Matter and Damping Effects in Neutrino Mixing and …theophys.kth.se/~mbl/lictalk.pdfNeutrino masses, mixing and oscillations Neutrino oscillations in experiments Solar neutrinos and

Matter and Damping Effects inNeutrino Mixing and

OscillationsLicentiate Thesis

Mattias Blennow

Division of Mathematical Physics

Department of Physics

Royal Institute of Technology (KTH)

Matter and Damping Effects in Neutrino Oscillations and Mixing – Mattias Blennow, KTH – Stockholm June 3, 2005 – p.1/37

OutlineGeneral overview – History of neutrinos

Neutrino masses, mixing and oscillations

Neutrino oscillations in experiments

Solar neutrinos and the day-night effect

Exact solution to the two-flavor problem

Neutrino oscillations in dense matter

Damping effects in neutrino oscillations

Summary and conclusions


Neutrinos, what are they?Elementary particles

Spin 1/2

Chargeless

Comes in three flavors, νe, νµ, ντ , one for eachcharged lepton

Interacts only through the weak interaction

Initially believed to be massless – has a masswhich is at least a 100000 times less than theelectron mass


The Standard ModelTwo types of particles, quarks and leptons

Three types of interaction, strong, weak andelectromagnetic – does not include gravity

Three generations of particles, each containingtwo quarks and two leptons

Particles:

(

u νed e−

)

,

(

c νµs µ−

)

,

(

t ντb τ−

)

Force carriers:

γ, W±, Z0, Gi

Mass through Higgs mechanism and Yukawacouplings to the Higgs field


The birth of neutrino physicsPostulated in a letter by Wolfgang Pauli (1930)

Originally named “neutron” by Pauli

After Chadwick’s discovery of the neutron, EnricoFermi renamed Pauli’s particle to “neutrino”,meaning “small and neutral”

Initially belived to be massless

Experimentally detected (νe) by Clyde CowanJr. and Frederick Reines in 1956

The νµ detected by the Brookhaven NationalLaboratory in 1962

The ντ detected by the DONUT collaboration in2001


Are neutrinos oscillating?Neutrino oscillations first proposed by BrunoPontecorvo in 1957 in analogy to K0 − K0

oscillations

Theory further developed to neutrino flavoroscillations

Apparent deficiency in the measured fluxes ofsolar and atmospheric neutrinos attributed toneutrino oscillations

First oscillation evidence published by theSuper-Kamiokande collaboration in 1998


Massive neutrinos?Neutrinos are massless in the SM

Therefore, neutrino masses is a window forphysics beyond the SM

There are a number of different ways ofintroducing neutrino masses


Neutrino mixingIn general, the neutrino mass eigenfields neednot be the same as the fields participating in theweak interaction (flavor eigenstates) with thecharged lepton mass eigenfields

Mass and flavor eigenfields related by a unitarytransformation U , the leptonic mixing matrix, as

ν1ν2...

= U †

νeνµ...

Mass and flavor eigenstates related as

|να〉 =∑

i

U∗αi |νi〉


Standard parameterizationWith two neutrino flavors:

U =

(

c s

−s c

)

c = cos(θ), s = sin(θ)

With three neutrino flavors:

U =

c13c12 c13s12 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13

s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13

cij = cos(θij), sij = sin(θij)


Neutrino oscillationsThe mass eigenstates are the eigenstates ofpropagation

The mass eigenstates obtain different phases ⇒quantum interference

The result: There is a probability of an initial αflavor neutrino to oscillate into another flavor β

The probability of finding the neutrino in the stateof flavor β after propagating the length L is thengiven by

Pαβ(L) =∑

i

∑

j

J ijαβ exp

(

−i∆m2

ij

2pL

)

,

where ∆m2ij = m2

i −m2j


Two-flavor oscillationsOnly one mixing parameter, θ

Only one mass squared difference, ∆m2

Oscillation formulas:

