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Phenomenology of Phenomenology of 1313
1313 half-day meeting half-day meeting
Oxford, UKOxford, UKSeptember 24, 2007September 24, 2007
Walter WinterWalter WinterUniversität WürzburgUniversität Würzburg
Sept. 24, 2007 Oxford 2007 - Walter Winter 2
ContentsContents
IntroductionIntroduction The measurement of The measurement of 1313: :
Reactor versus beam experimentsReactor versus beam experiments Performance indicators for Performance indicators for 1313
… and comparison of experiments… and comparison of experiments The “farer” future: what if The “farer” future: what if 1313 is very small? is very small?
Beyond Beyond 1313: Mass hierarchy and CP violation: Mass hierarchy and CP violation
SummarySummary
Sept. 24, 2007 Oxford 2007 - Walter Winter 3
Neutrino mixingNeutrino mixingUse standard parameterization - as for CKM matrix:Use standard parameterization - as for CKM matrix:
( ) ( ) ( )= xx
Three mixing angles Three mixing angles , , one CP phase one CP phase CPCP
Difference to quarks: Two mixing angles large: Difference to quarks: Two mixing angles large:
(s(sijij = sin = sin ij ij ccijij = cos = cos ijij))
Sept. 24, 2007 Oxford 2007 - Walter Winter 4
Neutrino massNeutrino mass
To independent mass To independent mass squared differences squared differences relevant for oscillations: |relevant for oscillations: |mm2121
2 2 | << || << |mm313122||
|| = = mm212122/|/|mm3131
22| ~ 3% | ~ 3%
Mass spectra: Difference to origin? Degenerate masses?Mass spectra: Difference to origin? Degenerate masses?
Mass hierarchy: Mass hierarchy: Normal or inverted?Normal or inverted?
Theory: Dirac or Theory: Dirac or Majorana mass terms?Majorana mass terms?
8
8
Sept. 24, 2007 Oxford 2007 - Walter Winter 5
Neutrino oscillations with two flavorsNeutrino oscillations with two flavorsMixing and mass squared difference:Mixing and mass squared difference:
“disappearance”: “disappearance”:
“appearance”: “appearance”:
Amplitude~Frequency
Baseline: Source - Detector
Energy
Sept. 24, 2007 Oxford 2007 - Walter Winter 6
Picture of three-flavor oscillationsPicture of three-flavor oscillations
Magnitude of Magnitude of 1313 is key tois key to
““subleading” effects: subleading” effects: Mass hierarchy Mass hierarchy
determinationdetermination CP violationCP violation
Use Use ee transitions on atmospheric oscillation scale transitions on atmospheric oscillation scale
(“Oscillation maximum”)(“Oscillation maximum”)
Coupling strength: 13
Atmosphericoscillation:Amplitude: 23
Frequency: m312
Solaroscillation:Amplitude: 12
Frequency: m212
Sub-leading
effect: CP
Sept. 24, 2007 Oxford 2007 - Walter Winter 7
Matter effects in Matter effects in -oscillations (MSW)-oscillations (MSW) Ordinary matter Ordinary matter
contains electrons, contains electrons, but no but no ,,
Coherent forward Coherent forward scattering in matter scattering in matter has net effect on electron flavor because of CC (rel. phase shift)has net effect on electron flavor because of CC (rel. phase shift)
Matter effects proportional to electron density and Matter effects proportional to electron density and baselinebaseline Hamiltonian in matter:Hamiltonian in matter:
The matter potential is The matter potential is notnot CP-inv.! Source of many problems! CP-inv.! Source of many problems!
