concha gonzalez-garcia - kth...global analysis concha gonzalez-garcia effects of mass: oscillations...

Global Analysis Concha Gonzalez-Garcia

GLOBAL ANALYSIS OF NEUTRINO DATA

Concha Gonzalez-Garcia(Stony Brook & IFIC-Valencia)

Nobel Symposium, August 2004

Introduction:

The Parameters of the New Minimal Standard Model

Orthodox Global Fits

Solar and Reactor Neutrinos

Atmospheric and LBL Neutrinos

3 � Mixing

Unorthodox Fits: Constraints on Extensions of the NMSM:

LSND+Karmen and Sterile neutrinos: 4 � Mixing

Tests of Fundamental Symmetries: CPT, LI, WEP

Summary

In collaboration with J. Bahcall, M. Maltoni, C.Pena-Garay and A. Smirnov


� in the SM

� The SM is a gauge theory based on the symmetry group

��

� � ��

��

� � � � ��

� ��

� !� " � � �

# �$ �� ! # � $ �

�%

� & � � �' �

( �� % ' � ) �

There is no * +

� Accidental global symmetry:

, - � - " - &

� � strictly massless

� When SM was built upper bounds on . /

0 1 2 0 1 � 3 � � 354 � �

νm

K (T)

QT

6 7 8:9 ;< ; = >

6 7 ? 9 @ AB C = > ( DE FHG I )

6 7 J 9 @ K < ;L = > ( ME N D G O )

� Neutrinos are conjured to be massless and left-handed

Global Analysis Concha Gonzalez-Garcia� We have learned:

� Atmospheric � " disappear ( � �� ) most likely to � &

� K2K: accelerator � " disappear at - � �� Km with � -distortion ( � � � – � )

� Solar � � convert to � " or � & ( � � )

� KamLAND: reactor � � disappear at - � � � Km with � -distortion ( � � � CL)

� LSND found evidence for � " 2 � �

All this implies that neutrinos are massive

Global Analysis Concha Gonzalez-Garcia� We have learned:

� Atmospheric � " disappear ( � �� ) most likely to � &

� K2K: accelerator � " disappear at - � �� Km with � -distortion ( � � � – � )

� Solar � � convert to � " or � & ( � � )

� KamLAND: reactor � � disappear at - � � � Km with � -distortion ( � � � CL)

� LSND found evidence for � " 2 � �All this implies that neutrinos are massive


Effects of � Mass� Neutrino masses must have kinematic effects at some level

� Also if neutrinos have a mass the charged current interactions of leptons are notdiagonal (same as quarks)

�� " � ��

� � �� " - �� 3 � � �� " -� � � 3 � # �

j

W+

l_

i

ν

W+

_

i

uj

d

� SM gauge invariance does not imply� � �� 8 � �� ? � � �� J symmetry

� Total lepton number� �� ?� � J can be or cannot be still asymmetry depending on whether neutrinos are Dirac or Majorana


� Mass Questions

�� " � ��

� � �� "�� 3 � � �� "� �� 3 � # �

� To fully determine the lepton flavour sector we want to know:

* How many, � , massive � � and their masses . �

* Their mixing: � angles � � � � � � �

�* Their CP properties: Dirac neutrino �� antineutrino

� lepton number is conserved � phases � � � � � � � � � � �

�

Majorana neutrino � antineutrino

� lepton number is violated � extra phases � � � � �

For example for 3 ’s : 3 Mixing angles + 1 Dirac Phase + +Majorana Phases


� Mass Questions

�� " � ��

� � �� "�� 3 � � �� "� �� 3 � # �

� To fully determine the lepton flavour sector we want to know:

* How many, � , massive � � and their masses . �

* Their mixing: � angles � � � � � � �

�* Their CP properties: Dirac neutrino �� antineutrino

� lepton number is conserved � phases � � � � � � � � � � �

�

Majorana neutrino � antineutrino

� lepton number is violated � extra phases � � � � �

� For example for 3 � ’s : 3 Mixing angles + 1 Dirac Phase + +Majorana Phases

� ��

� � � � � �

� � � � � ��

� � � � � � � �

� � �

� � � � � � � � ��

� � � � � �

� � � � � �

� � �

� ��

� � � � �

� � � � ��


Effects of � Mass: Oscillations� If neutrinos have mass, a weak eigenstate � � � � produced in � � 3 � 2 � � 3 � �

is a linear combination of the mass eigenstates ( � � � � ) : � � � � ��

��

� After a distance - it can be detected with flavour � with probability

� � � � � ��

� ��

Re �� ; � ;� ��

Im ��

! "�

� �� !� � " ��

� � �$# � ! � # �" �

eV � � % �

Km/GeV

� & � ' depends on Theoretical Parameters and on Two Experimental Parameters:

