Neutrino phenomenologyLecture 2: Precision physics with neutrinos

Winter school Schladming 2010“Masses and constants”01.03.2010

Walter WinterUniversität Würzburg

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Contents (overall)

Lecture 1:Testing neutrino mass and flavor mixing

Lecture 2:Precision physics with neutrinos

Lecture 3:Aspects of neutrino astrophysics

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Contents (lecture 2)

Repetition Matter effects in neutrino oscillations CP violation phenomenology Mass hierarchy measurement Experiments: The near future Experiments for precision.

Example: Neutrino factory

New physics searches (some examples) Summary

Repetition

… from yesterday

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With three flavors: six parameters(three mixing angles, one phase, two mass squared differences)

Established by two flavor subsector measurements In the future: measure unknown 13 and CP, MH

Three flavor oscillation summary

Coupling: 13

Atmosphericoscillations:Amplitude: 23

Frequency: m312

Solaroscillations:Amplitude: 12

Frequency: m212

Suppressed

effect: CP

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

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Global fits

Schwetz, Tortola, Valle, 20081

90%CL, 3

A new ingredient:Matter effects in neutrino oscillations

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Matter effect (MSW) Ordinary matter:

electrons, but no , Coherent forward

scattering in matter: Net effect on electron flavor

Matter effects proportional to electron density ne and baseline

Hamiltonian in matter (matrix form, flavor space):

Y: electron fraction ~ 0.5

(electrons per nucleon)

(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)

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Numerical evaluation

Evolution operator method:

H(j) is the Hamiltonian in constant density

Note that in general

Additional information by interference effects compared to pure absorption phenomena

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Matter profile of the Earth… as seen by a neutrino

(PR

EM

: Prelim

inary R

eference E

arth M

odel)

Core

Innercore

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Two flavor limit (=const.)

Multiplied out, two flavors, global phase substracted:

Compare to vacuum

Idea: write matter Hamiltonian in same form as in vacuum with effective parameters

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Parameter mapping

Oscillation probabilities invacuum:matter:

Matter resonance: In this case: - Effective mixing maximal- Effective osc. frequency minimal

~ 4.5 g/cm3 (Earth’s mantle)Solar osc.: E ~ 100 MeV !!!Atm osc.: E ~ 6.5 GeV

Resonance energy:

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Mass hierarchy

Matter resonance for

Will be used in the future to determine the mass ordering:

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8

Normalm31

2 >0Inverted m31

2 <0

Normal Inverted

Neutrinos Resonance Suppression

Antineutrinos Suppression Resonance

Neutrinos/Antineutrinos

Three flavor effects:CPV phenomenology

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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

Why interesting?Lecture Xing!

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Three flavor effects

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

Antineutrinos: Magic baseline: Silver: Platinum, T-inv.:

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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

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CP violation discovery … 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

~ Cabibbo-angleprecision at 2 BENCHMARK!

Best performanceclose to max.

CPV (CP = /2 or 3/2)

Mass hierarchy measurement

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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-ph/0608137)

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8

Normal Inverted

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Magic baseline:Restore two flavor limit ( ~ 1 – A for small 13)

Resonance: 1-A 0 (NH: , IH: anti-)Damping: sign(A)=-1 (NH: anti-, IH: )Energy close to resonance energy helps (~ 7 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)

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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

Peak neutrino energy ~ 14 GeV

Experiments: The near future

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There are three possibilities to artificially produce neutrinos

Beta decay:Example: Nuclear reactors

Pion decay:From accelerators:

Muon decay:Muons produced by pion decays!

Muons,neutrinos

Artificial neutrino sources

Protonen

Target Selection,focusing

Pions

Decaytunnel

Absorber

Neutrinos

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New reactor experimentsExamples: Double Chooz, Daya Bay

Identical detectors, L ~ 1.1 km

(Quelle: S. Peeters, NOW 2008)

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Idea: The event rate N close to the reactor is high, ~ 1/R2

A few thousand events/day for “small” detector ~ 25 m away from reactor core

Anticipated precision: ~ O(10) kgfor extraction of radioactive material

Spin-off: Nuclear monitoring?(A

dam B

ernstein, LL

NL

)(A

dam B

ernstein, LL

NL

)

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Narrow band superbeams

Off-axis technology to suppress backgrounds

Beam spectrum more narrow

Examples:T2KNOA

T2K beamOA 1 degreeOA 2 degreesOA 3 degrees

(hep-ex/0106019)

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GLoBES

AEDL„Abstract ExperimentDefinition Language“

Define and modifyexperiments

AEDL files

User InterfaceC library,

reads AEDL files

Functionality forexperiment simulation

Simulation of future experiments

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

(Huber, Lindner, Winter, 2004; Huber, Kopp, Lindner, Rolinec, Winter, 2007) Application software

linked with user interfaceCalculate sensitivities …

Comes with a 180 pages manual with step-by-step intro!

