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Probing the intrinsic Lorentz Invariance Violation with DUNE

Mehedi Masud(IFIC-CSIC, U. Valencia)

(work done with G. Barenboim, C. A. Ternes, M. Tortola: PLB(2018))

DISCRETE2018, Austrian Academy of Sciences, Vienna, November 27, 2018

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 1 / 22

Table of contents

Background: Lorentz Invariance Violation (LIV) model Effect of LIV in the probability level Simulation Result: Correlations in the new parameter space Result: New/ improved constraints on LIV parameters Conclusion

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 2 / 22

Present status of oscillation parameters

Table: de Salas, Forero, Ternes, Tortola, Valle: 1708.01186

Oscillation parameter Best fit value 3σ range θ12/◦ 34.5 31.5 → 38.0 θ23/◦ 47.7 41.8 → 50.4 θ13/◦ 8.45 8.0 → 8.9 δCP/π −0.68 [−π, π] ∆m2

21/10−5eV 2

7.55 7.05 → 8.14 ∆m2

31/10−3eV 2

2.5 2.41 → 2.6

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 3 / 22

Theory background (Kostelecky et al. (2012)

L = 1

2 ¯

Ψ(i / ∂ − M + ˆ Q)Ψ + h.c. with Ψ = (νe, νµ, ντ, νC

e , νC µ , νC τ )T

ˆ Q is a general Lorentz violating operator: ˆ Q = ˆ S + iPγ5 + ˆ νλγλ + ˆ Aλγ5γλ + 1

2 ˆ

T λησλη LLIV = − 1

2

• aµ

αβ ¯

ψαγµψβ + bµ

αβ ¯

ψαγ5γµψβ − icµν

αβ ¯

ψαγµ∂νψβ − idµν

αβ ¯

ψαγ5γµ∂νψβ

• CP-odd LIV: (aL)µ

αβ = (a + b)µ αβ → probed in our analysis

CP-even LIV: (cL)µν

αβ = (c + d)µν αβ → already constrained tightly (Kostelecky et al.). Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 4 / 22

Theory background (Kostelecky et al. (2012)

H = Hvac + Hmat + HLIV, Hvac =

1 2E U

  ∆m2

21

∆m2

31

  U†, Hmat = A   1   HLIV =   aee aeµ aeτ a∗

eµ

aµµ aµτ a∗

eτ

a∗

µτ

aττ   − 4

3E

  cee ceµ ceτ c∗

eµ

cµµ cµτ c∗

eτ

c∗

µτ

cττ  

• not considered

Similar to: H = Hvac + Hmat + HNSI where, HNSI = √ 2GFNe   ǫee ǫeµ ǫeτ ǫ∗

eµ

ǫµµ ǫµτ ǫ∗

eτ

ǫ∗

µτ

ǫττ   aαβ ↔ √ 2GFNeǫαβ But LIV is an intrinsic effect and nonzero even in vacuum NSI is an exotic matter effect, not present in vacuum

(Diaz (2015)) Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 5 / 22

What is DUNE (Deep Underground Neutrino Experiment)?

• R. Acciarri et. al.(DUNE Collaboration): 1512.06148

A proposed long baseline experiment (the erstwhile LBNE) with 1300 km baseline likely to have a 40 kt FD with 3.5 yrs. of ν and 3.5 yrs. of ¯ ν run. The incident νµ beam is generated by 80 GeV proton beam delivered at 1.07 MW with a POT of 1.47 × 1021 Total exposure : 300 kt-MW-yr.

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 6 / 22

Simulation

We use GLoBES and the latest configuration files (Alion et al. (2016)) Modify the GLoBES add-on snu.c to implement LIV scenario ∆χ2 ≃

channels

• i

bins

• j

[Nij

true(SI) − Nij test(aαβ)]2

Nij

true(SI)

∆χ2

total = ∆χ2 νµ→νe

+ ∆χ2

¯ νµ→¯ νe

+ ∆χ2

νµ→νµ

+ ∆χ2

¯ νµ→¯ νµ

marginalisation over θ23, δCP, ∆m2

31 and hierarchy and the phase φαβ Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 7 / 22

Impact of LIV parameters (non-diagonal) at probability level

Top row: PSI

µe (black) and PLIV µe (red), Bottom row: |PLIV µe − PSI µe|

aeµ and aeτ modify Pµe in opposite direction. aµτ has very small effect on νe appearance channel.

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 8 / 22

Impact of LIV parameters (diagonal) at probability

Top row: PSI

µe (black) and PLIV µe (red), Bottom row: |PLIV µe − PSI µe|

aee and aµµ increase or decrease the probability depending on the sign.

