Research
Neutrino phenomenology
Neutrino phenomenology · Particle physics beyond the Standard Model · Astroparticle physics · Cosmology
Research statement
Overview
I have been a researcher in theoretical physics from 2005 to 2015 and associate professor until 2023. I am currently Full Professor of Theoretical Physics at the University of Bari "Aldo Moro".
My research lies at the interface between neutrino physics, particle phenomenology and cosmology. With the Bari group I have contributed to a long line of global analyses of neutrino oscillation data, combining solar, atmospheric, reactor and accelerator experiments to extract the fundamental parameters of leptonic mixing with state-of-the-art precision.
As measurements enter the subpercent regime, these results sharpen the picture of the neutrino mass ordering, of leptonic CP violation and of the absolute neutrino mass scale, while probing possible signatures of physics beyond the three-neutrino paradigm.
Where this work sits
Full Professor of Theoretical Physics, Università degli Studi di Bari “Aldo Moro” and INFN Sezione di Bari. Researcher from 2005, associate professor to 2023.
Overview
Lines of research
Six lines of work, each with its question, its method, what we found and where to read more.
- 01Global analysis of neutrino oscillationsWhat are the six oscillation parameters, and how precisely do the world data fix them?
- 02Mass ordering and leptonic CP violationIs the ordering normal or inverted, and do leptons violate CP?
- 03Absolute neutrino masses and cosmologyHow heavy are neutrinos, when β decay, 0νββ and cosmology each see a different combination of the masses?
- 04Supernova neutrinosHow do neutrinos change flavour where they are dense enough to refract off each other?
- 05Beyond the three-neutrino paradigmIs the three-neutrino picture complete?
- 06Modular invariance and the flavour puzzleIs there a symmetry behind the masses and mixings of quarks and leptons?
Research theme 01
Global analysis of neutrino oscillations
Three-flavour fits to the world neutrino data, with a self-consistent treatment of solar, atmospheric, reactor and long-baseline accelerator experiments.
- Question
- What are the values of the three mixing angles, the two mass-squared splittings and the CP phase, and how precisely do the world data fix them?
- Method
- One self-consistent three-flavour fit of solar, atmospheric, reactor and long-baseline accelerator data, with the full matter-effect treatment and a careful statistical combination of datasets with very different systematics.
- Our part
- The Bari group's long line of global analyses, released and updated as new data arrive.
- Main result
- In the March 2025 release |Δm²| is known to 0.8 %, the first three-neutrino parameter below 1 %. The November 2025 update, dominated by the first JUNO results, takes δm² from 2.3 % to 1.3 %.
- Read
- Neutrino masses and mixing: entering the era of subpercent precision, Phys. Rev. D 111, 093006 (2025)
- Updated bounds on the (1, 2) neutrino oscillation parameters after first JUNO results, Phys. Rev. D 114, 016026 (2026)
- Go deeper
- Analysis results · full tables on global-nu.org · the two figures below
The observables are the two mass-squared splittings $\Delta m^2_{21}$ and $|\Delta m^2_{3\ell}|$ and the three mixing angles $\theta_{12}$, $\theta_{13}$, $\theta_{23}$ of the PMNS matrix, together with the CP-violating phase $\delta_{\rm CP}$. In vacuum the survival probability of a flavour eigenstate takes the familiar form
$$ P(\nu_\alpha \to \nu_\alpha) = 1 - 4\sum_{i<j} |U_{\alpha i}|^2 |U_{\alpha j}|^2 \sin^2\!\left(\frac{\Delta m^2_{ij} L}{4E}\right), $$but the precision now attainable requires the full matter-effect treatment and a careful statistical combination of datasets with very different systematics.
Interactive figure · Oscillations
How do three neutrino flavours oscillate?
Exact three-flavour oscillation probabilities in vacuum as a function of L/E, with the parameters of the Bari global analysis.
Interactive figure · Detectors
What does a neutrino look like in a water-Cherenkov detector?
The neutrino itself is invisible: the ring of light comes from the charged lepton it produces.
Current best fits
The six parameters, as we measure them
What the global analysis returns for the three mixing angles, the two mass-squared splittings and the CP phase, from the Bari Release 2026.a after the second JUNO data release — preliminary, the paper is in preparation.
Preliminary. Bari Release 2026.a, after the second JUNO data release: the paper is in preparation and these values may still change. Final combination of long-baseline accelerator, solar, reactor and atmospheric data; normal ordering, favoured over inverted at 3.9σ (Δχ²IO−NO = 15.34). δm² = m₂² − m₁², Δm² = m₃² − (m₁² + m₂²)/2. The 1σ precision is the 1σ error divided by the best fit; for sin²θ₂₃, whose 3σ range spans both octants, one sixth of the 3σ range divided by the best fit.
