particle-physics

The renormalization-group running of neutrino mixing is undetectable

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Do neutrinos mix differently depending on how they are made or detected?

Today, solar, reactor, accelerator, and atmospheric neutrino experiments measure neutrino mixing at energies from MeV to TeV. Global fits combine all of them into a single set of mixing angles and a CP phase. That this works rests on an assumption so basic that it is rarely stated: every experiment sees the same mixing.

In quantum field theory, the parameters of a theory, like the strength of a force or the mixing angles, depend on the energy scale at which we choose to describe them. This “renormalization-group running” is a standard and powerful tool. It connects theories defined at very high energies, like grand unified theories, to the values we measure in the lab.

In recent years, a growing number of papers, including some of our own, went a step further. They assumed that the running is directly observable. In this view, a neutrino made or detected in a collision carries the mixing evaluated at the momentum transfer of that collision, roughly, at how hard the collision is. This would lead to striking signals:

  • neutrinos changing flavor right at their source;
  • different values of the CP phase in different experiments;
  • unusual flavor ratios of the high-energy astrophysical neutrinos seen by IceCube.

In a new paper with Gabriela Barenboim (IFIC, University of Valencia) and Qinrui Liu (Simon Fraser University), we show that this premise is incorrect. The mixing is a property of the neutrino itself. It is fixed by quantum corrections to the neutrino as it travels freely from source to detector.

For the mixing to depend on the momentum transfer, the momentum transfer would have to enter those corrections. It does not: in the collisions that create and detect the neutrino, the momentum is exchanged through a W boson, not through the traveling neutrino. One can still choose to evaluate the mixing at the momentum transfer, as earlier works did. But then the corrections to the traveling neutrino, which those works left out, undo the running. Apart from tiny corrections at the collision points, every experiment, at any energy, measures the same mixing.

Neutrinos are made and detected in collisions with different momentum transfers (top). Earlier works assumed that the mixing changes with it (red). In fact, the traveling neutrino fixes the mixing, and it is the same in every experiment (blue).

The running itself is real, and it remains useful for testing theories at high energies. What cannot be seen is a dependence of the mixing on the momentum transfer of the experiment. Even setting the theory aside, old data rule this out. The NuTeV and NOMAD experiments looked for neutrinos changing flavor close to their source. They limit any change in the mixing angles between production in pion decay and detection at a few GeV to below 0.7°–2.4°.

This tells us where not to look. If future measurements deviate from expectations, for example of the flavor composition of high-energy astrophysical neutrinos, the cause will be genuinely new physics, not the running of the mixing.

Read more at:

The renormalization-group running of neutrino mixing is undetectable
Gabriela Barenboim, Mauricio Bustamante, Qinrui Liu
2610.28744 hep-ph

Measurement of the neutrino cross section across the TeV scale using IceCube data

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How likely is a neutrino to interact? Below a few hundred GeV, accelerator experiments have measured the neutrino–nucleon cross section to within a few percent. Above that, measurements have been scarce. Collider neutrinos from FASER reached about 2 TeV in 2024, and astrophysical neutrinos detected by IceCube have been used to measure the cross section in energy bins above about 10 TeV (including in my own paper with Amy Connolly from a while back, 1711.11043).

In between, across the TeV scale, previous measurements each obtained a single value of the cross section over a wide energy range, so how it changes with energy remained largely unmeasured. That matters, because deviations from the Standard Model, whether from the structure of the nucleon or from new physics, would in general depend on energy and could be diluted in a single value.

In a new paper led by star postdoc Rasmi Hajjar, from CCAPP at Ohio State, and co-authored with Sergio Palomares-Ruiz, we resolve how the cross section changes across this range. Using eight years of public IceCube data, 305,735 events from upward-going muon neutrinos and antineutrinos that crossed the Earth before reaching the detector, we measure the muon-neutrino charged-current cross section in five energy bins, from 150 GeV to 40 TeV.

The measurement relies on two effects. The Earth absorbs part of the upward-going flux, more so for neutrinos that cross more of it, and more so at higher energies, where the cross section is larger. And the energy distribution of the events tracks how the cross section changes from one energy bin to the next. Together with independent knowledge of the atmospheric neutrino flux, these effects let us tell the cross section apart from the flux.

