Three-flavour neutrino oscillation update

We review the present status of three-flavour neutrino oscillations, taking into account the latest available neutrino oscillation data presented at the Neutrino 2008 Conference. This includes the data released this summer by the MINOS collaboration, the data of the neutral current counter phase of the SNO solar neutrino experiment, as well as the latest KamLAND and Borexino data. We give the updated determinations of the leading 'solar' and 'atmospheric' oscillation parameters. We find from global data that the mixing angle $\theta_{13}$ is consistent with zero within $0.9\sigma$ and we derive an upper bound of $\sin^2\theta_{13}<0.035 (0.056)$ at 90% CL (3$\sigma$).


Introduction
Thanks to the synergy amongst a variety of experiments involving solar and atmospheric neutrinos, as well as man-made neutrinos at nuclear power plants and accelerators [1] neutrino physics has undergone a revolution over the last decade or so. The long-soughtfor phenomenon of neutrino oscillations has been finally established, demonstrating that neutrino flavor states (ν e , ν µ , ν τ ) are indeed quantum superpositions of states (ν 1 , ν 2 , ν 3 ) with definite masses m i [2]. The simplest unitary form of the lepton mixing matrix relating flavor and mass eigenstate neutrinos is given in terms of three mixing angles (θ 12 , θ 13 , θ 23 ) and three CP-violating phases, only one of which affects (conventional) neutrino oscillations [3]. Here we consider only the effect of the mixing angles in current oscillation experiments, the sensitivity to CP violation effects remains an open challenge for future experiments [4,5]. Together with the mass splitting parameters ∆m 2 21 ≡ m 2 2 − m 2 1 and ∆m 2 31 ≡ m 2 3 − m 2 1 the angles θ 12 , θ 23 are rather well determined by the oscillation data. In contrast, so far only upper bounds can be placed upon θ 13 , mainly following from the null results of the short-baseline CHOOZ reactor experiment [6] with some effect also from solar and KamLAND data, especially at low ∆m 2 31 values [7]. Here we present an update of the three-flavour oscillation analyses of Refs. [7] and [8]. This new analysis includes the data released this summer by the MINOS collaboration [9], the data from the neutral current counter phase of the SNO experiment (SNO-NCD) [10], the latest KamLAND [11] and Borexino [12] data, as well as the results of a recent re-analysis of the Gallex/GNO solar neutrino data presented at the Neutrino 2008 conference [13]. In Section 2 we discuss the status of the parameters relevant for the leading oscillation modes in solar and atmospheric neutrinos. In Section 3 we present the updated limits on θ 13 and discuss the recent claims for possible hints in favour of a non-zero value made in Refs. [14,15,16]. We summarize in Section 4.

The leading 'solar' and 'atmospheric' oscillation parameters
Let us first discuss the status of the solar parameters θ 12 and ∆m 2 21 . The latest data release from the KamLAND reactor experiment [11] has increased the exposure almost fourfold over previous results [17] to 2.44 × 10 32 proton·yr due to longer lifetime and an enlarged fiducial volume, corresponding to a total exposure of 2881 ton·yr. Apart from the increased statistics also systematic uncertainties have been improved: Thanks to the full volume calibration the error on the fiducial mass has been reduced from 4.7% to 1.8%. Details of our KamLAND analysis are described in appendix A of Ref. [8]. We use the data binned in equal bins in 1/E to make optimal use of spectral information, we take into account the (small) matter effect and carefully include various systematics following Ref. [18]. As previously, we restrict the analysis to the prompt energy range above 2.6 MeV where the contributions from geo-neutrinos [19] as well as backgrounds are small and the selection efficiency is roughly constant [11]. In that energy range 1549 reactor neutrinos events and a background of 63 events are expected without oscillations, whereas the observed number of events is 985 [20].
