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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, 214 Introduction

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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, 214 Introduction In neutrino oscillation one flavor evolves into another. This is because the flavor eigenstates and mass eigenstates are not same and related by ν α = N U αi ν i i=1 Where U is the unitary PMNS matrix which diagonalize the neutrino mass matrix m ν = Umν diag U T where m diag ν = diag(m 1, m 2, m 3 ) In standard three generation framework U can be parametrized by three mixing angles i.e θ 12, θ 13, θ 23 and one phase δ CP. Continue... Neutrino oscillation also involves two independent mass squared difference i.e the solar mass square difference (m 2 2 m2 1 = 21) and the atmospheric mass squared difference (m 2 3 m2 1 = 31). The undetermined sign of 31 give rise to two possible mass orderings i.e. Normal Hierarchy(NH i.e m 3 m 1 ) and Inverted hierarchy(ih i.e m 3 m 1 ) Unknowns Hierarchy(NH or IH) Octant of θ 23 (LO: θ 23 45 or HO: θ 23 45) δ CP (violation and precision) Current status of δ CP Recently, an indication for δ CP = -9 o 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 ( protons on target (pot)) The question In this work we ask the following questions: If the T2K hint of -9 o is confirmed by the further T2K neutrino runs, then can it indicate the true hierarchy and true octant? what are the role of anti-neutrinos? The T2K experiment T2K is a long-base experiment in Japan currently running in neutrino mode ν µ 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.6 GeV The appearance channel For T2K, the probability relevant for the measurement of CP can be expressed in terms of α = 21 / 31 as P µe = 4s13s sin 2 [(1 Â) ] + (1 Â)2 sin Â sin [(1 Â) ] α sin 2θ 13 sin 2θ 23 cos ( + δ CP ) Â (1 Â) = 31 L/4E = +ve for NH & -ve for IH A = Â 31 = ρ(gm/cc)e(gev ) For anti-neutrinos( ν) both Â and δ CP changes sign Degeneracies in P µe The determination of CP in T2K is affected by degeneracies: a)hierarcy-δ CP degeneracy i.e P µe (δ CP, NH) = P µe (δ CP, IH) b)octant-δ CP degeneracy i.e P µe (LO, δ CP ) = P µe (HO, δ CP ) Due to (a) and (b) there exist 3 fake solutions: i)wrong hierarchy-right octant ii)right hierarchy-wrong octant iii)wrong hierarchy-wrong octant As for ν, Â and δ CP both changes sign, addition of ν resolves (b) but not (a) which in turn removes (ii) and (iii) but not (i) CP Precision True value: -9 o (motivated by T2K hint)-(39 o ), (= (N true N test ) 2 /N true ) vs δ CP (test) for different test combinations of hierarchy and octant 8+ correspond to running T2K in only ν mode with total POT True NH,True LO δ CP (True)=-9 o T2K(8+) best fits: -9,, 135, 135 arises due to the fake and solutions(wrong octant i.e HO(51 o )) Conclusion: If true combination is, then clear hint at -9 is not possible. Continue... The same fig plotted for all 4 possible true combinations i.e,,, T2K config: True NH, True LO δ CP (True) = -9 o 2 True NH, True HO δ CP (True) = -9 o 2 True IH, True LO δ CP (True) = -9 o 2 True IH, True HO δ CP (True) = -9 o Only gives clear hint at -9 This is because for ν, -9- give to highest event rates Conclusion: If T2K runs only in ν and gives δ CP = -9, then true hierarchy = NH, true octant = HO Impact of anti-neutrino run T2K config: True NH, True LO δ CP (True) = -9 o 2 True NH, True HO δ CP (True) = -9 o 2 True IH, True LO δ CP (True) = -9 o 2 True IH, True HO δ CP (True) = -9 o 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 Conclusion: If T2K runs in equal ν- ν and gives δ CP = -9, then true hierarchy = NH, true octant =LO, HO The CP violation discovery To quantify the ν run we study CPV discovery The CPV discovery is defined as = min (N ex(δ tr CP ) N th(δ test CP =, 18o )) 2 N ex (δ tr CP ) = at δcp tr = &18(CP conserving values) = max at δcp tr Continue... CPV discovery is plotted vs δ CP (true) for all 4 possible true combinations 8 NH, LO NH, HO IH, LO IH, HO δ CP (True) δ CP (True) δ CP (True) δ CP (True) For and, 8+ is best: addition of ν reduce sensitivity For, 5+3 and for 6+2 is best: further addition of ν reduce sensitivity Conclusion: ν only removes wrong octant solution if it is present otherwise it reduces sensitivity The Answer In conclusion we give the following answers: If T2K runs only in ν mode and gives δ CP = -9, then true hierarchy is NH and true octant is HO If T2K runs in equal ν- ν mode and gives δ CP = -9, then true hierarchy is NH ν only removes wrong octant solution if it is present otherwise it reduces sensitivity Ghosh, Goswami, Raut : arxiv The Answer In conclusion we give the following answers: If T2K runs only in ν mode and gives δ CP = -9, then true hierarchy is NH and true octant is HO If T2K runs in equal ν- ν mode and gives δ CP = -9, then true hierarchy is NH ν only removes wrong octant soluion if it is present otherwise it reduces sensitivity Thank You

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