� ( . �� . �� . �� The mass differences � � The neutrino energy

� � � � The mixing angles � - Distance � source to detector(and Dirac phases)

No information on mass scale nor Majorana versus Dirac * nature


Global Fits: Solar Neutrinos� � �� (SNU)

� � �� (SNU)

� SK Zenith spectrum (44 Data points)

� SNO Ph-I D-N Spectrum (34 Points)

0

0.5

1

1.5

5 6 7 8 9 10 11 12 13 20

NightDay

Kinetic energy (MeV)

Cou

nts/

day/

0.5

MeV (a)

Kinetic energy (MeV)

Cou

nts/

day/

0.5

MeV (b)

-0.2

-0.1

0

0.1

0.2

5 6 7 8 9 10 11 12 13 20� SNOII spectrum unconstrained fluxes

� � � � � � �� (stat)� �� (syst)

� � � � � � �� 0 �� (stat) � � � � (syst)

� � � � � �� (stat) � � � � � (syst)


Solar Neutrinos: Oscillation Solutions

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-4 10-3 10-2 10-1 1 10.

RATES ONLY GLOBALSK and SNO E and t dependence

SMA

LMA

LOW

VAC

SMA, LOW, VACat � �

LMA

( . � � � � � �� eV � (1� )

� � � � � � � � � ��


Terrestrial Test of LMA: KamLAND� Search on � � at L � 180 km reactors, � / � few MeV: 4

� � 3 � 2 ) 3 ��

In 2002: Deficit Observed

� � �� 1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nob

s/N

exp

101 102 103 104 105

Distance to Reactor (m)

ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz

KamLAND

In 2004: Significant Energy Distortion

(M

eV)

dela

yed

E 2

3

4

5

Fri Jun 11 11:43:30 2004 (MeV)promptE0 1 2 3 4 5 6 7 8

Eve

nts

/ 0.4

25 M

eV

0

20

40

60

80

no-oscillation

best-fit oscillation

accidentals

KamLAND data


Test of LMA: KamLAND Oscillation Analysis∆m

2 (eV

2 )∆m

2 (eV

2 )

tan2θ tan2θ

Our binned analysis (1� ):

( . � � � �� 0 � � � � eV �

� � � � � � � � � ��


CHOOZ

Negative search with � � source: Nuclear Reactor at - � km


Combined Solar and KamLAND Analysis

∆m (

10-5

eV

2 )

tan2θ

All free + Lum. constraint

Before Nu2004468

101214161820

0.2 0.4 0.6tan2θ

All free + Lum. constraint

After Nu2004

0.2 0.4 0.6

( . ��

� � �� eV �

� � � � � �

� � � � � � � � � �


Atmospheric Neutrinos� Complete SKI data:

� �

�

�

� �

p, He

π , K

µ

e

νeνµ

detector

atmosphere

EARTH

νµ

down-going

up-going

zenithangle

L ≈1.2×104 km

L −~ 10-30 km

L ≈104 km

L ≈500 km

[not to scale]

+−

+− +−

+−


Atmospheric Neutrinos: Oscillation Solutions

� � " 2 � & : best channel

★

10-1

100

101

tan2 θ

10-3

10-2

∆m2

[eV

2 ]

3-dim

1-dim

( . � � � � � �� 0 eV �

� � � � � � � �� 0 ��

: Excluded at 5 (Bad fit to observed SM like distributions)

Strongly limited subdominant contribution in 3 mixing because of CHOOZ

: Disfavoured at ( Matter effects Flatter upgoing- distribution )

Limited subdominant contribution in 4 mixing


Atmospheric Neutrinos: Oscillation Solutions

� � " 2 � & : best channel

★

10-1

100

101

tan2 θ

10-3

10-2

∆m2

[eV

2 ]

3-dim

1-dim

( . � � � � � �� 0 eV �

� � � � � � � �� 0 ��

� � " 2 � � : Excluded at � 5� (Bad fit to observed SM like � � distributions)

Strongly limited subdominant contribution in 3 � mixing because of CHOOZ

� � " 2 � �� : Disfavoured at � � � ( Matter effects � Flatter upgoing- ! distribution )

Limited subdominant contribution in 4 � mixing


ATM Test at Long Baseline Experiments: K2K

K2K G I at KEK Kamiokande L=250 km

MINOS G I at Fermilab Soundan L=730 km

Opera/Icarus G I at CERN Gran Sasso L=740 km

K2K 2004: spectral distortion Confirmation of ATM oscillations


Solar+Atmospheric+Reactor+LBL 3 � Oscillations

� : 3 angles, 1 CP-phase+ (2 Majorana phases)

