Exploring CP sensitivity in the presence of Lorentz invariance violations at T2HK/T2HKK Supriya Pan1 Srubabati Goswami 1 Kaustav Chakraborty 1 1Physical Research Laboratory, Ahmedabad, Gujarat, India Abstract Breaching of Lorentz invariance can lead to CPT violations. Conservation/violation of CP symmetry in leptonic sector is essential in understanding the universe’s evolution. We examine how CPT-violating LIV parameters aeµ, aeτ, aµτ impact CP violation within two proposed setups for the forthcoming T2HK experiment: (i) individual detectors placed at 295 km and 1100 km [T2HKK], and (ii) a detector with double capacity positioned at 295 km [T2HK]. We explore[1] the role of different beam channels and baseline and their synergy in the context of CP sensitivity. Lorentz Invariance Violations (LIV) The total Hamiltonian in presence of LIV is given by, H = 1 2E  U    0 0 0 0 ∆21 0 0 0 ∆31   U† +    A 0 0 0 0 0 0 0 0     + HLIV , (1) A = 2E √ 2GFNe = 7.6 × 10−5ρ(g/cc)E(GeV) eV2, GF: Fermi Constant, Ne: No. density of e−in matter, ρ: matter density. 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   (2) aαβ: CPT violating, cαβ: CPT conserving. Oscillation Probability Pµe = 2αs13 sin 2θ12 sin 2θ23 sin[ ˆA∆] ˆA sin[( ˆA −1)∆] ˆA −1 cos(∆+ δ13) + 4s2 13s2 23 sin2[( ˆA −1)∆] ( ˆA −1)2 + P aeµ µe + P aeτ µe (3) Pµµ = 1 −sin2 2θ23 sin2 ∆+ P aµτ µµ (4) P aeµ µe ≃4|aeµ| ˆA∆s13 sin 2θ23 sin ∆ √ 2GFNe [Zeµ sin ψeµ + Weµ cos ψeµ](5) P aeτ µe ≃4|aeτ| ˆA∆s13 sin 2θ23 sin ∆ √ 2GFNe [Zeτ sin ψeτ + Weτ cos ψeτ](6) P aµτ µµ = 4|aµτ| ˆA∆sin 2θ23 sin ∆ √ 2GFNe [Zµτ cos φµτ + Wµτ cos φµτ](7) where ∆= ∆31L/4E, α = ∆21/∆31, ˆA = 2 √ 2GFNeE/∆31, sij = sin θij, cij = cos θij, ψeµ = δ13 + φeµ, ψeτ = δ13 + φeτ Zeµ = −cos θ23 sin ∆, Weµ = c23(s2 23 sin ∆ ∆.c2 23 + cos ∆) (8) Zeτ = sin θ23 sin ∆, Weτ = s23(sin ∆ ∆ −cos ∆) (9) Zµτ = −sin2 2θ23 cos ∆, Wµτ = −cos2 2θ23 sin ∆ ∆ (10) Pµe[2] depends on aeµ, aeτ and their respective phases. Pµµ[2, 3] depends on aµτ and φµτ at leading order. Tokai to Hyper-Kamiokande (T2HK) and Tokai to Hyper-Kamiokande and Korea (T2HKK) Figure 1. Schematic of T2HK and T2HKK experiment [neutrino.skku.edu] T2HK[4]: Detector of 374 kt at 295 km (2.5◦off-axis beam) in Hyper-K site. The 1st oscillation maxima is at 0.6 GeV. T2HKK[5]: One Detector of 187 kt at 295 km in Hyper-K site and another similar detector in Korea at 1100 km (1.5◦ off-axis beam), the 2nd oscillation maxima is at 0.6 GeV. 1.3 MW beam with an exposure of 27 × 1021 POT. Channel 295 km 1100 km νe Appearance 3.2%(5%) 3.8%(5%) νµ Disappearance 3.6%(5%) 3.8%(5%) ¯νe Appearance 3.9%(5%) 4.1%(5%) ¯νµ Disappearance 3.6%(5%) 3.8%(5%) Table 1. The signal (background) normalization uncertainties Numerical Analysis GLoBES[6, 7] has been used with the values in tables 1,2. Parameter True Value Marginalization Range θ12 33.4◦ N.A. θ13 8.62◦ N.A. θ23 49◦ (39◦, 51◦) δ13 (−180◦, 180◦) 0◦, 180◦ ∆21 7.4 × 10−5 eV2 N.A. |∆31| 2.5 × 10−3 eV2 (2.4, 2.6) × 10−3 eV2 aαβ 10−23 GeV (10−22, 10−24) GeV φαβ (−180◦, 180◦) 0◦, 180◦ Table 2. True values and range of marginalization of all the parameters Single Detector Analysis 295 km (δ13 test,φeμ test):0°,180° Fixed: aeμ:10-23GeV True: θ23:49°,δ13:-90°,φeμ:180° Δ χ2 0 20 40 60 80 100 θ23 test (°) 40 42 44 46 48 50 295 km Fixed: θ23:49° (δ13 test,φeμ test):0°,180° True: δ13:-90°,φeμ:180°,aeμ:10-23GeV Total νe νμ νe νμ Δ χ2 20 40 60 80 100 aeμ test (× 10-23 GeV) 0 2 4 6 8 10 Total νe νμ νe νμ 1100 km (δ13 test,φeμ test):0°,180° Fixed: aeμ:10-23GeV True: θ23:49°,δ13:-90°,φeμ:180° Δ χ2 0 20 40 60 80 100 θ23 test (°) 40 42 44 46 48 50 1100 km Fixed: θ23:49° (δ13 test,φeμ test):0°,180° True: δ13:-90°,φeμ:180°,aeμ:10-23GeV Δ χ2 20 40 60 80 100 aeμ test (× 10-23 GeV) 0 2 4 6 8 10 Figure 2. Sensitivity of CP conservation versus θtest 23 (left) and atest eµ (right) The marginalization in θ23, aαβ enhances sensitivity. Major contribution of χ2 comes from νe, ¯νe channels and ν