CP violation and mass hierarchy searches

Neutrinos in particle physics and astrophysics (lecture)

June 2009

Walter WinterUniversität Würzburg

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Contents

Phenomenology Simulation tools Experiments and CP violation

measurement CP precision measurement CPV from non-standard physics? Mass hierarchy measurement Summary

Phenomenology

(partly repetition from lecture)

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Neutrino mixing with three flavors

( ) ( ) ( )= xx

(sij = sin ij cij = cos ij)Potential CP violation

From observations:

• 23, 12 large

• 13 small, unknown

Atmospheric mixing Reactor mixing Solar mixing

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Neutrino masses: three flavors

Normal or inverted mass ordering

Neutrino oscillations driven by |m31

2| (atm.) >> m212 (solar)

Flavor content in mass eigenstate i given by |Ui|2

Absolute mass scale unknown (< eV): Tritium endpoint Neutrinoless double beta decay Cosmology

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8

Normal Inverted

|Ue3|2 ~ s132

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Three Flavors: six parameters(three angles, one phase; two independent mass squared differences)

Describes atmospheric, solar, reactor data in two flavor limits:

Neutrino oscillations

Coupling: 13

Atmospheric oscillations:Amplitude: 23

Frequency: m312

Solar oscillations:Amplitude: 12

Frequency: m212

Suppressed

effect: CP

(Super-K, 1998;Chooz, 1999; SNO 2001+2002; KamLAND 2002)

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Two flavor limits (lecture!) Atmospheric neutrinos

Solar neutrinosAdiabatic evolution (MSW), mostly sensitive to 12

Reactor experiments Atmospheric oscillation length (L ~ 1-2 km)

Solar oscillation length (L ~ 30-100 km)

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Three flavor effectsWith the following definitions

expand to second order in small quantities and 13:

Test: for = 0, 13 = 0: Pe = 0Problem: The info has to be disentangled from this expression!

Masshierarchy!

Quantities of interest

Spectral terms

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CP violation (CPV)

CP violation: Matter and antimatter behave „differently“ (in a well defined way including the peculiarities of the Standard Model, i.e., V-A interactions)

Necessary requirement for baryogenesis Here: CP violation ~ Im (ei) ~ sin CP

Define: we discover CP violation if we can exclude CP = 0 and (where sin CP=0, or U is real) at the chosen confidence level

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Terminology

Any value of CP

(except for 0 and )violates CP

Sensitivity to CPV:Exclude CP-conservingsolutions 0 and for any choiceof the other oscillationparameters in their allowed ranges

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CPV - statistics

2(12,13,23,,m212,m31

2)

For future experiments: we have to simulate data (Oi) assuming a set of (12,13,23,,m21

2,m312)

implemented by nature: „true values“, „simulated values“

Mostly the unknown 13 and relevant

Compute 2(13,)=Min12,13,23,m212,m312 2(12,13,23,0/,m21

2,m312

,13,)

(marginalization over unwanted parameters) Discovery potential as a function of (13,)

Our „theory“ (fit values), describe Ti

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CPV discovery reach … in (true) sin2213 and CP

Sensitive region as a

function of true 13 and CP

CP values now stacked for each 13

Read: If sin2213=10-3, we

expect a discovery for 80% of all values of CP

No CPV discovery ifCP too close to 0 or

No CPV discovery forall values of CP3

Best performanceclose to max.

CPV (CP = /2 or 3/2)

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Measurement of CPV

(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)

Antineutrinos: Magic baseline: Silver: Platinum, Superb.:

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Degeneracies

CP asymmetry

(vacuum) suggests the use of neutrinos and antineutrinos

One discrete deg.remains in (13,)-plane

(Burguet-Castell et al, 2001)Burguet-Castell et al, 2001)

Additional degeneracies: Additional degeneracies: (Barger, Marfatia, Whisnant, 2001)(Barger, Marfatia, Whisnant, 2001) Sign-degeneracy Sign-degeneracy

(Minakata, Nunokawa, 2001)(Minakata, Nunokawa, 2001) Octant degeneracy Octant degeneracy

(Fogli, Lisi, 1996)(Fogli, Lisi, 1996)

Best-fit

Antineutrinos

Iso-probability curves

Neutrinos

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Intrinsic vs. extrinsic CPV The dilemma: Strong matter effects (high E, long L),

but Earth matter violates CP Intrinsic CPV (CP) has to be

disentangled from extrinsic CPV (from matter effects)

Example: -transitFake sign-solutioncrosses CP conservingsolution

Typical ways out: T-inverted channel?

