-mass momentum in π → µ decay has the important consequence that kaons become the main source of neutrinos above Eν ∼ 100 GeV [4]. Calculation and the 1-D approximation There has been considerable activity in the field of calculating neutrino fluxes recently with several new calculations reported and refinements to some of the older calculations [5–12]. The basic technique used by all authors is to use the MonteCarlo technique to start the propagation of particles above the top of the atmosphere, let them interact, track secondaries through the atmosphere, including energy loss, bending in the Earth’s magnetic field, decay and interaction. Particles which hit the Earth are assumed to have stopped. It was important in early calculations to make what is called the “one-dimensional approximation” in which showers are generated with the direction of secondaries adjusted to be along the same direction as primaries. The showers can be started in a direction pointing at the detector with the certainty that all the secondaries will hit. This is a tremendous advantage from the point of view of calculation time. The first “3–D” calculation to remove this approximation [13] showed that there is an important enhancement of the fluxes near the horizon which may be understood geometrically [14] as being a consequence of the small scale of the depth of the atmosphere compared to the radius of the Earth. One way to picture the effect, which is de-
Figure 2. Illustration of the origin of the enhancement of the flux near the horizon when simulation is done in 3-D (see text).
scribed in [14], is to view the situation from two extremes (a) no change of direction is introduced between primary and secondary direction (this is just the 1-D approximation) and (b) a completely random direction change is introduced so that the neutrino direction is distributed isotropically with respect to the primary direction. Now consider that the direction change occurs at a single height h in the atmosphere at the extreme (b); in this extreme situation, there is a shell enclosing the Earth, height h above the surface emitting neutrinos isotropically. The flux from any given direction is proportional to the size of the patch in the sky at height h cut out by a cone of given solid angle. This patch is larger for horizontal directions because the cone is sliced at an angle. The origin of the geometrical effect is that, even taking into account the 1/(distance)2 factor associated with an isotropic source, the horizontal flux is larger than the vertical flux. This is illustrated in figure 2 where the distance h has been enlarged; with the correct value of h ∼ 20km the 3-D enhancement is considerably larger. Reality is somewhere between the two extremes (a) and (b), becoming more like (a) as the energy increases. Flux variations Figure 3 shows the fluxes as a function of zenith angle for different energy ranges, the solid lines are for a 3D calculation and the dashed lines are
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Figure 3. Zenith angle distributions for various energies at Kamioka (left) and Soudan (right). Solid lines show the results of a 3-D calculation and dashed lines show the change when the 1-dimensional approximation is used. for a 1-D calculation. The peak near the horizon (cosθ ∼ 0) due to the 3-D geometrical effect is clearly visible at energies below Eν = 1 GeV. At higher energies, the difference between 1-D and 3-D becomes small. The left panel of figure 3 shows the fluxes at Kamioka which is at a location where the geomagnetic cutoff is high and the right plot shows the fluxes in North America (at Soudan, the site of the Soudan-2 and MINOS detectors; the SNO fluxes are similar) near the magnetic pole where cutoffs are much lower. The main change in the flux between the two locations is that the downward (cosθ > 0) fluxes are considerably lower
at Kamioka than Soudan at low energy. The variation in the cutoffs also cause an important azimuthal variation of the fluxes which diminishes at high energy as shown in figure 4 for Kamioka. The fluxes when the 1-D approximation is used are governed only by the geomagnetic cutoffs which cause a large asymetry at low energy. Without the 1-D approximation, the bending of muons in the atmposphere creates a variation with neutrino species. Back with figure 3, the fluxes from below the horizon are more similar at the two sites because the cosmic ray interactions take place at a larger variety locations across the globe and some averaging of the geomagnetic ef-
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
Path length The three dimensional simulations show a reduction in the path length L between the neutrino production point and the detector, when compared to the older calculations with the 1-D approximation. The 3-D calculations include the possibility for a vertical shower to descend into the atmosphere close to the detector and produce a neutrino sideways. The best illustration of this effect is given in [12]. Flux Ratios A detailed discussion of the flux ratios: horizontal to vertical, upward to downward, νe /ν e , νµ /ν µ and νµ /νe is beyond the scope of this article. See for example [7,10]. Ratios are considerably less sensitive than absolute fluxes to the uncertainties of primary cosmic ray fluxes and hadron production, which are to be described later in this paper. Figure 5 shows that the νµ /νe ratio, which is dominated by the appearance of two muon type versus one electron type neutrino in the decay chain π → µ → e. There is no difference when using the 1-D approximation, or a 3-D calculation with the Earth’s field switched off (NM). At high energy, the ratio increases due to muons which hit the Earth’s surface which causes loss of one muon type neutrino and the only electron type neutrino in the above decay chain. Systematics The following section briefly describes the uncertainties in the fluxes produced by these calculations which are principally connected with hadron production due to lack of control data. Historically, the primary cosmic ray flux was also a large contributor to the uncertainty due to
0.8 0.7
Kamioka νe 1D
0.6
dAEW/d log10(Eν)
fects occurs. At high energies, the effect of muons hitting the earth can be seen. This produces the gentle peak in the zenith angle distribution of muon neutrinos near the horizon which is reproduced well even when using the 1-D approximation. Only the neutrinos from muon decay are removed by this effect, the neutrinos produced in the decay of mesons remain for all zenith angles. The same effect also heavily suppresses electron neutrinos at high energy (see figure 5).
