Non-standard in tf rac tj ons in atmospheric neu ts ino experiments - - PowerPoint PPT Presentation

Non-standard intfractjons in atmospheric neutsino experiments

Arman Esmaili

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Brasil

Standard high energy atm oscillation

✔

Arman Esmaili PANE 2018 @ ICTP 29/May/2018 The standard oscillation of neutrinos disappear with the increase

• f energy

sin2 2θm ∝ 1 (2 √ 2GF Eνne)2 → 0

For νe (although the osc. length converges to the refraction length ~ Earth’s radius): For νµ and ντ the mixing angle is unsuppressed, but the osc. length increases with energy and becomes much larger than the Earth’s diameter.

For energies >~ 100 GeV, no standard oscillation

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

Any oscillation at energies >~ 100 GeV can testify NSI (generally new physics)

✔ Oscillation in the presence of NSI (for anti-nu: V -> -V and U -> U*)

H3ν = 1 2Eν UPMNS @ ∆m2

21

∆m2

31

1 A U †

PMNS +

@ √ 2GF ne 1 A + X

f

Vf✏f

Vf = √ 2GF nf

where

✏f =   ✏f

ee

✏f

eµ

✏f

eτ

✏f∗

eµ

✏f

µµ

✏f

µτ

✏f∗

eτ

✏f∗

µτ

✏f

ττ

 

and

να + f → νβ + f

✏f

αβ

quantifies

VCC

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Normalizing by the d-quark density

✏ = X

f

nf nd ✏f

X

f

Vf✏f = 3✏VCC

✓nd ne ' 3 ◆

H3ν = 1 2Eν UPMNS   ∆m2

21

∆m2

31

  U †

PMNS +

  √ 2GF ne   + 3VCC ✏

✏ =   ✏ee ✏eµ ✏eτ ✏∗

eµ

✏µµ ✏µτ ✏∗

eτ

✏∗

µτ

✏ττ  

where

✏αβ = ✏∗

αβ

and we assume:

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Two-neutrino approximation:

✏ee, ✏eµ, ✏eτ ⌧ 1

for and Eν > Eres,13 (>~ 20 GeV)

ν3m ' νe and ¯ ν1m ' ¯ νe

The two-neutrino approximation can be used

H2ν = ∆m2

31

2Eν U(✓23) ✓ 0 1 ◆ U(✓23)† + Vd ✓ ✏µµ ✏µτ ✏µτ ✏ττ ◆

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔At the very high energy

H2ν = ∆m2

31

2Eν U(✓23) ✓ 0 1 ◆ U(✓23)† + Vd ✓ ✏µµ ✏µτ ✏µτ ✏ττ ◆

∆m2

31

2Eν ⌧ Vd✏αβ

Oscillation is completely matter dominated Diagonalizing:

sin 2⇠ = 2✏µτ q 4✏2

µτ + ✏02

∆Hm = VNSI = Vd q 4✏2

µτ + ✏02

mixing angle level splitting ɛ’ = ɛττ - ɛµµ

P(⌫µ → ⌫τ) = sin2 2⇠ sin2 ✓V dL 2 q 4✏2

µτ + ✏02

◆

• Osc. Prob.

φmatt

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ With the decrease of ɛ the potential VNSI and the matter phase decrease.

When ϕmatt << 1

matt = 35 ✓ ¯ ⇢ 5.5 g cm3 ◆ ✓ L 2R ◆ q 4✏2

µτ + ✏02

P(⌫µ → ⌫τ) ≈ (✏µτV dL)2

No dependence on ɛ’ : With the high energy neutrinos we can just constrain ɛµτ No dependence on the sign of ɛµτ. The same result for anti-neutrinos.