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Calculation of event rates

In practice:Secondary particles

integrated out

Detector response R(E,E´)

E E´

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Next generation CPV reach

Includes Double Chooz, Daya Bay, T2K, NOvA

(Huber, Lindner, Schwetz, Winter, arXiv:0907.1896)

90% CL

Experiments for precisionExample: Neutrino factory

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Neutrino factory:International Design Study (IDS-NF)

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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Steve Geer‘s vision

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Science fiction or science fact?http://www.fnal.gov/pub/muon_collider/

New physics searches(some examples, using neutrino factory near detectors)

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Effective operator picture if mediators integrated out:

Describes additions to the SM in a gauge-inv. way! Example: 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

Interesting dimension six operatorsFermion-mediated Non-unitarity (NU)Scalar or vector mediated Non-standard int. (NSI)

New physics from heavy mediators

mass d=6, 8, 10, ...: NSI, NU, CLFV, …

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Example 1:

Non-standard interactions Typically described by effective four

fermion interactions (here with leptons)

May lead to matter NSI (for ==e)

May also lead to source/detector NSI(e.g. NuFact:

s for ==e, =)These source/det.NSI are process-dep.!

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Lepton flavor violation… and the story of SU(2) gauge invariance

Strongbounds

e e

e

NSI(FCNC)

e e

e CLFV e

4-NSI(FCNC)

Ex.:

e e

Affects neutrino oscillations in matter (or neutrino production)

Affects environments with high densities (supernovae)

BUT: These phenomena are connected by SU(2) gauge invariance

Difficult to construct large leptonic matter NSI with d=6 operators (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!

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On current NSI bounds (Source NSI for NuFact)

The bounds for the d=6 (e.g.scalar-mediated) operators are strong (CLFV, Lept. univ., etc.)(Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)

The model-independent bounds are much weaker(Biggio, Blennow, Fernandez-Martinez, arXiv:0907.0097)

However: note that here the NSI have to come from d=8 (or loop d=6?) operators ~ (v/)4 ~ 10-4 natural?

„NSI hierarchy problem“?

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Source NSI with at a NuFact

Probably most interesting for near detectors: e

s, s (no intrinsic beam BG)

Near detectors measure zero-distance effect ~ |s|2

Helps to resolve correlations

(Tang, Winter, arXiv:0903.3039)

ND5: OPERA-like ND at d=1 km, 90% CL

This correlation is always present if:- NSI from d=6 operators- No CLFV (Gavela et al,arXiv:0809.3451;see also Schwetz, Ohlsson, Zhang, arXiv:0909.0455 for a particular model)

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Example 2:

Non-unitarity of mixing matrix Integrating out heavy fermion fields (such as in a type-I TeV

see-saw), one obtains neutrino mass and the d=6 operator (here: fermion singlets)

Re-diagonalizing and re-normalizing the kinetic terms of the neutrinos, one has

This can be described by an effective (non-unitary) mixing matrix with N=(1+) U

Similar effect to NSI, but source, detector, and matter NSI are correlated in a particular, fundamental way (i.e., process-independent)

also: „MUV“

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Impact of near detector

Example: (Antusch, Blennow, Fernandez-Martinez, Lopez-Pavon, arXiv:0903.3986)

near detector important to detect zero-distance effect

Curves: 10kt, 1 kt, 100 t, no ND

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Example 3:

Search for sterile neutrinos

3+S schemes of neutrinos include (light) sterile states, i.e., neutral fermion states light enough to be produced

The mixing with the active states must be small, the mass squared difference can be very different

The effects on different oscillation channels depend on the model test all possible two-flavor short baseline (SBL) cases, which are standard oscillation-free

Example: e disappearance

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SBL e disappearance

Averaging over straight important (dashed versus solid curves)

Location matters: Depends on m2

(Giunti, Laveder, Winter, arXiv:0907.5487)

90% CL, 2 d.o.f.,No systematics,

m=200 kg

Two baseline setup?

d=50 m

d~2 km(as long as possible)

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SBL systematics

Systematics similar to reactor experiments:Use two detectors to cancel X-Sec errors

(Giunti, Laveder, Winter, arXiv:0907.5487)

10% shape

error

arXiv:0907.3145

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Summary

Matter effects key ingredient to measure the mass orderingHow do neutrinos behave in environments with strongly varying matter density (Sun, Supernovae)?

Man-made terrestrial sources can measure all of the remaining standard neutrino oscillation properties (13, CPV, MH) even for very small 13

Are all parameters best measured using terrestrial sources? Where did the „solar sector“ get its name from?

Some new physics „neutrino properties“ can be tested as wellAre there neutrino properties which are best tested using astrophysical environments?

Lecture 3

Lecture 3

Lecture 3

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Transition amplitude in matrix form:

For instance, in = (1,0,0)T for e

With , we have

or

Matrix form in flavor space