��

� � �

� � � � � �

� � � � � ��

��

��

� � �

� � � � � � � � ��

��

��

� � � � � �

� � ��

�

Two mass schemes

M

sola

r

sola

r

atm

osm m 1 3

∆ 2

∆ m

2

m 3

m 2

∆ m

m 1

m 2

NORMAL INVERTED

2

2 � oscillation analysis � � 6 �� 6 � � � �� 6 �� 6 ��

Generic 3 mixing effects:

– Interference of two wavelength oscillations

– Effects due to

– Difference between Inverted and Normal

– CP violation due to phase


Solar+Atmospheric+Reactor+LBL 3 � Oscillations

� : 3 angles, 1 CP-phase+ (2 Majorana phases)

��

� � �

� � � � � �

� � � � � ��

��

��

� � �

� � � � � � � � ��

��

��

� � � � � �

� � ��

�

Two mass schemes

M

sola

r

sola

r

atm

osm m 1 3

∆ 2

∆ m

2

m 3

m 2

∆ m

m 1

m 2

NORMAL INVERTED

2

2 � oscillation analysis � � 6 �� 6 � � � �� 6 �� 6 ��

Generic 3 � mixing effects:

– Interference of two wavelength oscillations

– Effects due to � � 0

– Difference between Inverted and Normal

– CP violation due to phase �

Global Analysis Concha Gonzalez-Garcia� In the Hierarchical approximation ( . �

� � (� �� #

� For � � 0 � � solar and atmospheric oscillations decouple � Normal � Inverted

– Solar and KamLAND 2 ( . �� ( . �

�

� � � � � �

– Atmospheric and K2K 2 ( . �0 � � (� �� # � � 0 � � �� #

For

– Solar and KamLAND:

Limit on

– Atmos + K2K: Independent of ,

some Limit on

Dependence on scheme but too small

– CHOOZ:

For eV limit on

All

data

pref

ers

smal

l

,

,

very similar to 2 analysis


� � (� �� #



�

� � � � � �


� For � � 0 ��


� � 7� � �� 7� � � � 6 � � � ��

� Limit on � � 0

– Atmos + K2K: Independent of � � � , ( . ��

� � 0 � some � " 2 � � � Limit on � � 0Dependence on scheme but too small

– CHOOZ:

� �� @� � � � � � � � � ��

For � � 6 �� K� @B � � eV � � limit on � � 0

All

data

pref

ers��

smal

l

,

,

very similar to 2 analysis


� � (� �� #



�

� � � � � �


� For � � 0 ��


� � 7� � �� 7� � � � 6 � � � ��

� Limit on � � 0

– Atmos + K2K: Independent of � � � , ( . ��

� � 0 � some � " 2 � � � Limit on � � 0Dependence on scheme but too small

– CHOOZ:

� �� @� � � � � � � � � ��

For � � 6 �� K� @B � � eV � � limit on � � 0

All

data

pref

ers��

smal

l

( . �� , � � � � � � �

� ( . �0 � � , � � � � � � 0

very similar to 2 � analysis


Global Analysis: Three Neutrino Oscillations

Projected allowed regions (2dof)

Best Fit:

( . �� eV �

� � � � � � � � � � � �

�� 0 � � � � �

( . �0 � � � � � � 0 eV �

� � � � � � 0 � � �


Global Analysis: Three Neutrino Oscillations

1-parameter allowed ranges � 3� ranges:

� � �

# ��

� � �

# ��

� � � � � � � � � � � � � � � �

� � �� 0 � �

�� 0 � � � �

� The leptonic mixing matrix:

��

�

B < A� B < K K B < � � B < � @ 9 B < ;B

B < @ A� B < � ; B < � ;� B < B < � A� B < K ;

B < ;B � B < � B < � �� B < � B < � �� B < K @�

�


Beyond Hierarchical: � effects in ATM Data

Best at electron samples

-1 -0.5 0 0.5 10.8

0.9

1

1.1

1.2

1.3

Ne /

Ne0

SK sub-GeV (e)

Normal

-1 -0.5 0 0.5 10.8

0.9

1

1.1

1.2

1.3

SK sub-GeV (e)

Inverted

-1 -0.5 0 0.5 1

cos θ

0.8

0.9

1

1.1

1.2

1.3

Ne /

Ne0

SK multi-GeV (e)

Normal

-1 -0.5 0 0.5 1

cos θ

0.8

0.9

1

1.1

1.2

1.3

SK multi-GeV (e)

Inverted

� For ( . �� and � � 0 � � :

� ��

� � �# �� 0 �

4 � �� ?�� 8� � �

� Sensitivity to Octant of � � 0 !!!