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Figure 4. East-West asymetry (E − W )/(E + W ) of fluxes at Kamioka as a function of neutrino energy for neutrinos (filled symbols) and antineutrinos (open symbols). Electron (muon) type neutrinos are shown in the upper (lower) plot. The lines show the results when the 1-D approximation is applied (solid for neutrinos, dashed for antineutrinos).
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Figure 5. Ratio of muon neutrinos to electron neutrinos as a functioin of neutrino energy for 1D and 3D calculations. The dashed lines (NM) indicate the results of a 3-D calculation with bending of secondary particles in the Earth’s magnetic field omitted.
inconsistencies between measurements, however several modern sets of data have recently become available. Figure 6 shows a summary of proton fluxes measured with balloon and satellite borne measuring devices (see [15] for references). The difference between the data and the values obtained from the parameterisation from [15] are plotted on figure 7. Helium and measurements of other higher mass nuclei are also available. Up to about 200 GeV, the measurements are generally made with magnetic spectrometers with a high level of particle identification and redundancy to avoid errors due to accidental tracks. Recent measurements by AMS [16], BESS [17], and CAPRICE [18] all agree to within 15% with the agreement between AMS and BESS proton data being particularly impressive. At higher energies where the measurement of the cosmic ray momentum with a magnetic field becomes impractical, the fluxes are measured with balloon borne sampling calorimetry using emulsions as the active
1e-10
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Figure 6. Compilation of primary proton flux measurements as a function of energy (GeV) showing that the fluxes are a steeply falling distribution as a function of energy.
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Figure 7. Compilation of primary proton flux masurements as a function of energy (GeV) plotted as the fractional difference between the data and the parameterisation from [15].
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
detection region. The limited statistics at these high energies is still a significant uncertainty in the prediction of neutrino induced through going events. Hadron production uncertainties represent the largest uncertainty in the neutrino fluxes at all energies. The existing data are available at only a few primary energy points, require extrapolation of the target to air nuclei (from adjacent nuclei, such as Be, C or Al) and only cover a small number of points in secondary phase space (xlab , pT ). For atmospheric neutrino studies, the main interest is in the xlab (= Esecondary /Eprimary in the lab frame) distributions for pions and kaons, integrated over the full pT range. The production of kaons, particularly above 100 GeV is extremely important. Figure 8 shows an example from ref. [19] of how the neutrino flux changes when a change is made in the hadron production model. In this case, the rate of associative production, (where the leading secondary baryon is a Λ and is accompanied by the production of a K + ) was reduced by 15% — well within the constraints of experimental data. This causes a reduction in the neutrino flux above 50 GeV. Several new measurements have been carried out, and results are being produced. Listed in order of primary energy, HARP at CERN [20] (3– 15 GeV), E910 at Brookhaven [21] (6–18 GeV), MIPP at FNAL [22] (5–120 GeV) and NA49 at CERN [23] (100 and 158 GeV) all use time projection chambers (TPCs) to allow most of the secondary particle phase space to be measured with a single experimental setting. Neither the atmospheric density profile nor the absolute cross section for hadron production have a large effect on neutrino production. Changes modify slightly the depth within the atmosphere that the neutrinos are produced, but don’t change the fact that they are produced anyway (this is not true for cosmic ray muon fluxes at a given altitude). Conclusions In recent years we have witnessed a rebirth in the use of cosmic rays to measure the properties of fundamental particles. The high statistics sample of cosmic ray induced neutrino events being
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collected by underground detectors, in particular Super Kamiokande has provided very striking evidence that muon neutrinos oscillate and that therefore [at least some of the flavours of] neutrinos have mass. A considerable activity by several groups of authors has generated more precise estimates of the neutrino fluxes and in particular on removing the 1-D approximation which was made in calculations from the last century. Super Kamiokande have recently devised an analysis in which the event selection depends on the resolution in L/E [1]. This eliminates low energy events near the horizon where the value of L changes very rapidly with zenith angle. Figure 9 shows symbolically the difference between the flux calculated with and without the 1-D approximation as a function of energy and cosθ and the Super Kamiokande cut has been superimposed. The areas where 3-D effects are large do not yield much information on oscillation parameters because the value of L/E can not be determined accurately. Primary flux measurements have improved considerably in recent years and good measurements are available over the energy range of interest to atmospheric neutrinos except for the neu-
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
trinos at the very highest energies. Hadron production is still a major limitation to the accuracy of the fluxes, however new measurements — some specifically devoted to this issue — are being carried out.