✔ ✔

Estimating the sensitivity to ɛµτ ✏µτ = 1 V dL q P(⌫µ → ⌫µ)

10% accuracy of P -> ɛµτ ~ 5x10-3 1% accuracy of P -> ɛµτ ~ 2x10-3

restricted sensitivity: quadratic dependence Akhmedov 2001

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

H2ν = ∆m2

31

2Eν  U(θ23) ✓ 0 1 ◆ U(θ23)† + R0U(ξ) ✓ 0 1 ◆ U(ξ)†

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R0 ≡ 2EνVNSI ∆m2

31

= √ 2GF nd q 4✏2

µτ + ✏02 2Eν

∆m2

31

where

relative strength of matter and vacuum contributions

R0 = 0.5 ✓ ¯ ⇢ 5.5 g cm3 ◆ ✓ Eν GeV ◆ q 4✏2

µτ + ✏02

the value Diagonalizing:

∆Hm = ∆m2

31

2Eν R

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

where

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

H2ν = ∆m2

31

2Eν  U(θ23) ✓ 0 1 ◆ U(θ23)† + R0U(ξ) ✓ 0 1 ◆ U(ξ)†

• <latexit sha1_base64="/AZj+EJ3qVN2rgDT7f04n3JTBck=">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</latexit><latexit sha1_base64="/AZj+EJ3qVN2rgDT7f04n3JTBck=">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</latexit><latexit sha1_base64="/AZj+EJ3qVN2rgDT7f04n3JTBck=">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</latexit>

Oscillation half-phase

Φm = ∆Hm L 2 = ✓∆m2

31L

4Eν ◆ ⇥ 1 + R2

0 + 2R0 cos 2(θ23 − ξ)

⇤1/2

Φm = (φvac + φmatt) s 1 − 2R0 (1 + R0)2 [1 − cos 2(θ23 − ξ)]

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

Oscillation probability

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

&

✏µτ → −✏µτ

ξ → −ξ

✏0 → −✏0

cos 2(θ23 − ξ) → − cos 2(θ23 + ξ)

✏µτ → −✏µτ

✏0 → −✏0

&

R0 → −R0

anti-neutrinos

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

& Resonance condition

R0 = − cos 2(θ23 − ξ)

minimum value of resonance factor

ξ = 0

MSW resonance

ER = − ∆m2

31

2Vd q 4✏2

µτ + ✏02 cos 2(✓23 − ⇠)

Resonance energy

✏αβ = 10−2

ER ' 100 GeV

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

& What happens in the Resonance? In the resonance:

R2 = sin2 2(θ23 − ξ) = 1 − R2

sin2 2Θm = cos2 2ξ

(ξ = 0 → sin2 2Θm = 1)

(ξ = π/4 → sin2 2Θm = 0)

The two limits: &

MSW matter dominated

• Osc. phase in

the Resonance

Φm = ∆m2

31L

4E sin 2(θ23 − ξ)

✏ > 0

anti-neutrino neutrino

✏ < 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

& What happens in the Resonance? Maximal interplay between vacuum and NSI E ' ER

• r

R0 = 1

E ' ER

In the range The probability depends linearly on ɛ

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

& R0 quantifies the relative effect of NSI

R0 → 0

Low energies

ξ → 0 and R → 1

vacuum osc. recovers

sin2 2Θm = sin 2θ23, ∆Hm → ∆m2

31

2Eν , Φm → ∆m2

31L

4Eν

High energies

R0 → ∞

R → R0

matter dominated

• sc. recovers

sin 2Θm → sin 2ξ, ∆Hm → VNSI

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ In the general case:

P(νµ → νµ) = 1 − sin2 2Θm sin2 ✓∆m2

31L

4Eν R ◆

• Osc. prob.

