The quest for q 13 : Parameter space and performance indicators

The quest for The quest for 1313: Parameter space : Parameter space

and performance indicatorsand performance indicators

Proton Driver General MeetingProton Driver General MeetingAt FermilabAt FermilabApril 27, 2005April 27, 2005

Walter WinterWalter WinterInstitute for Advanced Study, PrincetonInstitute for Advanced Study, Princeton

April 27, 2005 PD General Meeting - Walter Winter

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ContentsContents

IntroductionIntroduction Simulation of future experimentsSimulation of future experiments Performance indicators for Performance indicators for 1313

What is “Fraction of What is “Fraction of CPCP”?”?

PD News: Neutrino oscillation landscapesPD News: Neutrino oscillation landscapes Some implications: Examples for Some implications: Examples for 1313 cases cases

SummarySummary


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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))


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Neutrino massNeutrino mass From oscillations: We know that neutrinos have mass!From oscillations: We know that neutrinos have mass! Dirac or Majorana?Dirac or Majorana? Absolute neutrino mass scale? Now: < eVAbsolute neutrino mass scale? Now: < eV Mass schemes: Degenerate or hierarchical?Mass schemes: Degenerate or hierarchical? Mass hierarchyMass hierarchy::

Normal or inverted?Normal or inverted?

In addition: Hierarchy is good model discriminator!In addition: Hierarchy is good model discriminator!

Adiabatic conversion in

SN

Better mass bounds from cosmology,

0-decay


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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


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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

e e flavor transitionsflavor transitions

in atmospheric oscillationsin atmospheric oscillations

(“Oscillation maximum”)(“Oscillation maximum”)

Coupling strength: 13

Atmosphericoscillation:Amplitude: 23

Frequency: m312

Solaroscillation:Amplitude: 12

Frequency: m212

Sub-leading

effect: CP


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Some “man-made” neutrino sourcesSome “man-made” neutrino sourcesSourceSource Production … and DetectionProduction … and Detection ““Limitation”Limitation” LL <E><E>

ReactorReactor SystematicsSystematics 1-2 km1-2 km ~4 MeV~4 MeV

Super-Super-beambeam

Intrinsic Intrinsic beam beam backgroundbackground

100-100-2,500 km2,500 km

0.5 – 5 0.5 – 5 GeVGeV

Neutrino Neutrino factoryfactory

Charge Charge identificationidentification

700-700-7,500 km7,500 km

15-30 15-30 GeVGeV

-beam-beam RadioactivityRadioactivity 100-100-2,000 km2,000 km

0.3 – 10 0.3 – 10 GeV GeV

For leading atm. params Signal prop. sin2213 Contamination


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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!


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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)


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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?

Simulation of future experiments = “Hypothesis testing”


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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 marginalized over marginalized 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


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1313 exclusion limit (1) exclusion limit (1) Describes the new Describes the new 1313 limit for the hyopthesis of no signal limit for the hyopthesis of no signal

((1313=0)=0) Define as largest fit value of Define as largest fit value of 1313=0, which fits true =0, which fits true 1313=0=0 Straightfoward inclusion of correlations Straightfoward 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!

(Huber et al hep-ph/0403068)


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1313 exclusion limit (2) exclusion 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 NOvA etc.;

Rate ~ 0

Look for any combination of

parameters which “fake” the smallest

rate


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1313 discovery limit discovery limit Simulated parameters:Simulated parameters:

Hypothesis:Hypothesis: Certain Certain 1313, , CPCP, mass hierarchy, mass hierarchy

Can we find a signal for Can we find a signal for this hypothesis?this hypothesis?

Maximize parameter Maximize parameter space for discoveryspace for 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


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1313 exclusion vs. exclusion vs. 1313 discovery discovery Two different performance indicatorsTwo different performance indicators 1313 exclusion interesting for pre-PD era: exclusion interesting for pre-PD era:

What will be the limits at PD startup? What will be the limits at PD startup? How far can we go for sure = can we exclude that we How far can we go for sure = can we exclude that we will not discover will not discover 1313??

1313 discovery interesting for PD era: discovery interesting for PD era:In what cases could we discover something?In what cases could we discover something?

Completely risk-minimized discovery potential Completely risk-minimized discovery potential corresponds approximately to corresponds approximately to 1313 exclusion limit exclusion limit

» Discovery limit has to be interpreted with care!Discovery limit has to be interpreted with care! Correlations and degeneracies in one case translate into Correlations and degeneracies in one case translate into

dependence on dependence on CPCP and mass hierarchy in the other and mass hierarchy in the other


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1313 exclusion limit at PD startup exclusion limit at PD startup 13 13 may or may not have been discovered at PD startup:may or may not have been discovered at PD startup:

Scenario 3:Discovery unlikely

until PD startup

Scenario 1:Certainly discovered

until PD startup

Scenario 2:Discovery likely before

PD startup

Could work on CP violation+mass hierarchy

with existing beamline + det.