Y: electron fraction ~ 0.5
(electrons per nucleon)
(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)
The measurement of The measurement of 1313
Experiment classesExperiment classes
Sept. 24, 2007 Oxford 2007 - Walter Winter 9
Experiment classes by sourceExperiment classes by sourceSourceSource Production … and DetectionProduction … and Detection LimitationsLimitations LL <E><E>
ReactorReactor SystematicsSystematics 1-2 km1-2 km ~4 MeV~4 MeV
Super-Super-beambeam
Intrinsic Intrinsic beam BG,beam BG,systematicssystematics
100-100-2,500 km2,500 km
0.5 – 5 0.5 – 5 GeVGeV
Neutrino Neutrino factoryfactory
Charge Charge identification,identification,NC BGNC BG
700-700-7,500 km7,500 km
5-50 5-50 GeVGeV
-beam-beam SourceSourceluminosityluminosity
100-100-2,000 km2,000 km
0.3 – 10 0.3 – 10 GeV GeV
For leading atm. params Signal prop. sin2213 Contamination
Sept. 24, 2007 Oxford 2007 - Walter Winter 10
Disappearance measurementsDisappearance measurements Use expansions in small parameters:Use expansions in small parameters:
Short baseline reactor experiments:Short baseline reactor experiments:
2 2ndnd term small for sin term small for sin22221313 >> 10 >> 10-3-3!!
Long baseline accelerator experiments:Long baseline accelerator experiments:
(see e.g. Akhmedov et al., hep-ph/0402175)
No CP, No mass
hierarchy!
31 = m312 L/(4E)
Sept. 24, 2007 Oxford 2007 - Walter Winter 11
A multi-detector reactor experimentA multi-detector reactor experiment… for a “clean” measurement of … for a “clean” measurement of 1313
Double Choozsize
Daya Baysize
(Minakata et al, 2002; Huber, Lindner, Schwetz, Winter, 2003)
Identical detectors, L ~ 1.1-1.7 km
Unknownsystematics
important for large
luminosity
NB: No sensitivity to CP and
mass hierarchy!
See also Lisa Falk-Harris‘ talk!
Sept. 24, 2007 Oxford 2007 - Walter Winter 12
Appearance channels: Appearance channels: ee
Complicated, but all interesting information there: Complicated, but all interesting information there: 1313, , CPCP, mass hierarchy (via A), mass hierarchy (via A)
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)
Antineutrinos
Sept. 24, 2007 Oxford 2007 - Walter Winter 13
Neutrino beamsNeutrino beams
Accelerator-based neutrino
source
Often: near detector (measures flux times
cross sections)
Far detector
Baseline: L ~ E/m31
2
(Osc. length)
?
See also Dave Wark‘s talk!
Sept. 24, 2007 Oxford 2007 - Walter Winter 14
Running example: MINOSRunning example: MINOS Measurement of atmosphericMeasurement of atmospheric
parameters with high precisionparameters with high precision Flavor conversion ?Flavor conversion ? Fermilab - Soudan
L ~ 735 km
Far detector: 5400 tNear detector: 980 t
735 km
Beam line
1313 performance indicators performance indicators…and comparison of experiments…and comparison of experiments
1313 exclusion/sensitivity limit exclusion/sensitivity limit
1313 discovery potential discovery potential
Sept. 24, 2007 Oxford 2007 - Walter Winter 16
Predictions for future experimentsPredictions for future experiments Existing experiments:Existing experiments: Future experiments:Future experiments:
Data
Fit parameters to data:Precision of quantity
of interest
Simulated data
Fit parameters to data:Precision of quantity
of interest
Input parameters?
Performance indicators depend on input param. hypothesis!
Sept. 24, 2007 Oxford 2007 - Walter Winter 17
Simulated versus fit parametersSimulated versus fit parameters
Determine the Determine the precision of the precision of the quantity of interestquantity of interest
““Unused” parameteres Unused” parameteres are usually are usually marginalizedmarginalized over over (projection onto (projection onto axis/plane of interest)axis/plane of interest)
Source of correlations!Source of correlations!
Represent the values Represent the values implemented by natureimplemented by nature
Known within current limitsKnown within current limits Change the event rates, top.Change the event rates, top. Have to be interpreted likeHave to be interpreted like
“If the value of … is …, then “If the value of … is …, then the performance will be …” the performance will be …” - - Luck or not luck?Luck or not luck?
Used for risk minimization!Used for risk minimization!
