Antonio MarroneTheoretical Physics · Bari
ν1 ν2 ν3 νe νμ ντ SOURCE ILLUSTRATIVE PROPAGATION DISTANCE →

Research

Neutrino phenomenology

Neutrino phenomenology · Particle physics beyond the Standard Model · Astroparticle physics · Cosmology

Publications Analysis results INSPIRE-HEP

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.

At a glance

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.

Publications → Analysis results

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.

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.

Solar Atmospheric Reactor Accelerator 3ν global fit δm² Δm² θ12 θ13 θ23 δCP DATA PARAMETERS ONE SELF-CONSISTENT ANALYSIS
Schematic. Four classes of experiment constrain overlapping combinations of the same six parameters, which is why they are fitted together rather than one at a time.

Interactive figure

Three-flavour oscillation lab

Exact coherent three-flavour vacuum oscillations. The amplitude is summed over the mass eigenstates with the complex PMNS matrix and only then squared, so no curve is an independent sine wave and the three sum to one at every point.

1.0 0.75 0.50 0.25 0 1 10 10² 10³ 10⁴ 10⁵ L / E (km / GeV) PROBABILITY FLAVOUR COMPOSITION AT THIS L/E
L/E = 500 km/GeV P(νe) — P(νμ) — P(ντ) — Σ = 1.0000000000
Source flavour
11010²10³10⁴10⁵

Parameters in use

sin²θ12
0.303
sin²θ13
0.0223
sin²θ23
0.473
δCP
1.20 π
δm²
7.37 × 10⁻⁵ eV²
Δm²
2.495 × 10⁻³ eV²
Δm²31
—
ordering
normal

Every value above is our own, from Table I of Phys. Rev. D 111, 093006 (arXiv:2503.07752), in this group's conventions: δm² = m2² − m1² and Δm² = m3² − (m1² + m2²)/2. They are not NuFIT's Δm²3ℓ and cannot be compared with it at a glance, which is why Δm²31, the splitting the phases actually need, is derived here rather than quoted: Δm²31 = Δm² + δm²/2. Normal ordering throughout — the same analysis favours it at 2.2σ. Propagation is parameterised by L/E; the scan is a way of reading the curve, not physical time.

Interactive figure — detector response

Water-Cherenkov event

The neutrino emits no Cherenkov light: it is neutral, it crosses the water unseen, and its direction is only inferred after the fact. Light appears when the charged lepton produced at the vertex travels faster than the phase velocity of light in water, c/n, which is well below c. The cone opens at cos θC = 1/(βn), and its intersection with the sensor wall is the ring.

SECTIONAL VIEW · WATER VOLUME SENSOR WALL, FACE ON SENSOR WALL VERTEX inferred ν direction — not an observed track — βn ≤ 1 — NO CHERENKOV LIGHT EARLY LATE RELATIVE ARRIVAL TIME · ILLUSTRATIVE, NOT PHYSICAL TIME
Event topology

A muon travels as a single straight track, so the ring edge stays sharp.

0.851.00 — threshold1.34

State

βn
—
cos θC
—
θC
—
stage
—
hit PMTs
—

Nothing here moves faster than light in vacuum. The charged lepton exceeds only c/n, the phase velocity of light in water, which is why the wavefronts pile up into a cone; below βn = 1 the condition fails and no light is produced. Distances are schematic and the sequence is paced for reading, not to scale in physical time.

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 — the quantities every figure above is drawn from.

Solar mixing angle
0.303 3σ: 0.264 – 0.345
sin²θ₁₂ · 4.5 % precision (1σ)
Reactor mixing angle
0.0223 3σ: 0.0206 – 0.0238
sin²θ₁₃ · 2.4 % precision (1σ)
Atmospheric mixing angle
0.473 3σ: 0.437 – 0.581
sin²θ₂₃ · first octant at 1.1σ, ambiguity persists
Solar splitting
7.37 ×10⁻⁵ eV²
δm² · 2.3 % precision (1σ)
Atmospheric splitting
2.495 ×10⁻³ eV²
|Δm²| · 0.8 % — the first 3ν parameter below 1 %
Leptonic CP phase
1.20 3σ: 0.73 – 2.03
δ/π · CP violation favoured at 1.3σ, still open

Normal-ordering best fits from Capozzi, Giarè, Lisi, Marrone, Melchiorri and Palazzo, Phys. Rev. D 111, 093006 (2025), Table 1; δm² = m₂² − m₁², Δm² = m₃² − (m₁² + m₂²)/2. NO is favoured over IO at 2.2σ. The 1σ precision is one sixth of the 3σ range.

Research theme 02

Mass ordering and leptonic CP violation

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.

Diagram comparing the normal and inverted neutrino mass orderings, with the flavour composition of each mass eigenstate shown as coloured fractions.
The neutrino mass spectrum, with the flavour composition $|U_{\alpha i}|^2$ of each eigenstate coded by colour. Whether $\nu_3$ sits at the top (normal) or at the bottom (inverted) is one of the open questions our global fits aim to resolve.

Interactive figure · JUNO · reactor antineutrinos at 52.5 km

How a reactor 52.5 km away reads the mass ordering

The reactor antineutrino spectrum at JUNO, built up one ingredient at a time: the slow solar oscillation, the fast atmospheric ripple on top of it, the phase shift that tells normal from inverted ordering, and what detector resolution and statistics leave of it. Step through the seven scenes, or take the controls yourself.

