- Email: [email protected]
Atmospheric neutrinos in MINOS
Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Atmospheric neutrinos in MINOS Peter J. Litch"eld Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK
Abstract A Monte Carlo analysis of atmospheric neutrinos in the MINOS Soudan detector is described. Measurements of dm and sin(2h) comparable with those of Super-K are obtained. 2000 Elsevier Science B.V. All rights reserved. Keywords: NUFACT99; Neutrino; Oscillations; Lyon; Atmospheric neutrino
1. Introduction Atmospheric neutrino interactions have been generated in the MINOS detector in the Soudan mine. The detector is a 5 kton steel-scintillator sandwich, 8 m in diameter with 2.5 cm thick steel plates. The active elements are 1;4 cm scintillator strips read out by wavelength shifting "bres. The Soudan 2 generator was used, together with the #ux predicted by Barr}Gaisser}Stanev (BGS) [1]. The normalisation of the #ux is such that a 1 kton-year exposure would produce a total of 385 events in the whole detector. A "le of 7000 neutrino interactions, corresponding to an 18 kton year exposure or approximately 4 years running, has been tracked through the detector geometry. The discrimination between m CC and m CC I atmospheric neutrino events in MINOS relies on topological di!erences between the two classes of event. m CC events tend to be long and track-like, I whereas m CC events tend to be shorter and shower-like. This distinction is less clear at low
E-mail address: p.litch"[email protected] (P.J. Litch"eld).
neutrino energies (E (1 GeV) where the muons J in m CC events are short- and low-energy elecI trons in m CC events do not produce energetic electromagnetic showers. The principle of this analysis is to select a highenergy sample and extract events with an outgoing muon of '1 GeV. Only high-energy events give good pointing of the neutrino direction and a good separation of m events. The neutrino direction and I energy are assumed the same as those of the muon as in the analyses of Super-Kamiokande (Super-K). The analysis gives a good discrimination of m Pm I O oscillations over the allowed region from Super-K, demonstrating that MINOS can con"rm the Super-K e!ect and provide new parameter measurements. If *m is less than 10\ eV atmospheric neutrinos may be the only means of detecting and studying the e!ect. 1.1. Analysis A sample of events with a measurement of the distance to the interaction point in the atmosphere (¸) and the neutrino energy (E) is obtained by the following procedure:
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 0 3 8 5 - 5
NEUTRINO BEAM/EXPERIMENTS
188
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 1. Neutrino energy distribution for the selected high-energy sample. The solid line is m CC events, dashed line is m CC I events and the dotted line neutral current events.
Fig. 2. Resolution on ¸/E due to the smearing of muon parameters (solid line) and the use of muon parameters instead of the incident neutrino (dashed line).
(1) A clustering algorithm searches for clusters of hits in each view in space and time. Hits are required to be within a 100 ns time window and within 100 cm of their nearest neighbour. The clustering is fairly loose but is su$cient to reject most noise and radioactive decay hits. (2) Clusters are required to have a summed pulse height of '100 pe and a length (de"ned as the square root of the sum of the squares of the distances between the maximum and minimum of each coordinate) '100 cm. These cuts effectively isolate a high-energy sample which is predominantly m events. Fig. 1 shows the neuI trino energy distribution of the selected m and I m charged current and neutral current events. (3) Hand scanning of a sample of these events shows that in almost all m charged current I events a muon track is easily visible. We have assumed in the following analysis that it will be possible to select events with a muon track above 1 GeV. Advances in the pattern recognition algorithms will probably achieve this by automatic means. If not the event sample is relatively small and it can be done by hand scanning.