Research theme 02
Mass ordering and leptonic CP violation
- Question
- Is the neutrino mass ordering normal or inverted, and is CP violated in the lepton sector?
- Method
- Statistical extraction of δCP and of the sign of Δm² from T2K, NOvA, reactor and atmospheric data together, and forecasts for JUNO, DUNE and Hyper-Kamiokande.
- Our part
- Combining datasets that pull in partly different directions, with their systematics treated jointly, since the significance depends delicately on it.
- Main result
- In the March 2025 release normal ordering is favoured at 2.2σ and, in normal ordering, CP violation at 1.3σ: both questions are still open.
- Read
- Unfinished fabric of the three neutrino paradigm, Phys. Rev. D 104, 083031 (2021)
- Current unknowns in the three neutrino framework, Prog. Part. Nucl. Phys. 102, 48 (2018)
Statistical extraction of the leptonic CP phase $\delta_{\rm CP}$ and of the sign of $\Delta m^2_{3\ell}$ from the interplay of T2K, NOvA, reactor and atmospheric data. The two datasets pull in partly different directions, and the resulting significance depends delicately on how their systematics are combined.
A related strand is forecasting the discovery reach of the next generation of experiments — JUNO, DUNE and Hyper-Kamiokande — and identifying which combinations of measurements would resolve the ordering and the $\theta_{23}$ octant with the least model dependence.
Interactive figure · Mass ordering
How can a reactor 52.5 km away tell the neutrino mass ordering?
The reactor antineutrino spectrum at JUNO in seven scenes: the fast ripple whose phase tells normal from inverted ordering, and what resolution and statistics leave of it.
Research theme 03
Absolute neutrino masses and cosmology
- Question
- How heavy are neutrinos? Oscillations measure only differences of squared masses.
- Method
- A joint statistical treatment of the three probes of the absolute scale — the β-decay endpoint (mβ), neutrinoless double-β decay (mββ) and cosmology (Σ) — together with the oscillation results.
- Our part
- Allowed regions in the (mβ, mββ, Σ) space, and how the tension between cosmological bounds and laboratory limits evolves as data improve.
- Main result
- Global constraints on the absolute masses and on their ordering from all these data at once, and Majorana-mass constraints that carry the spread of nuclear matrix elements through.
- Read
- Global constraints on absolute neutrino masses and their ordering, Phys. Rev. D 95, 096014 (2017)
- Majorana neutrino mass constraints in the landscape of nuclear matrix elements, Phys. Rev. D 106, 013009 (2022)
Oscillation experiments are sensitive only to mass-squared differences. The absolute scale is constrained instead by three complementary probes: the endpoint of the β-decay spectrum, which measures the effective mass $m_\beta$; searches for neutrinoless double-β decay, sensitive to the Majorana mass $\langle m_{\beta\beta} \rangle$; and cosmological observations of the CMB and of large-scale structure, which bound the sum $\Sigma = \sum_i m_i$.
Combining these with the oscillation results is a genuinely statistical problem, since the three observables depend on different combinations of the same underlying parameters and carry very different systematics. Our analyses map the allowed regions in the $(m_\beta,\ \langle m_{\beta\beta}\rangle,\ \Sigma)$ space, and quantify how the tension between cosmological bounds and laboratory limits evolves as data improve.
Current bounds
Where the absolute scale stands
The three probes, as they constrain the scale today — one laboratory limit each from β decay and from neutrinoless double-β decay, and the cosmological sum.
Interactive figure · Absolute masses
What do β decay, 0νββ and cosmology each measure?
mβ, mββ and Σ as functions of the lightest mass, the ordering and the Majorana phases, set against the current bounds.
Interactive figure · Cosmology
What happened to the neutrinos of the Big Bang?
A scrubbable history of the relic neutrinos, from the primordial plasma to the sea that fills every cubic centimetre of space today.
Research theme 04
Supernova neutrinos
Flavour evolution in the one place where neutrinos are dense enough to refract off each other.
- Question
- How do neutrinos change flavour near a collapsing core, where the flux is dense enough for neutrinos to refract off each other — and what will the next galactic supernova's events tell us?
- Method
- Non-linear, collective flavour evolution: multi-angle geometry instead of a single-angle approximation, three flavours together, and the dispersion relation of the flavour field.
- Our part
- With the Bari group: trajectory averaging, three-flavour collective evolution, spectral splits, and the low-energy features in inverted ordering.
- Main result
- Spectral-split patterns mapped against the relative luminosities of the species, and a classification of fast flavour conversions through dispersion relations.