R2 = [R0 + cos 2(θ23 − ξ)]2 + sin2 2(θ23 − ξ)

sin2 2Θm = 1 R2 (sin 2θ23 + R0 sin 2ξ)2

&

With the decrease of ɛ the energy where the NSI effect becomes dominating increases

Also: lm ∝ 1/∆Hm ∼ 1/✏

At very small ɛ the oscillation length becomes much larger than the Earth’s diameter

P(νµ → νµ) = 1 − (sin 2θ23 + R0 sin 2ξ)2 · ✓∆m2

31L

4Eν ◆2

In this case:

For ξ = 0 the “vacuum mimicking” result can be

• btained (Akhmedov 2001)

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

In this case sin 2ξ = 1, and: sin2 2Θm =

1 1 + cos2 2θ23(R0 + sin 2θ23)−2

converges to maximal for large R0 The resonance factor becomes

R2 = [R0 + sin 2θ23]2 + cos2 2θ23

In the resonance

Φm = ∆m2

31L

4Eν cos 2θ23

Far from the resonance

Φm ≈ vac + matt = ∆m2

32L(1 + R0)

4Eν = ∆m2

32L

4Eν + VdL✏µτ

modification of the phase is energy independent

matt = 70 ✓ ¯ ⇢ 5.5 g cm−3 ◆ ✓ L 2R⊕ ◆ ✏µτ

In the high energy the vacuum term is negligible, while:

✏µτ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

For cos θz = -1

matt = 62✏µτ

φmatt = π/2

minimum of muon survival prob.

✏µτ = 2.5 × 10−2

cos θz = -1

For ✏µτ & 2.5 × 10−2

the minimum of probability occurs at cos θz > -1

✔ In asymptotic, i.e. high energies or very small ɛµτ, we have: P = 𝜚2matt.

✏µτ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

cos Θz 1 10 20 50 100 200 500 1000 0.0 0.2 0.4 0.6 0.8 1.0 EΝ GeV PΝΜ ΝΜ

ΕΜΤ 0.01 , Ε 0 ΕΜΤ Ε 0

cos Θz 1 10 20 50 100 200 500 1000 0.0 0.2 0.4 0.6 0.8 1.0 EΝ GeV PΝΜ ΝΜ

ΕΜΤ 0.01 , Ε 0 ΕΜΤ Ε 0

Equivalent to negative ɛµτ

✔

For Ev < 100 GeV, the NSI leads to shift of the oscillatory pattern to lower (neutrino) and higher (anti-neutrino) energies for ɛµτ > 0 .

✔ A small change in the depth of minimum, due to the change in mixing angle. ✔ In the resonance, ER ~ 60 GeV, the mixing is zero, sin Θm = 0 —> no osc. for anti-neutrino. ✔

With the increase of energy, both nu and anti-nu oscillation probabilities converge to the same asymptotic value, P = 𝜚2matt.

✏µτ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

P(νµ → νµ)

✏µτ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

✏ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Equivalent to anti-nu

P(νµ → νµ)

resonance matter dominated

• scillation

(sin2 2Θm = 0)

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor off-diagonal NSI (Universal NSI)

P(νµ → νµ)

P STD(⌫µ → ⌫µ) − P(⌫µ → ⌫µ; {✏µτ, ✏0 = 0})

the difference change sign

Equivalent to anti-nu

Ev,min = 38 GeV Ev,min = 18 GeV

depth decreases

(nu+anti-nu) decreases the sensitivity Energy integration decreases the sensitivity

✏µτ 6= 0 , ✏0 = ✏ττ ✏µµ = 0

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor conserving NSI (non-Universal NSI)

In this case sin 2ξ = 0, and the mixing and mass-splitting formulas can be obtained from the usual MSW formulas with the potential VNSI = Vd ɛ’. Where resonance condition R0 = -cos 2θ23

✏µτ = 0 , ✏0 = ✏ττ ✏µµ 6= 0

sin2 2Θm = sin2 2θ23 (R0 + cos 2θ23)2 + sin2 2θ23

∆Hm = ∆m2

31

2E ⇥ (R0 + cos 2θ23)2 + sin2 2θ23 ⇤1/2

and

R0 = 0.5 ✓ ¯ ⇢(✓z) 5.5 g cm3 ◆ ✓ Eν GeV ◆ ✏0

ER = 2 GeV ✓5.5 g cm3 ¯ ⇢(✓z) ◆ ✓cos 2✓23 ✏0 ◆

For small ɛ’ = 5x10-2, ER ~ 10 GeV for mantle crossing trajectories. However, the resonance enhancement of oscillation is very weak because the mixing angle is already large. The main effect of NSI is the suppression of oscillation at Ev > ER .