Fit parameters Simulated/true params
Sept. 24, 2007 Oxford 2007 - Walter Winter 18
1313 exclusion/sensitivity limit (1) exclusion/sensitivity limit (1) Describes the new Describes the new 1313 limit for the simulation of no signal limit for the simulation of no signal
((1313=0)=0) Define as largest fit value of Define as largest fit value of 1313, which fits true , which fits true 1313=0=0 Straightforward inclusion of correlations Straightforward inclusion of correlations
and degeneraciesand degeneracies Does not depend on the simulated Does not depend on the simulated CPCP
and mass hierarchy!and mass hierarchy!
(from hep-ph/0403068, App. C)
Sept. 24, 2007 Oxford 2007 - Walter Winter 19
1313 exclusion/sensitivity limit (2) exclusion/sensitivity limit (2) Simulated parameters:Simulated parameters:
1313=0, =0, CPCP meaningless meaningless Relatively “simple” Relatively “simple”
parameter dependenciesparameter dependencies No dependence on No dependence on CPCP, ,
mass hierarchymass hierarchy
Fit parameters:Fit parameters:All six parametersAll six parameters
Correlations and Correlations and degeneracies affect degeneracies affect this performance this performance indicatorindicator
Small for T2K etc.;Rate ~ 0
Look for any combination of
parameters which “fake” the smallest
rate
Sept. 24, 2007 Oxford 2007 - Walter Winter 20
1313 exclusion: Problems with degeneracies exclusion: Problems with degeneracies Connected (green) or Connected (green) or
disconnected (yellow) disconnected (yellow) degenerate solutions in degenerate solutions in parameter spaceparameter space
Affect measurementsAffect measurementsExample: Example: 1313-sensitivity-sensitivity
(exclusion limit)(exclusion limit)
(Huber, Lindner, Winter, 2002)(Huber, Lindner, Winter, 2002)
Discrete degeneracies: Discrete degeneracies: ((,,1313)-degeneracy)-degeneracy(Burguet-Castell et al, 2001)(Burguet-Castell et al, 2001)
sgn-degeneracy sgn-degeneracy (Minakata, Nunokawa, 2001)(Minakata, Nunokawa, 2001)
((2323,,/2-/2-2323)-degeneracy )-degeneracy (Fogli, Lisi, 1996)(Fogli, Lisi, 1996)
Degeneracy resolution importanttopic in recent years!
Example: Neutrino factory (later)
Sept. 24, 2007 Oxford 2007 - Walter Winter 21
1313 discovery limit discovery limit Simulated parameters:Simulated parameters:
Hypothesis:Hypothesis: Certain Certain 1313>0, >0,
CPCP, mass hierarchy, mass hierarchy
Can we establish Can we establish 1313>0 for >0 for
this hypothesis?this hypothesis? Maximize parameter space Maximize parameter space
for discoveryfor discovery
Fit parameters:Fit parameters:Relatively simple as Relatively simple as long as “solar term” long as “solar term” negligiblenegligible
Small impact of Small impact of correlationscorrelations
Simulated rate depends on all
parametersSmall for
NOvA etc.;
Rate ~ 0
Sept. 24, 2007 Oxford 2007 - Walter Winter 22
1313 discovery: CP fraction plots discovery: CP fraction plots
Sensitive region as
function of true 13 and CP
CP values now stacked for
each 13
Fraction of
CP for
successful discoveryRead: For
sin2213=0.04, we expect a discovery
for 20% of all values of CP
“Typical CP”:CP fraction
50%
Sept. 24, 2007 Oxford 2007 - Walter Winter 23
Evolution of Evolution of 1313 discovery limit? discovery limit?
Specific scenarioSpecific scenario Bands reflect Bands reflect
dependence on dependence on CPCP
(from: FNAL Proton Driver Study)
GLoBES 2005
(NOvA)
Sept. 24, 2007 Oxford 2007 - Walter Winter 24
Discovery versus exclusion powerDiscovery versus exclusion power
Beams: discovery machines? Reactor experiments: Exclusion instruments?
