The Modest Excess Higgs Boson Production Explained

The Standard Model is stochastic (i.e. probabilistic) and not deterministic. It doesn't say, if you do X then Y will happen. It says, if you do X, Y with happen Z percent of the time.

One of the many things that the Standard Model predicts is the Higgs boson production rate, as a probability distribution of the rate at which Higgs bosons are produced in given circumstances. The calculation is in the form of an infinite series of terms with leading order, next to leading order, next to next to leading order, etc. terms.

You haven't read much about the physics of Higgs boson production at this blog because its a lot less simple and intuitive than Higgs boson decays, which are much more straightforward and rely on simpler, less complicated processes and rules. This makes Higgs boson production harder to write good blog posts about than Higgs boson decays. Also, the experimental anomalies compared to Standard Model predictions for Higgs boson production have been less striking, with more uncertainty and not very striking discrepancies, even though the discrepancies in Higgs boson production rates have been quite persistent.

In practice, scientists calculate the Standard Model prediction for the Higgs production rate with as many terms as are practically feasible for them to calculate, and then they try to estimate the uncertainty arising from the omitted terms as best they can.

Usually, each slight incremental improvement in the accuracy of the calculation takes disproportionately more work to calculate than the amount of work that was necessary to make the previous improvement of that magnitude. 

But, now and then, scientists unexpectedly find a previous omitted term from their calculations that is really important, although figuring out which terms will be especially fruitful to include is still at a more art than science level right now. Research programs like the amplituhedron approach and related developments from it are trying to bring more science to that search, but we aren't quite there yet.

Experiments since 2012, when the Higgs boson was first discovered, have shown that Higgs production usually exceeds the rate calculated by the best available Standard Model prediction calculations, although either not by a statistically significant amount, or with only a mild statistical tension with the best available predicted value for the Standard Model Higgs boson production rate.

Initially, some scientists though that this could be because the Higgs boson was detected sooner than it would have been otherwise because of a statistical fluke of higher than expected Higgs production. At first, that was a plausible proposal.

But it has been 14 years now, so it probably wasn't that, because the slight bias towards higher the expected Higgs boson production rates hasn't completely gone away, as the sample size of Higgs bosons detected has surged and reduced statistical uncertainties (but not always systemic uncertainties in the measurements of the Higgs boson production rates). 

Of course, like every anomaly in high energy particle physics, some theorists have, instead, tried to explain this persistent, not very large anomaly, with beyond the Standard Model physics.

But, a new paper now explains most or all of what has been going on. It turns out that the Higgs boson that physicists have observed is behaving more like than Standard Model Higgs boson to higher precision than ever, once again.

The new paper recalculates the Standard Model predicted Higgs boson production rate and determines that some next to leading order terms contributing to the predicted Higgs boson production rate were more important than had been expected. It turns out that these omitted terms can led to up to 10% more Higgs bosons being produced than would have been predicted without them in some circumstances.

Including the omitted terms explains most or all of the excess of experimentally observed Higgs boson production over the old calculation of the SM predicted value. This also, by the way, tends to imply that the uncertainties in the old experimental measurements were probably overestimated, which is a common reality in electroweak physics (as opposed to QCD or astronomy where uncertainties are often underestimated).

This new discovery feels like a reprise of the comparisons between the experimentally measured values of muon g-2 and state of the art calculations of the Standard Model prediction. In both cases, the gap has been mostly bridged by improving the quality of the calculations of the Standard Model predictions with an immense amount of hard calculation work, rather than by improving experimental accuracy or discovery new beyond the Standard Model physics. And, like the muon g-2 discrepancies, the part of the Higgs boson production calculation that has impaired the accuracy of the Standard Model prediction has mostly been the very hard to calculate strong force/hadronic/quark based part of what is primarily an extremely precise electroweak calculation.

The new paper and its abstract are as follows:

We present the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. 

The virtual amplitudes are computed fully analytically using the method of differential equations. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We implement the results in the POWHEG-BOX framework for phenomenological studies. 

The corrections are found to have a significant impact on the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold. This channel has not been considered before in calculations of the next-to-leading order electroweak corrections to Higgs boson pair production.

Marco Bonetti, Gudrun Heinrich, Philipp Rendler, William J. Torres Bobadilla, "Electroweak corrections to Higgs boson pair production: The quark channel" arXiv:2606.25928 (June 24, 2026) (contribution to the proceedings of Loops and Legs in Quantum Field Theories 2026, Bayreuth, Germany).

The new paper above is a physics conference summary of a more detailed paper on the same topic released in January of this year.