(4) The events are checked for containment. If a track leaves the detector it is required that the event be at least 3 m in length to allow the muon momentum and direction to be measured in the magnetic "eld. After these cuts a total of 407 events remain for subsequent analysis. (5) The muon direction and energy are smeared by the expected measurement errors and de"ned as the neutrino direction and energy. The measurement error due to smearing is not critical as the major error in ¸ and E is due to the assumption that the neutrino direction and muon direction are the same. Fig. 2 shows the di!erence in ¸/E produced by the smearing and the muon-neutrino approximation. The latter is clearly much larger. It may be possible to improve the measurement of the neutrino direction by using the hadron shower (if one is visible). However, very often the hadron `showera at these low energies is nothing but a few isolated hits. (6) A critical parameter in the calculation of ¸ is the direction of travel of the event. In about 70% of the events extra hits are produced around the vertex which enables the
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 3. Histograms of the measured m energy (top), m zenith angle (middle) and log (¸/E) when unoscillated (solid histograms) and for dm"10\ and sin(2h)"1.0 (points with error bars) (bottom).
production end of the event to be de"ned. In addition, the "t of the muon trajectory in the magnetic "eld is very direction dependent due to the slowing of the particle and the increase in multiple scattering towards the stopping end of the track. We assume that the combination of these two e!ects will correctly de"ne the direction in the vast majority of events. For this analysis we assume 100% correct direction determination. It is possible, at least for long muon tracks, that the timing will also give directionality. Having obtained the event sample and calculated the measured ¸/E for the unoscillated sample we then weight the events by the oscillation probability, assuming two #avour m Pm oscillations with I O various values of the oscillation parameters *m and sin(2h). Fig. 3 shows the neutrino energy distribution, the zenith angle distribution and the log (¸/E) distribution for the unoscillated sample (histogram) and for oscillations with dm"10\ and sin(2h)"1.0 (points with errors).
189
Fig. 4. Histograms of measured unoscillated log (¸/E) (solid histograms) and the oscillated values (points with errors) for various values of *m and sin(2h)"1.0.
Fig. 4 shows the ¸/E distribution for four values of *m spanning the range where we are sensitive to the shape of the ¸/E distribution (dm"10\} 10\). The change in shape of the oscillated samples, depleting the distributions from right to left, is clearly visible, demonstrating our sensitivity to the oscillation parameters. Fig. 5 shows the ratio of the oscillated to unoscillated distributions (R) for the four values of dm. The points with errors at R&1.0 are for dm"10\. There is only any oscillation e!ect visible in the highest bin of log (¸/E). The points at R&0.5 are for dm"10\ where the oscillations are completely saturated from all directions. The vertical error bars are the typical statistical errors from the four year exposure. In between these values of dm the ¸/E distribution is suppressed from the right as dm increases. The "rst line from the right joins the points for dm"10\ and the second for dm"10\. It can be seen that with the typical statistical errors MINOS will obtain a good discrimination between these values of dm. Fig. 6 shows a lego plot of the s di!erence between the oscillated and unoscillated samples for
NEUTRINO BEAM/EXPERIMENTS
190
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 5. The ratio of the oscillated to unoscillated numbers of selected m charged current events as a function of log (¸/E). I The upper points with errors are for dm"10\, the lower points for dm"10\. The dashed line joins the points for dm"10\ and the solid line for dm"10\.
Fig. 6. Top: Lego plot of the s as a function of *m and sin(2h) assuming the data normalisation is known perfectly. Bottom: 90% contour line, we are sensitive to regions above and to the right of the line.
a grid of *m and sin(2h) assuming that the normalisation of the two samples is known exactly. The bottom plot shows the 90% con"dence contour. We are sensitive to regions to the above and right of the line. Fig. 7 has the same plots for a shape only comparison, i.e., the unoscillated sample is normalised to the same number of events as in the oscillated sample. It can be seen that access to high values of *m and low values of sin(2h) are dependent on the normalisation. The current best estimate of the normalisation error is &$20%. However, experiments are in progress measuring the cosmic-ray #uxes in orbit which promise much to improve the normalisation error in the next few years. The normalised and shape only limit plots give the full range of possible results but we expect the "nal answer to be close to the normalised limits. The region that can be accessed in a 4 year exposure of MINOS covers completely the present Super-K preferred region (10\(dm(10\) and would enable the search for oscillations to be extended down to a dm of nearly 10\.