The Sudbury Neutrino Observatory (SNO) has released the data of its last phase, where the neutrons produced in the neutrino NC interaction with deuterium are detected mainly by an array of 3 He proportional counters to measure the rate of neutralcurrent interactions in heavy water and precisely determine the total active boron solar neutrino flux, yielding the result 5.54 +0. 33 −0.31 (stat) +0.36 −0.34 (syst) × 10 6 cm −2 s −1 [10]. The independent 3 He neutral current detectors (NCD) provide a measurement of the neutral current flux uncorrelated with the charged current rate from solar ν e , different from the statistical CC/NC separation of previous SNO phases. Since the total NC rate receives contributions from the NCD as well as from the PMTs (as previously) a small (anti-) correlation between CC and NC remains. Following Ref. [16] we assume a correlation of ρ = −0.15. In our SNO analysis we add the new data on the CC and NC fluxes to the previous results [21] assuming no correlation between the NCD phase and the previous salt phase, see Ref. [7] for further details. The main impact of the new SNO data is due to the lower value for the observed CC/NC ratio, (φ CC /φ NC ) NCD = 0.301 ± 0.033 [10], compared to the previous value (φ CC /φ NC ) salt = 0.34 ±0.038 [21]. Since for 8 B neutrinos φ CC /φ NC ≈ P ee ≈ sin 2 θ 12 , adding the new data point on this ratio with the lower value leads to a stronger upper bound on sin 2 θ 12 .
We also include the direct measurement of the 7 Be solar neutrino signal rate performed by the Borexino collaboration [12]. They report an interaction rate of the 0.862 MeV 7 Be neutrinos of 49±3(stat)±4(syst) counts/(day·100 ton). This measurement constitutes the first direct determination of the survival probability for solar ν e in the transition region between matter-enhanced and vacuum-driven oscillations. The survival probability of 0.862 MeV 7 Be neutrinos is determined to be P 7 Be,obs ee = 0.56 ± 0.1. We find that with present errors Borexino plays no significant role in the determination of neutrino oscillation parameters. Apart from the fact that the uncertainty on the survival probability is about a factor 3 larger than e.g., the uncertainty on the SNO CC/NC ratio measurement, it turns out that the observed value for P ee quoted above practically coincides (within 0.1σ) with the prediction at the best fit point: P 7 Be,pred ee = 0.55. The new data from SNO and Borexino are combined with the global data on solar neutrinos [22,23,24,25], where we take into account the results of a recent re-analysis of the Gallex data yielding a combined Gallex and GNO rate of 67.6±4.0±3.2 SNU [13].
The numerical χ 2 profiles shown in Fig. 1 have to very good accuracy the Gaussian shape χ 2 = (x − x best ) 2 /σ 2 , when the different σ for upper an lower branches are used as given in Eq.
(1). Spectral information from KamLAND data leads to an accurate determination of ∆m 2 21 with the remarkable precision of 8% at 3σ, defined  Figure 1. Determination of the leading "solar" oscillation parameters from the interplay of data from artificial and natural neutrino sources. We show χ 2 -profiles and allowed regions at 90% and 99.73% CL (2 dof) for solar and KamLAND, as well as the 99.73% CL region for the combined analysis. The dot, star and diamond indicate the best fit points of solar data, KamLAND and global data, respectively. We minimise with respect to ∆m 2 31 , θ 23 and θ 13 , including always atmospheric, MINOS, K2K and CHOOZ data.
as (x upper − x lower )/(x upper + x lower ). We find that the main limitation for the ∆m 2 21 measurement comes from the uncertainty on the energy scale in KamLAND of 1.5%. KamLAND data start also to contribute to the lower bound on sin 2 θ 12 , whereas the upper bound is dominated by solar data, most importantly by the CC/NC solar neutrino rate measured by SNO. The SNO-NCD measurement reduces the 3σ upper bound on sin 2 θ 12 from 0.40 [8] to 0.37.
