Transcript Document 7168088

Constraints on Solar Neutrino Mixing
Parameters with the SNO Data
Alain Bellerive
Canada Research Chair in Particle Physics
Carleton University
On behalf of the SNO
Collaboration
Thanks to the Experts: Yasuo Takeuchi,
Mark Chen, Duncan Fraser, Mark Boulay,
Scott Oser, and Gordana Tesic
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Outline
• Introduction and Motivation
 Solar Neutrinos & the Standard Solar Model (SSM)
 Neutrino Oscillations
 Sudbury Neutrino Observatory
•
•
•
•
•
•
SNO Multivariate Signal Extraction
Global Analysis of all Solar Neutrino Experiments
Constraints on Oscillation Parameters
TSigEx tool in ROOT
Open Questions for Global Analysis
Summary and Conclusion
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Neutrino Production in the Sun
Light Element Fusion Reactions
p + p 2H + e+ + e
99.75 %
p + e- + p  2H + e
0.25 %
3He
+ p 4He + e+ + e ~10-5 %
7Be
+ e- 7Li + e
8B
 8Be* + e+ + e
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15 %
0.02 %
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Solar Neutrino Oscillations
Pee = sin2(2q) sin2(1.27Dm2 L / E)
• Physics:
Dm2 & sin(2q)
• Experiment:
Distance (L) & Energy (E)
 e 
 
  
 
  
U e1 U e2 U e 3  1 

  
U 1 U  2 U  3   2 

  
U1 U 2 U 3   3 
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Dm2  Dm122 and q  q12
3 Parameters !
Dm  m  m
q  Mixing angle
2
2
2
2
1
The state evolves with
time or distance
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Underground laboratory in Sudbury
SNOLAB
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Sudbury Neutrino Observatory
Salt Phase
PMT Support Structure, 17.8 m
9456 20 cm PMTs
Acrylic Vessel, 12 m diameter
1000 tonnes D2O + 2 tonnes NaCl
1700 tonnes H2O - Inner Shield
5300 tonnes H2O - Outer Shield
Urylon Liner and Radon Seal
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Neutrino Reactions in SNO [salt phase]
CC
e + d  p + p + e−
- Q = 1.445 MeV
- good measurement of e energy spectrum
- some directional info (V-A)
- e only
NC
 x + d  p + n + x
- Q = 2.22 MeV
- measures total 8B  flux from the Sun
- equal cross section for all  types
ES
 x + e−   x + e−
Produces Cherenkov
Light Cone in D2O
Neutral Current
n captures on deuteron
35Cl(n, g)36Cl
Observe 8.6 MeV g’s
Elastic Scattering
- low statistics
- mainly sensitive to e, some  and 
- strong directional sensitivity
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Charged Current
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Produces Cherenkov
Light Cone in D2O
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Neutrino Reactions in SNO [salt phase]
CC
ES
NC
Kinetic
Energy
Distribution
Te (MeV)
Radial
Distribution
(RAV=1)
 = (R/RAV)3
Solar
Direction
Distribution
Cos qsun
14
Isotropy
Distribution
i.e. light pattern
Covariances between Direction and Energy actually require 2D PDFs
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Multivariate Signal Extraction in SNO
Covariance Matrix for Signals
VCC
 0.992  0.011

  0.011 0.994

0.003
0.001

  0.015 0.027

CC & ES Energy Constrained Fit (2D)
0.003  0.015 

0.001 0.027 
0.993 0.014 

0.014 0.991 
 0.994  0.014 0.143  0.011


  0.014 0.994  0.011 0.026 
VES  
0.143  0.011 1.004  0.214 


  0.011 0.026  0.214 0.991 


VNC
 0.991  0.012  0.002  0.131



0
.
012
0
.
993

0
.
002
0
.
009



 0.002  0.002 0.993
0.001 


  0.131 0.009
0.001
0.992 

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
P( x )  p( x1 ) p( x2 ) p( x3 ) p( x4 )

with x  (Te ,  , cosq sun , 14 )
CC & ES Energy Unconstrained Fit (2D)

