Optimization of a neutrino factoryOptimization of a neutrino factoryfor non-standard neutrino interactionsfor non-standard neutrino interactions

IDS plenary meetingIDS plenary meetingRAL, United KingdomRAL, United Kingdom

January 16-17, 2008January 16-17, 2008

Walter WinterWalter WinterUniversität WürzburgUniversität Würzburg

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ContentsContents IntroductionIntroduction Our setupOur setup Main questions:Main questions:

– What does the silver channel help?What does the silver channel help?– How small can the muon energy be?How small can the muon energy be?– Standard versus non-standard baseline optimizationStandard versus non-standard baseline optimization

SummarySummary

In collaborationwith Joachim Kopp and

Toshihiko Ota

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Non-standard neutrino interactionsNon-standard neutrino interactions Consider effective four-point interactionsConsider effective four-point interactions

This leads to a Hamiltonian for This leads to a Hamiltonian for propagation: propagation:

matter potential: matter potential:

For antineutrinos: H For antineutrinos: H H*, a H*, aCCCC -a -aCCCC

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NSI constraintsNSI constraints Limits depend Limits depend

on chirality and on chirality and fermionfermion

Neutrino Neutrino propagation in propagation in principle principle sensitive to sensitive to 33uu+3+3dd++ee

We ignore We ignore potential potential production and production and detection effects, detection effects, which can be which can be parameterized parameterized similarly!similarly!

(ISS Physics report, arXiv:0710.4947)

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Relevant parameters for a NFRelevant parameters for a NF

Uninteresting:limited by matter

density uncertainty

Relatively strong constraints

Weak constraints

Complex numbers

Real number

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Our setup: close to IDS baseline!Our setup: close to IDS baseline! Two detectors at Two detectors at

LL11 and L and L22, 50 kt each, 50 kt each 50% E50% E0.50.5 energy resolution energy resolution Backgrounds 0.001/EBackgrounds 0.001/E22

2.5% signal uncertainty, 2.5% signal uncertainty, 20% BG uncertainty20% BG uncertainty

4 yr + 4 yr running time4 yr + 4 yr running time 10102121 useful muon useful muon

decays/year/detector!decays/year/detector! EE=50 GeV, unless stated =50 GeV, unless stated

otherwise otherwise

Old analysis/det.

Our detector

New analysis (diff. L) (Cervera@

Golden 07)

Silver channel:Silver channel:10 kt Silver* from10 kt Silver* fromhep-ph/0606119hep-ph/0606119(Autiero et al ECC with (Autiero et al ECC with 5xSG, 3xBG)5xSG, 3xBG)

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Performance indicators usedPerformance indicators used Definition of Definition of sensitivity similar to sensitivity similar to 1313 sens.: sens.:

Largest fit |Largest fit | which fits a true which fits a true =0 =0 Corresponds to a conservative case discovery Corresponds to a conservative case discovery

potentialpotential All oscillation parameters, NSI phases All oscillation parameters, NSI phases

marginalized over (exceptions: for marginalized over (exceptions: for , which is , which is real, or if real, or if is assumed to be real) is assumed to be real)

Typically only one or two NSI parameters Typically only one or two NSI parameters considered, such as |considered, such as |ee, , , |, |ee---plane-plane

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NSI with magic baselineNSI with magic baseline

Combing the two baselines Combing the two baselines reduces the impact of reduces the impact of correlations drasticallycorrelations drastically(only real (only real ee assumed!) assumed!)

Does one still need the silver Does one still need the silver channel in that case?channel in that case?

3000 km7000 km

Com

bined

arXiv:0709.1980

Close to worst case for degeneracies: CP=3/2, sin2213=0.001

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Correlations at magic baselineCorrelations at magic baseline Including NSI, the magic baseline is not exactly Including NSI, the magic baseline is not exactly

correlation/degeneracy-freecorrelation/degeneracy-free Example: Approximation Example: Approximation

aaCCCC ~ E: ~ E: Standard term drops as 1/EStandard term drops as 1/E44, NSI-Term as 1/E, NSI-Term as 1/E33 High energies important for NSIHigh energies important for NSI!!