The average of the neutrino and antineutrino cross sections, shown in red, agrees with the Standard Model prediction across the whole energy range and is measured with an uncertainty below 20% in every bin. It overlaps with the collider measurements at low energies and with the astrophysical ones at high energies, bridging the gap between them. It is the most precise measurement of the neutrino–nucleon cross section across the TeV scale to date.

IceCube cannot tell a neutrino from an antineutrino event by event. Still, the two leave different imprints on the data:

  • the atmospheric flux contains fewer antineutrinos;
  • the antimuons they produce carry on average a larger share of their energy;
  • the Earth absorbs them less.

Exploiting these differences, we find a first, albeit mild (1.6σ), indication that the neutrino and antineutrino cross sections can be measured separately above 1 TeV, where they had never been resolved. With ten times more data, within reach of next-generation neutrino telescopes, the uncertainty on the average cross section would fall below 10%. A non-zero antineutrino cross section above 360 GeV could then be established at more than 7σ.

Read more at:

Measurement of the neutrino cross section across the TeV scale using IceCube data
Rasmi Hajjar, Mauricio Bustamante, Sergio Palomares-Ruiz
2610.24068 hep-ph

The Magnus paper is out!

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I have posted the paper that accompanies Magνs, the code I released in August for computing neutrino oscillation probabilities.

In vacuum and in matter of constant density, the oscillation probability has an exact formula. Where the density changes along the path, as through the Earth, the Sun, or a supernova, it does not, and the equation of motion has to be integrated. The usual approaches both become slow at high accuracy. Cutting the matter profile into a staircase of constant-density steps gives an error that falls only as the square of the step width. Handing the equation to a general-purpose solver means resolving every oscillation, so the cost grows with the number of oscillations along the path, which can reach millions for a neutrino leaving the Sun. On top of that, each new experiment or model often means writing and validating a new solver.

Magνs uses the Magnus expansion instead. Over a stretch of the path within which the density may vary, it writes the evolution of the neutrino as a single exponential built from integrals of the Hamiltonian. The error falls as up to the tenth power of the stretch’s length, and the cost is set by how fast the density changes, not by how many times the neutrino oscillates. Three advantages follow, whatever the Hamiltonian contains.

Robust. The evolution is exactly unitary at any order and any accuracy setting, so the probabilities always add up to one, to round-off.

Fast. A typical probability takes a few milliseconds, and a scan over energy or arrival direction is a single batched call, one to two orders of magnitude cheaper per point than computing the points one at a time.

Flexible. The Hamiltonian is any Hermitian matrix, at any number of flavors. Non-standard interactions, sterile neutrinos, Lorentz-invariance violation, pseudo-Dirac neutrinos, or an interaction nobody has written down yet all go through the same call.

Magνs also chooses its own method. You state a tolerance, and it decides how finely to divide the path. Where a cheaper route exists, it takes it, such as following the slowly changing eigenstates of the Hamiltonian across the Sun. Besides oscillating probabilities, it returns phase-averaged ones, the quantity solar and astrophysical neutrino experiments measure. The aim is to move the effort of studying a new experiment or model from writing a solver to specifying its physics.

The paper works through examples across the field: the Earth’s layers and core, the Sun, a supernova shock front, geoneutrinos, the flavor composition of astrophysical neutrinos, a jet inside a collapsing star, turbulent matter, and a Hamiltonian supplied by the user. Each is a variation on one call.

Install Magνs via PyPI:

pip install magnuspy

Documentation: https://mbustama.github.io/Magnus/

Notebooks: https://mbustama.github.io/Magnus/tutorials.html

Read more at:

Magνs: neutrino oscillation probabilities for any Hermitian Hamiltonian, any number of flavors, and any matter profile
Mauricio Bustamante
2610.07159 hep-ph

Electron stability constrains neutrino time delays

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The search for Lorentz-invariance violation (LIV) is one of our best paths toward uncovering the quantum nature of spacetime. One of its most famous potential manifestations is the modification of neutrino propagation speeds.

For years, the community has known that superluminal (faster-than-light) neutrinos are heavily constrained. LIV would cause them to rapidly lose energy by radiating electron-positron pairs in a vacuum. Because of this, when anomalous time delays between cosmic neutrinos and gamma rays are observed, phenomenologists have naturally favored subluminal (slower-than-light) LIV propagation as the most viable explanation.

In a new paper co-authored with José Manuel Carmona, José Luis Cortés, Ardit Gkioni, and Maykoll A. Reyes, we demonstrate that this apparent subluminal loophole is actually an illusion.