P( x )  p( x1 ) p( x2 ) p( x3 )

with x  (  , cos q sun , 14 )
Extended Maximum Likelihood Fit
 m
 

log L(  )    j +  log    j Pj ( xi ) 
j 1
i 1
 j 1

with j  type idex and i  event index
 j  mean number of events of type j

m
n
Systematic uncertainties incorporated
by smeared joint PDFs in the fit
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Multidimensional Joint PDFs and 2D PDFs
• To take into account
correlations between
direction and energy
we build 2D PDFs
• Small effect for ES
events (c.f. forward
peaked)
• For each energy bin
one computes a PDF
for the isotropy
parameter 14
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Te
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14
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Extended Maximum Likelihood Fit
With Binned Data


log L( tot ,q )   tot +  ni log q j Pij ( x )
N
m
i 1
j 1
with i  bin index, j  type index, and ni  number of events in bin i
 tot  i 1  j  niq j with q j  fraction of events of type j
N
m
CC & ES Energy Constrained Fit (2D)

Pij ( x )  pij ( x1 ) pij ( x2 ) pij ( x3 ) pij ( x4 )

with x  (Te ,  , cos q sun , 14 )
Unconstrained
More Model
Independent

Pij ( x )  pij ( x1 ) pij ( x2 ) pij ( x3 )