Need substantially more thanexisting beamline + detectorBut: superbeams way to go

Probably need neutrino factory

Conceptual casesin PD study

NUE=“NuMI Up-graded Experiment”

~ NOvA


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1313 discovery and CP fraction plots discovery and CP fraction plots

Sensitive region as

function of true 13 and CP

CP values now stacked for

each 13

Fraction of

CP for

successful discoveryNew primer in PD-NOD!Read: For

sin2213=0.04, we expect a discovery

for 20% of all values of CP


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““Fraction of Fraction of CPCP”” = Measure for luck?= Measure for luck? Discovery potentialDiscovery potential depends on depends on

true true CPCP, mass hierarchy, mass hierarchy

For uniform distribution in For uniform distribution in CPCP::

Fraction of Fraction of CPCP = Probability to = Probability to

discoverdiscover CPCP

Remember: Remember: CP CP comes from a comes from a

complex phase factor ecomplex phase factor eii in the in the mixing matrix mixing matrix Thus: a distribution in sin Thus: a distribution in sin would be theoretically would be theoretically “unnatural”“unnatural” (FNAL Proton Driver study, to appear in 2005)

No luck needed;

works for all hier.

Best case , hierarchy

“Typical”

chance


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Discovery limit landscapes: Discovery limit landscapes: 1313

Assume that each experiment Assume that each experiment runs five years (most in runs five years (most in neutrino mode only)neutrino mode only)

Characterize dependence on Characterize dependence on CPCP as bands reflecting all as bands reflecting all possible chasespossible chases

Choose starting times as close Choose starting times as close as possible to values in as possible to values in respective LOIs/proposalsrespective LOIs/proposals

Include statistics+systematics+correlationsInclude statistics+systematics+correlations Assume that disappearance channels give best Assume that disappearance channels give best

information on leading atmospheric paramsinformation on leading atmospheric params


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Evolution of Evolution of 1313 discovery limit discovery limit

Branching point between Scenarios

2 and 3 (not for PD!)

MINOS and CNGSHave approximately equal performance

(depends somewhat onassumptions)

Reactor experiments:No dependence on CP!

Reactor-IIcorresponds to “large”

reactor experiment(Braidwood or similar).

Actual performance depends on control of systematics!

Proton driver + NUE(NuMI Upgraded Experiment): Pass

branching point almost for sure

Based on T2HK;assume start 10 years

after T2K starts

Starts about 10 years after branching point;changes polarity after

2.5 years(normal mass hierarchy assumed)

Superbeamshave a better discovery

potential than reactor exps for a large number of CP

values!


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Evolution of Evolution of 1313 discovery limit discovery limit Obviously different Obviously different

generations of experimentsgenerations of experiments New generation will New generation will

quickly determine potentialquickly determine potential Reactor experiments Reactor experiments

provide complementary provide complementary information!information!

Antineutrino running could Antineutrino running could help for risk minimizationhelp for risk minimization

For inverted hierarchy: For inverted hierarchy: Beam limits shift Beam limits shift somewhat down!somewhat down!

(from: FNAL Proton Driver Study, to appear in 2005)


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Examples for Examples for 1313 cases (1) cases (1) Assume: Actual value of sinAssume: Actual value of sin22221313 = 0.03 = 0.03

~2012-2013: ~2012-2013: 1313

signal likely at signal likely at superbeams or reactor superbeams or reactor

experimentsexperiments

PD+NUE+2nd NUE very competitiveFast+cost efficient alternative to T2HK!?



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Examples for Examples for 1313 cases (2) cases (2) Assume: Actual value of sinAssume: Actual value of sin22221313 = 0.007 = 0.007

Discovery of Discovery of 1313

unlikely without unlikely without PD and impossible PD and impossible

for T2Kfor T2K

But: One could have done almost of all the physics with a superbeam program!

If no PD at Fermilab, probably no further superbeam program!



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SummarySummary NUE discovery potential for NUE discovery potential for 1313 greatly increased by greatly increased by

Proton DriverProton Driver NUE and NUE+PD have “very likely” better NUE and NUE+PD have “very likely” better 1313

discovery potential then reactor experimentsdiscovery potential then reactor experiments Predictions for reactor experiments more robust: Do not Predictions for reactor experiments more robust: Do not

depend on depend on CPCP and mass hierarchy and mass hierarchyThus: Very competitive exclusion limits expected (if no Thus: Very competitive exclusion limits expected (if no signal)signal)

Dependence of PDependence of Pee on on CPCP and mass hierarchy implies and mass hierarchy implies that genuine potential of PD-based experiments in these that genuine potential of PD-based experiments in these quantitiesquantities


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Special topic: Special topic: Why does worst-case limit Why does worst-case limit hardly improve for superbeam upgrades?hardly improve for superbeam upgrades?

Assume oscillation maximum, neglect solar termAssume oscillation maximum, neglect solar term Then for one specific value of Then for one specific value of CPCP (typically (typically /2):/2):

This means: For sin2This means: For sin21313 ~ ~ (or sin (or sin22221313 ~ ~ 22 ~ 0.001) ~ 0.001)

PPee is very small independent of the total number of is very small independent of the total number of

eventsevents Therefore: The closer the experiment performance to Therefore: The closer the experiment performance to

sinsin22221313 = 0.001, the broader the band and the more = 0.001, the broader the band and the more

unaffected the lower end of the band (equivalent to good unaffected the lower end of the band (equivalent to good performance in performance in CPCP!)!)

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The quest for q 13 : Parameter space and performance indicators

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