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Comparison to our simulation (1)Comparison to our simulation (1)3000 km

7000 kmC

ombined

arXiv:0709.1980Our simulation,

similar setupOur simulation,

our setupOur simulation + our setup,all osc. params marginalized

Only 13 and CP marginalized!

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Comparison to our simulation (2)Comparison to our simulation (2)

3000 km +7000 km

3000 km +7000 km +

Silver*@3000km

3000 km +7000 km +

Disappearance

3000 km + 7000 kmSilver*@3000km +

Disappearance

Disappearance important for , !

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When does the silver channel helpWhen does the silver channel help… in a two baseline setup?… in a two baseline setup?

Assume oneAssume oneNSI parameterNSI parameterat first, such as at first, such as ee

Fix golden Fix golden detectorsdetectors

Where is the Where is the optimaloptimalsilver baseline?silver baseline?

Place Silver* at Place Silver* at golden baseline 1!golden baseline 1!EE >= 50 GeV! >= 50 GeV!

0.01

0.004

Golden detector 1 = Silver baseline

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Minimum muon energy?Minimum muon energy?

Higher muon energy helps; low-E NF not an optionHigher muon energy helps; low-E NF not an option Silver channel: Not relevant for IDS baseline; helps for ESilver channel: Not relevant for IDS baseline; helps for E ~ 50 GeV ~ 50 GeV

IDS baseline?

High-E N

F

IDS baseline?

High-E N

F

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What if more parameters?What if more parameters? Marginalize over phase of Marginalize over phase of ee as well: as well:

Absolute limits: |Absolute limits: || < 0.03, || < 0.03, |ee| < 0.006 (3| < 0.006 (3))Two orders of magnitude improvement of current Two orders of magnitude improvement of current bounds!bounds!

3000km+7000km 3000km+7000km+Silver*@3000km

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Standard versus non-standard Standard versus non-standard optimizationoptimization

Obviously, the main NSI sensitivity comes Obviously, the main NSI sensitivity comes from the golden and disappearance channelsfrom the golden and disappearance channels

Changing the golden baselines will affect Changing the golden baselines will affect the NSI sensitivitiesthe NSI sensitivities

What if there is no silver channel, do the What if there is no silver channel, do the standard and non-standard optimizations standard and non-standard optimizations coincide?coincide?

Perform optimizations in LPerform optimizations in L11-L-L22-space-space

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Standard optimization revisitedStandard optimization revisited All regions:All regions:

Sensitivity for Sensitivity for sinsin22221313>10>10-4.2-4.2 (5(5) for the ) for the shown shown performance performance indicatorindicator

True True CPCP chosen chosen close to worst close to worst casecase

Robust optimum Robust optimum for ~ 4000 + 7500 for ~ 4000 + 7500 kmkm(not <= 3000 (not <= 3000 km!) km!)

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NSI optimization: one parameterNSI optimization: one parameter

Similar to matter effects (which increase with baseline!), Similar to matter effects (which increase with baseline!), NSI sensitivities want one very long baselineNSI sensitivities want one very long baseline

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Combined optimization: ExampleCombined optimization: Example 4000 + 7500 km4000 + 7500 km

consistent withconsistent withNSI optimizationNSI optimization

But: In general,But: In general,choose both choose both baselines rather baselines rather longer than shorter!longer than shorter!

Standard opt: combined

NSI example(CP=/2, sin2213=0.01)

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Summary and conclusionsSummary and conclusions The leading NSI sensitivity comes from the golden + The leading NSI sensitivity comes from the golden +

disappearance channelsdisappearance channels The silver channel might help if EThe silver channel might help if E > 40 GeV > 40 GeV

Return to high-E NF for IDS baseline? Return to high-E NF for IDS baseline? A low-E NF (EA low-E NF (E << 20 GeV) probably has very little NSI << 20 GeV) probably has very little NSI

sensitivity beyond the current limitssensitivity beyond the current limits The currently used IDS baseline setup 4000 km + 7500 The currently used IDS baseline setup 4000 km + 7500

km is consistent for both standard and non-standard km is consistent for both standard and non-standard effects; the baselines be rather longer than shorter!effects; the baselines be rather longer than shorter!

NSI are important to establish the physics case for a very NSI are important to establish the physics case for a very long baselinelong baseline