7. Atmospheric neutrinos and Neutrino oscillations

7. Atmospheric neutrinos and

Neutrino oscillations

Corso “Astrofisica delle particelle”

Prof. Maurizio SpurioUniversità di Bologna. A.a.

2011/12

Outlook Some history Neutrino Oscillations How do we search for neutrino

oscillations Atmospheric neutrinos 10 years of Super-Kamiokande Upgoing muons and MACRO Interpretation in terms on neutrino

oscillations Appendix: The Cherenkov light

At the beginning of the ’80s, some theories (GUT) predicted the proton decay with measurable livetime

The proton was thought to decay in (for instance) pe+p0ne

Detector size: 103 m3, and mass 1kt (=1031 p) The main background for the detection of proton

decay were atmospheric neutrinos interacting inside the experiment

7.1 Some history

Proton decay

gg

e Neutrino Interaction

Water Cerenkov Experiments (IMB, Kamiokande)

Tracking calorimeters (NUSEX, Frejus, KGF)

Result: NO p decay ! But some anomalies on the neutrino measurement!

7.2 Neutrino Oscillations

|ne , |nm , |nt =Weak Interactions (WI) eigenstats

|n1 , |n2 , |n3 =Mass (Hamiltonian) eigenstats

Idea of neutrinos being massive was first suggested by B. Pontecorvo

Prediction came from proposal of neutrino oscillations

• Neutrinos propagate as a superposition of mass eigenstates

Neutrinos are created or annihilated as W.I. eigenstates

Weak eigenstates (ne, nm, nt) are expressed as a combinations of the mass eigenstates (n1, n2,n3).

These propagate with different frequencies due to their different masses, and different phases develop with distance travelled. Let us assume two neutrino flavors only.

The time propagation: |n(t)= (|n1 , |n2 )

02

222

ij

iiii

ME

mEmpMn

n

M = (2x2 matrix)

(eq.2)

)(tMdt

di n

n (eq.1)

eq.1 becames, using eq.2)

)(2

2

tvE

mEdt

di i

nn

n

whose solution is :ti

iiievtv )0()(

nn

EmE i

i 2

2

with

During propagation, the phase difference is:

nEtmm

i 2)( 2

122

(eq.4)

(eq.6)

(eq.5)

Time propagation

|ne = cosq |n1 + sinq |n2

|nm = -sinq |n1 + cosq |n2

q = mixing angle

(eq.3)

Time evolution of the “physical” neutrino states:

• Let us assume two neutrino flavors only (i.e. the electon and the muon neutrinos).

• They are linear superposition of the n1,n2 eigenstaten:

titi

titie

i

i

evevv

evevv21

21

)0(cos)0(sin

)0(sin)0(cos

21

21

m

qq

qq

(eq.7)

• Using eq. 5 in eq. 3, we get:

• At t=0, eq. 7 becomes:

)0(cos)0(sin

)0(sin)0(cos

21

21

vvv

vvve

qq

qq

m

)0(cos)0(sin)0(

)0(sin)0(cos)0(

2

1

m

m

qq

qq

vvv

vvv

e

e

• By inversion of eq. 8:

(eq.8)

• For the experimental point of view (accelerators, reactors), a pure muon (or electron) state a t=0 can be prepared. For a pure nm beam, eq. 9:

)0(cos)0(

)0(sin)0(

2

1

m

m

q

q

vv

vv

(eq.9)

(eq.10)

The time evolution of the nm state of eq. 8:titi ievevv 21 )0(cos)0(sin 22

m

mm qq

By definition, the probability that the state at a given time is a nm is:

20 tP mmnn nnmm

(eq. 12)• Using eq. 11, the probability:

titi

t

ee

P)()(22

4420

2121cossin

cossin

mmnn

qq

qqnnmm

2

)(sin2sin1 2122 tP qmmnn

i.e. using trigonometry rules:

(eq.11)

(eq. 13)

(eq. 14)

nn

EmE i

i 2

2

Finally, using eq.5:

nnn qmm E

tmmP4

)(sin2sin121

2222

With the following substitutions in eq.15:- the neutrino path length L=ct (in Km)- the mass difference m2 = m2

2 – m12

(in eV2)- the neutrino Energy En (in GeV)

nnn qmm E

LmP

222 27.1sin2sin1

To see “oscillations” pattern: 2

27.1

02 p

q

n

ELm

(eq. 15)

(eq. 16)

7.3 How do we search

for neutrino oscillatio

ns?