- Read
- Fast flavor conversions of supernova neutrinos: classifying instabilities via dispersion relations, Phys. Rev. D 96, 043016 (2017)
- Supernova neutrinos and antineutrinos: ternary luminosity diagram and spectral split patterns, JCAP 10, 002 (2009)
A core-collapse supernova releases almost all of its gravitational binding energy as neutrinos, and it does so before anything is visible at the surface. They leave the collapsing core while the shock is still buried, which makes them the only messengers that carry direct information about the proto-neutron star and about the mechanism that revives the explosion. SN 1987A remains the sole detection: a couple of dozen events, and still the observational basis of most of what can be said. The next galactic supernova will be recorded by detectors that did not exist then, and the question is what those events can be made to say.
What makes the problem hard — and what our work has been about — is that the neutrino flux near the core is dense enough that neutrinos refract off each other. The flavour evolution stops being a one-particle problem and becomes a non-linear, collective one: the state of the ensemble enters the Hamiltonian that evolves it. With the Bari group we studied how these collective flavour transitions behave once the geometry is treated honestly rather than in a single-angle approximation, and how the multi-angle structure of the emission changes the outcome; how the transitions look when all three flavours evolve together instead of two; and how the resulting spectral splits depend on the relative luminosities of the species. We also worked out the consequences for the low-energy end of the spectrum in inverted ordering, and, more recently, on classifying the fast flavour conversions — instabilities that develop on scales far shorter than the ones set by the mass splittings — through the dispersion relation of the flavour field.
Selected work
Papers on collective flavour transitions
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Fast flavor conversions of supernova neutrinos: classifying instabilities via dispersion relations
Phys. Rev. D 96, 043016 (2017) arXiv:1706.03360
-
Supernova neutrinos and antineutrinos: ternary luminosity diagram and spectral split patterns
JCAP 10, 002 (2009) arXiv:0907.5115
-
Supernova neutrino three-flavor evolution with dominant collective effects
JCAP 04, 030 (2009) arXiv:0812.3031
-
Low-energy spectral features of supernova (anti)neutrinos in inverted hierarchy
Phys. Rev. D 78, 097301 (2008) arXiv:0808.0807
-
Collective neutrino flavor transitions in supernovae and the role of trajectory averaging
JCAP 12, 010 (2007) arXiv:0707.1998
Interactive figure · Supernovae
What would a galactic supernova look like in neutrinos?
The neutrino burst of a core collapse in time and energy, and what three detector technologies would record at a distance you choose.
Research theme 05
Beyond the three-neutrino paradigm
Tests of the standard 3ν framework against possible extensions.
- Question
- Is the three-neutrino picture complete, or do the data leave room for something more?
- Method
- Fits that add light sterile states (new splittings and mixing angles), non-standard interactions (a modified matter potential), and checks of the consistency among datasets.
- Main result
- The three-neutrino picture describes the data remarkably well; tensions among datasets are followed as statistics grow, since a persistent one may be the first sign of new physics rather than of underestimated systematics.
- Read
- Four neutrino oscillation solutions of the atmospheric neutrino anomaly, Phys. Rev. D 63, 053008 (2001)
The three-neutrino picture describes the data remarkably well, but it is not guaranteed to be complete. We test it against light sterile states, which would appear as additional mass-squared splittings and mixing angles; against non-standard neutrino interactions, which modify the matter potential and therefore the effective mixing in the Sun and in the Earth; and against tensions among datasets, which — if they persist as statistics grow — may be the first indication of new physics rather than of underestimated systematics.
Research theme 06
Modular invariance and the flavour puzzle
- Question
- Is there a symmetry behind the masses and mixings of quarks and leptons?
- Method
- Modular-invariant flavour models, in which Yukawa couplings are modular forms of a complex modulus τ, confronted with data in a global fit.
- Our part
- The first joint fit of quark and lepton observables — 22 quantities with 14 real parameters, in a model based on the binary octahedral group 2O — and modular invariance as an answer to the strong CP problem.
- Main result
- Strong correlations, invisible in separate analyses, between quark mass ratios and the leptonic CP phase, which become sharp predictions for KATRIN, neutrinoless double-β decay, JUNO and DUNE.
- Read
- Interplay and correlations between quark and lepton observables in modular symmetry models, Phys. Rev. D 111, 075024 (2025)
- Solving the strong CP problem in string-inspired theories with modular invariance, JHEP 08 (2025) 076
Following the proposal by F. Feruglio that the Yukawa couplings of leptons could be modular forms of a complex modulus $\tau$ living in the upper half-plane, modular invariance has emerged as a powerful candidate symmetry for the flavour structure of quarks and leptons.