Step 1 / 7

Reactor antineutrinos

Fission in the reactor cores emits ν̄e up to about 10 MeV. JUNO detects them through inverse beta decay, and flux times cross section gives a spectrum that peaks near 3 MeV of visible energy.

no oscillation normal ordering (NO) inverted ordering (IO) pseudo-data ± stat.
Mass ordering

Switch NO ↔ IO and watch the fast ripple slide in phase — more at low energy than at high.

idealJUNO 3%8%

No smearing: every ripple is resolved.

Ordering signal retained

100%

RMS of the NO − IO difference (lower panel), relative to perfect resolution.

P(ν̄e→ν̄e) = 1 − cos⁴θ13 sin²2θ12 sin²Δ21 − sin²2θ13 (cos²θ12 sin²Δ31 + sin²θ12 sin²Δ32),  Δij = 1.267 Δm²ij[eV²] L[m] / E[MeV]

Bari global analysis: δm² = 7.48×10⁻⁵ eV², sin²θ12 = 0.3085 (Phys. Rev. D 114, 016026); sin²θ13 = 0.0223, Δm² = 2.495×10⁻³ eV² (NO; Phys. Rev. D 111, 093006), with δm² = m₂² − m₁² and Δm² = m₃² − (m₁² + m₂²)/2. IO is drawn with the same effective Δm²ee = cos²θ12|Δm²31| + sin²θ12|Δm²32| as NO, as a fit would choose it, so the difference that remains is the ordering alone. Flux: Mueller et al. (2011) with fission fractions 0.58, 0.07, 0.30, 0.05 (²³⁵U, ²³⁸U, ²³⁹Pu, ²⁴¹Pu); inverse-beta-decay cross section at leading order; Evis ≈ Eν − 0.78 MeV. Single baseline, no backgrounds, no systematics; pseudo-data drawn with a fixed random seed.

Research theme 03

Absolute neutrino masses and cosmology

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.

m1, m2, m3 β-decay endpoint mβ 0νββ decay ⟨mββ⟩ Cosmology Σ THE SAME THREE MASSES · THREE DIFFERENT COMBINATIONS
Schematic. Each probe measures a different combination of the same three masses, so the three bounds have to be combined statistically rather than compared directly.

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.

Direct kinematic mass
< 0.45 eV
mβ · KATRIN, 90 % C.L.
Majorana mass
≲ 28–122 meV
⟨mββ⟩ · KamLAND-Zen, ¹³⁶Xe
Cosmological sum
Σ mν
CMB, large-scale structure and DESI

Cosmology · relic neutrinos

The cosmic neutrino background

from the primordial plasma to today

Stage 1 / 4 · thermal equilibrium

10.00MeV

≈ 0.01 s

νe νμ ντ e⁻ e⁺ γ links = weak interactions
DRAG THE TRACK · CLICK AN EPOCH · ← →

—

Thermal equilibrium

—

Comoving temperature aT

1.40 1.26 1.12 0.98 10 MeV today aTγ aTν

Annihilating pairs heat the photons and not the decoupled neutrinos. That gap is the whole content of (4/11)1/3.

Momentum distribution

0 p / Tν → maintained by collisions

In comoving variables the shape is frozen. What changes is the physical scale: —

Tγ

—

Tν

—

Tν/Tγ

—

scale factor a

—

Γν/H

—

epoch

—

Research theme 04

Supernova neutrinos

Flavour evolution in the one place where neutrinos are dense enough to refract off each other.

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

Educational visualization · configurable templates

A galactic supernova in neutrinos

Two example emission templates are supplied below. Neither is a prediction: both are illustrative shapes with uncertainty bands, kept in a replaceable data object so that real collaboration output can be dropped in. What the figure is for is the structure of the burst in time and energy, and the way different detector technologies see different flavours of it.

—

1 · Collapsing stellar core

INFALL radius, logarithmic — km

2 · Emission timeline

arbitrary normalized units

TIME AFTER CORE BOUNCE — LINEAR TO 20 ms, THEN LOGARITHMIC νe ν̄e νx

3 · Energy–time map

model dependent · arb. units

−20 msEν vertical: 0 → 60 MeV10 s

4 · Detector response

Liquid argon

—

—

Research theme 05

Beyond the three-neutrino paradigm

Tests of the standard 3ν framework against possible extensions.

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.

THREE NEUTRINOS 3 + 1 ν1 ν2 ν3 ν1 ν2 ν3 ν4 mostly sterile MASS SCHEMATIC · NOT TO SCALE
Schematic, not to scale. A light sterile state would add a fourth mass eigenstate far above the three active ones, and with it new splittings and mixing angles for the data to constrain.

Research theme 06

Modular invariance and the flavour puzzle

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.

The upper half-plane with the shaded fundamental domain of the modular group SL(2,Z), bounded by the unit circle and the lines Re(tau) = ±1/2, with the fixed points i, omega and −omega-bar marked.
The complex modulus $\tau$ lives in the shaded fundamental domain $\mathcal{F}$ of $SL(2,\mathbb{Z})$. Special points $i$, $\omega$, $-\bar\omega$ and $i\infty$ are fixed by residual symmetries and play a distinguished role in flavour model building.

Selected recent publications

The complete list is maintained on INSPIRE-HEP.

Full publication list →
Conferences

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.

Workshop series →
Opportunities

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.

Teaching and theses → Write to me →

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.

Facsimile of the typewritten German original of Pauli's 1930 open letter to the Tübingen conference.
Facsimile of the German original, addressed to the group of radioactives at the Tübingen meeting.
Historical photograph of Wolfgang Pauli, Werner Heisenberg and Enrico Fermi together.
Pauli, Heisenberg and Fermi.