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 9 / 22

Constraining LIV-SI parameter space

Shows the correlations between aαβ and standard oscillation parameters (δ, θ23) The sensitivity to δ gets modified in presence of aeτ

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 10 / 22

Constraining LIV-SI parameter space

Shows the correlations between aαα and standard oscillation parameters New degeneracy around aee ≈ −22 × 10−23 GeV : - an effect of marginalisation

• ver both mass orderings.

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 11 / 22

Correlations among LIV parameters (aαα vs. aαβ)

New degeneracy around aee ≈ −22 × 10−23 GeV aee − aeτ correlation: A pair of linear branches around aee ≈ 0 and ≈ −22 × 10−23 GeV = ⇒ a consequence of (aee − |aeτ|)-like term.

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 12 / 22

Correlations among LIV parameters

Indication of |aeµ| and |aeτ| acting in opposite directions is apparent

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 13 / 22

• ne dimensional projection for the LIV parameters

95% C.L.

Δχ2

2 4 6 8 10

aee [10-23 GeV]

−40 −20 20 95% C.L.

aμμ [10-23 GeV]

−10 −5 5 10 95% C.L.

Δχ2

2 4 6 8 10

|aeμ| [10-23 GeV]

0.5 1 1.5 2 2.5 3 95% C.L.

|aeτ| [10-23 GeV]

0.5 1 1.5 2 2.5 3 95% C.L.

|aμτ| [10-23 GeV]

0.5 1 1.5 2 2.5 3

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 14 / 22

Constraints on LIV parameters

Parameter Existing bounds Our work

(Abe et al. 2015 (SK collab.))

|aeµ| [GeV] 2.5 × 10−23 7 × 10−24 |aeτ| [GeV] 5 × 10−23 1 × 10−23 |aµτ| [GeV] 8.3 × 10−24 1.7 × 10−23 aee [GeV] − −2.5 × 10−22 < aee < −2 × 10−22 and −2.5 × 10−23 < aee < 3.2 × 10−23 aµµ [GeV] − −3.7 × 10−23 < aµµ < 4.8 × 10−23 3 times Improvement of bound for |aeµ| and 5 times for |aeτ|

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 15 / 22

Conclusion

Realization of a Plank suppressed effect such as LIV in a much anticipated neutrino experiment Correlations in the new LIV parameter space Improvement of the bounds on eµ and eτ sector LIV parameters New bounds on diagonal LIV parameters aee and aµµ

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 16 / 22

Thank You!

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 17 / 22

Backup

∆Pµe(εeµ) = PNSI

µe (εeµ) − PSI µe

≈ −4A∆ sin ∆|εeµ|s13s2(23)c23Deµ

1

sin(δ + ϕeµ − γeµ

1 )

& ∆Pµe(εeτ) ≈ 4A∆ sin ∆|εeτ|s13s2(23)s23Deτ

1 sin(δ + ϕeτ + γeτ 1 )

where, Deµ

1

= [sin2 ∆ + (tan2 θ23 sin ∆ ∆ + cos ∆)2]1/2 γeµ

1

= tan−1(tan2 θ23 ∆ + cot ∆) Deτ

1

= [sin2 ∆ + (sin ∆ ∆ − cos ∆)2]1/2; γeτ

1

= tan−1( 1 ∆ − cot ∆)

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 18 / 22

Backup

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25 0.3

E [GeV] |εeµ|

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

|εeτ|

0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

|εµτ|

0.05 0.1 0.15 0.2 0.25 0.3-0.3

• 0.2
• 0.1

0.1 0.2 0.3

εee

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3-0.3

• 0.2
• 0.1

0.1 0.2 0.3

|∆Pµµ| εττ

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 1 2 3 4 5 6 7 8 9 10

E [GeV]

1 2 3 4 5 6 7 8 9 10

|∆P| |∆Pµe|

0.005 0.01 0.015 0.02

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 19 / 22

Backup

5 GeV 2.5 GeV

D1

eμ

D1

eτ

0.5 1 1.5 2 2.5

E [GeV]

2 4 6 8 10

5 GeV 2.5 GeV

γ1

eμ / π

γ1

eτ / π

−0.4 −0.2 0.2 0.4

E [GeV]

2 4 6 8 10

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 20 / 22

Backup

ˆ Q = ˆ S + iPγ5 + ˆ νλγλ + ˆ Aλγ5γλ + 1

2 ˆ

T λησλη

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 21 / 22

Backup

hab = Eδab + (mab)2 2E + (aL)α

abpα − (cL)α abpαpβE

h¯

a¯ b = Eδ¯ a¯ b + (m¯ a¯ b)2

2E + (aL)α

¯ a¯ bpα − (cR)α ¯ a¯ bpαpβE

ha¯

b ∼ i

√ 2(Hα

a¯ b − gαβ a¯ b pβE)

(1)

Mehedi Masud(IFIC-CSIC, U. Valencia) (work done with G. Barenboim, C. A. Ternes, Probing the intrinsic Lorentz Invariance Violation with DUNE 22 / 22