Let us now move to the discussion of the status of the leading atmospheric parameters θ 23 and ∆m 2 31 . The Main Injector Neutrino Oscillation Search experiment (MINOS) has reported new results on ν µ disappearance with a baseline of 735 km based on a two-year exposure from the Fermilab NuMI beam. Their data, recorded between May 2005 and July 2007 correspond to a total of 3.36×10 20 protons on target (POT) [9], more than doubling the POT with respect to MINOS run I [26], and increasing the  Figure 2. Determination of the leading "atmospheric" oscillation parameters from the interplay of data from artificial and natural neutrino sources. We show χ 2 -profiles and allowed regions at 90% and 99.73% CL (2 dof) for atmospheric and MINOS, as well as the 99.73% CL region for the combined analysis (including also K2K). The dot, star and diamond indicate the best fit points of atmospheric data, MINOS and global data, respectively. We minimise with respect to ∆m 2 21 , θ 12 and θ 13 , including always solar, KamLAND, and CHOOZ data. exposure used in the latest version of Ref. [8] by about 34%. The latest data confirm the energy dependent disappearance of ν µ , showing significantly less events than expected in the case of no oscillations in the energy range 6 GeV, whereas the high energy part of the spectrum is consistent with the no oscillation expectation. We include this result in our analysis by fitting the event spectrum given in Fig. 2 of Ref. [9]. Current MINOS data largely supersedes the pioneering K2K measurement [27] which by now gives only a very minor contribution to the ∆m 2 31 measurement. We combine the long-baseline accelerator data with atmospheric neutrino measurements from Super-Kamiokande [28], using the results of Ref. [8], see references therein for details. In this analysis sub-leading effects of ∆m 2 21 in atmospheric data are neglected, but effects of θ 13 are included, in a similar spirit as in Ref. [29]. Fig. 2 illustrates how the determination of the leading atmospheric oscillation  parameters θ 23 and |∆m 2 31 | emerges from the complementarity of atmospheric and accelerator neutrino data. We find the following best fit points and 1σ errors: The determination of |∆m 2 31 | is dominated by spectral data from the MINOS longbaseline ν µ disappearance experiment, where the sign of ∆m 2 31 (i.e., the neutrino mass hierarchy) is undetermined by present data. The measurement of the mixing angle θ 23 is still largely dominated by atmospheric neutrino data from Super-Kamiokande with a best fit point at maximal mixing. Small deviations from maximal mixing due to subleading three-flavour effects have been found in Refs. [30,31], see, however, also Ref. [32] for a preliminary analysis of Super-Kamiokande. A comparison of these subtle effects can be found in Ref. [33]. At present deviations from maximality are not statistically significant.

Status of θ 13
The third mixing angle θ 13 would characterize the magnitude of CP violation in neutrino oscillations. Together with the determination of the neutrino mass spectrum hierarchy (i.e., the sign of ∆m 2 31 ) it constitutes a major open challenge for any future investigation of neutrino oscillations [4,5]. Fig. 3 summarizes the information on θ 13 from present data. Similar to the case of the leading oscillation parameters, also the bound on θ 13 emerges from an interplay of different data sets, as illustrated in the left panel of Fig. 3. An important contribution to the bound comes, of course, from the CHOOZ reactor experiment [6] combined with the determination of |∆m 2 31 | from atmospheric and long-baseline experiments. Due to a complementarity of low and high energy solar neutrino data, as well as solar and KamLAND data, one finds that also solar+KamLAND provide a non-trivial constraint on θ 13 , see e.g., Refs. [7,8] [34]. We obtain at 90% CL (3σ) the following limits ‡: In the global analysis we find a slight weakening of the upper bound on sin 2 θ 13 due to the new data from 0.04 (see Ref. [33] or v5 of [8]) to 0.056 at 3σ. The reason for this is two-fold. First, the shift of the allowed range for |∆m 2 31 | to lower values due to the new MINOS data implies a slightly weaker constraint on sin 2 θ 13 (cf. Fig. 3, left), and second, the combination of solar and new KamLAND data prefers a slightly non-zero value of sin 2 θ 13 which, though not statistically significant, also results in a weaker constraint in the global fit (cf. Fig. 3, right).
As has been noted in Ref. [16] the slight downward shift of the SNO CC/NC ratio due to the SNO-NCD data leads to a "hint" for a non-zero value of θ 13 . From the combination of solar and KamLAND data we find a best fit value of sin 2 θ 13 = 0.03 with ∆χ 2 = 2.2 for θ 13 = 0 which corresponds to a 1.5σ effect (86% CL). We illustrate the interplay of solar and KamLAND data in the left panel of Fig. 4. The survival probability in KamLAND is given by leading to an anti-correlation of sin 2 θ 13 and sin 2 θ 12 [8], see also [14,34]. In contrast, for solar neutrinos one has P solar ee ≈ cos 4 θ 13 1 − 1 2 sin 2 2θ 12 low energies cos 4 θ 13 sin 2 θ 12 high energies .
