Neutrino Oscillation Phenomenology using atmospheric …Problem 29 • The neutrino oscillograms are...

Neutrino Oscillation Phenomenology using atmospheric neutrinos

Ioana Anghel1), Joshua Hignight2), Junting Huang3), Derek Rountre4)

1) Iowa State University/Argonne National Lab2) Stony Brook University3) University of Texas at Austin4) Virginia Tech

International Neutrino Summer School 2012 - Virginia Tech, July 20, 2012

(Group 9)

Problem 29

• The neutrino oscillograms are a useful way to explore the phenomenology of neutrino oscillations

• The goal: using the atmospheric neutrino oscillograms, determine the neutrinos mass hierarchy

• Approach:

- use the prob3++ package to make the oscillograms for different processes when neutrino

traverse the Earth

- compare the atmospheric neutrino oscillograms of the event rate for appearance channels

for different mass hierarchies

- by studying the resonances in the oscillograms for both neutrinos and anti-neutrinos, identify the

neutrinos mass hierarchy

⌫e

International Neutrino Summer School 2012 - July 20, 2012 2

Atmospheric neutrinos

ATMOSPHERIC NEUTRINOS

• The atmospheric neutrinos result from the interaction of cosmic rays with

atomic nuclei in the Earth atmosphere

• A shower of particles results from the interaction, the unstable particles

produce neutrinos when they decay

ATMOSPHERIC NEUTRINOS

• Neutrinos reach the Earth

at a certain Zenith angle (downward)✓ = 0✓ = ⇡ (upward)

3

Neutrino Oscillograms

4International Neutrino Summer School 2012 - July 20, 2012

• The neutrino oscillograms plot contours of equal oscillation probability in the neutrino energy -

zenith Earth angle

• Oscillograms - represented in (Energy, )✓

Probability

sin2(2✓13) = 0 sin2(2✓13) = 0.05 sin2(2✓13) = 0.1

P⌫µ!⌫e


Y. Itow’s talk from Neutrino 2012

• The existence of a non-zero causes the appearance of high energy upward going neutrinos due to

the resonance effect✓13

Probability

sin2(2✓13) = 0 sin2(2✓13) = 0.05 sin2(2✓13) = 0.1

P⌫µ!⌫e

~ recently measured International Neutrino Summer School 2012 - July 20, 2012

Y. Itow’s talk from Neutrino 2012

• The existence of a non-zero causes the appearance of high energy upward going neutrinos due to

the resonance effect✓13

6

Resonances in Neutrino Oscillograms


• Resonances in oscillation probabilities occur when sin(2✓ij) = 1

• For different (i,j), the resonances occur at different energies. For resonances occur at energies

of ~ 4-10 GeV

• Resonance equation:

✓13

• The resonance condition:

where , GF is the Fermi constant and ne is the electron density in matter

• A > 0 for neutrinos, A < 0 for anti-neutrinos

• for normal mass hierarchy, for inverted mass hierarchy

-The resonance for neutrino energies from ~4-10 GeV occurs for neutrinos if normal hierarchy is correct while it would occur for anti-neutrinos if inverted-hierarchy is true. - By measuring the resonances for neutrino and anti-neutrinos in this energy range, one could distinguish normal from inverted hierarchy.

D. Indumathi and M. V. N. Murthy, "Question of hierarchy: Matter effects with atmospheric neutrinos and antineutrinos", Phys Rev D 71, 013001 (2005)

�23 > 0 �23 > 0

Neutrino Oscillations Parameters


• We used Prob3++ package to produce the neutrino oscillogramshttp://www.phy.duke.edu/~raw22/public/Prob3++/

• Oscillation parameters

sin2(2✓13) = 0.1

sin2(2✓12) = 0.825

sin2(2✓23) = 1.0

�CP = 0

�m122 = 7.9⇥ 10�5

�m232 = 2.5⇥ 10�3

- When neutrinos are traveling

in a vacuum, the oscillations are

seen directly in the oscillogram

for P

P in (Energy, ) plane for neutrinos in vacuum ✓


normal Hierarchy

P in (Energy, ) plane for neutrinos in vacuum ✓

- Earth matter density is not zero, it varies with distance:

7/19/12 1:00 AM

Page 1 of 1http://upload.wikimedia.org/wikipedia/commons/e/ee/Earth-crust-cutaway-english.svg

Earth layer Distance (km) Density (g/cm3)

Crust 0-35 2.2-2.9

Mantle 35-2890 3.4-5.6

Core 2890-6378 9.9-13.1


normal Hierarchy

- When neutrinos are traveling

in vacuum, the oscillations are

seen directly in the oscillogram

for P

Vacuum

Earth density

P comparison for vacuum / Earth density

11

normal Hierarchy

- the matter effect is seen for a

non 0 zenith angle, for neutrinos

travelling distance d > 1000 km

Vacuum

Earth density

P comparison for vacuum / Earth density

12

normal Hierarchy

Normal Mass Hierarchy

P (E, ) for different mass hierarchies - neutrinos✓

• For energies of a few GeV, is large, while is quite low for normal mass hierarchy P⌫µ!⌫e P⌫e!⌫e