(Huber, Kopp, Lindner, Rolinec, Winter, 2006)
The „farer“ future?The „farer“ future?
Experiments for very small Experiments for very small 1313
Sept. 24, 2007 Oxford 2007 - Walter Winter 26
Superbeam upgrades: ExamplesSuperbeam upgrades: Examples
Bands reflect Bands reflect variation of variation of systematical errors: systematical errors: 2%-5%-10%2%-5%-10%
Dots: Nominal LDots: Nominal L Typical Typical CPCP, 3, 3 Discovery of sinDiscovery of sin22221313
downto ~10downto ~10-3-3
(Barger, Huber, Marfatia, Winter, hep-ph/0610301, hep-ph/0703029)
discovery
Sept. 24, 2007 Oxford 2007 - Walter Winter 27
Neutrino factoryNeutrino factory Ultimate “high precision” instrument!?Ultimate “high precision” instrument!? Muon decays in straight sections of storage Muon decays in straight sections of storage
ringring Technical challenges: Target power, muon Technical challenges: Target power, muon
cooling, charge identification, maybe steep cooling, charge identification, maybe steep decay tunnelsdecay tunnels
(from: CERN Yellow Report )
p
Target
, K
Decays
-Accelerator
Cooling
“Right sign”
“Wrong sign”
“Right sign”
“Wrong sign”
(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)
Sept. 24, 2007 Oxford 2007 - Walter Winter 28
IDS-NF launched at NuFact 07IDS-NF launched at NuFact 07International design study for a neutrino factoryInternational design study for a neutrino factory
Successor of the International Scoping Study for a „future Successor of the International Scoping Study for a „future neutrino factory and superbeam facility“:neutrino factory and superbeam facility“:Physics case made in physics WG report (~368 pp) Physics case made in physics WG report (~368 pp) http://www.hep.ph.ic.ac.uk/idshttp://www.hep.ph.ic.ac.uk/ids
Initiative from ~ 2007-2012 to present a design report, Initiative from ~ 2007-2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino schedule, cost estimate, risk assessment for a neutrino factoryfactory
In Europe: Close connection to „EuroIn Europe: Close connection to „Eurous“ proposal us“ proposal within the FP 07; currently ranked #1, negotiating contract within the FP 07; currently ranked #1, negotiating contract
In the US: „Muon collider task force“In the US: „Muon collider task force“How can a neutrino factory be „upgraded“ to a muon How can a neutrino factory be „upgraded“ to a muon collider?collider?
Ken Long (Imperial, RAL)
Sept. 24, 2007 Oxford 2007 - Walter Winter 29
Resolving degeneraciesResolving degeneraciesExample: „Magic“ baseline for NFExample: „Magic“ baseline for NF
L= ~ 4000 km (CP) + L= ~ 4000 km (CP) + ~7500 km (degs) today ~7500 km (degs) today baseline configuration of baseline configuration of a neutrino factory a neutrino factory (ISS study, 2006)(ISS study, 2006)
(Huber, Winter, 2003)(Huber, Winter, 2003)
Beyond Beyond 1313 discovery discovery
Mass hierarchy and CP violationMass hierarchy and CP violation
Precision measurementsPrecision measurements
Sept. 24, 2007 Oxford 2007 - Walter Winter 31
Perspectives for MH and Perspectives for MH and CPCP
for the coming 5 to 10 years?for the coming 5 to 10 years? A mass hierarchy or CP violation measurement A mass hierarchy or CP violation measurement
will be unlikely or impossible fromwill be unlikely or impossible from– Beams+Reactor experimentsBeams+Reactor experiments– Any other source alone (supernova etc.) Any other source alone (supernova etc.)
