# Gianluigi Fogli: Past, Present and Future of Neutrino Oscillations

The past saw two protagonists, Bruno Pontecorvo and Raymond Davis Jr. Pontecorvo mentions for the first time neutrino oscillations in 1957, the same year when parity violation is discovered and the two-component theory of massless neutrinos is proposed. Pontecorvo comes back to the topic several years later, 1967, where he fixes the conditions for oscillations to occur. Two years later, with Gribov, he considers explicitly a model with a mixing matrix.

Quite independently, in 1962 Maki, Nagakawa and Sakata also had introduced the mixing of two neutrinos. This is the origin of today’s PMNS mixing matrix.

In the meantime, Davis was preparing his famous Homestake experiment on the detection of solar neutrinos. The Davis experiment operated continuously until 1994, finding a flux of only a third of the expected flux, calculated by Bahcall.

Further experiments also found a deficit, but until the nineties the situation was not clear.

In 1994 the situation was pointing at two possible solution,s, a large and a small angle one. The first breakthrough came from the atmospheric neutrino anomaly: a unexpected difference about the muon to electron neutrino composition in the flux of atmospheric neutrinos (coming from cosmic rays). Finally, in 1998 a strong zenith angle dependence was shown by Super-Kamiokande.

In the meantime we also understood the solar neutrino problem: SNO, using a heavy-water target measured charged as well as neutral current events, proving that the solar model was okay, and evidence of mixing of neutrinos as the origin of the riddles.

In 2002, KamLand could reproduce the neutrino oscillation results in laboratory. So we are going toward a solution of the solar neutrino problem. A incredible reduction of the allowed parameter space is obtained in 2001-2003. So there is direct proof of electron into tau neutrino oscillations, and a confirmation of the solar model. In 2004, by combining solar and KamLand data only one solution (the large mixing angle one) is found compatible with all data.

The MSW effect is confirmed in 2006, and in 2008 Borexino measures a decreasing survival probability of electron neutrinos with energy. In the meantime, long baseline neutrino experiments aim at reproducing atmospheric results. Results of K2K and Minos are in agreement with SuperKamiokande ones.

The missing piece is the appearance of tau neutrinos: Opera fills that missing piece, using the neutrino beam from the CNGS at CERN. 4 candidates are seen, with 0.23 expected from background sources. The no-oscillation hypothesis is thus excluded at 4.2 standard deviations.

In 2007 one can write the matrix as a composition of an atmospheric sector, an interference sector, and a solar sector. The angles start to be measured more precisely. But how to measure theta_13 and delta ? Also, the sign of the large mass-squared difference is to be determined.

The hutn to theta_13 is crucial. In 2006 the upper bound on it still comes from CHOOZ. Some weak hints appear of lower bounds, from a 3-nu analsis of atmospheric data by considering subleading solar mixing effects. Also, an old but persistent hint for theta_13>0 comes from the 3-nu analysis of atmospheric+LBL+CHOOZ data.

The other point is a slight disagreement between solar data from SNO and KamLand data. The disagreement is reduced if one takes sin^2 theta_13>0. This is due to the different correlation of theta_13 and theta_12 in the two experiments. So all in all there is a indication of theta_13>0 at the level of 1.6 standard deviations.

What happened after 2008 ? New experimental results come from T2K and MINOS, who in 2011 find some electron event ecesses in appearance mode. Both favor theta_13 sizably greater than 0. This before the arrival of short-baseline reactor data. The combination is sin^2 theta_13 = 0.21+-0.07. Then short-baseline experiments come in: double chooz, daya bay. In 2012 the experimental discovery is obtained.

Nowadays we have a wealth of datasets, including appearance and disappearance experiments. The accelerator LBL data are dominantly sensitive to delta m^2, theta_23 and theta_13, but accurate constraints do need delta_m^2 and theta_12 from solar and KL, in order to include and compute sub-dominant effects.

Adding the other data one gets from a global analysis also a value of delta, which however remains unconstrained. Adding short-baseline reactor data one gets a preference for a non-maximal value of theta_23. Delta remains not constrained. Adding Super-Kamiokande data, delta is preferred at the value of 1.4 pi.

Fogli stressed that one should appreciate the relative contribution of each set of data, and he did so by showing one after the other the measurement of the main parameters.

So nowadays we have no significant hierarchy preference from the global fit, a weak preference for the 1st octant, and a intriguing hint of non-zero CP violation, with sin(delta)<0. But CP violation requires a genuine 3-nu odscillations.

The future means the possibility to measure theta_13, delta, and the mass hierarchy. For theta_13, it is already well-measured, but it is important to improve its precision, as it affects the other parameters. Daya Bay has a recently improved estimation. The error has improved in one year by a factor of two, and the total uncertainty is dominated by statistics. So there is further room for improvement.

From the muon neutrino disappearance of long baseline experiments one can estimate delta m^2 and sin^2 theta_23, using sin^2 teta_13 measured by reactors. The most recent measurement is from T2K a few days ago. The best fit point is near the boundary of maximal disappearance. So the octant degeneracy in theta_23 seems to be easier to be resolved.

As far as delta is concerned, the appearance of muon neutrino experiments in long-baseline experiments are sensitive. T2K reports a recent estimate, but a similar analysis has little power to constrain the parameter without reactor measurements of sin^2 theta_13.

T2K has no sufficient sensitivity to determine the mass hierarchy by itself. But a similar sensitivity is achieved by NOvA, which has a longer baseline.

The sign of delta_m^2 is maybe the most fascinating of the items in neutrino physics. No indications are available so far from the current experiments, but we hope to solve this dilemma within the next ten years.

We need medium baseline reactor neutrino experiment,s specifically Juno, atmospheric neutrino epxeriments as Pingu and Ino, and long baseline accelerator experiments studying matter effects in muon to electron neutrino appearance experiments.

Fogli closed his talk by showing a recent detailed comparison of the sensitivity of each of several experiments in terms of the number of standard deviations to the hierarchy, as a function of time. It is maybe even more informative to look at the probability of rejecting at 3-sigma the wrong hierarchy, as a function of time. It looks like in a decade this problem might find a solution.

If you’ll forgive a layman’s curiosity: why didn’t KATRIN warrant a mention?

This should be addressed to Fogli. I will ask him and let you know – but my transcript might be incomplete…

Cheers,

T.