Eq. (5) shows a similar anti-correlation as in KamLAND for the vacuum oscillations of low energy solar neutrinos. For the high energy part of the spectrum, which undergoes the adiabatic MSW conversion inside the sun and which is subject to the SNO CC/NC measurement, a positive correlation of sin 2 θ 13 and sin 2 θ 12 emerges. As visible from Fig. 4 (left) and as discussed already in Refs. [8,34], this complementarity leads to a non-trivial constraint on θ 13 and it allows to understand the hint for a non-zero value of θ 13 , which helps to reconcile the slightly different best fit points for θ 12 for solar and KamLAND separately [14,16]. This trend was visible already in pre-SNO-NCD data, though with a significance of only 0.8σ, see Fig. 4 (right) showing the present result together with our previous one from v6 of [8].
Let us briefly comment on a possible additional hint for a non-zero θ 13 from atmospheric neutrino data [15,30]; Refs. [16,30] find from atmospheric+long-baseline+CHOOZ data a 0.9σ hint for a non-zero value: sin 2 θ 13 = 0.012 ± 0.013. In our atmospheric neutrino analysis (neglecting ∆m 2 21 effects) combined with CHOOZ data the best fit occurs for θ 13 = 0 (cf. Fig. 3, right), in agreement with Ref. [29]. Also, in the atmospheric neutrino analysis from Ref. [31] (which does include ∆m 2 21 effects, as Refs. [16,30]) the preference for a non-zero θ 13 is much weaker than the one from [30], with a ∆χ 2 0.2. In our global analysis the hint from solar+KamLAND gets diluted by the constraint coming from atmospheric+CHOOZ data, and we find the global χ 2 minimum at sin 2 θ 13 = 0.01, but with θ 13 = 0 allowed at 0.9σ (∆χ 2 = 0.87). Hence, we conclude that at present there is no significant hint for a non-zero θ 13 . As already stated, the origin of slightly different conclusions of other studies is related with including or neglecting the effect of solar terms in the atmospheric neutrino oscillation analysis, and translates also into a possibly nonmaximal best fit value for θ 23 . Note, however, that all analyses agree within ∆χ 2 values of order 1 and therefore there is no significant disagreement. A critical discussion of the impact of sub-leading effects in atmospheric data on θ 13 and θ 23 as well as a comparison of the results of different groups can be found in Ref. [33].
Before summarizing let us update also the determination of the ratio of the two mass-squared differences, which is relevant for the description of CP violation in neutrino oscillations in longbaseline experiments.

Summary
In this work we have provided an update on the status of three-flavour neutrino oscillations, taking into account the latest available world neutrino oscillation data presented at the Neutrino 2008 Conference. Our results are summarized in Figures 1,  2 and 3. Table 1 provides best fit points, 1σ errors, and the allowed intervals at 2 and 3σ for the three-flavour oscillation parameters. Appendix A.1. Updates in the solar neutrino analysis SSM: We consider the recently updated standard solar model from [35]. Among the different models presented in that reference, we use the low metallicity model, labelled as AGSS09, that incorporates the most recent determination of solar abundances [36] as our standard choice. The solar abundances in that model are a bit higher than previous determinations by the same group, alleviating the disagreement with helioseismic data. From the point of view of solar neutrinos, the most important changes with respect to the previous SSM used in our analysis (BS05(OP), with high metallicities [37]) is the 15% and 5% reduction in the Boron and Beryllium fluxes respectively. This is due to the reduced central temperature in the new model with respect to the previous one. Given the condition of fixed solar luminosity, this reduction is compensated by a slight increase in the pp and pep neutrino fluxes. We discuss also the impact of a new SSM with high metallicity, the GS98 model (presented in [35] as well), see also the recent discussion in [38].  [40]. Note that the recently published reanalysis of GALLEX data [41] has been reported already at Neutrino 2008 [13] and was therefore included in the original version of this paper. SNO: In our update we include also the results from the recent joint re-analysis of data from the Phase I and Phase II (the pure D 2 O and salt phases) of the Sudbury Neutrino Observatory (SNO) [42]. In this analysis, an effective electron kinetic energy threshold of 3.5 MeV has been used (Low Energy Threshold Analysis, LETA), and the total flux of 8 B neutrinos has been determined to be  [10], one can see that the determination of the total neutrino flux has been improved by about a factor 2. These improvements have been possible thanks mainly to the increased statistics, in