how to extract neutrino factory flux from imd and neutrino elastic scattering? near detector...
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How to extract Neutrino Factory flux How to extract Neutrino Factory flux from IMD and neutrino elastic from IMD and neutrino elastic
scattering?scattering?
How to extract Neutrino Factory flux How to extract Neutrino Factory flux from IMD and neutrino elastic from IMD and neutrino elastic
scattering?scattering?
Near Detector Workshop, CERN, 30 July 2011
Paul Soler
Near Detector workshop, CERN, 30 July 2011
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OutlineOutline
Spectra at near detector of a neutrino factory Outline method to extract fluxes at ND Inverse Muon Decay Muon-neutrino electron elastic scattering Electron-neutrino electron elastic scattering Combination of channels to extract fluxes
Near Detector workshop, CERN, 30 July 2011
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Spectra at Near Detector Spectra at Near Detector
e
o Near Detector sees a line source (600 m long decay straight)o Far Detector sees a point source
e1 km
100 m
2500 km
2500 kmND
NDFD
FD
Need to take into account these differences for flux measurement
100 m
1 km
Near Detector workshop, CERN, 30 July 2011
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How to extract the neutrino factory flux from the measurements of IMD and nue elastic scattering?
Use channels with very small theoretical error in the cross-sections and measure them at near detector:– Inverse muon decay (Charged Current):
– Elastic neutrino scattering:• Neutral Current:
• Interference Charged Current/Neutral Current:
These processes have cross-sections about 10-3 of total CC cross-section but can still expect ~106 events in a near detector at a neutrino factory
MethodMethod
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ee ee
ee ee ee ee
Near Detector workshop, CERN, 30 July 2011
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Charged current processes:
Cross-section ~1.7x10-41 E(GeV) cm2, threshold = 11 GeV We cannot distinguish between the two channels so we measure N1(E) +
N2(E):
Inverse Muon DecayInverse Muon Decay
ee ee
)()()(1 EEEN CC
ee
W
ee
W
e
e
s
msGE FCC
e
222 )()(
213
1)()(
222
EEEE
s
msGE e
FCC
ee
)()()(2 EEEN CC
ee ee
Near Detector workshop, CERN, 30 July 2011
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Charged current processes:
Inverse Muon DecayInverse Muon Decay
)()()(1 EEEN CC
ee
)()()(2 EEEN CC
ee ee
Near Detector workshop, CERN, 30 July 2011
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Neutral current processes:
Cross-section 0.16x10-41 E(GeV) and 0.13x10-41 E(GeV) cm2 We can only distinguish between the two channels since each come from a different muon decay :
Accuracy of cross-section depends on sin2W
Muon-neutrino electron Muon-neutrino electron scatteringscattering
ee ee
0Z
e
e
0Z
e
e
WW
FNC
e
sGE
4
22
2
sin3
1sin
2
1)(
WW
FNC
e
sGE
4
22
2
sinsin2
1
3
1)(
)()()(3 EEEN NC
ee )()()(4 EEEN NC
ee
Near Detector workshop, CERN, 30 July 2011
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Interference neutral and charged current processes:
Cross-section 0.96x10-41 E(GeV) and 0.40x10-41 E(GeV) cm2 We can only distinguish between the two channels since each come from a different muon decay :
Accuracy of cross-section depends on sin2W
Electron-neutrino electron Electron-neutrino electron scatteringscattering
)()()(5 EEEN NCCC
ee ee
)()()(6 EEEN NCCC
ee ee
0Z
e e
ee
W
e
ee
e
ee ee
0Z
e e
ee
W
e
ee
e
ee ee
WWFNCCC
e
sGE
e
42
22
sinsin2
1
3
1)(
WWFNCCC
e
sGE
e
42
22
sin3
1sin
2
1)(
Near Detector workshop, CERN, 30 July 2011
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So, if we consider the IMD and neutrino elastic scattering channels together we obtain:– For the NF decay:
– We can extract the fluxes when we have IMD and elastic scattering:
– Below 11 GeV we cannot resolve since we only have N3+N6
Combination of all channelsCombination of all channels
ee
)()()()()()( 21 EEEEENEN CC
ee
CC
ee ee
NC
e
CC
e
CC
e
NCCC
e
CC
e
NCCC
e
e
ee
eeNNNN
E
)()()(
6321
)()()()()()( 63 EEEEENEN NCCC
ee
NC
ee ee
NC
e
CC
e
CC
e
NCCC
e
CC
e
NC
e
e
ee
e
NNNNE
)()()(
6321
Near Detector workshop, CERN, 30 July 2011
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So, if we consider the IMD and neutrino elastic scattering channels together we obtain:– For the NF decay:
– We cannot resolve the two fluxes because they are together:
So, we can only resolve the fluxes when we are in an energy bin in which we have both IMD and elastic scattering for - decay. For + decay, we cannot resolve fluxes with this method – maybe we can do ratio of +/ - or fit shapes Are there any other neutrino processes that we can use? We need to look at these possibilities to extract final fluxes
Combination of all channelsCombination of all channels
ee
)()()()()()( 45 EEEEENEN NC
ee
NCCC
ee ee
Near Detector workshop, CERN, 30 July 2011
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Method for extracting neutrino fluxes at NF relies on using channels in which cross-sections are known very well theoretically Channels identified include:
– Inverse Muon Decay– Muon-neutrino electron elastic scattering– Electron-neutrino electron elastic scattering
Combination of IMD+neutrino elastic scattering works very well for - decay above IMD threshold (11 GeV) For + decay cannot resolve two fluxes Might have to rely on fitting shapes or other processes (quasi-elastic scattering?)
ConclusionsConclusions