Most important for Sub-GeV e� For ( . �

� � � � and � � 0 �� the opposite:

� ��

� � � $ �� 0 �

4 � �

Most important for Muli-GeV e


� effects in ATM Data: Present

★

10-3

10-2

∆m2 31

[eV

2 ]

∆m221 = 8.2×10

-5 eV

2

★

∆m221 = 10

-4 eV

2

0 0.25 0.5 0.75 1

sin2 θ23

55

60

65

70

χ2 SK

+C

HO

OZ

0 0.25 0.5 0.75 1

sin2 θ23

� � 0 � � � � � � � � 0 � � � � � � � �

★

10-4

10-3

10-2

∆m2 31

[eV

2 ]

Sub-GeV (e+µ)

★

Contained (µ)

★

0 0.25 0.5 0.75 1

sin2 θ23

10-4

10-3

10-2

∆m2 31

[eV

2 ]

Multi-GeV (e+µ)

★

0 0.25 0.5 0.75 1

sin2 θ23

Upgoing (µ)


Neutrino Mass Scale

Oscillation analysis � lower bound on heaviest � mass. Upper bounds from:

0 1 2 0 1 � 3 � 3 � � : for both Dirac or Majorana � ’s. ' � . � �� (at 95 % CL)

� -less Double- � decay: �� E � � � � � ; � � � � � � �

�

�

�

� �

only for Majorana � ’s

Sensitive to Majorana CP phases

. ' ' � � � �� . � � � � � � � � �

3 theor. uncert. � � � � � � (90% CL)

COSMO:WMAP+LSS � � . � � � � � � � � � � � � � � � �

Global Analysis Concha Gonzalez-GarciaNeutrino Mass Scale

Global oscillation analysis � Correlated ranges for . ' , . ' ' and � (Fogli et al hep-ph/0408045)

Normal Mass Scheme ( � � �� )

Inverted Mass Scheme ( � � �� )


LSND

� The only short distance signal for oscillation: - � � � m with � � / � � � � MeV

� Observed � " 2 � � with probability � & � " � � ��

� � � � . � ) searched for the same signal and did not observe oscillations

LSND+Karmen Combined Analysis

sin22Θ

∆m

2[e

V2/c

4]

10-2

10-1

1

10

102

10-3

10-2

10-1

1

68% C.L.

95% C.L.

90% C.L.


Sterile Neutrinos and 4 � Models� Motivation: To explain LSND

( . �� ( . �� # � ( . �

�

� To fit solar, atmospheric and LSND � 3 ( . � � 4th sterile �

� � : 6 mixing angles and 3 CP Dirac phases and 3 Majorana phases

� 6 mass spectra of two type:

LSND

atmos

solar

LSND

atmos

solar

LSND LSND

LSND

atmos

solar

LSND

atmos

solaratmos

solar atmos

solar

3 + 1 2 + 2


Sterile Neutrinos and 4 � Models� �

�� "� � �

�� constrained by Bugey

�� "� � � constrained by CDHSW+ATM

10-4

10-3

10-2

10-1

100

sin22θLSND

10-1

100

101

∆m2 LS

ND [e

V2 ]

LSND DAR

LSND global

NEV + atm + K2K

95% C

L

99% C

L

Only tiny regions at 99%CL

Also constrained by cosmo bound on 6 7 !

Mal

toni

etal

hep-

ph/0

1071

50

Mixed active-sterile oscillations

Naively: Solar:

Atm:

Disagreement at more than 4


Sterile Neutrinos and 4 � Models� �

��

�� constrained by Bugey

�� constrained by CDHSW+ATM

10-4

10-3

10-2

10-1

100

sin22θLSND

10-1

100

101

∆m2 LS

ND [e

V2 ]

LSND DAR

LSND global

NEV + atm + K2K

95% C

L

99% C

L

Only tiny regions at 99%CL

Also constrained by cosmo bound on � � !

Mal

toni

etal

hep-

ph/0

1071

50

� �

Mixed active-sterile oscillations

Naively: Solar: ��

Atm: � ��

Disagreement at more than 4 �


Tests of Symmetries: CPT

CPT violation:

� ’s and � ’s can have different masses

� Possibility of accommodating LSND?

