2025 · Journal of High Energy Physics · Open access

Leptogenesis and neutrino mass with scalar leptoquarks

Two of the biggest open questions in particle physics are why the universe contains matter but almost no antimatter, and why neutrinos have tiny, non-zero masses. This paper shows that one family of hypothetical particles — scalar leptoquarks — can account for both at the same time, while staying clear of every experiment that has looked for them so far.

Published in: Kåre Fridell, Leptogenesis and neutrino mass with scalar leptoquarks, JHEP 05 (2025) 096. doi:10.1007/JHEP05(2025)096 · free preprint on arXiv

Background: two cosmic puzzles, one connection

The Big Bang should have produced matter and antimatter in equal amounts, and yet today's universe is made almost entirely of matter. How much matter is left over is measured very precisely from the cosmic microwave background: the baryon asymmetry, the excess of baryons (protons and neutrons) over antibaryons divided by the number of photons, is η_B = (6.20 ± 0.15) × 10⁻¹⁰. That is one leftover baryon for roughly every billion photon pairs — a tiny number that still needs explaining.

Neutrinos pose a second puzzle. Neutrino oscillations prove that at least two of the three neutrino types have non-zero mass, but the Standard Model predicts that neutrinos are exactly massless. One option is that neutrinos are like ordinary matter particles (Dirac), which would need absurdly tiny Yukawa couplings of order 10⁻¹². The other option is that neutrinos are Majorana particles — their own antiparticles — in which case their mass is tied to a process that violates lepton number, the quantity that counts electrons, muons, taus and neutrinos. The classic realization is the type-I seesaw, whose new heavy neutrinos would need masses above about 10⁹ GeV — far out of reach of any experiment.

The connection between the two puzzles is a process called leptogenesis. In the hot early universe, certain interactions (sphalerons) change the sum of baryon and lepton number, B + L, while conserving their difference. So a theory that violates lepton number and generates more leptons than antileptons can have part of that lepton asymmetry converted into the observed excess of matter. In this way, the same new physics could explain both the baryon asymmetry and the smallness of neutrino masses.

What the paper does

The paper studies a concrete model built from scalar leptoquarks: hypothetical particles that interact with both quarks and leptons, and which have been searched for at the LHC and in rare-decay experiments. Three of them are added to the Standard Model — S₁, R̃₂ and S₃. All three are scalars (spin-0 particles) that couple directly to a lepton and a quark, and all three carry lepton number L = −1.

The key ingredients are two so-called tri-scalar couplings. Each lets two leptoquarks and the Higgs field interact in a way that changes lepton number by two units — what physicists call a ΔL = 2 interaction. That single source of lepton-number violation is enough to do two jobs at once:

Generate neutrino masses. The ordinary neutrinos start out massless, but the ΔL = 2 couplings let them acquire mass through a quantum loop, as shown in figure 1 below. No right-handed neutrinos or other new fermions are needed.
Generate the matter–antimatter asymmetry. The heaviest leptoquark, S₃, is assumed to be heavier than S₁; the S₁ particles then decay out of equilibrium in the early universe. Quantum interference between two decay paths gives these decays a slight preference for matter over antimatter — the CP violation that leptogenesis requires (figure 2 below).

The model is designed with a clear hierarchy: S₃ is heavier than S₁, and both are much heavier than R̃₂. In this limit the neutrino mass and the final asymmetry become almost independent of the lightest leptoquark, R̃₂ — which is convenient, because R̃₂ is the only one that current experiments could realistically produce.

The central technical point of the paper is the washout: processes in the early universe that can erase a freshly generated asymmetry before it freezes in. The author shows that the relevant ΔL = 2 washout rate is proportional to the size of the neutrino mass. That means neutrino mass generation and the erasure of the asymmetry are controlled by the same couplings, and they must be treated together to know whether leptogenesis can succeed. The paper then solves the set of Boltzmann equations — the bookkeeping that tracks how many of each particle exist as the universe cools — together with the neutrino-mass calculation, and checks the result against a long list of experimental constraints.

Feynman diagram: two neutrinos connected by a loop of two leptoquarks S1 and R2-tilde with a down-quark loop and a Higgs insertion — **Paper figure 1 — How neutrinos get mass.** A neutrino (ν) converts into a neutrino through a loop containing the two leptoquarks S₁ and R̃₂ and a down-type quark (d), with an insertion of the Higgs field h⁰. The two leptoquarks mix after the Higgs field takes its vacuum value, and the quark mass insertion flips its chirality — together these break the symmetry in a way that lets this loop act as a neutrino mass. Because the mass appears only at the quantum-loop level, its size is naturally much smaller than the masses of the particles in the loop.

Two Feynman diagrams: left, S1 decays to H and R2-tilde dagger; right, a one-loop diagram where S1 turns into S3 with a lepton and a quark in the loop — **Paper figure 2 — Where the matter–antimatter preference comes from.** Left: the tree-level decay of S₁ into a Higgs boson and an anti-leptoquark. Right: a one-loop version of the same decay in which the S₃ leptoquark and a lepton–quark pair run around the loop. The two diagrams interfere in a way that gives the decay of S₁ a slightly different rate than the decay of its antiparticle — this CP violation is what allows a net excess of matter to build up. Without S₃ (or a similar extra particle) the effect would vanish.

What they found

The central result is shown below: there are regions of parameter space where the model reproduces the observed baryon asymmetry η_B and the observed neutrino mass scale simultaneously. A representative benchmark point has S₁ with a mass of 10⁸ GeV, R̃₂ at 5 TeV, and couplings around 10⁻³–0.025 — that is, none of the couplings or masses has to be fine-tuned to an absurd value.