..with atmospheric neutrinos

nnn qmm E

LmP

222 27.1sin2sin1

• m2, sin22Q from Nature;

• En = experimental parameter (energy distribution of neutrino giving a particular configuration of events)

• L = experimental parameter (neutrino path length from production to interaction)

Appearance/

Disappearance

nnn qmm E

LmP

222 27.1sin2sin1

7.4- Atmospheric neutrinos

The recipes for the evaluation of the atmospheric neutrino

flux-

ee nnm

nmp

m

m

\

E-3 spectrum

GZK cut

1015 < E< 1018 eVgalactic ?

E < 1015 eVGalactic

E 5. 1019 eVExtra-Galactic?Unexpected?

5. 1019 < E< 3. 1020 eV

i) The primary spectrum

ii)- CR-air cross section

pp Cross section versus center of mass energy.

Average number of charged hadrons produced in pp (andpp) collisions versus center of mass energy

It needs a model of nucleus-nucleus interactions

iii) Model of the atmosphere

ATMOSPHERIC NEUTRINO PRODUCTION: • high precision 3D calculations,• refined geomagnetic cut-off treatment (also

geomagnetic field in atmosphere)• elevation models of the Earth• different atmospheric profiles• geometry of detector effects

Output: the neutrino (ne,nm) flux

See for instance the FLUKA MC: http://www.mi.infn.it/~battist/neutrino.html

iv) The Detector responseFully Contained

n Partially Contained

Energy spectrum of n for each event categoryn

m

Through going mStopping m

n

m

n

m

Energy spectrum (from Monte Carlo) of atmospheric neutrinos seen with different event topologies (SuperKamiokande)

up-stop m up-thru m

nnn qmm E

LmP

222 27.1sin2sin1

Rough estimate: how many ‘Contained events’ in 1 kton

detector

1. Flux: n ~ 1 cm-2 s-1

2. Cross section (@ 1GeV): sn~0.5 10-38 cm2

3. Targets M= 6 1032 (nucleons/kton)4. Time t= 3.1 107 s/y

Nint = n (cm-2 s-1) x sn (cm2)x M (nuc/kton) x t (s/y) ~ ~ 100 interactions/ (kton y)

nm

ne

7.5 10 years of Super-Kamiokande1996.4 Start data taking

1999.6 K2K started

2001.7 data taking was stopped for detector upgrade2001.11 Accident

partial reconstruction2002.10 data taking was resumed

2005.10 data taking stopped for full reconstruction

2006.7 data taking was resumed

2001 Evidence of solar n oscillation (SNO+SK)

1998 Evidence of atmospheric n oscillation (SK)

2005 Confirm n oscillation by accelerator n (K2K)

SK-I

SK-II

SK-III

SK-IV 2009 data taking

Measurement of contained events and

SuperKamiokande (Japan)

1000 m Deep Underground

50.000 ton of Ultra-Pure Water

11000 +2000 PMTs

As a charged particle travels, it disrupts the local electromagnetic field (EM) in a medium.

Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle.

Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed.

In a conductor, the EM disruption can be restored without emitting a photon.

In normal circumstances, these photons destructively interfere with each other and no radiation is detected.

However, when the disruption travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed Cerenkov radiation.

Cherenkov Radiation

Cherenkov Radiation

One of the 13000 PMTs of

SK

How to tell a nm from a ne : Pattern recognition

nm

ne

e or m

Fully Contained (FC)

m

No hit in Outer Detector One cluster in Outer Detector

Partially Contained (PC)

Reduction

Automatic ring fitterParticle IDEnergy reconstruction

Fiducial volume (>2m from wall, 22 ktons) Evis > 30 MeV (FC), > 3000 p.e. (~350 MeV) (PC)

Fully Contained8.2 events/dayEvis<1.33 GeV : Sub-GeVEvis>1.33 GeV : Multi-GeV

Partially Contained0.58 events/day

Contained event in SuperKamiokande

Contained events. The

up/down symmetry in SK and nm/ne ratio.