Atmospheric

Atmospheric, LSND

SolarKamLAND

Neutrinos Antineutrinos

m 1

m 3

m

m

m

3

2

1

m 2

★

10-4

10-3

10-2

10-1

100

∆m231 [eV

2]

10-4

10-3

10-2

10-1

100

∆m2 31

[eV

2 ]

★

0 0.2 0.4 0.6 0.8 1

sin2 θ23

0

0.2

0.4

0.6

0.8

1

sin2

θ 23

★★★0 0.2 0.4 0.6 0.8 1

sin2 θ13

0

0.2

0.4

0.6

0.8

1

sin2

θ 13

But Data does not support this:

ATM and ’s similar wavelength

Solar and KamLAND similar

Best fit near

CPT conservation

★

LSN

D★

10-3

10-2

10-1

100

sin2 2θLSND

10-4

10-3

10-2

10-1

100

101

102

∆m2 31

All-but-LSND

All-But-LSND and LSND regions

incompatible at



CPT violation:



Atmospheric

Atmospheric, LSND

SolarKamLAND


m 1

m 3

m

m

m

3

2

1

m 2

★

10-4

10-3

10-2

10-1

100

∆m231 [eV

2]

10-4

10-3

10-2

10-1

100

∆m2 31

[eV

2 ]

★

0 0.2 0.4 0.6 0.8 1

sin2 θ23

0

0.2

0.4

0.6

0.8

1

sin2

θ 23

★★★0 0.2 0.4 0.6 0.8 1

sin2 θ13

0

0.2

0.4

0.6

0.8

1

sin2

θ 13


ATM � � and � � ’s similar wavelength

Solar � and KamLAND � � similar � ��

Best fit near

CPT conservation

★

LSN

D★

10-3

10-2

10-1

100

sin2 2θLSND

10-4

10-3

10-2

10-1

100

101

102

∆m2 31

All-but-LSND


incompatible at



CPT violation:



Atmospheric

Atmospheric, LSND

SolarKamLAND


m 1

m 3

m

m

m

3

2

1

m 2

★

10-4

10-3

10-2

10-1

100

∆m231 [eV

2]

10-4

10-3

10-2

10-1

100

∆m2 31

[eV

2 ]

★

0 0.2 0.4 0.6 0.8 1

sin2 θ23

0

0.2

0.4

0.6

0.8

1

sin2

θ 23

★★★0 0.2 0.4 0.6 0.8 1

sin2 θ13

0

0.2

0.4

0.6

0.8

1

sin2

θ 13


ATM � � and � � ’s similar wavelength

Solar � and KamLAND � � similar � ��

Best fit near

CPT conservation

★

LSN

D★

10-3

10-2

10-1

100

sin2 2θLSND

10-4

10-3

10-2

10-1

100

101

102

∆m2 31

All-but-LSND


incompatible at � � �


Tests of Symmetries: LI, WEP...� These New Physics Effects can also lead to -Oscillations

But in general oscillation wavelegth has different � � dependence

Violation of Lorentz Invariance:

Non universal asymptotic velocity of neutrinos

90% CL Limit from ATM data

Violation of Weak Equivalence Principle:

Non universal coupling of neutrinos to graviational potential



Tests of Symmetries: LI, WEP...� These New Physics Effects can also lead to � -Oscillations


� Violation of Lorentz Invariance:

Non universal asymptotic velocity of neutrinos � � ��

� � �

90% CL Limit from ATM data �

� � � ��

Violation of Weak Equivalence Principle:

Non universal coupling of neutrinos to graviational potential



Tests of Symmetries: LI, WEP...� These New Physics Effects can also lead to � -Oscillations


� Violation of Lorentz Invariance:

Non universal asymptotic velocity of neutrinos � � ��

� � �

90% CL Limit from ATM data �

� � � ��

� Violation of Weak Equivalence Principle:

Non universal coupling of neutrinos � � �� to graviational potential � � � ��

90% CL Limit from ATM data � ��


Summary� Solar, Reactor, Atmospheric and LBL data: Perfect in 3 � -oscillations

(3 � ranges)

� �� eV�

� �� eV�

and leptonic mixing matrix:

� � � � ��

� � �� @ � � ��

� � @� � � � � � � ��

� �� @�

�

� Accommodating LSND: A problem

3+1 still marginally at 99%CL with � � � � ! " # � � � eV�

2+2 sterile limits from Solar and ATM incompatible $ � �

CTP violation incompatible at more than 3 � .

� Neutrino data provides interesting limits on fundamental symmetries

CPT, LI, WEP...

concha gonzalez-garcia - kth...global analysis concha gonzalez-garcia effects of mass: oscillations...

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