With G.-J. Ding (USTC), E. Lisi (INFN Bari) and S. T. Petcov (SISSA/IPMU) we have carried out the first joint fit of quark and lepton observables — 22 quantities in total — within a modular flavour model based on the binary octahedral group $2O$, with just 14 real parameters. The fit reveals strong correlations among observables, notably between quark mass ratios and the leptonic CP phase $\delta_{\rm CP}$, that are invisible in separate analyses and that translate into sharp predictions for KATRIN, neutrinoless double-β decay, JUNO and DUNE.
In a complementary direction, with F. Feruglio (Padova), A. Strumia and A. Titov (Pisa), we have shown that modular invariance can also address the strong CP problem in string-inspired settings, where quarks have positive modular weights and gauge kinetic functions are non-trivial.
Interactive
Interactive figures
Eight figures that compute what they show, each on its own page with its assumptions, sources, a PNG for slides and a licence to reuse. The full collection, with filters by topic and level, is on the Interactive page.
How do three neutrino flavours oscillate?
Exact three-flavour oscillation probabilities in vacuum as a function of L/E, with the parameters of the Bari global analysis.
Advanced undergraduate: quantum mechanics and the idea of flavour mixing.
What does a neutrino look like in a water-Cherenkov detector?
The neutrino itself is invisible: the ring of light comes from the charged lepton it produces.
Undergraduate: special relativity and the refractive index.
What happened to the neutrinos of the Big Bang?
A scrubbable history of the relic neutrinos, from the primordial plasma to the sea that fills every cubic centimetre of space today.
Graduate: the thermal history of the early Universe.
What would a galactic supernova look like in neutrinos?
The neutrino burst of a core collapse in time and energy, and what three detector technologies would record at a distance you choose.
Graduate: neutrino astrophysics.
What must we add to the Standard Model to give neutrinos mass?
A map of the theoretical choices, from the minimal Standard Model to SO(10), with the fields, the mass matrix and the observable consequences of each.
Graduate: the Standard Model and basic quantum field theory.
How do three different seesaws become one operator?
The type I, II and III seesaw diagrams collapse onto the same dimension-five operator as the energy scale runs below the heavy mass.
Graduate: quantum field theory and effective field theory.
What do β decay, 0νββ and cosmology each measure?
mβ, mββ and Σ as functions of the lightest mass, the ordering and the Majorana phases, set against the current bounds.
Advanced undergraduate to graduate.
How can a reactor 52.5 km away tell the neutrino mass ordering?
The reactor antineutrino spectrum at JUNO in seven scenes: the fast ripple whose phase tells normal from inverted ordering, and what resolution and statistics leave of it.
Advanced undergraduate to graduate.
Selected recent publications
The complete list is maintained on INSPIRE-HEP.
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Solving the strong CP problem in string-inspired theories with modular invariance
JHEP 08 (2025) 076 arXiv:2505.20395
-
Interplay and correlations between quark and lepton observables in modular symmetry models
Phys. Rev. D 111, 075024 (2025) arXiv:2409.15823
-
Neutrino masses and mixing: entering the era of subpercent precision
Phys. Rev. D 111, 093006 (2025) arXiv:2503.07752
-
Unfinished fabric of the three neutrino paradigm
Phys. Rev. D 104, 083031 (2021) arXiv:2107.00532
-
Current unknowns in the three neutrino framework
Prog. Part. Nucl. Phys. 102, 48 (2018) arXiv:1804.09678
-
Global constraints on absolute neutrino masses and their ordering — Addendum
Phys. Rev. D 101, 116013 (2020)
Results and data
Where the numbers live
Publications
Selected and recent work, a citation summary from INSPIRE-HEP, and the complete list with filters.
Results
The latest release of the Bari global analysis in brief: what changed, the main numbers, the papers.
GLOBAL-NU
The authoritative home of the Bari global analyses: full tables, ranges, χ² profiles, comparisons and downloadable data, release by release.
NOW — Neutrino Oscillation Workshop
Otranto, biennial. One of the longest-running European workshops in neutrino physics, gathering theorists and experimentalists for in-depth discussions on the frontiers of the field. I am among the organizers.
For prospective students and postdocs
I welcome motivated students and young researchers interested in neutrino phenomenology, statistical analysis of particle physics data, and the interplay between particle physics and cosmology.
A historical note
Pauli’s letter, 1930
The story of neutrinos began with one of the most famous letters in twentieth-century physics. On 4 December 1930 Wolfgang Pauli postulated a new neutral particle of tiny mass to rescue energy conservation in β-decay — a hypothesis he himself called “a desperate remedy”.
Dear Radioactive Ladies and Gentlemen, as the bearer of these lines will explain to you in more detail, because of the “wrong” statistics of the N and Li⁶ nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the “exchange theorem” of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin ½ and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. […]
But only the one who dare can win, and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles: “Oh, it is best not to think about this at all, like new taxes”. […]
Unfortunately, I cannot appear in Tübingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back.
Your humble servant, W. Pauli.