Difference between 3D and 1D calculations
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Figure 9. Change in the calculation when the one dimensional approximation is applied as a function of both neutrino energy and zenith angle. The cut from the Super Kamiokande L/E analysis is indicated.
Acknowledgements I would like to thank N. Brooks, T. Gaisser, S. Robbins, T. Stanev and N. Tagg for discussions and assistance with graphics. REFERENCES 1. E. Kearns, these proceedings 2. H. Gallagher, these proceedings 3. N.J. Tagg, Ph.D thesis, Guelph University, 2001, UMI-NQ-65836; C. Currat and J. Formaggio, these proceedings 4. T.K. Gaisser Astropart. Phys. 16 (2002) 285. 5. G. Battistoni et al., Astropart. Phys. 19, 269 (2003)
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6. Y. Tserkovnyak et al., Astropart. Phys. 18, 449 (2003) 7. J. Wentz et al., Phys. Rev. D67, 073020 (2003) 8. Y. Liu, L. Derome and M. Bu´enerd Phys. Rev. D 67, 073022 (2003) 9. J. Favier, R. Kossakowski and J.P. Vialle, Phys. Rev. D 68, 093006 (2003) 10. G. Barr, T. Gaisser, P. Lipari, S. Robbins and T. Stanev, Phys. Rev. D 70, 023006 (2004) 11. M. Honda, T. Kajita, K. Kasahara and S. Midorikawa, Phys. Rev. D 64, 053011 (2001) 12. M. Honda, T. Kajita, K. Kasahara and S. Midorikawa, Phys. Rev. D 70, 043008 (2004) 13. G. Battistoni et al., Astropart. Phys. 12, 315 (2000) 14. P. Lipari, Astropart. Phys. 14, 153 (2000) 15. T.K. Gaisser, M. Honda, P. Lipari & T. Stanev, Proc. 27th Int. Cosmic Ray Conf. (2001) 1643. 16. J. Alcaraz et al., Phys. Lett. B490, 27 (2000) 17. T. Sanuki et al., Ap. J. 545, 1135 (2002) 18. M. Boezio et al., Astropart. Phys. 19, 583 (2003) 19. S. Robbins, D.Phil thesis, Oxford 2004 20. J.J. Gomez-Cadenas, these proceedings 21. E910 experiment, http://www.phy.bnl.gov/ e910/html/home.html 22. MIPP experiment, http://ppd.fnal.gov/experiments/e907/ 23. G. Barr et. al. “Hadroproductrion in Proton Carbon Collisions at the NA49 Experiment” proceedings of the 28th International Cosmic Ray Conference Tsukuba, Aug 2003
Atmospheric Neutrino Fluxes Giles Barra a
University of Oxford, Department of Physics, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, United Kingdom Introduction Atmospheric neutrinos, originally considered a background to nucleon decay searches have become an exciting study in their own right — the Earth, it turns out, is just about the most convenient size to see neutrino oscillations [1,2]. With the large statistics sample now available from Super Kamiokande, it is important to push the accuracy of the predictions of neutrino fluxes as far as possible. This paper discusses the progress which has been made since the previous neutrino conference in the neutrino flux calculations, with emphasis on three dimensional calculations which have received considerable interest recently. Cosmic rays which are composed mainly of protons, but with a significant (25%) component of fully ionised heavier nuclei interact hadronically with the air molecules in the upper atmosphere of the Earth. Neutrinos are produced in the decay of muons, pions and kaons in the resulting cascades. The Earth’s magnetic field is important in determining the flux of cosmic rays in the vicinity above the Earth’s atmosphere and in the propagation of the cascade, particularly the muons through the atmosphere. The solar wind, which represents a potential barrier to the cosmic rays as they enter the solar system, varies through the 11 year solar cycle and must be taken into account when computing neutrino fluxes. Figure 1 displays a pictograph of various important features in the production of neutrinos as a function of energy. Firstly, the energy ranges for the different types of events observed underground are indicated. Events where the vertex and all the secondary particles in the neutrino interaction are contained in the detector correspond to neutrino energies from a few hundred 0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.01.092
Pions interact Kaons interact Vertical muons reach Earth’s surface Through going muons Partially C Contained
Energy (GeV) 0.1
1
10
100
1000
3D effects
Osc Max Down
Osc Max Horizontal
Osc Max Up
Figure 1. Features of important effects related to atmospheric neutrino fluxes displayed on an energy chart.