Pαα = Pββ = 1− sin2(2θ) sin2(

∆m2

4EL

)

Pαβ = Pβα = sin2(2θ) sin2(

∆m2

4EL

)


Three-flavor oscillationsFour mixing parameters, θ12, θ13, θ23, and δ

Two independent mass squared differences,∆m2

21 and ∆m231

No simple analytic formula for the neutrinooscillation probabilities

Formulas can be simplified in some special casesor Taylor expanded in small parameters

In general, Pαβ 6= Pβα (T-violation)


Current bounds on parametersThe current bounds on the neutrino oscillationparameters:

Parameter Best-fit 3σ confidence

∆m221 [10−5 eV2] 8.1 7.2-9.1

|∆m231| [10−3 eV2] 2.2 1.4-3.3

θ12 [◦] 33.2 28.6-38.1

θ23 [◦] 45.0 35.7-53.1

θ13 [◦] 0.0 ≤ 12.5M. Maltoni, et al., New J. Phys. 6, 122 (2004), hep-ph/0405172


Matter effectsInteraction with matter gives rise to an effectiveaddition to the Hamiltonian operator

All flavors interact via neutral-current interaction

Only νe interacts via charged-current interaction

e νe

νe e

W±

e e

να να

Z0

Affects the effective neutrino masses and mixing


Atmospheric neutrinosNeutrinos produced when cosmic rays hit theEarth’s atmosphere

Typical reaction:

π± −→ µ± +(−)

ν µ

followed by

µ± −→ e± +(−)

ν e +(−)

ν µ.

Typical neutrino energies are in the GeV range

At relatively low energies, φνµ/φνe ' 2 withoutoscillations


Super-KamiokandeSuccessor of the KamiokaNDE – the KamiokaNucleon Decay Experiment

Detects fast charged leptons from neutrinointeractions through Cherenkov radiation

Deep underground – reduces background

First experiment to present evidence for neutrinooscillations


The 1998 findingsAn apparent deficiency in the νµ flux for longerbaseline lengths

0

50

100

150

200

250

0

50

100

150

200

250

0

10

20

30

40

50

0

15

30

45

60

75

-1 -0.6 -0.2 0.2 0.6 10

40

80

120

160

200

-1 -0.6 -0.2 0.2 0.6 10

60

120

180

240

300

-1 -0.6 -0.2 0.2 0.6 10

20

40

60

80

100

e-likep < 0.4 GeV/c

e-likep > 0.4 GeV/c

e-likep < 2.5 GeV/c

e-likep > 2.5 GeV/c

µ-likep < 0.4 GeV/c

cosΘ

µ-likep > 0.4 GeV/c

cosΘ

µ-like

cosΘ

Partially Contained

cosΘ

sub-GeV multi-GeV

-1 -0.6 -0.2 0.2 0.6 10

25

50

75

100

125

Super-Kamiokande collaboration, Phys. Rev. Lett. 81, 1562 (1998), hep-ex/9807003

No deficiency or enhancement in the νe flux – νµoscillates mainly to ντ


Super-Kamiokande reanalysisIn a more recent analysis, neutrino oscillationsare compared to neutrino decay and neutrinodecoherence as descriptions of the νµdisappearance

Decay and decoherence are strongly disfavored

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

redi

ctio

n (n

ull o

sc.)