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor conserving NSI (non-Universal NSI)

For the core-crossing neutrinos (cos θz = -1), approximately:

✏µτ = 0 , ✏0 = ✏ττ ✏µµ 6= 0

Φm = 38 ✓GeV Eν ◆ s 1 + cos 2✓23 ✓ Eν GeV ◆ ✏0 + 0.25 ✓ Eν GeV ◆2 ✏02

sin2 2Θm = sin2 2✓23 1 + cos 2✓23 Eν

GeV

• ✏0 + 0.25

Eν

GeV

2 ✏02

small in high energies

approximating the sensitivity to ɛ’ : the effect is linear in ɛ’ with a coefficient given by:

≡ 2 cos 2✓23R0 = 2✏0 cos 2✓232EνVd ∆m2

31

For maximal 2-3 mixing the linear term is zero and the effect is very small (ɛ’2)

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor conserving NSI (non-Universal NSI)

In the linear approximation of 𝜺,

✏µτ = 0 , ✏0 = ✏ττ ✏µµ 6= 0

∆P ≈ δ

• − sin2 φvac + φvac sin φvac cos φvac
• <latexit sha1_base64="E1g4IA9g6JOyZ+FTRnkr6HiYsM=">ACX3icbZFPbxMxEMW92wJp6J8FToiLRYRUhIg2FRJwqygHjqnUtJXiEM06s4lVr23Zs4VolS/JjUMvfBKcNAdIOpKlp9+80djPhdMqUJ7/TtKd3UePn7T2k/3Dw6PsmfPL4OtvcSBtNr6wICamVwQIo0XjuPUBUar4qbs2X/6hZ9UNZc0NzhqIKpUaWSQBGNsx/iK2oC3ucCnP2JxeTFRAaSzp+z0VQ5vsJF26mxo3wFb8FueDveHuDLH2bLiFt2GJeTWf0dpx18m6+Kr4temvRYevqj7NfYmJlXaEhqSGEYS93NGrAk5IaF21RB3Qgb2CKwygNVBhGzSqgBX8TyYSX1sdjiK/ovxMNVCHMqyI6K6BZ2Owt4UO9YU3lp1GjKsJjbxfVNak+XLtPlEeZSk51GA9CrelcsZeJAU/6QdQ+htPnlbDE6n7v5+YfO6Zd1Gi32ir1mx6zHPrJT9o312YBJdpfsJPvJQfInbaWHaXZvTZP1zAv2X6Uv/wIuRbS</latexit><latexit sha1_base64="E1g4IA9g6JOyZ+FTRnkr6HiYsM=">ACX3icbZFPbxMxEMW92wJp6J8FToiLRYRUhIg2FRJwqygHjqnUtJXiEM06s4lVr23Zs4VolS/JjUMvfBKcNAdIOpKlp9+80djPhdMqUJ7/TtKd3UePn7T2k/3Dw6PsmfPL4OtvcSBtNr6wICamVwQIo0XjuPUBUar4qbs2X/6hZ9UNZc0NzhqIKpUaWSQBGNsx/iK2oC3ucCnP2JxeTFRAaSzp+z0VQ5vsJF26mxo3wFb8FueDveHuDLH2bLiFt2GJeTWf0dpx18m6+Kr4temvRYevqj7NfYmJlXaEhqSGEYS93NGrAk5IaF21RB3Qgb2CKwygNVBhGzSqgBX8TyYSX1sdjiK/ovxMNVCHMqyI6K6BZ2Owt4UO9YU3lp1GjKsJjbxfVNak+XLtPlEeZSk51GA9CrelcsZeJAU/6QdQ+htPnlbDE6n7v5+YfO6Zd1Gi32ir1mx6zHPrJT9o312YBJdpfsJPvJQfInbaWHaXZvTZP1zAv2X6Uv/wIuRbS</latexit><latexit sha1_base64="E1g4IA9g6JOyZ+FTRnkr6HiYsM=">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</latexit>