Four panels showing the green baryon-asymmetry contour overlaid on the orange neutrino-mass band in the g1 versus S1-mass plane, for lambda1 equal to 1, 0.1, 0.01 and 0.001 — **Paper figure 4 — The main result.** Each panel scans the coupling g₁ (vertical axis) against the mass of S₁ (horizontal axis, 10⁴–10¹⁴ GeV), for four different values of the coupling λ₁. The orange band marks where the model produces the observed neutrino mass scale; the green curve marks where it generates the observed baryon asymmetry. Wherever the two overlap, both observations come out right at once — and such overlap regions exist for λ₁ between 1 and 10⁻³. For smaller λ₁ the CP violation becomes too weak and the green curve disappears entirely; for larger couplings at the top left, the asymmetry is washed out before it can survive.

Both puzzles, one model

Parameter regions exist where the observed η_B = 6.2 × 10⁻¹⁰ and the observed neutrino mass scale are produced together, using a benchmark with S₁ at 10⁸ GeV and R̃₂ at 5 TeV.

Washout knows about neutrino mass

The ΔL = 2 washout rate is proportional to the neutrino mass. A big neutrino mass inevitably brings strong washout that erases the asymmetry — so the two effects must be computed together, consistently, rather than separately.

A narrow window for couplings

If the coupling λ₁ drops below about 10⁻⁴, there is too little CP violation and no asymmetry at all. If the couplings are too large, washout wins instead. In between lies the viable window, and for small couplings the asymmetry grows as the square of g₁.

Constraints can be dodged

Experimental bounds depend either on the mass of R̃₂ or on couplings the mechanism does not need. For example, sidestepping the proton-decay bound requires a diquark coupling below about 10⁻⁹, and rare kaon decays (NA62) push the S₁ mass above 32 GeV for the benchmark point.

Heavy enough to hide — for now

Neutrinoless double beta decay (KamLAND-Zen) requires S₁ heavier than 4.3 × 10⁴ GeV at the benchmark point, or 5.7 × 10⁸ GeV with order-one couplings. The ATLAS search for leptoquarks decaying to a bottom quark and a tau already excludes masses below 1460 GeV for a coupling of 3.

Future experiments could see it

The mechanism barely depends on R̃₂, so a light, strongly coupled R̃₂ could show up at future colliders or in next-generation neutrinoless double beta decay searches — while the rest of the model stays out of reach.

Left panel: particle abundances and baryon asymmetry versus inverse temperature z; right panel: decay and washout rates compared with the Hubble expansion rate — **Paper figure 6 — Watching the asymmetry build.** Left: as the universe cools (moving right along z = m_S1/T), the S₁ abundance (solid orange) falls away around z ≈ 1, and the baryon asymmetry (green) is generated by the decays. Washout processes then trim the asymmetry slightly for 1 ≲ z ≲ 10 before it freezes out. Right: the decay rate (solid orange) dominates while the asymmetry is created, while the washout rate (dashed orange) approaches the expansion rate of the universe (green) but does not overtake it — if it did, the asymmetry would be largely erased.

In one line: A single scalar-leptoquark model can generate both the observed matter–antimatter asymmetry and the observed neutrino mass scale through the same lepton-number-violating interactions, without conflicting with any existing experiment.

Why it matters

The origin of matter and the origin of neutrino mass are usually treated as separate mysteries. This paper shows that a well-motivated class of models — radiative neutrino mass models built from leptoquarks — can solve both at once, and explains why earlier attempts had failed: the washout processes that erase the asymmetry are themselves proportional to the neutrino mass, so the two calculations cannot be separated. The result also sharpens a philosophical point: because a large neutrino mass would wash out the asymmetry, the smallness of the observed neutrino mass might partly be a selection effect — a universe with heavier neutrinos could have ended up with no matter at all. The author argues that similar conclusions likely hold for other radiative neutrino-mass models, making this a template rather than a one-off.

Key concepts

Leptoquark: A hypothetical scalar or vector particle that couples to both a quark and a lepton, so it can turn quarks into leptons and vice versa. Leptoquarks are searched for at the LHC and in rare decays such as K → πνν.
Leptogenesis: The idea that the universe's matter–antimatter asymmetry was generated by lepton-number-violating processes in the early universe, with electroweak sphalerons later converting part of the lepton asymmetry into a baryon asymmetry.
Majorana neutrino: A neutrino that is its own antiparticle. Its mass violates lepton number, which is why the same interactions that give neutrinos mass can also help explain the matter–antimatter asymmetry.
CP violation: A difference in the behaviour of particles and antiparticles. Leptogenesis requires the decays of a heavy particle and its antiparticle to happen at slightly different rates; here the difference comes from interference between a tree-level decay and a one-loop decay of the leptoquark S₁.
Washout: Scattering processes in the early universe that can erase a newly generated asymmetry before it becomes permanent. In this model the ΔL = 2 washout rate is proportional to the neutrino mass.
ΔL = 2: A process that changes lepton number by two units. It is the hallmark of Majorana neutrino masses, and in this model it comes from couplings between two leptoquarks and the Higgs field.

Citation

Kåre Fridell, Leptogenesis and neutrino mass with scalar leptoquarks, Journal of High Energy Physics 05 (2025) 096. arXiv:2411.03282 [hep-ph] · doi:10.1007/JHEP05(2025)096. Figures reproduced from the paper, which is published open access under a CC BY 4.0 license; this page is a plain-language summary and any simplification is the fault of the summary, not the author.