Fig. 8 shows a lego plot of the s di!erence between the oscillated distribution at dm" 10\, sin(2h)"1.0 and those at the other points in the dm, sin(2h) plane, for known normalisation. The contour plot shows the 90% con"dence level region if these were the true parameter values. Similar plots for other values of dm show that MINOS will give measurements of the atmospheric neutrino oscillation parameters comparable with those of Super-K.
2. Conclusions An analysis of atmospheric neutrino interactions in MINOS has been carried out assuming an 18 kton year exposure (4 years running). It selects only high-energy events with muons above 1 GeV. This sample is essentially all m events. Neutrino paramI eters are taken to be the same as those of the muon. The dominant errors are due to this assumption, not the identi"cation and measurement of the muon.
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 7. Top: Lego plot of the s as a function of *m and sin(2h) assuming the data normalisation is completely unknown and the expected rate is normalised to the measured rate (a `shape onlya test). Bottom: 90% contour line, we are sensitive to regions to the right of the line.
Oscillation (¸/E) analyses have been carried out for both methods. Error contours that are comparable in size to those of Super-K are found, demonstrating that MINOS will be able to con"rm the Super-K results in a detector with completely different systematic errors and provide new measurements of the oscillation parameters. If the value of *m is signi"cantly (10\ the study of atmospheric neutrinos by these types of analyses may be
191
Fig. 8. Top: Lego plot of the s di!erence between the oscillated distribution for dm"10\, sin(2h)"1.0 and that at the other points in the plane, assuming the data normalisation is known. Bottom: 90% con"dence contour line for a measurement of the parameters if they had this true value.
the only method of observing the neutrino oscillations postulated by Super-Kamiokande.
References [1] G. Barr, T.K. Gaisser, T. Stanev, Phys. Rev. D 39 (1989) 3532.
NEUTRINO BEAM/EXPERIMENTS
Atmospheric neutrinos in MINOS Peter J. Litch"eld Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK
Abstract A Monte Carlo analysis of atmospheric neutrinos in the MINOS Soudan detector is described. Measurements of dm and sin(2h) comparable with those of Super-K are obtained. 2000 Elsevier Science B.V. All rights reserved. Keywords: NUFACT99; Neutrino; Oscillations; Lyon; Atmospheric neutrino
1. Introduction Atmospheric neutrino interactions have been generated in the MINOS detector in the Soudan mine. The detector is a 5 kton steel-scintillator sandwich, 8 m in diameter with 2.5 cm thick steel plates. The active elements are 1;4 cm scintillator strips read out by wavelength shifting "bres. The Soudan 2 generator was used, together with the #ux predicted by Barr}Gaisser}Stanev (BGS) [1]. The normalisation of the #ux is such that a 1 kton-year exposure would produce a total of 385 events in the whole detector. A "le of 7000 neutrino interactions, corresponding to an 18 kton year exposure or approximately 4 years running, has been tracked through the detector geometry. The discrimination between m CC and m CC I atmospheric neutrino events in MINOS relies on topological di!erences between the two classes of event. m CC events tend to be long and track-like, I whereas m CC events tend to be shorter and shower-like. This distinction is less clear at low
E-mail address: p.litch"[email protected] (P.J. Litch"eld).
neutrino energies (E (1 GeV) where the muons J in m CC events are short- and low-energy elecI trons in m CC events do not produce energetic electromagnetic showers. The principle of this analysis is to select a highenergy sample and extract events with an outgoing muon of '1 GeV. Only high-energy events give good pointing of the neutrino direction and a good separation of m events. The neutrino direction and I energy are assumed the same as those of the muon as in the analyses of Super-Kamiokande (Super-K). The analysis gives a good discrimination of m Pm I O oscillations over the allowed region from Super-K, demonstrating that MINOS can con"rm the Super-K e!ect and provide new parameter measurements. If *m is less than 10\ eV atmospheric neutrinos may be the only means of detecting and studying the e!ect. 1.1. Analysis A sample of events with a measurement of the distance to the interaction point in the atmosphere (¸) and the neutrino energy (E) is obtained by the following procedure:
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 0 3 8 5 - 5
NEUTRINO BEAM/EXPERIMENTS
188
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 1. Neutrino energy distribution for the selected high-energy sample. The solid line is m CC events, dashed line is m CC I events and the dotted line neutral current events.
