Transcript Energy measurement in quasi-elastics Unfolding detector

Energy measurement in quasi-elastics
Unfolding detector and physics effects
Alain Blondel
Mario Campanelli
Maximilien Fechner
A. Blondel, M.Campanelli, M.Fechner
Introduction
Quasi-elastic events, dominant at low energy
(< 1 GeV) easier to reconstruct than DIS.
Very important for low-energy Super-Beams, in
particular for Cerenkov detectors.
For a target nucleon at rest, the neutrino energy
can be reconstructed exactly from lepton
information only (proton below Cerenkov
threshold):
m  m  m
2
E 
mn El 
2
n
2
l
2
mn  El  Pl cos( )
A. Blondel, M.Campanelli, M.Fechner
Experiment/Physics effects
In order to use this formula in a real experiment, we have
to account for:
• Resolution on lepton measurement
• Nuclear effects (Fermi motion, Pauli blocking)
• efficiencies
All these effects lead to a widening of neutrino energy
resolution, and to a clear bias on the reconstructed energy
We consider the case of a large water Cerenkov detector, illuminated by a
low energy super-beam (CERN SPL-> Frejus), for a 200 kton*year
exposure.
However, most of the following considerations have general application.
A. Blondel, M.Campanelli, M.Fechner
Event simulation
Standard SPL+UNO event rates considered
Lepton energy and angle resolution are taken from
SuperKamiokande:
s(Ee)/Ee=0.5%+2.5%/E
s(Eμ)/Eμ=3%
s()=3o
•Fermi motion: neutrons are assumed having momentum
uniformly distributed on a sphere with kF=225 MeV
•Pauli blocking: to have a quasi-elastic event, we need the
produced proton to be outside the Fermi sphere
n
ν
p
kF
μ
A. Blondel, M.Campanelli, M.Fechner
Energy reconstruction from leptons
Using the above formula, for e, at SPL energies:
Perfect detector
Lepton resolution
Erec
Erec
Nuclear effects only
Egen
All effects included
Egen
A. Blondel, M.Campanelli, M.Fechner
Biases and Energy resolution
Erec-Egen
20% average resolution, with 5% bias
resolution
A. Blondel, M.Campanelli, M.Fechner
Effects on neutrino oscillations
The dip due to neutrino oscillations almost
disappears after smearing effects are considered
dip
A general bias towards higher energies is observed
no dip
A. Blondel, M.Campanelli, M.Fechner
Fitting for oscillation parameter
in presence of distorting effects
Classical problem in HEP; here we follow the approach of the
MonteCarlo re-weighting with box method (used eg for W
physics at LEP)
Basic idea: produce a large MonteCarlo correspondence table
between the real quantity (Eνgen) and measured one (Eνrec),
and consider for each data event all those with reconstructed
energy sufficiently close to the data event.
Since normally the MC sample is produced with a given set of
parameters θ0, events are reweighted according to the ratio
of oscillation probabilities
N ( )
wi ( ) 
N ( 0 )
A. Blondel, M.Campanelli, M.Fechner
Box reweighting at work
Box!
Reconstructed MC
distribution
Data event
MC events
in the box
weights
reconstructed
generated
Image of the box
A. Blondel, M.Campanelli, M.Fechner
Fits with reweighting
The final fit is performed from a likelihood containing two
terms, one for the shape (box method) and one describing
the Poisson probability for the number of events:
N data
Nj
N MC
1
1
log L   log(   (i; ))  log(N exp ( 0 ) 
 (i, ))
V j i 1
j 1
i 1 N MC
 ( N data log(N exp ( ))  N exp ( ))
box
counting
The two parts of the likelihood can be studied separately
to isolate contributions from the spectrum and from the
simple counting of the number of events
A. Blondel, M.Campanelli, M.Fechner
Fits
2
to Δm
The algorithm was
tested for the whole
relevant range of
Dm2 and showed
good linearity and
precision
A. Blondel, M.Campanelli, M.Fechner
2d results
Using this method, we fit
several quantities, using the
following oscillation
parameters:
Dm23=2.5 10-3
Dm12=5.44 10-5
tan2 12=0.4
sin2223=0.95
sin2 213=0.02
d=0
As expected, Dm2 determination
benefits much from spectrum, while
13 is basically counting events
Counting only
spectral information also
A. Blondel, M.Campanelli, M.Fechner
Atmospheric
parameters
Even more spectacular is
the improvement on
the fit of both
atmospheric
parameters, where the
lack of spectral
information results in
large correlations and
a “banana-shaped”
contour.
Counting only
spectral information also
A. Blondel, M.Campanelli, M.Fechner
Conclusions
• Spectral information is essential to fully exploit the
capabilities of a Super-beam oscillation experiment
• At low energy, detector and especially nuclear effects
introduce large spectral distortions, to be corrected for
• The MC re-weighting is one of the most powerful
methods to deal with such situations
• Very good precision on the main oscillation parameters
obtained; no systematics yet; applicability to CP violation
under study
A. Blondel, M.Campanelli, M.Fechner