MeV to a few GeV depending on the granularity and size of the detector respectively. Through going muons (observable only in the upward direction due to the background of high energy muons in the downward direction1 are induced by neutrinos from about 10 GeV to almost 1 TeV. An intermediate class of “partially contained” events is also observable. The primary cosmic ray energies involved are generally about 2 orders of magnitude higher in energy than the neutrinos [4]. The energies at which the first oscillation maximum assuming ∆m2 ∼ 2.4 × 10−3eV2 are shown 1 SNO, which is deep underground is able to see atmospheric neutrinos induced muons from near but above the horizon.[3]
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on figure 1 for propagation lengths L corresponding to vertically downward (L ∼ 20km), horizontal (L ∼ 500km) and vertically upward (L ∼ 13000km) directions. At an energy of about 3 GeV, vertical muons in the cosmic ray shower have enough energy to penetrate to the ground. This effect causes an important feature of the neutrino fluxes as a function of energy and zenith angle. Another important consideration is the competition between decay and interaction for charged mesons, low energy mesons always decay, whereas above 100 GeV, interaction becomes dominant for π ± . Due to the shorter lifetime of the K± , the point at which kaon interactions dominate does not occur until higher energies. This fact, coupled with the small centre-of-mass momentum in π → µ decay has the important consequence that kaons become the main source of neutrinos above Eν ∼ 100 GeV [4]. Calculation and the 1-D approximation There has been considerable activity in the field of calculating neutrino fluxes recently with several new calculations reported and refinements to some of the older calculations [5–12]. The basic technique used by all authors is to use the MonteCarlo technique to start the propagation of particles above the top of the atmosphere, let them interact, track secondaries through the atmosphere, including energy loss, bending in the Earth’s magnetic field, decay and interaction. Particles which hit the Earth are assumed to have stopped. It was important in early calculations to make what is called the “one-dimensional approximation” in which showers are generated with the direction of secondaries adjusted to be along the same direction as primaries. The showers can be started in a direction pointing at the detector with the certainty that all the secondaries will hit. This is a tremendous advantage from the point of view of calculation time. The first “3–D” calculation to remove this approximation [13] showed that there is an important enhancement of the fluxes near the horizon which may be understood geometrically [14] as being a consequence of the small scale of the depth of the atmosphere compared to the radius of the Earth. One way to picture the effect, which is de-
Figure 2. Illustration of the origin of the enhancement of the flux near the horizon when simulation is done in 3-D (see text).