particular the NC event sample in the LETA is increased by about 70%, since the previously used higher energy thresholds of 5 MeV in phase I and 5.5 MeV in phase II have cut away a significant portion of the NC events. Furthermore, energy resolution, backgrounds suppression, and systematic uncertainties have been improved. We include the LETA SNO data by fitting the predicted energy-dependent neutrino survival probability and day-night asymmetry in terms of the polynomials given by the SNO collaboration, see Tabs. XXVI and XXVII in [42]. We have checked that our results agree with the analysis including all solar neutrino experiments made by SNO. Note that we have adopted in our present analysis of the SNO-NCD phase data the detailed correlations between the CC, NC and ES neutrino fluxes recently given by the SNO collaboration [43], thereby improving our previous treatment presented in Sec. 2. Fig. A1 shows the impact of the updates in the solar analysis on the determination of the solar parameters. The left panel compares solar and solar+KamLAND allowed regions for the previous and updated analyses, the middle panel illustrates the impact of the SNO LETA analysis, and the right panel shows the effect of changing between the low (AGSS09) and high (GS98) metallicity solar models. We observe that the main changes come from the SNO LETA analysis, whereas the impact of solar metallicity is small. In general changes are rather small, once KamLAND data is added to the solar data, with a small tightening of the lower bound on sin 2 θ 12 . The best fit point value for the solar mixing angle has been shifted to a slightly higher value mainly due to the lower values reported for the total boron neutrino flux, either from the SNO LETA measurements as well as from the updated SSM with low metallicities. The allowed range for ∆m 2 21 of solar only data has been somewhat reduced, however this effect gets completely diluted after combining with KamLAND data. The updated best fit values and allowed ranges for sin 2 θ 12 and ∆m 2 21 can be found in Tab. A1. The impact of the updated solar analysis on θ 13 is illustrated in Fig. A2. Our  Figure A1. Impact of the changes in the solar neutrino analysis. In all panels the blue (shaded) regions corresponds to the 3σ regions from solar and solar+KamLAND updated analysis. The regions delimited by the red contour curves correspond to our previous analysis (left), an analysis using the previous high-threshold SNO phase I and II analysis but the same solar model (middle), and an analysis using the high metallicity GS98 instead of our standard low metallicity AGSS09 solar model (right).
analysis of solar + KamLAND data gives sin 2 θ 13 = 0.022 +0.018 −0.015 in excellent agreement with the value obtained by the SNO Collaboration [42], sin 2 θ 13 = 0.0200 +0.0209 −0.0163 . Hence, we obtain a lower best fit value with respect to the one we obtained in our previous analysis (sin 2 θ 13 = 0.03). This is due to the fact that now solar data prefer a somewhat higher value of θ 12 (as KamLAND does), and therefore, a smaller value of θ 13 is required to reconcile solar and KamLAND data, as can be seen by comparing left panels of Figs. 4 and A2. The fact that now solar data prefer a larger value for sin 2 θ 12 results in a stronger bound on θ 13 from the combination of solar + KamLAND data. The allowed solar region in the panel (sin 2 θ 12 , sin 2 θ 13 ) is more shifted to the right (because of the higher θ 12 preferred by the new smaller boron neutrino flux), where the allowed KamLAND region is narrower. At θ 13 = 0 we find ∆χ 2 = 2.2, same value as before.
As stated above, the small improvement in the θ 13 bound is related to the solar model used. For models with higher solar metallicities like GS98, a slightly weaker bound is obtained [38], see Fig. A2 (right). In that case we obtain a slightly larger best fit point, sin 2 θ 13 = 0.027 +0.019 −0.015 and ∆χ 2 = 3.05 at θ 13 = 0.
Appendix A.2. MINOS ν e appearance data In Ref. [44] a search for ν µ → ν e transitions by the MINOS experiment has been presented, based on a 3.14 × 10 20 protons-on-target exposure in the Fermilab NuMI beam. 35 events have been observed in the far detector with a background of 27 ± 5(stat) ± 2(syst) events predicted by the measurements in the near detector. This corresponds to an excess of about 1.5σ which can be interpreted as a weak hint for ν e appearance due to a non-zero θ 13 . We fit the MINOS ν e spectrum by using the GLoBES simulation software [45], where we calibrate our predicted spectrum by using the information given in [46]. A full three-flavour fit is performed taking into account a 7.3% uncertainty on the background normalization (Tab. I of [44]), and a 5% uncertainty on the matter density along the neutrino path.