Up/Down asymmetry interpreted as neutrino oscillations

Expectations: events inside the detector. For En > a few GeV,Upward / downward = 1

En=0.5GeV En=3 GeV En=20 GeV

Zenith angle

distributionSK:1289 days

(79.3 kty)

m /eDATA

m /e M C= 0.638 0.017 0.050

Data

• Electron neutrinos = DATA and MC (almost) OK!

• Muon neutrinos = Large deficit of DATA w.r.t. MC !

Zenith angle distributions for e-like and µ-like contained atmosphericneutrino events in SK. The lines show the best fits with (red) and without (blue) oscillations; the best-fit is m2 = 2.0 × 10−3 eV2 and sin2 2θ = 1.00.

Zenith Angle Distributions (SK-I + SK-II)nm–nt oscillation (best fit)

null oscillation

m-likee-like

P<400MeV/c

P>400MeV/c

P<400MeV/c

P>400MeV/c

NOTE: All topologies, last results (September 2007)

Livetime• SK-I 1489d (FCPC) 1646d (Upmu)• SK-II 804d (FCPC) 828d(Upmu)

Main features of Macro as n detector

• Large acceptance (~10000 m2sr for an isotropic flux)

• Low downgoing m rate (~10-6 of the surface rate )

• ~600 tons of liquid scintillator to measure T.O.F. (time resolution ~500psec)

• ~20000 m2 of streamer tubes (3cm cells) for tracking (angular resolution < 1° )

More details in Nucl. Inst. and Meth. A324 (1993) 337.

7.6 Upgoing muons and MACRO (Italy)

R.I.P December 2000

The Gran Sasso National Labs

http://www.lngs.infn.it/

Up stopIn down

1) 2) 3) 4)

Neutrino event topologies in MACRO

In upUp throughgoing

AbsorberStreamerScintillator

• Liquid scintillator counters, (3 planes) for the measurement of time and dE/dx.

• Streamer tubes (14 planes), for the measurement of the track position;

• Detector mass: 5.3 kton• Atmospheric muon

neutrinos produce upward going muons

• Downward going muons ~ 106 upward going muons

• Different neutrino topologies

Energy spectra of nm events in MACRO

• <E>~ 50 GeV throughgoing m

• <E>~ 5 GeV, Internal Upgoing (IU) m;

• <E>~ 4 GeV , internal downgoing (ID) m and for upgoing stopping (UGS) m;

+1 m-1 m

T1

T2Streamer tube track

Neutrino induced events are upward throughgoing muons, Identified by the time-of-flight method

Atmospheric m: downgoing

m from n: upgoing

LcTT 211

LcTT 211

MACRO Results: event deficit and distortion of the angular

distribution

Observed= 809 eventsExpected= 1122 events (Bartol)Observed/Expected= 0.721±0.050(stat+sys)

±0.12(th)

- - - - No oscillations____ Best fit m2= 2.2x10-3 eV2

sin22q=1.00

MACRO Partially contained events

consistent with up throughgoing muon results

Obs. 262 eventsExp. 375 eventsObs./Exp. = 0.70±0.19)

Obs. 154 eventsExp. 285 eventsObs./Exp. = 0.54±0.15

IU

ID+UGS

MC with oscillations

underground detector

Effects of nm oscillations on upgoing events

n

Earth

m

nnn qmm E

LmP

222 27.1sin2sin1

q

• If q is the zenith angle and D= Earth diameter

L=Dcosq• For throughgoing neutrino-induced

muons in MACRO, En = 50 GeV (from Monte Carlo)

q cos(q) m2=0.0002 m2=0.00010 -1,000 0,62 0,89

-10 -0,985 0,63 0,90-20 -0,940 0,66 0,91-30 -0,866 0,71 0,92-40 -0,766 0,77 0,94-50 -0,643 0,83 0,96-60 -0,500 0,89 0,97-70 -0,342 0,95 0,99-80 -0,174 0,99 1,00-90 0,000 1,00 1,00

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

-1,00 -0,80 -0,60 -0,40 -0,20 0,00

cosq

mmnnP

Oscillation Parameters• The value of the “oscillation parameters” sin2q and m2 correspond to the values which provide the best fit to the data

• Different experiments different values of sin2q and m2

• The experimental data have an associated error. All the values of (sin2q, m2) which are compatible with the experimental data are “allowed”.