scribed in [14], is to view the situation from two extremes (a) no change of direction is introduced between primary and secondary direction (this is just the 1-D approximation) and (b) a completely random direction change is introduced so that the neutrino direction is distributed isotropically with respect to the primary direction. Now consider that the direction change occurs at a single height h in the atmosphere at the extreme (b); in this extreme situation, there is a shell enclosing the Earth, height h above the surface emitting neutrinos isotropically. The flux from any given direction is proportional to the size of the patch in the sky at height h cut out by a cone of given solid angle. This patch is larger for horizontal directions because the cone is sliced at an angle. The origin of the geometrical effect is that, even taking into account the 1/(distance)2 factor associated with an isotropic source, the horizontal flux is larger than the vertical flux. This is illustrated in figure 2 where the distance h has been enlarged; with the correct value of h ∼ 20km the 3-D enhancement is considerably larger. Reality is somewhere between the two extremes (a) and (b), becoming more like (a) as the energy increases. Flux variations Figure 3 shows the fluxes as a function of zenith angle for different energy ranges, the solid lines are for a 3D calculation and the dashed lines are
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Figure 3. Zenith angle distributions for various energies at Kamioka (left) and Soudan (right). Solid lines show the results of a 3-D calculation and dashed lines show the change when the 1-dimensional approximation is used. for a 1-D calculation. The peak near the horizon (cosθ ∼ 0) due to the 3-D geometrical effect is clearly visible at energies below Eν = 1 GeV. At higher energies, the difference between 1-D and 3-D becomes small. The left panel of figure 3 shows the fluxes at Kamioka which is at a location where the geomagnetic cutoff is high and the right plot shows the fluxes in North America (at Soudan, the site of the Soudan-2 and MINOS detectors; the SNO fluxes are similar) near the magnetic pole where cutoffs are much lower. The main change in the flux between the two locations is that the downward (cosθ > 0) fluxes are considerably lower
at Kamioka than Soudan at low energy. The variation in the cutoffs also cause an important azimuthal variation of the fluxes which diminishes at high energy as shown in figure 4 for Kamioka. The fluxes when the 1-D approximation is used are governed only by the geomagnetic cutoffs which cause a large asymetry at low energy. Without the 1-D approximation, the bending of muons in the atmposphere creates a variation with neutrino species. Back with figure 3, the fluxes from below the horizon are more similar at the two sites because the cosmic ray interactions take place at a larger variety locations across the globe and some averaging of the geomagnetic ef-
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
Path length The three dimensional simulations show a reduction in the path length L between the neutrino production point and the detector, when compared to the older calculations with the 1-D approximation. The 3-D calculations include the possibility for a vertical shower to descend into the atmosphere close to the detector and produce a neutrino sideways. The best illustration of this effect is given in [12]. Flux Ratios A detailed discussion of the flux ratios: horizontal to vertical, upward to downward, νe /ν e , νµ /ν µ and νµ /νe is beyond the scope of this article. See for example [7,10]. Ratios are considerably less sensitive than absolute fluxes to the uncertainties of primary cosmic ray fluxes and hadron production, which are to be described later in this paper. Figure 5 shows that the νµ /νe ratio, which is dominated by the appearance of two muon type versus one electron type neutrino in the decay chain π → µ → e. There is no difference when using the 1-D approximation, or a 3-D calculation with the Earth’s field switched off (NM). At high energy, the ratio increases due to muons which hit the Earth’s surface which causes loss of one muon type neutrino and the only electron type neutrino in the above decay chain. Systematics The following section briefly describes the uncertainties in the fluxes produced by these calculations which are principally connected with hadron production due to lack of control data. Historically, the primary cosmic ray flux was also a large contributor to the uncertainty due to
0.8 0.7
Kamioka νe 1D
0.6
dAEW/d log10(Eν)
fects occurs. At high energies, the effect of muons hitting the earth can be seen. This produces the gentle peak in the zenith angle distribution of muon neutrinos near the horizon which is reproduced well even when using the 1-D approximation. Only the neutrinos from muon decay are removed by this effect, the neutrinos produced in the decay of mesons remain for all zenith angles. The same effect also heavily suppresses electron neutrinos at high energy (see figure 5).
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Figure 4. East-West asymetry (E − W )/(E + W ) of fluxes at Kamioka as a function of neutrino energy for neutrinos (filled symbols) and antineutrinos (open symbols). Electron (muon) type neutrinos are shown in the upper (lower) plot. The lines show the results when the 1-D approximation is applied (solid for neutrinos, dashed for antineutrinos).
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Figure 5. Ratio of muon neutrinos to electron neutrinos as a functioin of neutrino energy for 1D and 3D calculations. The dashed lines (NM) indicate the results of a 3-D calculation with bending of secondary particles in the Earth’s magnetic field omitted.
inconsistencies between measurements, however several modern sets of data have recently become available. Figure 6 shows a summary of proton fluxes measured with balloon and satellite borne measuring devices (see [15] for references). The difference between the data and the values obtained from the parameterisation from [15] are plotted on figure 7. Helium and measurements of other higher mass nuclei are also available. Up to about 200 GeV, the measurements are generally made with magnetic spectrometers with a high level of particle identification and redundancy to avoid errors due to accidental tracks. Recent measurements by AMS [16], BESS [17], and CAPRICE [18] all agree to within 15% with the agreement between AMS and BESS proton data being particularly impressive. At higher energies where the measurement of the cosmic ray momentum with a magnetic field becomes impractical, the fluxes are measured with balloon borne sampling calorimetry using emulsions as the active
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Figure 6. Compilation of primary proton flux measurements as a function of energy (GeV) showing that the fluxes are a steeply falling distribution as a function of energy.