We show that the same LIV modifications that slow down neutrinos inevitably render high-energy electrons unstable. Under subluminal LIV, electrons undergo a catastrophic decay process: e− → e− + ν + anti-ν. This triggers rapid and severe energy degradation.

By demanding that electrons survive up to the extreme energies we observe in astrophysics—specifically, the 15.5-TeV candidates from H.E.S.S. and the 2.34-PeV electrons inferred by LHAASO in the Crab Nebula—we placed stringent new limits on subluminal LIV.

Our results firmly invalidate the subluminal parameter space previously invoked to explain years-long cosmic neutrino time delays. Consequently, any observable delays must either have purely astrophysical origins, rely on a universal LIV deformation across all particle species, or require physics well beyond the standard effective-field-theory framework.

Read more at:

Electron stability constrains neutrino time delays
Mauricio Bustamante, José Manuel Carmona, José Luis Cortés, Ardit Gkioni, Maykoll A. Reyes
2607.01339 hep-ph

IV NBI Neutrino Summer School “Here, There & Everywhere”

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Registration is now open for the fourth edition of our NBI Neutrino Summer School, “Here, There & Everywhere”.

Like in previous editions (2021, 2022, 2023), the school is aimed at PhD students and advanced MSc students from all over the world that work on neutrinos, are planning to work on them, or are simply interested in them! The school is a one-week series of lectures on neutrino phenomenology, astrophysics, and cosmology delivered by carefully chosen world experts on these subjects.

When? July 7-11, 2025

Where? Niels Bohr Institute, Copenhagen, Denmark

How to register? Go to our Indico page here

Registration deadline: March 31, 2025 (register early!)

Can you present a student talk? Accepted in-person participants are encouraged to submit an abstract

Is there a participation fee? Yes, there is a fee of 130 EUR for in-person participants

Questions? Find our contact information (Markus Ahlers, Mauricio Bustamante) on the Indico page

The school provides lunch (Monday to Friday), two coffee breaks a days, reception and a school dinner.

Testing Lorentz invariance with a flare of high-energy astrophysical neutrinos

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Lorentz invariance is one of the pillars of modern physics, underlying special relativity—and, with that, the Standard Model—and general relativity. It posits that the laws of physics are the same for all observers moving in their own inertial frame. Yet, at high energies and short distances, Lorentz invariance may no longer hold.

To date, Lorentz invariance remains unbroken in all experimental tests. If it were violated, however, it could have many and varied consequences. Accordingly, there have been multiple searches for Lorentz invariance violation, using atom interferometry, gamma rays, cosmic rays, and neutrinos, etc. See, for instance, the data tables in 0801.0287.

High-energy astrophysical neutrinos, with TeV-PeV, are powerful probes of Lorentz invariance, thanks to their high energies and long traveled distances from their sources to Earth, of Mpc-Gpc scales. If Lorentz invariance is violated, it could imply that, en route to Earth, higher-energy neutrinos would travel more slowly than lower-energy neutrinos.

In a new paper, we introduce methods to look for these temporal distortions. We use the high-energy joint time and energy distribution of the neutrino flare detected by IceCube in 2014/2015 from the blazar TXS 0506+056 to look for specific signatures from Lorentz-invariance violation. We do this by borrowing non-parametric statistical methods previously used to look for signs of Lorentz-invariance violation in the gamma rays from gamma-ray bursts (1807.00189).

And, in doing so, we account for the significant energy and directional uncertainty associated to the detection of high-energy astrophysical neutrinos. Doing this makes our analysis realistic and robust, even if it erodes some of its sensitivity.

As a result, we set new lower limits on the energy scale of Lorentz-invariance violation in neutrino propagation. If Lorentz invariance is broken, this must happen at energies beyond 10^{14} GeV, if the effects depend linearly on the neutrino energy, or beyond 10^9 GeV, if they depend quadratically on it.

Read more at:

Probing Lorentz invariance with a high-energy neutrino flare
Mauricio Bustamante, John Ellis, Rostislav Konoplich, and Alexander S. Sakharov
2408.15949 astro-ph

Discovering Majorons from the neutrinos of the next galactic supernova

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In the hot, dense cores of core-collapse supernova, neutrinos could coalesce to make new, heavy particles, like Majoron-like bosons, with masses from tens of MeV to more than 100 MeV. After escaping the supernova, these Majorons would decay into energies comparable to the parent Majoron mass, far more energetic than the standard supernova neutrinos emitted from the neutrinosphere, and arriving at Earth later than them.

