NSI Sensitivities: Octant-NSI degeneracy N. R. Khan Chowdhury, Tarak - - PowerPoint PPT Presentation

NSI Sensitivities: Octant-NSI degeneracy

• N. R. Khan Chowdhury, Tarak Thakore

May 9, 2019 | N. R. Khan Chowdhury | Weekly Meeting | IFIC, Valencia |

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Sensitivity in the Hybrid model: 𝛇𝜈𝜐 , Normal Ordering

Proposed public plot Runtime comparisons: ORCA: 3 years IceCube: 3 years (5174 events) Super Kamiokande I (1996- 2001) and II (2003-2005) 2 Flavor Hybrid model approximation, 𝜾12, 𝜾13, 𝜠m2

12 = 0; Fixed in the fit.

𝛇ei = 0.

90% CL May 8, 2019 | N. R. Khan Chowdhury | Group Meeting | IFIC, Valencia |

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2 Flavor Hybrid model approximation, 𝜾12, 𝜾13, 𝜠m2

12 = 0; Fixed in the fit.

𝛇ei = 0.

Correlated sensitivities in the Hybrid Model: NO

Proposed public plot

May 8, 2019 | N. R. Khan Chowdhury | Group Meeting | IFIC, Valencia |

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3 Flavor Hybrid model approximation, 𝜾12, 𝜾13, 𝜠m2

12 = 0; Fixed in the fit.

𝛇𝜈i = 0.

Correlated sensitivities in the Hybrid Model: NO

Old Plot New Plot New Plot 𝞋ee = 0 Proposed public plot

May 8, 2019 | N. R. Khan Chowdhury | Group Meeting | IFIC, Valencia |

Chi_sq table for different theta23 starting points

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Theta23 (true) Eps_mt (test) Theta23 (start) Theta23 (fitted) Chi_sq (stat) Chi_sq (min) 47.2

• 0.001

42.8 43.92 2.28 0.94869 45 46.06 0.94867 47.2 46.08 0.94869 1) Although the starting values and the fitted values of theta23 are different, the minimised chi_sq are almost similar for a given true value of theta23. 2) If you compare a row 1 with row 3, although the fitted values of theta23 are in different

• ctants, the minimised chi_sq is same since rest of the fitted parameter values are same

and there is no prior on theta_23 leading to the exact same value of minimised chi_sq.

Chi_sq table for different theta23 starting points

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Theta23 (true) Eps_mt (test) Theta23 (start) Theta_23 (fitted) Chi_sq (stat) Chi_sq (min) 47.2

• 0.001

42.8 43.92 2.28 0.94869 45 46.06 0.94867 47.2 46.08 0.94869 This implies for a value of Eps_mt = -0.01, there are 2 minima for theta23 = 43.92 & 46.08

• degrees. Surprisingly, the rest of the fitted parameters came out of exactly similar.

Let’s consider the case when the rest of the systematic parameters are fixed. So theta23 is only varied in the fit with different starting points.

Chi_sq table for different theta23 starting points

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Theta23 (true) Eps_mt (test) Theta23 (start) Theta23 (fitted) Chi_sq (stat) Chi_sq (min) 47.2

• 0.001

42.8 43.37 2.28 1.86831 45 46.62 1.86827 47.2 46.63 1.86831 1) Although the starting values and the fitted values of theta_23 are different, the minimised chi_sq are almost similar. 2) Chi_sq value is again exactly similar for 2 values of theta23 in either octants. Rest of the systematics parameters are fixed. This leads to the uncertainty of chosing the starting point of the fit in case of sea data!

Statistical sens. using fitted theta23 values

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| NSI (Eps_mt=-0.001, theta23 = 43.37) - STD (theta23=47.2) |

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| NSI (Eps_mt=-0.001, theta23 = 46.63) - STD (theta23=47.2) |

Statistical sens. using fitted theta23 values

Chi_sq table for different true theta23 values

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Theta23 (true) Eps_mt (test) Theta23 (start) Theta23 (fitted) Chi_sq (stat) Chi_sq (min) 47.2

• 0.001

47.2 46.63 2.28 1.86831 45 45 45 2.29 2.29747 42.8 42.8 43.37 2.28 1.86831 40 40 40.24 2.22 1.78453 50 50 49.76 2.22 1.78453

Inferences:

1) For a given value of true23, the chi_sq minimum is independent of the starting value of theta23 in the fit, since the fit converges to values on either octants such that theta23 (low oct.) = 90 - theta23 (high

• ct.).

2) This might be an inherent symmetry in the hybrid model (2 flavor approximation) even in presence of

• NSI. The osc. proba. in the 2 flv approximation is proportional to sin^2(2theta23).

3) It makes more sense to give a starting value close to the true minima of the fitting parameter. But this leads to uncertainty while dealing with sea data. 4) The NSI plots are “not wrong” but may be called a “cheat” due to apriori information about the true

• ctant of theta23, with which the data is simulated.

5) For different true values of theta23, the NSI sensitivity is different even after marginalisation over theta23.

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