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Figure 7. Compilation of primary proton flux masurements as a function of energy (GeV) plotted as the fractional difference between the data and the parameterisation from [15].
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
detection region. The limited statistics at these high energies is still a significant uncertainty in the prediction of neutrino induced through going events. Hadron production uncertainties represent the largest uncertainty in the neutrino fluxes at all energies. The existing data are available at only a few primary energy points, require extrapolation of the target to air nuclei (from adjacent nuclei, such as Be, C or Al) and only cover a small number of points in secondary phase space (xlab , pT ). For atmospheric neutrino studies, the main interest is in the xlab (= Esecondary /Eprimary in the lab frame) distributions for pions and kaons, integrated over the full pT range. The production of kaons, particularly above 100 GeV is extremely important. Figure 8 shows an example from ref. [19] of how the neutrino flux changes when a change is made in the hadron production model. In this case, the rate of associative production, (where the leading secondary baryon is a Λ and is accompanied by the production of a K + ) was reduced by 15% — well within the constraints of experimental data. This causes a reduction in the neutrino flux above 50 GeV. Several new measurements have been carried out, and results are being produced. Listed in order of primary energy, HARP at CERN [20] (3– 15 GeV), E910 at Brookhaven [21] (6–18 GeV), MIPP at FNAL [22] (5–120 GeV) and NA49 at CERN [23] (100 and 158 GeV) all use time projection chambers (TPCs) to allow most of the secondary particle phase space to be measured with a single experimental setting. Neither the atmospheric density profile nor the absolute cross section for hadron production have a large effect on neutrino production. Changes modify slightly the depth within the atmosphere that the neutrinos are produced, but don’t change the fact that they are produced anyway (this is not true for cosmic ray muon fluxes at a given altitude). Conclusions In recent years we have witnessed a rebirth in the use of cosmic rays to measure the properties of fundamental particles. The high statistics sample of cosmic ray induced neutrino events being
10 5
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Figure 8. Effect of reducing the associative ΛK + in the hadron production model by 15%
collected by underground detectors, in particular Super Kamiokande has provided very striking evidence that muon neutrinos oscillate and that therefore [at least some of the flavours of] neutrinos have mass. A considerable activity by several groups of authors has generated more precise estimates of the neutrino fluxes and in particular on removing the 1-D approximation which was made in calculations from the last century. Super Kamiokande have recently devised an analysis in which the event selection depends on the resolution in L/E [1]. This eliminates low energy events near the horizon where the value of L changes very rapidly with zenith angle. Figure 9 shows symbolically the difference between the flux calculated with and without the 1-D approximation as a function of energy and cosθ and the Super Kamiokande cut has been superimposed. The areas where 3-D effects are large do not yield much information on oscillation parameters because the value of L/E can not be determined accurately. Primary flux measurements have improved considerably in recent years and good measurements are available over the energy range of interest to atmospheric neutrinos except for the neu-
G. Barr / Nuclear Physics B (Proc. Suppl.) 143 (2005) 89–95
trinos at the very highest energies. Hadron production is still a major limitation to the accuracy of the fluxes, however new measurements — some specifically devoted to this issue — are being carried out.
Difference between 3D and 1D calculations
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Figure 9. Change in the calculation when the one dimensional approximation is applied as a function of both neutrino energy and zenith angle. The cut from the Super Kamiokande L/E analysis is indicated.
Acknowledgements I would like to thank N. Brooks, T. Gaisser, S. Robbins, T. Stanev and N. Tagg for discussions and assistance with graphics. REFERENCES 1. E. Kearns, these proceedings 2. H. Gallagher, these proceedings 3. N.J. Tagg, Ph.D thesis, Guelph University, 2001, UMI-NQ-65836; C. Currat and J. Formaggio, these proceedings 4. T.K. Gaisser Astropart. Phys. 16 (2002) 285. 5. G. Battistoni et al., Astropart. Phys. 19, 269 (2003)
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