with x  (  , cosq sun , 14 )
NTe
m
NTe
fix
fix
k
k
q

q
+
q
+
q
+
q
+
q
+
q
 j NC ext(n) int(n) int(g )  CC  ES
i
j 1
Energy Shape
is free to float
CC & ES Energy Unconstrained Fit (2D)
i
i
i
k 1
i
k 1
i
where q ' s for NC/CC/ES depend on Xsection & luminosity
NTe NTe
NTe NTe
 1  1
 1  1
2
2
 CC
  cov CC ( ,  ) and  ES
  cov ES ( ,  ) and
#EVENTS
Unconstrained Signal Extraction Results
CC 1339.6
ES
+63.8
- 61.5
170.3 +23.9
- 20.1
NC 1344.2
+69.8
- 69.0
Shape-unconstrained Neutrino Fluxes
Signal Extraction in FCC,
FNC, FES with
Te > 5.5 MeV
Fcc(e) =
+0.08
+0.06
1.59 -0.07 (stat.) -0.08 (syst.)
x106 cm-2s-1
Fes(x) =
+0.31
+0.10
2.21 -0.26 (stat.) -0.10 (syst.)
x106 cm-2s-1
Fnc(x) =
+0.27
5.21 -0.27
x106 cm-2s-1
+0.38
(stat.) -0.38 (syst.)
Submitted to Phys. Rev. Lett.
nucl-ex/0309004
Contact person: Mark Boulay
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Data Sets Used for Global Analysis
SNO:
• Pure D2O Day/Night fluxes and the Salt fluxes
How to use the SNO data to produce MSW contour plots is described; e.g.
how to include the required correlations for including the new salt data in a
global oscillation analyses; enumeration of improvements; etc…
All Solar Neutrino Experiments:
• Chlorine flux
• Gallium fluxes (SAGE and GALLEX/GNO)
• SuperKamiokande (SK) zenith spectra
KamLAND:
• KamLAND reactor anti-neutrino results
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SNO: Pure D2O Phase
• The CC, ES and NC fluxes presented in the earlier SNO papers that analyzed data
from the pure D2O phase were in derived under the explicit assumption of an
undistorted 8B spectral shape (i.e.an energy-independent survival probability).
• At each grid point in the Dm2 and tan2q plane, we calculated the expected summed
energy spectra (CC+NC+ES+bkgd events, day and night), and compared the
calculated energy spectra to the SNO data.
• The assumption of a 8B spectrum was appropriate for testing the null hypothesis of
neutrino oscillations. We assumed no oscillations, then showed that our data under
this assumption would imply a non-zero of , thus refuting the null hypothesis.
• However using fluxes derived assuming an undistorted spectrum is not appropriate for
calculating constraints on MSW mixing parameters, since MSW oscillations generally
allow for spectral distortions. We did not use the reported integral fluxes when making
the contour plots, but instead used the summed energy spectra. During the pure D2O
phase, the spectral shape was particularly important for distinguishing CC from NC
events, since our best handle on detecting neutrons was to look for a bump in the
energy spectrum, due to the neutrons.
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SNO: Salt Phase
• In salt, we do not need to make assumptions about the shapes of the CC or ES
energy spectra when deriving these fluxes (independent of assumptions about the
energy dependence of the survival probability).
• Appropriate for use in global oscillation analyses. We use only the integral CC, ES
and NC fluxes. We did not include spectral information because it will lead to double
counting and CC/NC (syst. Mostly cancel) provided tighter constraints.
• A more advanced MSW oscillation analysis is being developed that jointly use the
isotropy and energy spectrum information in a maximum-likelihood.
Statistical Correlations
Here the statistical errors on the fluxes have been symmetrized.
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Systematic Correlations Between Fluxes
Improvements for the Salt Phase
●
New numerical integration for MSW in both Sun and Earth
●
ES radiative correction (previous: 2%  new:3~6% in 5-20MeV)
●
Better treatment of systematic errors
Estimate energy-dependent systematic errors at each grid point
implement 8B shape errors and new Ga/Cl cross-section correlated
errors
Better treatment of SK results
energy(kinetic  total), energy resolution, systematic errors
1258day day/night spectra 1496day zenith spectra (newest results)
●
Updated the following inputs:
pp and hep neutrino energy spectrum
electron density in the Earth (Bahcall's chemical composition)
Newest GNO and SAGE results (SAGE result@LowNu2003 used)
●
Improve calculation precision
no gap and finer grid for VO region
●
Contact person: Yasuo Takeuchi
Numerical integration in the Sun
●
Previous method: MVA approxmation
● Cannot handle off-center neutrino generation completely
● Has a few, known inaccuracies in QVO region
Typical numerical integration of neutrino wave
function
●
typical
non-adiabatic
MSW
Pee
(survival
probability
of electron
neutrino)
R/Rsun
center
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Numerical integration in the Sun: QVO region
use this
Dm2/E
-8
-9
-12
log(tan2q)
original
(D2O)
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reproduce
integration
(at 1AU)
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integration
(annual
average)
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Energy Dependence
8B
●
●
●
Spectrum:
Bahcall: PRC54(1996)411
Ortiz: PRL(2000)2909
Bahcall provide both experimental and theoretical errors
Ortiz provide only experimental error. It is slightly better than
Bahcall (difference are very small).
Use Bachcall as 8B spetrum uncertainties (larger uncertainty)
SNO Energy Scale and Resolution:
●
calculate energy scale and resolution errors at each oscillation
parameter point, like B8 spectrum error
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SNO: Constraint on mixing parameters
SNO only
8B Free
2/d.o.f=26.2/34
Allowed Regions
Best Fit (1.03xSSM 8B)
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Combination of Several Experiments
• Each electron type comes from different fusion reactions (pp,pep,hep,7Be,8B,…)
and is generated over some production region in the Sun’s interior.
• Correlation between the theoretical uncertainties on the solar fluxes and on the
cross-sections are included.
• Energy Scale and Resolution for SK are calculated at each MSW point (like SNO).
• Assumed (for the moment) that SNO D2O and Salt phases are uncorrelated; which
is a good approximation (but it is the same detector!).
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All: Constraint on mixing parameters
Solar Neutrino Experiments
8B Free 1.04xSSM 8B
2/d.o.f=70.2/81
Solar Neutrino Experiments
+
KamLAND
LMA
Allowed
Region
Exclude maximal mixing
at 5.4; implies Dm2>0
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8B
Free
1.02xSSM 8B
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SNO Contribution to Global Analysis
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ROOT Module
Provide all the info in TObject
format (i.e. ROOT)
QSigExDirHandler Abstract base class for TDirectory handler classes
QSigExCuts Loads equivalences/cuts in the TDirectory structure;
treats regular 1D selections and/or expressions
QSigExCleanData Applies cuts on raw data events and fills a TTree
with clean data
QSigExProbs Computes the marginal probability densities using
marginal PDFs and data TTtree
QSigExPDFs Abstract base class for QSigExDirHandler derived
classes that load marginal PDFs in the TDirectory structure
QSigExJointProbs Computes the joint probability densities of
variables with/without correlation (full or multi-dim)
QSigExFit Evaluates the population parameters and their errors using
Minuit minimization package (binned/unbinned/analytic)
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– Lisi – Marrone – Montanino – Palazzo
OPEN Questions Fogli
hep-ph/0206162
Pull Method: Split the residuals from observables and the systematics
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Diagram of
Pull for
Observables
for LMA
hep-ph/0206162
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Diagram of
Pull for
Systematics
for LMA
hep-ph/0206162
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Conclusion
• New SNO results from the salt phase: confirm the pure D2O
evidence for solar neutrino oscillations
• How to use SNO data in global analysis - LMA solutions are
favored by a global analysis
• TQsigEx module with all documentation on the web and
distributed with ROOT for extended maximum likelihood fits
• Are we allowed to let the systematic uncertainties float in a
global analysis? Likelihood functions might be a better
approach for global combination?
• More from SNO: full salt data set will increase the statistic
by ~ 2 – Day/Night – Spectral analysis
• Course on Statistical Analysis – Comp. Phys. 4807/5002 on
the web:
www.physics.carleton.ca/~alainb/teaching.html
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