• The “allowed” values span a region in the parameter space of (sin2q, m2)

nnn qmm E

LmP

222 27.1sin2sin1

1.9 x 10-3 eV2 < m2 < 3.1 x 10-3 eV2

sin2 2q > 0.93 (90% CL)

“Allowed” parameters region

90% C. L. allowed regions for νm → νt oscillations of atmospheric neutrinos for Kamiokande, SuperK, Soudan-2 and MACRO.

Why not νμνe ?

Apollonio et al., CHOOZ Coll.,Phys.Lett.B466,415

nm disappearance: History Anomaly in

R=(m/e)observed/(m/e)predicted Kamiokande: PLB 1988, 1992 Discrepancies in various

experiments Kamiokande: Zenith-angle

distribution Kamiokande: PLB 1994

Super-Kamiokande/MACRO: Discovery of nm oscillation in 1998 Super-Kamiokande: PRL 1998 MACRO, PRL 1998

K2K: First accelerator-based long baseline experiment: 1999 – 2004 Confirmed atmospheric neutrino results Final result 4.3s: PRL 2005, PRD

2006 MINOS: Precision

measurement: 2005 - First result: PRL2006

Kajita: Neutrino 98

See for review: The “Neutrino Industry”

http://www.hep.anl.gov/ndk/hypertext/ Janet Conrad web pages:

http://www.nevis.columbia.edu/~conrad/nupage.html

Fermilab and KEK “Neutrino Summer School” http://projects.fnal.gov/nuss/

Torino web Pages: http://www.nu.to.infn.it/Neutrino_Lectures

/

Progress in the physics of massive neutrinos, hep-ph/0308123

Appendice:La radiazione Cerenkov

Effetto CerenkovPer una trattazione classica dell’effetto Cerenkov:Jackson : Classical Electrodynamics, cap 13 e par. 13.4 e 13.5La radiazione Cerenkov e’ emessa ogniqualvolta una particella carica attraversa un mezzo (dielettrico) con velocita’ c=v>c/n, dove v e’ la velocita’ della particella e n l’indice di rifrazione del mezzo.Intuitivamente: la particella incidente polarizza il dielettrico gli atomi diventano dei dipoli. Se >1/n momento di dipolo elettrico emissione di radiazione.

<1/n 1/n

L’ angolo di emissione qc puo’ essere interpretato qualitativamente come un’onda d’urto come succede per una barca od un aereo supersonico.

Esiste una velocita’ di soglia s = 1/n qc ~ 0 Esiste un angolo massimo qmax= arcos(1/n) La cos(q) =1/n e’ valida solo per un radiatore infinito, e’ comunque una buona approssimazione ogniqualvolta il radiatore e’ lungo L>>l essendo l la lunghezza d’onda della luce emessa

lpart=ct

llight=(c/n)tq

wave front

1)(with1cos l

q nnnC

qC

Numero di fotoni emessi per unita’ di percorso e intervallo unitario di lunghezza d’onda. Osserviamo che decresce al crescere della l

.with 1

sin2112

2

2

2

22

2

222

22

constdxdE

NdEhcc

dxdNd

zn

zdxd

NdC

nl

ll

qlp

lp

l

dN/dl

l

dN/dE

Il numero di fotoni emessi per unita’ di percorso non dipende dalla frequenza

L’ energia persa per radiazione Cerenkov cresce con . Comunque anche con 1 e’ molto piccola.Molto piu’ piccola di quella persa per collisione (Bethe Block), al massimo 1% .

dnc

zdxdE

22

2 11

medium n qmax (=1) Nph (eV-1 cm-1)

air 1.000283 1.36 0.208isobutane 1.00127 2.89 0.941water 1.33 41.2 160.8quartz 1.46 46.7 196.4

1) Esiste una soglia per emissione di luce Cerenkov

2) La luce e’ emessa ad un angolo particolareFacile utilizzare l’effetto Cerenkov per identificare le particelle. Con 1) posso sfruttare la soglia Cerenkov a soglia. Con 2) misurare l’angolo DISC, RICH etc.La luce emessa e rivelabile e’ poca.Consideriamo un radiatore spesso 1 cm un angolo qc = 30o ed un E = 1 eV ed una particella di carica 1. 5.9225.0370sin370

sin

2

22

ELNc

zdEdxdN

cph

c

Considerando inoltre che l’efficienza quantica di un fotomoltiplicatore e’ ~20% Npe=18 fluttuazioni alla Poisson