Thanks to large upcoming neutrino detectors, we might observe these high-energy neutrinos from the next galactic core-collapse supernova. Combining all available detection channels provides us with information on the energy, flavor, and arrival times of these neutrinos.

In a new paper, led by NBI PhD student Bernanda Telalovic, we have shown for the first time that we can combine this information use to clearly distinguish neutrinos from Majoron decay from the standard neutrinos of the next galactic supernova.

And, on top of that, we fold in the large uncertainty that exists in supernova physics by using two sophisticated supernova simulations (hot and cold) from the Garching group, obtained for two different assumptions for the mass of the proto-neutron star. However, our results do not hinge on us knowing what the real model, since we marginalize over it.

Should we detect no high-energy neutrinos, we will be able to place upper bounds on the Majoron coupling to neutrinos that are more than an order of magnitude stronger than the ones inferred from the observation of neutrinos from SN 1987A:

We show explicitly how the bounds are different depending on the flavor texture of the Majoron.

Conversely, should we detect high-energy neutrinos with late arrival times (tens of seconds post-bounce), we will be able to measure the mass and flavor-universal coupling of the Majoron:

Read more at:

The next galactic supernova can uncover mass and couplings of particles decaying to neutrinos
Bernanda Telalovic, Damiano F.G. Fiorillo, Pablo Martíinez-Miravé, Edoardo Vitagliano, Mauricio Bustamante
2406.15506 astro-ph

New limits on neutrino decay from high-energy astrophysical neutrinos

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In the Standard Model, neutrinos are effectively stable, their lifetimes orders of magnitude longer than the age of the Universe. In proposed extensions of the Standard Model, however, neutrinos might decay faster, and so observing them decay would constitute evidence of new neutrino physics.

Regardless, neutrino lifetimes, even augmented by new physics, are likely very long, and the effects of decay are likely manifest only in neutrinos that travel a long distance, during which the chances of them decaying becomes appreciable even if they are long-lived.

In a new paper, we have searched for signs of neutrino decay using the neutrinos from farthest away: the high-energy astrophysical neutrinos detected by IceCube, which travel cosmological-scale distances of Mpc-Gpc from their sources to Earth. Neutrino decay, in principle, alters the shape of the neutrino energy spectrum—introducing a step-like jump—and the flavor composition of the neutrinos upon reaching Earth—taking it outside the region expected from standard oscillations alone.

We find no signs of decay in present-day IceCube data, but place new, competitive lower limits on the lifetimes of the nu_2 and nu_3 neutrino mass eigenstates. We report, for the first time, limits inferred using the neutrinos from the first candidate steady-state astrophysical source of high-energy neutrinos, the active galaxy NGC 1068, and limits inferred from the diffuse flux of high-energy neutrinos.

These are arguably the most robust neutrino lifetime bounds garnered from high-energy astrophysical neutrinos so far! In addition, we make forecasts for the year 2035, combining multiple upcoming neutrino telescopes.

While similar studies have been performed before, ours brings two new perspectives, often overlooked or understudied, that make our results robust.

First, we consider broadly the large astrophysical uncertainties that plague the prediction of the flux of high-energy astrophysical neutrinos. This includes the size and shape of the neutrino energy spectrum, the flavor composition of the neutrino flux, the number or source populations and their distribution in redshift, and whether we have prior constraints on the size of the neutrino flux normalization. The impact of considering these uncertainties ranges from appreciable to critical. In some cases, they nearly make the sensitivity to neutrino decay vanish! Surprisingly, with present data, it is not possible to constrain neutrino decay using neutrinos from NGC 1068 due to the astrophysical unknowns!

Second, we model in detail the detection of neutrinos in IceCube and other neutrino telescopes. Their limited resolution to measure the energy, direction, and flavor of detected neutrinos blurs potential signs of neutrino decay in the flux of high-energy astrophysical neutrinos. We model experimental nuance using either tools provided publicly by the IceCube Collaboration (for the diffuse flux, using High Energy Starting Events), or using the PLEnuM (for the flux from NGC 1068, using tracks).