(from: Huber, Lindner, Rolinec, Schwetz, Winter, 2004)(from: Huber, Lindner, Rolinec, Schwetz, Winter, 2004)
Sept. 24, 2007 Oxford 2007 - Walter Winter 32
Help from outer space?Help from outer space? Astrophysical neutrino sources produceAstrophysical neutrino sources produce
certain flavor ratios of neutrinos (certain flavor ratios of neutrinos (ee::::):):
Neutron decays: (1:0:0)Neutron decays: (1:0:0)Muon damped sources: (0:1:0)Muon damped sources: (0:1:0)Pion decays: (1:2:0)Pion decays: (1:2:0)
These ratios are changed at Earth through These ratios are changed at Earth through averaged neutrino oscillations:averaged neutrino oscillations:
Measure muon track to shower ratio at neutrino Measure muon track to shower ratio at neutrino telescope: R = telescope: R = /(/(ee))
(conservative, since in future also flavors!?)(conservative, since in future also flavors!?)
~ cos
Sept. 24, 2007 Oxford 2007 - Walter Winter 33
Complementarity to beamsComplementarity to beams Use R to obtainUse R to obtain
information oninformation onosc. parameters?osc. parameters?Difficult, sinceDifficult, since– Low statisticsLow statistics– No spectral infoNo spectral info
(Serpico, Kachelriess, 2005;(Serpico, Kachelriess, 2005;Serpico, 2005)Serpico, 2005)
But: ComplementaryBut: Complementarydependencedependenceon on CPCP
Combine the Combine the information from information from multiple low multiple low statistics exps?statistics exps?
(Winter, 2006)
R
TotalRates
Sept. 24, 2007 Oxford 2007 - Walter Winter 34
Early measurement of Early measurement of CPCP ... using Double Chooz?... using Double Chooz?
Double ChoozDouble Choozmight be the first might be the first experiment toexperiment toobserve observe CPCP
If more information: If more information: possibly even CP possibly even CP violation measurement:violation measurement:
(Winter, 2006)
(Blum, Nir, Waxman, 2007)
Sept. 24, 2007 Oxford 2007 - Walter Winter 35
Future discovery of MH and Future discovery of MH and CPCP
Mass hierarchy discovery CP violation discovery
(ISS study)Left end of band: Optimistic setupRight end of band: Conservative setup
Sept. 24, 2007 Oxford 2007 - Walter Winter 36
Beyond discovery:Beyond discovery:
Precision measurements at a NFPrecision measurements at a NF
(Gandhi, Winter, 2006)(Huber, Lindner, Winter, 2004)
CP precision 13 precision
CP dep.
3
Sept. 24, 2007 Oxford 2007 - Walter Winter 37
SummarySummary 1313 will be tested in the near future by reactor will be tested in the near future by reactor
experiments and superbeamsexperiments and superbeams Reactor experiments provide very good limits Reactor experiments provide very good limits
on on 1313, while a discovery may be more likely at , while a discovery may be more likely at
a beam experimenta beam experiment If not found, neutrino factories may probe If not found, neutrino factories may probe
sinsin22221313 down to the level of 10 down to the level of 10-4-4 or 10 or 10-5-5
The measurements of the mass hierarchy and The measurements of the mass hierarchy and CPCP will require the next generation of will require the next generation of
experimentsexperiments
BackupBackup
Sept. 24, 2007 Oxford 2007 - Walter Winter 39
Matter effects (two flavors, Matter effects (two flavors, const.) const.)
Parameter mapping (same form):Parameter mapping (same form):Vacuum:Vacuum:Matter:Matter:
“Matter resonance”: In this case: - Effective mixing maximal- Effective osc. frequency min.
~ 4.5 g/cm3 (Earth’s mantle)LBL osc.: E ~ 6.5 GeV
Resonance energy:
Describes e – transitionsto 0th order in
13
m2 m312
(except factor 0.5)
Sept. 24, 2007 Oxford 2007 - Walter Winter 40
Curves: Errors on R5%10%20%No constraint
Early mass hierarchy measurement?Early mass hierarchy measurement? Fake solution is running in Fake solution is running in CPCP
as function of as function of 1313
Astrophysical source may help Astrophysical source may help mass hierarchy measurementmass hierarchy measurementby constraining this runningby constraining this running
(Winter, 2006)
MINOS+Double Chooz+T2K+NOvA