Phenomenology of 13 13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität...

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


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))


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


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


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


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


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


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)


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!


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


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!


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


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!


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


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)


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


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)


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


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%


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)


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


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


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)


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)


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


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)


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


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


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)


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


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


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


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)


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

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Phenomenology of 13 13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität...

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