✏0 ∼ ∆P ∆m2

31

2EνVd

• − sin2 vac + vac sin vac cos vac

1

sensitivity

10% accuracy of P and Ev = 30 GeV -> ɛ’ ~ 2x10-2

Non-standard neutrino interactions

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Flavor conserving NSI (non-Universal NSI)

✏µτ = 0 , ✏0 = ✏ττ ✏µµ 6= 0

P(νµ → νµ)

P STD(⌫µ → ⌫µ) − P(⌫µ → ⌫µ; {✏µτ, ✏0 = 0})

The important energy range (20 — 40) GeV Stronger effect for positive ɛ’

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ SuperKamiokande, µ-τ sector ✔ 1 GeV < Ev < 30 GeV (lower and higher also

included)

SK collaboration, 2011

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ IC-79 dataset + DeepCore data, µ-τ sector ✔ (100 GeV - 10 TeV) + (20 GeV - 100 GeV)

A.E., Alexei Smirnov, 2013

✔ Considering both ve -> vµ and vµ -> vµ

• 0.01

0.01 0.1 0.1 ΕΜΤ Ε

SK , 90 C.L. IC40 , 90 C.L. IC79 , 90 C.L.

• b.f. , SK
• b.f. , IC40
• b.f. , IC79

Marginalized 1-D limits (90% C.L.):

−6.1 × 10−3 < ✏µτ < 5.6 × 10−3

−3.6 × 102 < ✏0 < 3.1 × 102

see also Salvado et al., 2016

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ IC-79 dataset + DeepCore data, µ-τ sector

A.E., Alexei Smirnov, 2013

1.0 0.8 0.6 0.4 0.2 0.0 1000 2000 3000 4000 5000 6000 7000 8000 cos Θz number of events

ΕΜΤ 102 , Ε 0 ΕΜΤ 0 , Ε 0

data

1.0 0.8 0.6 0.4 0.2 0.0 1000 2000 3000 4000 5000 6000 7000 8000 cos Θz number of events

ΕΜΤ 102 , Ε 0 ΕΜΤ 0 , Ε 0

data

1.0 0.8 0.6 0.4 0.2 0.0 20 40 60 80 100 120 cos Θz number of events

ΕΜΤ 102 , Ε 0 ΕΜΤ 0 , Ε 0

data

1.0 0.8 0.6 0.4 0.2 0.0 20 40 60 80 100 120 cos Θz number of events

ΕΜΤ 0 , Ε 5102 ΕΜΤ 0 , Ε 0

data

High energy data 100 GeV - 100 TeV Low energy data 20 GeV - 100 GeV

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ IceCube collaboration results (1 NSI parameter analysis, ɛµτ):

Three years DeepCore data

IceCube collaboration, 2017

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ IceCube collaboration results (1 NSI parameter analysis, ɛµτ):

Three years DeepCore data

IceCube collaboration, 2017

90% CL, A.E., A. Yu. Smirnov

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ 3 years of DeepCore data (future reach)

• 0.01

0.01 0.1 0.1 ΕΜΤ Ε

SK , 90 C.L. IC79 , 90 C.L. DC , 90 C.L.

