T2K and Aggressive Oscillation

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Can the hint of

δ

CP

from T2K also indicate

the hierarchy and octant ?

Monojit Ghosh

Physical Research Laboratory Ahmedabad

XXI DAE-BRNS High Energy Physics Symposium IITG, 8-12 December, 2014

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Introduction

In neutrino oscillation one flavor evolves into another.

This is because the flavor eigenstates and mass eigenstates are not same and related by

|ναi=

N

X

i=1

Uαi|νii

Where U is the unitary PMNS matrix which diagonalize the neutrino mass matrix

mν =Umdiagν UT

wheremνdiag =diag(m1,m2,m3)

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Continue...

Neutrino oscillation also involves two independent mass squared difference i.e the solar mass square difference (m2₂−m2₁ = ∆21) and the atmospheric mass squared

difference (m2₃−m2₁= ∆31).

The undetermined sign of ∆31 give rise to two

possible mass orderings i.e. Normal

Hierarchy(NH i.e m3 >m1) and Inverted

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Unknowns

Hierarchy(NH or IH)

Octant of θ23(LO:θ23<45 or HO:θ23<45)

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Current status of

δ

CP

Recently, an indication forδCP = -90o has been obtained from T2K data

This hint comes from T2K running in the “neutrino mode” with 8% of the expected total flux of T2K (7.8×1021 _protons

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The question

In this work we ask the following questions: If the T2K hint of -90o is confirmed by the further T2K ‘neutrino’ runs, then can it indicate the true hierarchy and true octant ?

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The T2K experiment

T2K is a long-base experiment in Japan currently running in neutrino mode

νµ’s are shot from J-PARC towards 295 km away

Super-Kamiokande detector, which is a Water Cerenkov detector having mass 22.5 kt.

The flux peaks sharply at the first oscillation maxima around 0.6 GeV

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The appearance channel

For T2K, the probability relevant for the measurement of CP can be expressed in terms ofα= ∆21/∆31as

Pµe = 4s132 s232

sin2[(1−Aˆ)∆] (1−Aˆ)2 +

αsin 2θ13sin 2θ23cos (∆ +δCP)

sin ˆA∆ ˆ A

sin [(1−Aˆ)∆] (1−Aˆ)

∆ = ∆31L/4E = +ve for NH & -ve for IH

A= ˆA∆31= 0.76×10−4ρ(gm/cc)E(GeV)

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Degeneracies in

P

µe

The determination of CP in T2K is affected by degeneracies:

a)Hierarcy-δCP degeneracy i.e Pµe(δCP,NH) =Pµe(δ_CP0 ,IH)

b)Octant-δCP degeneracy i.ePµe(LO, δCP) =Pµe(HO, δCP0 )

Due to (a) and (b) there exist 3 fakesolutions: i)wrong hierarchy-right octant

ii)right hierarchy-wrong octant iii)wrong hierarchy-wrong octant

As for ¯ν, ˆAandδCP both changes sign, addition of ¯ν resolves

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CP Precision

True value: -90o(motivated by T2K hint)-NH-LO(39o),

χ2(= (Ntrue −Ntest)2/Ntrue) vsδCP(test) for differenttest

combinations of hierarchy and octant

8+0 correspond to running T2K in only ν mode with total

8×1021 POT 10 20 30 40 χ 2 T2K(8+0) True NH,True LO δCP(True)=-90o NH-LO NH-HO IH-LO IH-HO 3 best fits: -90, 0, 135 0, 135 arises due to the fake IH-HO and NH-HO solutions(wrong octant i.e HO(51o₎₎

Conclusion: If true

combination is NH-LO, then clear hint at -90 is

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The same fig plotted for all 4 possible true combinations i.e NH-LO, NH-HO, IH-LO, IH-HO

T2K config: 8+0 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2 True NH, True LO δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2 True NH, True HO δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2

True IH, True LO

δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2

True IH, True HO

δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO

Only NH-HO gives clear hint at -90

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Impact of anti-neutrino run

T2K config: 4+4 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2 True NH, True LO δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2 True NH, True HO δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2

True IH, True LO

δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO 0 10 20 30 40 -180 -120 -60 0 60 120 180 δCP (Test) χ 2

True IH, True HO

δCP (True) = -90o NH-LO NH-HO IH-LO IH-HO ¯

ν removes the wrong octant fits but not wrong hierarchy fits 2nd panel remains unaltered as it does not have any wrong octant best fit

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The CP violation discovery

χ

2

To quantify the ¯ν run we study CPV discovery The CPV discoveryχ2 is defined as

χ2= min(Nex(δ

tr

CP)−Nth(δCPtest = 0,180o))2 Nex(δtr_CP)

χ2 = 0 atδtr_CP = 0&180(CP conserving values) = max atδ_CPtr =±90

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CPV discovery χ2 is plotted vsδCP(true) for all 4 possible

true combinations 0 2 4 6 8 -180 -120 -60 0 60 120 180 δCP (True) χ 2 NH, LO 4+4 8+0 5+3 6+2 7+1 0 2 4 6 8 -180 -120 -60 0 60 120 180 δCP (True) χ 2 NH, HO 4+4 8+0 5+3 6+2 7+1 0 2 4 6 8 -180 -120 -60 0 60 120 180 δCP (True) χ 2 IH, LO 4+4 8+0 5+3 6+2 7+1 0 2 4 6 8 -180 -120 -60 0 60 120 180 δCP (True) χ 2 IH, HO 4+4 8+0 5+3 6+2 7+1

For NH-HO and IH-HO, 8+0 is best: addition of ¯ν reduce sensitivity

For NH-LO, 5+3 and for IH-HO 6+2 is best: further addition of ¯ν reduce sensitivity

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The Answer

In conclusion we give the following answers:

If T2K runs only in ν mode and givesδCP = -90, then true

hierarchy is NH and true octant is HO

If T2K runs in equal ν-¯ν mode and givesδCP = -90, then true

hierarchy is NH ¯

ν only removes wrong octant solution if it is present otherwise it reduces sensitivity

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The Answer

In conclusion we give the following answers:

If T2K runs only in ν mode and givesδCP = -90, then true

hierarchy is NH and true octant is HO

If T2K runs in equal ν-¯ν mode and givesδCP = -90, then true

hierarchy is NH ¯

ν only removes wrong octant soluion if it is present otherwise it reduces sensitivity