Daya Bay, Double Chooz and RENO combined analy- sis J. Garc´ıa Belloa, B. Vargas Perezb, J. Garc´ıa-Raveloc, Dionisio Tund, Carlos L´opez Limae Instituto Polit´ecnico Nacional, Escuela Superior de F´ısica y Matem´aticas, Departamento de F´ısica, Unidad Profesional Adolfo L´opez Mateos, Mexico City, Mexico. Jes´us Escamilla Roaf Instituto Polit´ecnico Nacional, Unidad Profesional Interdisci- plinaria de Ingenier´ıa, Ciudad del Conocimiento y la Cultura, Hidalgo, Mexico. afisjorge@live.com, bfis.vargas.perez@gmail.com, cg.ravelo@hotmail.com, ddtun@outlook.com, ecarlosomega40@hotmail.es fjesus.escamilla.roa@gmail.com Abstract Through a global statistical analysis from the public experimental data of the three LBL reactor experiments, Daya Bay, Double Chooz and RENO. We obtain the Daya Bay, Double Chooz and RENO conﬁdence regions for the neutrino oscil- lation mixing angle θ13 and the effective squared mass difference ∆m2ee in the three neutrino mixing model. Our single results are consistent with those published by the collaborations and corroborate that this statistical analysis improves individual results. Introduction The main objectives of Double Chooz, RENO and Daya Bay experiments are the precise measurement of the mixing angle θ13 and the ∆m2ee, [1][2]. These experiments detect reactor Anti-neutrinos by means of Inverse Beta Decay, mea- suring the positron kinetic energy produced. The three-ﬂavor survival probability P of a νe with energy Eν(MeV) after traveling a distance L(m), is given by P(ee) = 1 −sin2(2θ13)sin2 (1.27∆m2eeL Eν ) −cos4 θ13 sin2(2θ12)sin2 (1.27∆m2 12L Eν ) (1) where θ12 and ∆m2 12 are ﬁxed by others experiments. The average survival probability in the ith energy bin, P i is used to determine oscillation parameters. 1 Double Chooz The Double Chooz collaboration determined sin2(2θee) = 0.090+0.032 −0.029, without showing conﬁdence regions and using the value obtained by MINOS of 2.44+0.09 −0.10 × 10−3eV2/c4 for ∆m2ee in a simpliﬁed two ﬂavor mixing model, [3]. Double Chooz was designed to run with two detectors located at LF = 1050 m, (Far), and LN = 400 m, (Near). We use only the Double Chooz far data in χ2 tests to determine both sin2(2θ13) and ∆m2ee as well as their conﬁdence regions1. The experiment measures visible energy between 0.5 and 20 MeV, divided into 40 bins. The Rate + Shape analysis is determined by the function χ2 DC = 40 ∑ i=1 40 ∑ j=1 (N obs i −N exp i )M −1 ij (N obs j −N exp j ) + χ2 δE(ϵa,ϵb,ϵc) + 5 ∑ k=1 ϵ2 k σ2 k + χ2 off. (2) N obs i (N exp i ) are the observed (expected) number of IBD in the ith energy bin, Mij is the co- variance Matrix and N exp i is proportional to the expected number of antineutrinos without oscillations, nexp i , and to the average survival probability. Also, we write N exp i as follows N exp i = nexp i Pi(θ13,∆m2ee,L) + f(ϵ1,...,ϵ4), where the last term is a correction due to the background sources. Eight systematic uncertainties are considered in the second and third terms of χ2 R+S, using pull parameters ϵx. The fourth term in (2) is the contribution when the two reactors are turned off. We report the minimization of the function χ2 R+S and its level curves Fig. 1. Figure 1: It is shown the behavior of the χ2 DC statistics for Double Chooz and its con- ﬁdence regions up to 68, 95 and 99% of C. L. for (sin2 2θ13, ∆m2ee) for Full Covariance Matrix analysis. This graph is an improvement of the shown in [2]. This is because we have used a three mixing model and we have taken in account the Double Chooz collab- oration suggestions. In this case, we do not obtain two disjoint regions and the value for ∆m2ee is in good agreement with the currently acepted value. 2 RENO analysis The RENO collaboration determined sin2(2θee) = 0.0896 ± 0.0067 and 2.68 ± 0.13 × 10−3eV2/c4 for ∆m2ee, [5]. RENO runs with two detectors and six nuclear reactors in a linear conﬁguration. We use only the RENO far data in χ2 tests to determine both sin2(2θ13) and ∆m2ee as well as their conﬁd