Fig. 2. Resolution on ¸/E due to the smearing of muon parameters (solid line) and the use of muon parameters instead of the incident neutrino (dashed line).
(1) A clustering algorithm searches for clusters of hits in each view in space and time. Hits are required to be within a 100 ns time window and within 100 cm of their nearest neighbour. The clustering is fairly loose but is su$cient to reject most noise and radioactive decay hits. (2) Clusters are required to have a summed pulse height of '100 pe and a length (de"ned as the square root of the sum of the squares of the distances between the maximum and minimum of each coordinate) '100 cm. These cuts effectively isolate a high-energy sample which is predominantly m events. Fig. 1 shows the neuI trino energy distribution of the selected m and I m charged current and neutral current events. (3) Hand scanning of a sample of these events shows that in almost all m charged current I events a muon track is easily visible. We have assumed in the following analysis that it will be possible to select events with a muon track above 1 GeV. Advances in the pattern recognition algorithms will probably achieve this by automatic means. If not the event sample is relatively small and it can be done by hand scanning.
(4) The events are checked for containment. If a track leaves the detector it is required that the event be at least 3 m in length to allow the muon momentum and direction to be measured in the magnetic "eld. After these cuts a total of 407 events remain for subsequent analysis. (5) The muon direction and energy are smeared by the expected measurement errors and de"ned as the neutrino direction and energy. The measurement error due to smearing is not critical as the major error in ¸ and E is due to the assumption that the neutrino direction and muon direction are the same. Fig. 2 shows the di!erence in ¸/E produced by the smearing and the muon-neutrino approximation. The latter is clearly much larger. It may be possible to improve the measurement of the neutrino direction by using the hadron shower (if one is visible). However, very often the hadron `showera at these low energies is nothing but a few isolated hits. (6) A critical parameter in the calculation of ¸ is the direction of travel of the event. In about 70% of the events extra hits are produced around the vertex which enables the
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 3. Histograms of the measured m energy (top), m zenith angle (middle) and log (¸/E) when unoscillated (solid histograms) and for dm"10\ and sin(2h)"1.0 (points with error bars) (bottom).
production end of the event to be de"ned. In addition, the "t of the muon trajectory in the magnetic "eld is very direction dependent due to the slowing of the particle and the increase in multiple scattering towards the stopping end of the track. We assume that the combination of these two e!ects will correctly de"ne the direction in the vast majority of events. For this analysis we assume 100% correct direction determination. It is possible, at least for long muon tracks, that the timing will also give directionality. Having obtained the event sample and calculated the measured ¸/E for the unoscillated sample we then weight the events by the oscillation probability, assuming two #avour m Pm oscillations with I O various values of the oscillation parameters *m and sin(2h). Fig. 3 shows the neutrino energy distribution, the zenith angle distribution and the log (¸/E) distribution for the unoscillated sample (histogram) and for oscillations with dm"10\ and sin(2h)"1.0 (points with errors).
189
Fig. 4. Histograms of measured unoscillated log (¸/E) (solid histograms) and the oscillated values (points with errors) for various values of *m and sin(2h)"1.0.