(e.g. beta beam+superbeam,platinum channel at NF, NF+SB)

Second (magic) baseline(Huber, Lindner, Winter, hep-ph/0204352)

NuFact, L=3000 km

Fit

True CP (violates

CP maximally)

Degeneracy above 2

(excluded)

True

Critical range

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The magic baseline

Simulation tools

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GLoBES

AEDL„Abstract ExperimentDefinition Language“

Define and modifyexperiments

AEDL files

User InterfaceC library,

loads AEDL files

Functionality for experiment simulation

Simulation of futureexperiments

http://www.mpi-hd.mpg.de/lin/globes/

(Huber, Lindner, Winter, 2004;Huber, Kopp, Lindner, Rolinec, Winter, 2006) Application software

linked with user interfaceCalculate sensitivities etc.

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Event rate engine

In practice: Secondary particles

integrated out

Detector response R(E,E´)

E E´

E: Incident neutrino energyE‘: Reconstructed energyE: Secondary particle energy(e.g. muon)

Experiments andCP violation measurement

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There are three principle possibilities to artificially create neutrinos:

Beta decay:Example: Nuclear fission reactors

Pion decay:From accelerators:

Muon decay:The muons are produced by pion decays!

Muons,Neutrinos

Reminder: „man-made“ neutrinos

Protons

Target Selection,Focusing

Pions

Decaytunnel

Absorber

Neutrinos

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Next generation experiments

Perspectives to constrain 13 and find CPV relatively weak

Focus on next-to-next generation!Example: Neutrino factory

(Huber, Lindner, S

chwetz, W

inter, in prep.)

CL

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Neutrino factory:International design study

IDS-NF: Initiative from ~ 2007-

2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory

In Europe: Close connection to „Eurous“ proposal within the FP 07

In the US: „Muon collider task force“ISS

(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)

Signal prop. sin2213

Contamination

Muons decay in straight sections of a storage ring

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IDS-NF baseline setup 1.0 Two decay rings E=25 GeV

5x1020 useful muon decays per baseline(both polarities!)

Two baselines:~4000 + 7500 km

Two MIND, 50kt each

Currently: MECC at shorter baseline (https://www.ids-nf.org/)(https://www.ids-nf.org/)

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NF physics potential Excellent 13, MH,

CPV discovery reaches (IDS-NF, 2007)

Robust optimum for ~ 4000 + 7500 km

Optimization even robust under non-standard physics(dashed curves)

(Kopp, Ota, Winter, arXiv:0804.2261; see also: Gandhi, Winter, 2007)

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Experiment comparison

The sensitivities are expected to lie somewhere between the limiting curves

Example: IDS-NF baseline(~ dashed curve)

(ISS physics WG report, arXiv:0810.4947, Fig. 105)

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On near detectors@IDS-NF

Define near detectors including source/detector geometry: Near detector limit:

Beam smaller than detector Far detector limit:

Spectrum similar to FD Compute spectrum, study

systematical errors, study impact of physics

(Tang, Winter, arXiv:0903.3039)

~ND limit ~FD limit

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Example: Systematics(Tang, Winter, arXiv:0903.3039)

CP precision measurement

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Performance indicator: CP coverage

Problem: CP is a phase (cyclic)

Define CP coverage (CPC):Allowed range for CP which fits a chosen true value

Depends on true 13 and true CP

Range: 0 < CPC <= 360

Small CPC limit:Precision of CP

Large CPC limit:360 - CPCis excluded range

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CP pattern

Performance as a function of CP (true)

Example: Staging.If 3000-4000 km baseline operates first, one can use this information to determine if a second baseline is needed

(Huber, Lindner, Winter, hep-ph/0412199)

Exclusion limitPrecision limit

CPV from non-standard physics?

