Joint short- and long-baseline constraints on light sterile neutrinos

Recent studies provide evidence that long-baseline (LBL) experiments are sensitive to the extra $CP$ phases involved with light sterile neutrinos, whose existence is suggested by several anomalous short-baseline (SBL) results. We show that, within the $3+1$ scheme, the combination of the existing SBL data with the LBL results coming from the two currently running experiments, $\mathrm{NO}\nu \mathrm{A}$ and T2K, enables us to simultaneously constrain two active-sterile mixing angles, ${\theta }_{14}$ and ${\theta }_{24}$, and two $CP$ phases, ${\delta }_{13}\equiv \delta$ and ${\delta }_{14}$, although the information on the second $CP$ phase is still weak. The two mixing angles are basically determined by the SBL data, while the two $CP$ phases are constrained by the LBL experiments, once the information coming from the SBL setups is taken into account. We also assess the robustness or fragility of the estimates of the standard 3-flavor parameters in the more general $3+1$ scheme. To this regard we find that (i) the indication of $CP$ violation found in the 3-flavor analyses persists also in the $3+1$ scheme, with ${\delta }_{13}\equiv \delta$ having still its best-fit value around $-\pi /2$, (ii) the 3-flavor weak hint in favor of the normal hierarchy becomes even less significant when sterile neutrinos come into play, (iii) the weak indication of nonmaximal ${\theta }_{23}$ (driven by $\mathrm{NO}\nu \mathrm{A}$ disappearance data) persists in the $3+1$ scheme, where maximal mixing is disfavored at almost the 90% C.L. in both normal and inverted mass hierarchy, and (iv) the preference in favor of one of the two octants of ${\theta }_{23}$ found in the 3-flavor framework (higher octant for inverted mass hierarchy) is completely washed out in the $3+1$ scheme.

Figure 1

Regions allowed by the combination of the SBL and LBL data (T2K and $\mathrm{NO}\nu \mathrm{A}$) together with the ${\theta }_{13}$-sensitive reactor results for the NH case. The left-bottom panel reports the projection on the plane of the two mixing angles (${\theta }_{14}$, ${\theta }_{24}$). The other two panels display the constraints in the plane formed by each one of these two mixing angles and the new $CP$ phase ${\delta }_{14}$. The confidence levels correspond to 68%, 90% and 95% for 2 d.o.f ($\mathrm{\Delta }{\chi }^2=2.3$, 4.6, 6.0), and the best-fit points are marked with a red point.

Figure 2

Regions allowed by the combination of the SBL and LBL data (T2K and $\mathrm{NO}\nu \mathrm{A}$) together with the ${\theta }_{13}$-sensitive reactor results for the IH case. The left-bottom panel reports the projection on the plane of the two mixing angles (${\theta }_{14}$, ${\theta }_{24}$). The other two panels display the constraints in the plane formed by each one of these two mixing angles and the new $CP$ phase ${\delta }_{14}$. The confidence levels correspond to 68%, 90% and 95% for 2 d.o.f ($\mathrm{\Delta }{\chi }^2=2.3$, 4.6, 6.0), and the best-fit points are marked with a red point.

Figure 3

Regions allowed by the combination of the SBL and LBL data (T2K and $\mathrm{NO}\nu \mathrm{A}$) together with the ${\theta }_{13}$-sensitive reactor results for NH (left panel) and IH (right panel) in the plane spanned by the two $CP$ phases ${\delta }_{13}$ and ${\delta }_{14}$. The confidence levels are the same ones used in Fig. 1.

Figure 4

Regions allowed in the plane [${\sin }^{2}2{\theta }_{13}$, ${\delta }_{13}$] by the joint analysis of all the SBL experiments and the LBL experiments (T2K and $\mathrm{NO}\nu \mathrm{A}$). The interval of ${\theta }_{13}$ identified by the reactor experiments (green vertical band) is displayed for the sake of comparison. The left (right) panels represent the NH (IH) case. The upper (lower) panels refer to the 3-flavor (4-flavor) scheme. The confidence levels are the same reported in Fig. 1.

Figure 5

Regions allowed in the plane [${\sin }^2{\theta }_{23}$, $\mathrm{\Delta }{m}_{32}^2$] by the joint analysis of all the SBL, the LBL data (T2K and $\mathrm{NO}\nu \mathrm{A}$), together with the ${\theta }_{13}$-sensitive reactor results. The left (right) panels represent the NH (IH) case. The upper (lower) panels refer to the 3-flavor (4-flavor) scheme. The confidence levels are the same reported in Fig. 1.

Figure 6

Marginalized $\mathrm{\Delta }{\chi }^2$ for the parameter ${\sin }^2{\theta }_{23}$ for NH (left panel) and IH (right panel). The black solid line indicates the 3-flavor case, while the red dashed line refers to the $3+1$ scheme.