Super-Kamiokande collaboration, Phys. Rev. Lett. 93, 101801 (2004), hep-ex/0404034


Solar neutrinosProduced as νe in thermonuclear reactions in thecenter of the Sun

The fluxes are predicted by the Standard SolarModel (SSM)

Homepage of John Bahcall, http://www.sns.ias.edu/˜jnb/


Solar neutrinos (2)Discrepancy between the detected and predictedfluxes (assuming no oscillations)

Homepage of John Bahcall, http://www.sns.ias.edu/˜jnb/

Discrepancy known as the “solar neutrinoproblem”


The SNOThe Sudbury Neutrino Observatory

Heavy water Cherenkov detector

Three types of detection:Elastic scatteringνα + e− → να + e−

Charged-currentνe + d→ e− + p+ p

Neutral-currentνα + d→ να + p+ n


Reactor neutrinosElectron anti-neutrinos produced in nuclearreactors

First neutrinos ever detected

Short-baseline – θ13 sensitivity

Long-baseline – ∆m212 sensitivity

Neutrino oscillation experiments mainly study thePee survival probability


CHOOZA short-baseline reactor neutrino experiment atthe Chooz power plant

Gives the current upper bound for θ13

No deficit of electron anti-neutrinos detected withany statistical significance

Analysis A

10-4

10-3

10-2

10-1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1sin2(2θ)

δm2 (e

V2 )90% CL Kamiokande (multi-GeV)

90% CL Kamiokande (sub+multi-GeV)

νe → νx

90% CL

95% CL

CH

OO

Zco

llabo

ratio

n,P

hys.

Lett.

B46

6,41

5(1

999)

,hep-ex/9907037


KamLANDA long-baseline reactor neutrino experiment

The Japanese nuclear power plants (and somenon-Japanese power plants close to Japan) areused as a neutrino source

Average baseline of about 180 km

Detects an electron anti-neutrino disappearance

)2 (

eV2

m∆

-510

-410

θ 2tan

-110 1 10

KamLAND

95% C.L.

99% C.L.

99.73% C.L.

KamLAND best fit

Solar

95% C.L.

99% C.L.

99.73% C.L.

solar best fit

θ 2tan

0.2 0.3 0.4 0.5 0.6 0.7 0.8

)2 (

eV2

m∆KamLAND+Solar fluxes

95% C.L.

99% C.L.

99.73% C.L.

global best fit-510×4

-510×6

-510×8

-410×1

-410×1.2

KamLAND collaboration, Phys. Rev. Lett. 94, 081801 (2005), hep-ex/0406035


KamLAND L/E analysisAs for the Super-Kamiokande, a fit to oscillationsas well as to neutrino decay and neutrinodecoherence

The results favor neutrino oscillations

20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

1.2

1.4

(km/MeV)eν/E0L

Rat

io2.6 MeV promptanalysis threshold

KamLAND databest-fit oscillationbest-fit decay

best-fit decoherence

KamLAND collaboration, Phys. Rev. Lett. 94, 081801 (2005), hep-ex/0406035


The day-night effectPaper 1 of the thesis

Earth matter effects on the solar neutrino flux

First treatment using three-flavor neutrinooscillations

Approximations:Third mass eigenstate essentially unaffectedConstant Earth matter densityNeutrinos produced at some average matterdensity inside the Sun


The day-night effect (2)The difference in the day and night electronneutrino survival probability scales essentially asc613

Three flavor day-night asymmetry at detectors

0.2 0.3 0.4 0.5

sin2θ

12

-5

-4.5

-4

-3.5

-3

log(

∆m2 /e

V2 )

θ13

= 0

θ13

= 9.2o

0

0.005

0.01

0.03

0.05

0.070.09

90% CL 95% CL 99% CL 99.73% CL


The day-night effect (3)Could be used to put constraints on θ13

Elaborated on by Akhmedov et.al. (arbitrarymatter density)

E. Kh. Akhmedov, JHEP 0405, 057 (2004), hep-ph/0412029

0.5 0.6 0.7 0.8 0.9 1

cos2θ

13

-0.01

0

0.01

0.02

0.03

0.04

0.05

AN

D

0.5 0.6 0.7 0.8 0.9 1

cos2θ

13

σ = 25% σSK

σ = 10% σSK

CHOOZ bound

CHOOZ bound

E. Kh. Akhmedov, hep-ph/0412029


Exact two-flavor solutionPaper 2 of the thesis

Deals with two-flavor neutrino oscillations inmatter with arbitrary density profile

