A 92 year old retired math professor (a woman), and a 15 year old girl, who both live in the same neighborhood in Manhattan, solve an important unsolved problem in the topology of knot theory together (via Not Even Wrong which links to the New York Times, the article that they published about their discovery, and Scientific American).
Read the whole thing, it is not very amenable to being summarized.
One of my long-standing to dos for a blog post, which keeps getting put off because it is a pretty big project, is to survey the current state of the literature regarding hadron and/or hadron molecule resonances that aren't simple pseudo-scalar valance quark-antiquark, and simple three valance quark baryons, with u, d, s, c, and b valance quarks.
These include scalar mesons, axial-vector mesons, tetraquarks, pentaquarks, hexaquarks (if any), quarkonia, toponium, glueballs, mixed/blended meson resonances, glueball-quark hybrids, hadron molecules, excited hadron resonances, and other XYZ resonances.
There are also "leptonic atoms" which substitute positively charged leptons for protons in an atomic nucleus and are bound by quantum electrodynamics (i.e. by electromagnetism) rather than by the strong force, that probably belong in the same discussion (and generally have a mass of less than 4 GeV).
As a prelude, the big bottom line is that there is not a global solution, really, even to any large group of unclassified resonances. Each resonance has to be figured out on its own. It is sometimes quite an epic effort to discriminate between plausible explanations of their structure.
But there is also no BSM physics. QCD can explain it, but you have to be open to more involved hadron and hadron molecule structures than the vanilla mesons and baryons display. Thus, we are slowly and painfully, but inexorably, reaching a point where essentially all resonances have a Standard Model explanation.
Also, except for toponium, this highly sophisticated analysis and classification of hadron resonances, while it requires lots of data points, doesn't require the extreme high energies of the 13-14 TeV LHC (Large Hadron Collider).
Generally speaking, all hadron resonances are somewhere between 135 MeV (the lightest pion) and about 30 GeV (a hypothetical six b quark hexaquark), and the lower middle part of this range is very crowded with all sorts of resonances. This is comfortably below the energy scale of even a W or Z or Higgs boson, and is also below the energy scale of a top quark-antitop quark pair.
Maybe a post just spelling out the possibilities would be a good prelude to a post putting forth the leading theories about which resonances are most likely matches to which possibilities.
The maxim "today's morphology is yesterday's syntax," coined by linguist Thomas Givon, means that grammatical word endings and affixes (morphology) evolve over time from separate, independent words once used together in phrases and sentences (syntax).
Via Language Log.
Vaguely related: Some karaoke machines display words sung with almost no gap between them as a single word (German style), which indeed does help in getting the phrasing of the words in a song that you don't know very well right.
A new study makes a state of the art prediction of the Higgs boson pair production rate from gluon fusion in the Standard Model.
Some day when Higgs boson pair production experiments are about 1000 times more precise than they are today, this prediction can be compared to the experimental data, which is one way to determine is the Higgs boson self-coupling is consistent with the Standard Model prediction or if it instead has a value more consistent with a beyond the Standard Model value.
Gluon fusion is one of the main mechanisms by which Higgs bosons and Higgs boson pairs are created, and combined with Standard Model predictions for the other possible mechanisms, can be compared to the actual experimentally observed rates of Higgs boson pair production at particle collider experiments.
Despite the lengths of many authors go to in order to make the calculation that considers all sorts of higher order corrections, however, the uncertainties are still large.
But the experimental measurements currently aren't any better. They show that the actual rate of Higgs boson pair production is merely less than 2.4 times the Standard Model expectation (i.e. less than about 87.3 fb) with a 95% confidence interval. Higgs boson pair production rates are 0.06% of the overall Higgs boson production. In the Standard Model, Higgs boson pair production predominantly (90%) comes from the gluon fusion mechanism that the new study calculates considering all feasible to calculate factors.
Total Higgs boson production at 13 TeV is about 55.6 pb (+6% -8% uncertainties at one sigma) of which 48.4 (87% of the total) comes from gluon fusion with the remaining 7.2 pb coming from six other main production mechanisms. Higgs boson pair production at 13 TeV using a gluon fusion rate of 33 fb is 36.36 fb, of which 3.36 fb come from five other main non-gluon fusion production mechanisms. And, 1 picobarn (pb) = 1,000 femtobarns (fb).
This study (see below) concludes that double Higgs boson pair production at 13 TeV from gluon fusion is actually 30.4 fb (but subject to a roughly + 10% -23% uncertainty, so its is consistent with the earlier less exhaustively calculated result quoted in the Particle Data Group review below the fold which has roughly the same uncertainty on a percentage basis; the new result has a central value which is about 8% smaller than the old one). A ± 0.2 GeV change in the Higgs boson mass from 125.0 GeV shifts the predicted value by only about + 0.3% (if it is lighter) - 0.4% (if it is heavier), so the gluon fusion Higgs boson pair production rate isn't very sensitive to tweaks to the Higgs boson mass within the current range of uncertainty, but is probably a little bit less than 30.4 fb.
The paper and its abstract are as follows:
In this contribution, the higher-order QCD and electroweak corrections to Standard Model Higgs boson pair production via the gluon-fusion mechanism, gg→hh, are summarized and the different sources of theoretical uncertainty are assessed. The discussion includes finite top quark mass effects, matching to parton showers, approximate NNLO and N3LO QCD corrections, NLO electroweak effects, and uncertainties associated with the top quark mass scheme and perturbative scale choices. In addition, we provide an updated state-of-the-art recommendation for the inclusive gluon-fusion Higgs boson pair production cross section and the corresponding Higgs boson pair invariant-mass distribution.
The conclusion explains:
This report has summarized the current status of precision predictions for Standard Model Higgs boson pair production via gluon fusion. The discussion brings together NLO QCD calculations with full top quark mass dependence, approximate NNLO QCD predictions, N3LO QCD corrections and soft-gluon resummation, NLO electroweak corrections, and details the main sources of theoretical uncertainty entering the theoretical prediction.
The final recommendations provide state-of-the-art SM reference predictions for phenomenological studies and LHC analyses. They combine higher-order QCD (exact NLO, approximate NNLO and N3LO + N3LL) and EW (NLO) corrections, together with a full uncertainty budget. The combined inclusive cross sections, including the dominant uncertainty associated with the top-quark mass scheme, are collected in Table 12, while their dependence on the Higgs-boson mass is given in Table 13. Additionally we provide differential distributions in m(hh) (Section 7.5), along with corresponding K-factors from the higher-order calculations. These numbers should be used as the definitive predictions of this report, superseding the intermediate results shown in the preceding sections where different input parameters or PDF choices are used. It is worth noting that while the present work does not reduce the overall uncertainty with respect to the previous recommendation, its central prediction includes N3LO+N3LL QCD corrections in the HTL, NLO electroweak effects and updated PDF sets, and should therefore provide a more accurate reference value.
Further improvements in the SM prediction will come from reducing uncertainties associated with finite top quark mass effects and mass-scheme choice, extending fully differential predictions with consistently combined higher-order QCD and electroweak effects, and updating the recommendations as parton distributions and input parameters evolve.
Background from the Particle Data Group (with somewhat icky formatting) appears below the fold.