Fig. 4 shows the ¸/E distribution for four values of *m spanning the range where we are sensitive to the shape of the ¸/E distribution (dm"10\} 10\). The change in shape of the oscillated samples, depleting the distributions from right to left, is clearly visible, demonstrating our sensitivity to the oscillation parameters. Fig. 5 shows the ratio of the oscillated to unoscillated distributions (R) for the four values of dm. The points with errors at R&1.0 are for dm"10\. There is only any oscillation e!ect visible in the highest bin of log (¸/E). The points at R&0.5 are for dm"10\ where the oscillations are completely saturated from all directions. The vertical error bars are the typical statistical errors from the four year exposure. In between these values of dm the ¸/E distribution is suppressed from the right as dm increases. The "rst line from the right joins the points for dm"10\ and the second for dm"10\. It can be seen that with the typical statistical errors MINOS will obtain a good discrimination between these values of dm. Fig. 6 shows a lego plot of the s di!erence between the oscillated and unoscillated samples for
NEUTRINO BEAM/EXPERIMENTS
190
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 5. The ratio of the oscillated to unoscillated numbers of selected m charged current events as a function of log (¸/E). I The upper points with errors are for dm"10\, the lower points for dm"10\. The dashed line joins the points for dm"10\ and the solid line for dm"10\.
Fig. 6. Top: Lego plot of the s as a function of *m and sin(2h) assuming the data normalisation is known perfectly. Bottom: 90% contour line, we are sensitive to regions above and to the right of the line.
a grid of *m and sin(2h) assuming that the normalisation of the two samples is known exactly. The bottom plot shows the 90% con"dence contour. We are sensitive to regions to the above and right of the line. Fig. 7 has the same plots for a shape only comparison, i.e., the unoscillated sample is normalised to the same number of events as in the oscillated sample. It can be seen that access to high values of *m and low values of sin(2h) are dependent on the normalisation. The current best estimate of the normalisation error is &$20%. However, experiments are in progress measuring the cosmic-ray #uxes in orbit which promise much to improve the normalisation error in the next few years. The normalised and shape only limit plots give the full range of possible results but we expect the "nal answer to be close to the normalised limits. The region that can be accessed in a 4 year exposure of MINOS covers completely the present Super-K preferred region (10\(dm(10\) and would enable the search for oscillations to be extended down to a dm of nearly 10\.
Fig. 8 shows a lego plot of the s di!erence between the oscillated distribution at dm" 10\, sin(2h)"1.0 and those at the other points in the dm, sin(2h) plane, for known normalisation. The contour plot shows the 90% con"dence level region if these were the true parameter values. Similar plots for other values of dm show that MINOS will give measurements of the atmospheric neutrino oscillation parameters comparable with those of Super-K.
2. Conclusions An analysis of atmospheric neutrino interactions in MINOS has been carried out assuming an 18 kton year exposure (4 years running). It selects only high-energy events with muons above 1 GeV. This sample is essentially all m events. Neutrino paramI eters are taken to be the same as those of the muon. The dominant errors are due to this assumption, not the identi"cation and measurement of the muon.
P.J. Litchxeld / Nuclear Instruments and Methods in Physics Research A 451 (2000) 187}191
Fig. 7. Top: Lego plot of the s as a function of *m and sin(2h) assuming the data normalisation is completely unknown and the expected rate is normalised to the measured rate (a `shape onlya test). Bottom: 90% contour line, we are sensitive to regions to the right of the line.
Oscillation (¸/E) analyses have been carried out for both methods. Error contours that are comparable in size to those of Super-K are found, demonstrating that MINOS will be able to con"rm the Super-K results in a detector with completely different systematic errors and provide new measurements of the oscillation parameters. If the value of *m is signi"cantly (10\ the study of atmospheric neutrinos by these types of analyses may be
191
Fig. 8. Top: Lego plot of the s di!erence between the oscillated distribution for dm"10\, sin(2h)"1.0 and that at the other points in the plane, assuming the data normalisation is known. Bottom: 90% con"dence contour line for a measurement of the parameters if they had this true value.
the only method of observing the neutrino oscillations postulated by Super-Kamiokande.
References [1] G. Barr, T.K. Gaisser, T. Stanev, Phys. Rev. D 39 (1989) 3532.
NEUTRINO BEAM/EXPERIMENTS