• b.f. , SK
• b.f. , IC79

A.E., Alexei Smirnov, 2013

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Disentangling between NSI and eV-scale sterile neutrino

A.E., Alexei Smirnov, 2013

EΝ20,40 GeV

1.0 0.8 0.6 0.4 0.2 0.0 0.8 0.9 1.0 1.1 1.2 1.3 1.4 cos Θz ratio

NSI, ΕΜΤ0.005 , Ε0 Sterile, m41

2 1 eV2 , sin22ΘΜΜ0.1

EΝ2560,5120 GeV

1.0 0.8 0.6 0.4 0.2 0.0 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 cos Θz ratio

NSI, ΕΜΤ0.005 , Ε0 Sterile, m41

2 1 eV2 , sin22ΘΜΜ0.1

In the energy bin containing the minimum

• f vµ survival probability, the NSI shifts

the minimum. In the energy bin containing the MSW resonance vµ -> vs, there is a strong suppression of signal compared to the NSI effect.

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Future sensitivity (PINGU, 3 years)

• S. Choubey, T. Ohlsson, 2014

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Opening up the e-tau sector:

• A. Friedland, C. Lunardini, 2004
• A. Friedland, C. Lunardini, M. Maltoni, 2005

✏ττ = |✏eτ|2 1 + ✏ee

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Opening up the e-tau sector:

• A. Friedland, C. Lunardini, 2004
• A. Friedland, C. Lunardini, M. Maltoni, 2005

✏ττ = |✏eτ|2 1 + ✏ee

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ Opening up the e-tau sector:

6 GeV - 80 TeV

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

✔ More general analysis:

• I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. Salvado; arXiv:1805.04530

Thank you !

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

N = T(2π) Z Aν

eff(Eν, cos θz)Φν(Eν, cos θz) dEν d cos θz + (ν → ¯

ν)

• Constraining sterile neutrino with IC-40 data

(atm flux (Honda+Volkova

102 103 104 105 104 103 102 101 1 10 102 EΝ GeV Aeff

Ν m2

IceCube40 ΝΜ effective area

0.5 cosΘz 0.4 0.4 cosΘz 0.3 0.3 cosΘz 0.2 0.2 cosΘz 0.1 0.1 cosΘz 0

102 103 104 105 104 103 102 101 1 10 102 EΝ GeV Aeff

Ν m2

IceCube40 ΝΜ effective area

0.5 cosΘz 0.4 0.4 cosΘz 0.3 0.3 cosΘz 0.2 0.2 cosΘz 0.1 0.1 cosΘz 0

102 103 104 105 104 103 102 101 1 10 102 EΝ GeV Aeff

Ν m2

IceCube40 ΝΜ effective area

1 cosΘz 0.9 0.9 cosΘz 0.8 0.8 cosΘz 0.7 0.7 cosΘz 0.6 0.6 cosΘz 0.5

102 103 104 105 104 103 102 101 1 10 102 EΝ GeV Aeff

Ν m2

IceCube40 ΝΜ effective area

1 cosΘz 0.9 0.9 cosΘz 0.8 0.8 cosΘz 0.7 0.7 cosΘz 0.6 0.6 cosΘz 0.5

• A. E., F. Halzen and O. L. G. Peres,

JCAP 1211 (2012) 041

Arman Esmaili PANE 2018 @ ICTP 29/May/2018

IceCube sensitivity to sterile neutrinos (muon-track events)

✔ We analyzed the zenith distribution of muon-track events

Nµ(θ24) Nµ(θ24 = 0)

uncertainty 24% ~

↻ ↺

uncertainty 4% ~

χ2(∆m2

41, θ24; α, β) =

X

i

{Ni(θ24 = 0) − α[1 + β(0.5 + (cos θz)i)]Ni(θ24)}2 σ2

i,stat + σ2 i,sys

+ (1 − α)2 σ2

α

+ β2 σ2

β

sin2 2Θ24 0.04

1.0 0.8 0.6 0.4 0.2 0.0 0.94 0.96 0.98 1.00 1.02 1.04 1.06 cos Θz ratio

m41

2 1 eV2

m41

2 0.5 eV2

Arman Esmaili PANE 2018 @ ICTP 29/May/2018