Read more at:

New limits on neutrino decay from high-energy astrophysical neutrinos
Victor B. Valera, Damiano F. G. Fiorillo, Ivan Esteban, Mauricio Bustamante
2405.14826 astro-ph

Download our digitized two-dimensional lifetime limits from this GitHub repository.

A plethora of long-range neutrino interactions probed by DUNE and T2HK

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If there are new neutrino interactions with matter, and if they affect neutrinos of different flavor differently, then they could impact neutrino oscillations. Long-baseline neutrino experiments are well-suited to look for them, thanks to their use of intense, well-characterized neutrino beams.

If the new interactions have a long range—i.e., if they are mediated by a new, ultra-light mediator—then neutrinos on Earth may experience a matter potential sourced by the vast amount of faraway matter elsewhere inside the Earth, Moon, Sun, Milky Way, and in the cosmological matter distribution, as pointed out in 1808.02042 [Universe’s Worth of Electrons to Probe Long-Range Interactions of High-Energy Astrophysical Neutrinos, by MB & Sanjib Agarwalla, PRL 2019]. This boosts the chances of discovering the new interaction even if it is supremely feeble.

In a recent paper (2305.05184 [Flavor-dependent long-range neutrino interactions in DUNE & T2HK: alone they constrain, together they discover, by Masoom Singh, MB, and Sanjib Agarwalla, JHEP 2023]), we explored the prospects of constraining or discovering these new, long-range neutrino interactions in the upcoming long-baseline experiments DUNE and T2HK. We found promising prospects. However, we explored only three different possible forms of the interaction, introduced by gauging three of the accidental global lepton-number U(1) symmetries of the Standard Model.

In a new paper (2404.02775), led by PhD students Masoom Singh and Pragyanprasu Swain, we now extend this to many other symmetries—a plethora of them!—that introduce new neutrino interactions with electrons, neutrons, and protons. Each symmetry affects oscillations differently.

Our new results cement and extend our original findings: DUNE and T2HK should be able to probe the existence of new interactions—and possibly discover and distinguish between alternatives—regardless of which symmetry is responsible for inducing them. The reach of DUNE and T2HK to probe new neutrino interactions is not only deep, but also broad!

Read more at

A plethora of long-range neutrino interactions probed by DUNE and T2HK
Sanjib Kumar Agarwalla, Mauricio Bustamante, Masoom Singh, Pragyanprasu Swain
2404.02775 hep-ph

Download the digitized data from out plots from this GitHub repository.

Measuring the ultra-high-energy neutrino flavor composition in in-ice radio detectors

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The flavor composition of high-energy cosmic neutrinos—i.e., the proportion of electron, muon, and tau neutrinos in the flux—is a versatile probe of neutrino physics and astrophysics (see, e.g., here, here, and here). So far, all measurements of it, by IceCube, have been in the TeV-PeV energy range. In the next decade, new neutrino telescopes might discover ultra-high-energy (UHE) neutrinos, with EeV-scale energies, opening up new possibilities. Yet, so far, the measurement of their flavor composition has remained largely unexplored (see, however, our recent paper here).

In a new paper led by postdoc Alan Coleman we propose new methods to measure the flavor composition of UHE neutrinos in upcoming large in-ice radio-detection neutrino telescopes, like RNO-G, under construction, and the planned radio array of IceCube-Gen2. 

The measurement is based on two flavor-sensitive channels: one sensitive to electron neutrinos, by looking for the elongation of radio Askaryan emission due to the Landau-Pomeranchuk-Migdal effect, and one sensitive mainly to muon and tau neutrinos, by looking for events that contain multiple showers, triggered by the stochastic losses of final-state muons and taus.

Our results, based on state-of-the-art simulations of IceCube-Gen2, show promising prospects. If the UHE neutrino flux is large (as in, informed by cosmic-ray measurements by the Telescope Array), we should achieve sensitivity enough to confirm standard predictions of the flavor composition and disfavor extreme deviations from them:

This would allow us, for instance, to infer the flavor composition at the point of production of the UHE neutrinos and thus indirectly probe their production mechanism and possibly the identity of the neutrino sources:

Read more at:

The flavor composition of ultra-high-energy cosmic neutrinos: measurement forecasts for in-ice radio-based EeV neutrino telescopes
Alan Coleman, Oscar Ericsson, Mauricio Bustamante, Christian Glaser
2402.02432 astro-ph