Data On Galaxies

Are active galactic nuclei (AGNs) exceptions to the Tully-Fischer rule or are they just hard to measure?

Active galactic nuclei have sometimes been excluded from Tully-Fischer fits because the underlying data points have high uncertainties, due to their low inclinations relative to solar system based observers leading, in turn, to "large scatter" although the magnitude of the scatter really isn't all that high for fairly imprecise astronomy measurements of distant galaxies.

The small data set in a new paper doesn't really bely that but these may also be galaxies which are out of equilibrium or have non-gravitational forces (e.g., the massive nuclear forces involved in star formation) that are relevant and significant in their dynamics. The authors of a new paper note that:

While the samples used to calibrate the canonical TF relations did not explicitly flag AGNs for removal (Tully& Pierce 2000; Tully et al. 2008; Tully&Courtois 2012; Kourkchi et al. 2020a), the selection criteria generally exclude active galaxies. Primarily, all works above select spirals with inclinations greater than 45◦. As Type 1 AGNs have been observed to be preferentially hosted by face-on (<45◦) galaxies (Keel 1980; Maiolino & Rieke 1995; McLeod & Rieke 1995; Simcoe et al. 1997; Gkini et al. 2021), this criterion naturally excludes a significant amount of Seyfert 1 hosts. The nuclear flux from unobscured Type 1 AGNs represents the primary expected source of photometric scatter in TF relations, whereas the high levels of nuclear obscuration inherent in Type 2 systems are expected to largely mitigate such contamination.

Visually, their data set does show high AGN scatter but also shows big error bars largely consistent with the baryonic Tully-Fischer relation.

We present an investigation of the Tully-Fisher (TF) relation solely for galaxies hosting an active galactic nucleus (AGN). Using 22 galaxies with primary, z-independent distances, we find that active galaxies exhibit significantly larger scatter about all TF relations compared to each respective calibration for (largely) inactive galaxies. 

The larger scatter persists despite removal of the AGN contamination from the photometry of the Type 1 AGNs via 1) careful surface brightness decompositions or 2) employing SEDs to constrain the light contribution of the AGN. These results suggest that the influence of an AGN on its host galaxy's surface brightness may extend beyond the nucleus. 

We also calculate the percentage difference between TF and primary distances, and find that TF-based distances are biased towards overestimation of the primary distances to active galaxies by anywhere from 5-10 percent for the optical/near-infrared and approximately 15 percent for distances predicted from inverting the Baryonic TF (BTF) relation. As TF-based distances (especially the I-band) are relied on heavily for analysis and modeling of the local peculiar velocity (Vpec) field, we suggest that active galaxies be removed from future Vpec modeling samples.

Justin H. Robinson, et al., "On the Tully-Fisher Relation for Active Galaxies -- I: Evidence of Larger Scatter" arXiv:2606.22575 (June 21, 2026) (Accepted for publication in ApJ).

In one context, a new paper (which also has a small sample size) finds that inferred spherical dark matter halos aren't ruled out, although slightly flattened halos are still preferred.

Wide-field surveys like Euclid mark a new era of extragalactic stellar stream studies. With a large number of streams, it is now possible to constrain the dark matter halos of galaxies in a cosmological volume and draw comparisons to theoretical expectations for the geometry of dark matter halos. 

This study combines Euclid imaging with visual detection and segmentation annotations to analyse streams. We use projected stream morphologies to constrain the shape and centre-of-mass position (CoM) of each host galaxy's potential, jointly probing baryonic and dark matter distributions. These inferences complement weak lensing methods, with sensitivity to halo profile and geometry on sub-virial scales. The method enables both stacked, population-level constraints on halo flattening and CoM position, and constraints on these quantities for individual halos. 

We also present a novel method for transforming segmentation maps of stellar streams into smooth, curvature-preserving tracks optimised for fast and robust dynamical inference. This approach enables rapid modelling of stream morphology, supports a statistically rigorous combination of constraints across multiple streams within a single galaxy, and enables joint inference across galactic hosts. 

From our study of 13 galaxies with prominent tidal streams, we find agreement with spherical halos, albeit a mild preference for flattening with q=0.95+0.05−0.10 at 68% confidence. This is promising early agreement with ΛCDM predictions. 

With thousands more discovered streams expected across Euclid's mission, our programme will enable precise measurements of halo shapes and CoM positions across large samples and redshifts, offering constraints on the geometry of dark matter halos.

Euclid Collaboration, "Euclid Quick Data Release (Q1): The geometry of dark matter halos from extragalactic streams" arXiv:2606.21774 (June 19, 2026) (Submitted to A&A).