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~ current bound

CPV from non-standard interactions

Example: non-standard interactions (NSI) in matter from effective four-fermion interactions:

Discovery potential for NSI-CPV in neutrino propagation at the NF

Even if there is no CPV instandard oscillations, we mayfind CPV!

But what are the requirements for a model to predict such large NSI?

(arXiv:0808.3583)3

IDS-NF baseline 1.0

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Effective operator picture:

Describes additions to the SM in a gauge-inv. way! Example: NSI for TeV-scale new physics

d=6: ~ (100 GeV/1 TeV)2 ~ 10-2 compared to the SMd=8: ~ (100 GeV/1 TeV)4 ~ 10-4 compared to the SM

Current bounds, such as from CLFV: difficult to construct large (= observable) leptonic matter NSI with d=6 operators (except for

m, maybe)

(Bergmann, Grossman, Pierce, hep-ph/9909390; Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003; Gavela, Hernandez, Ota, Winter,arXiv:0809.3451)

Need d=8 effective operators!Finding a model with large NSI is not trivial!

Models for large NSI?

mass d=6, 8, 10, ...: NSI

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Systematic analysis for d=8

Decompose all d=8 leptonic operators systematicallyThe bounds on individual

operators from non-unitarity, EWPD, lepton universality are very strong!

(Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)

Need at least two mediator fields plus a number of cancellation conditions(Gavela, Hernandez, Ota, Winter, arXiv:0809.3451)

Basis (Berezhiani, Rossi, 2001)

Combinedifferent

basis elements

C1LEH, C3

LEH

Canceld=8

CLFV

But these mediators cause d=6 effects Additional cancellation condition

(Buchmüller/Wyler – basis)

Avoid CLFVat d=8:

C1LEH=C3

LEH

Feynman diagrams

Mass hierarchy (MH)

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Motivation

Specific models typically come together with specific MH prediction (e.g. textures are very different)

Good model discriminator(Albright, Chen, hep-h/0608137)

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8

Normal Inverted

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Magic baseline:Removes all degeneracy issues (and is long!)

Resonance: 1-A 0 (NH: , IH: anti-)Damping: sign(A)=-1 (NH: anti-, IH: )Energy close to resonance energy helps (~ 8 GeV)

To first approximation: Pe ~ L2 (e.g. at resonance)Baseline length helps (compensates 1/L2 flux drop)

Matter effects

(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)

Lecture:

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Baseline dependence

Comparison matter (solid) and vacuum (dashed)

Matter effects (hierarchy dependent) increasewith L

Event rate (, NH) hardly drops with LGo to long L!

(Freund, Lindner, Petcov, Romanino, 1999)

(m212 0)

Eve

nt

rate

s (A

.U.)

Vacuum, NH or IH

NH matter effect

NH matter effect

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Mass hierarchy sensitivity

For a given set of true 13 and CP: Find the sgn-deg.solution

Repeat that for all true true 13 and CP (for this plot)

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Small 13 optimization: NF

Magic baseline good choice for MH E ~ 15 GeV sufficient (peaks at 8 GeV)

(Huber, Lindner, Rolinec, Winter, 2006) (Kopp, Ota, Winter, 2008)

E-L (single baseline) L1-L2 (two baselines)

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Summary

CP violation measurement requires next-to-next generation of experiments

Example: Neutrino factory Other relevant quantities:

CP precision measurement CP violation from non-standard physics Mass hierarchy

CP violation discovery in the lepton sector may be an interesting hint for leptogenesis!

This talk at: http://www.physik.uni-wuerzburg.de/~winter/Teaching/neutrinos.html