Inverted Mass Hierarchy

• Both and

are close to 0 at E ~ few GeV

P⌫µ!⌫eP⌫e!⌫e

14

P (E, ) for different mass hierarchies - neutrinos✓



• The case is reversed for

electron anti-neutrino channels

( e.g. > 0 for

inverted mass hierarchy )

P⌫µ!⌫e

15

P (E, ) for different mass hierarchies - anti-neutrinos✓

From Probability to Event Rate


From Probability to Event Rate

(s−1m

−2GeV

−1Sr

−1)

The number of event in the detector can be written as

Δ N=−N σ nL

=−(∫FL2dEdΩdT )σ nL

=−(∫FdEdΩdT )σ (n L3)

Total number of target in detector

L: detector size

σ: cross section n: the number of target per unit volume

F: Azimuth angle averaged

flux

(Honda flux table)

K. Hagiwara et al., Phys. Rev. D 66 (Review of Particle Physics 2002)

http://www.icrr.u-tokyo.ac.jp/~mhonda/

An EstimationFor a 50 kiloton water Cerenkov detector (Super K),

Event Rate =(∫FdEdΩdT )σ (nL3)=0.11 per year

nL3=3×10

33

F∼1 s−1

m−2

GeV−1

Sr−1

(for cosθ=−0.7∼−0.8, E=6.3GeV)

∫dE∼2GeV

∫dΩ=∫dcosθd φ∼0.1×π=0.628

∫dT=1 year∼3×107s

σ=10−42

m2

Total # of nuclei

Flux

Resonance width

Solid angle

1 year data

Cross section

With those numbers, one has

An Estimation


An EstimationFor a 50 kiloton water Cerenkov detector (Super K),

Event Rate =(∫FdEdΩdT )σ (nL3)=0.27 per year

nL3=3×10

33

F∼1 s−1

m−2

GeV−1

Sr−1

(for cosθ=−0.7∼−0.8, E=6.3GeV)

∫dE∼2GeV

∫dΩ=∫dcosθd φ∼0.3×2π=1.9

∫dT=1 year∼3×107s

σ∼0.8×10−42

m2for ν

(2 to 3 times smaller for ν̄)

Total # of nuclei

Flux

Resonance width

Solid angle

1 year data

Cross section

With those numbers, one has

Flux (E, ) Distribution✓

• The atmospheric neutrino flux for SuperK is relatively high for low energies (~102 MeV) and

decreases while the zenith angle approaches 0 or ⇡• For neutrinos with energies ~ GeV, the flux is ~ 10-3.



Event Rate (E, ) for different mass hierarchies✓

• The event rate for neutrinos with energies ~ GeV is

very low (~ 10-2) compared to low energies neutrinos.


5Normal Mass Hierarchy






21

• At resonance, there is an

excess in the event rate for

normal wrt inverted

hierarchies

• After one year of running,

integrating over the entire

area of resonance, we can

observe ~ 1 event

5

5




22

• For anti-neutrinos, the

excess in the event rate is

observed for the inverted

hierarchy

5

5

Differences in the Event Rate for different hierarchies

• Without identifying between neutrinos and anti-neutrinos, the

differences between the mass hierarchies

is quite low.

• To compute the event rates we need to

use the cross sections for neutrinos and

anti-neutrinos (2-3 lower than neutrinos)

• Need for a much higher statistics !!!

23

Normal H

Inverted H

5

5

Differences in the Event Rate for different hierarchies

24

Normal H

Inverted H • Separating neutrinos from anti-neutrinos, the

differences between the

mass hierarchies are larger.

5

5

5

5


• Our calculations are slightly better than the real world

• In the current configuration of SuperK many years of running are necessary to get the needed statistics

• What would be necessary?

- higher statistics- charge separation detector- neutrino beam

Requirements for identifying mass hierarchy using oscillograms






Inverted Mass HierarchyMuon Neutrino

beam


55 26


4





Muon anti-

Neutrino beam



5

5

5

5

5

5

27

Back-up

36° 20' 24'' North , 137° 19' 48'' East

SuperK

54° 20' 24'' South , 43° 19' 48'' West

29

30

sin2(2✓13) = 0.08 sin2(2✓13) = 0.1 sin2(2✓13) = 0.12

Probability in (Energy, ) plane✓

31

sin2(2✓13) = 0.1 sin2(2✓13) = 0.12sin2(2✓13) = 0.08

Probability in (Energy, ) plane✓

Mass Hierarchy Effect on the Event Rate

32



Mass Hierarchy Effect on the Event Rate

33



34

�CP = 0 �CP = ⇧/4 �CP = ⇧/2Normal H

Inverted H


35

�CP = ⇧/2�CP = ⇧/4�CP = 0Normal H

Inverted H


Neutrino Oscillation Phenomenology using atmospheric …Problem 29 • The neutrino oscillograms are...

Documents

Transcript of Neutrino Oscillation Phenomenology using atmospheric …Problem 29 • The neutrino oscillograms are...