In the MINOS detector, being optimized for muons, it is rather difficult to identify ν e CC events, since they lead to an electromagnetic shower. NC and ν µ CC events often have a similar signature, and hence lead to a background for the ν e appearance search. Indeed, in Ref. [47] an analysis of "NC events" has been performed, where "NC events" in fact include also ν e CC events due to the similar event topology. Therefore, a possible ν µ → ν e oscillation signal would contribute to the "NC event" sample of [47] and these data can be used to constrain θ 13 . We have performed a fit to the observed spectrum, again using the GLoBES software, by summing the NC events induced from the total neutrino flux with the ν e CC appearance signal due to oscillations. We include a 4% error on the predicted NC spectrum and a 3% error on the ν µ CC induced background (Tab. II of [47]).
In Fig. A2 (right) we show the constraint on sin 2 θ 13 from these MINOS data. The χ 2 has been marginalized with respect to all parameters except θ 13 , where for the solar and atmospheric parameters we imposed Gaussian errors taken from Tab. A1, without including any other information on θ 13 except from MINOS. We show the ∆χ 2 profiles for ν e appearance data and NC data, for a fixed neutrino mass hierarchy. The best fit point is always obtained for the inverted hierarchy (IH, ∆m 2 31 < 0), and in that case in general the constraint on sin 2 θ 13 is weaker, since for IH the matter effect tends to suppress the ν e appearance probability. The ∆χ 2 for normal hierarchy (NH, ∆m 2 31 > 0) is given with respect to the best fit for IH. In the global analysis we also marginalize over the two hierarchies, and hence, the actual information from MINOS comes from the IH. We see from the figure that MINOS ν e appearance data shows a slight preference for a non-zero value of θ 13 , with a best fit point of sin 2 θ 13 = 0.032(0.043) for NH (IH) with ∆χ 2 = 1.8 at sin 2 θ 13 = 0. In contrast, no indication for a non-zero θ 13 comes from the NC data. Furthermore, one observes that NC gives a slightly more constraining upper bound on sin 2 θ 13 than ν e appearance, while both are significantly weaker than the bound from ν µ disappearance data + CHOOZ or solar+KamLAND. Let us mention that the result for the NC analysis strongly depends on the value assumed for the systematic uncertainty, whereas the ν e appearance result is more robust with respect to systematics, being dominated by statistics.
In the global analysis we do not combine the χ 2 's from MINOS ν e and NC data, since presumably the data are not independent and adding them would imply a double counting of the same data. Therefore, we adopt the conservative approach and use only ν e appearance data without the information from NC data in the global analysis. We have checked, however, that adding both MINOS data sets leads to practically the same result in the global fit, both for the "hint" for θ 13 > 0 as well as the global bound, the latter being dominated by other data sets.
The present situation on the mixing angle θ 13 is summarized in Fig. A3. We obtain the following bounds at 90% (3σ) CL: We note a slight tightening of the bounds from solar+KamLAND as well as the global bound, due to the update in the solar analysis, see Appendix A.1, whereas the bound from CHOOZ+atm+K2K+MINOS gets slightly weaker, due to MINOS appearance data. In the global analysis we obtain the following best fit value and 1σ range: This corresponds to a 1.5σ hint for θ 13 > 0 (∆χ 2 = 2.3 at θ 13 = 0). As discussed in sec. 3 above, in our previous analysis the 1.5σ hint for θ 13 > 0 from solar+KamLAND data was diluted after the combination with atmospheric, long-baseline and CHOOZ data, resulting in a combined effect of 0.9σ. Now, thanks to the new MINOS appearance data, we find that the atmospheric + long-baseline + CHOOZ analysis already gives a nonzero best fit value of θ 13 (see Fig. A3), leading to the above global result, eq. A.3.
Finally, let us comment on the possible hint for a non-zero θ 13 from atmospheric data [16,30], as discussed in sec. 3. The possible origin of such a hint has been investigated in Ref. [48] and recently in [38], see also [49]. From these results one may conclude that the statistical relevance of the claimed hint for non-zero θ 13 from atmospheric data depends strongly on the details of the rate calculations and of the χ 2 analysis. Furthermore, the origin of that effect might be traced back to a small excess (at the 1σ level) in the multi-GeV e-like data sample in SK-I, which however, is no longer present in the combined SK-I and SK-II, as well as SK-I+II+III data. Tab. A1 gives an updated summary of the present best fit values and allowed ranges for the three-flavor oscillation parameters.