The problem of neutrino oscillations in matter isrewritten as a real second order non-lineardifferential equation:

(p+Gp)2 = F (t)[G(1− p2)− p2]

Presents a series solution for p


Exact two-flavor solution (2)Convergence of the solution:

0 5 10 15 20E [GeV]

0

0.1

0.2

0.3

0.4

0.5

Pex

L = 3000 km

0 1000 2000 3000t [km]

0

0.2

0.4

Pex

5 10

15

20

25

30


Neutrinos in dense matterPaper 3 of the thesis

Three-flavor formulas → two-flavor formulasIf the mixing matrix has a zero entryIf one mass squared difference is zero

May be used as approximation in vacuum(θ13 → 0 or ∆m2

12 → 0)

In matter with high density, νe effectivelydecouples

We use degenerate perturbation theory to treatthe remaining νµ − ντ oscillations


Neutrinos in dense matter (2)Accuracy of the first-order approximation:

-3 -2 -1

log(VE / 1 eV2)

0

5

10

15

θ 13 [

o ]

< 0.25 % < < 0.5 % < < 1 %


Damping effectsPaper 4 of the thesis

Treatment of sub-leading effects on the probabilitylevel, e.g.,

Neutrino wave-packet decoherenceNeutrino quantum decoherenceNeutrino decayNeutrino absorption

Introduces “damping factors” in the neutrinooscillation formulas

Pαβ =∑

i

∑

j

DijJijαβ exp

(

−i∆m2

ij

2pL

)


Damping effects (2)The effect of damping on the neutrino survivalprobability Pαα:

0 2 4 6 8 10

Oscillation phase (∆)

0

0.2

0.4

0.6

0.8

1Su

rviv

al p

roba

bilit

yPure oscillationOscillation + decoherenceOscillation + decay IOscillation + decay II


Damping effects (3)Damping effects may alter the precisedetermination of the neutrino oscillationparameters

For example, the upper bound on θ13 fromshort-baseline reactor experiments (CHOOZ)

0 0.01 0.02 0.03 0.04 0.05Fit value of sin2 2Θ13

0

2

4

6

8

10

Fitv

alue

ofΣ

E@MeVD

sin22Θ13 -ΣE sensitivity for Reactor-I

1Σ

2Σ

3Σ

0 0.01 0.02 0.03 0.04Fit value of sin2 2Θ13

0

1

2

3

4

5

Fitv

alue

ofΣ

E@MeVD

sin22Θ13 -ΣE sensitivity for Reactor-II

1Σ

2Σ

3Σ


Damping effects (4)How to identify the specific effect?

Energy dependence is a better candidate:

10 20 30 40 50E @GeVD0

0.2

0.4

0.6

0.8P

ΜΜ

Decoherence

ΣE =H0,1,2,3,4,5L GeV

10 20 30 40 50E @GeVD0

0.2

0.4

0.6

0.8

PΜΜ

Decay

Α=H0,2,4,6,8,10L×10-4 GeV��km

10 20 30 40 50E @GeVD0

0.2

0.4

0.6

0.8

PΜΜ

Oscillations

Ε=H0,1,2,3,4,5L×10-6 eV2


Summary and conclusionsThree-flavor effects in the solar day-nightasymmetry

Possible information on θ13 from day-nightdata

Non-linear differential equation and exact solutionof the two-flavor neutrino evolution in an arbitrarymatter density profile

The effective two-flavor scenario for matter withhigh density

Sub-leading effects on neutrino oscillationsentering on probability level

Implications for measurements of neutrinooscillation parametersHow to distinguish between different dampingeffects


Documents

Matter and Damping Effects in Neutrino Mixing and …theophys.kth.se/~mbl/lictalk.pdfNeutrino masses, mixing and oscillations Neutrino oscillations in experiments Solar neutrinos and