[bjornsing]

Thanks. But weird… The previous error bounds on the top quark mass were grossly incorrect then? I mean a new estimate for the top quark mass, which is within the bounds of the previous estimate, shouldn’t make the predicted mass of the Higgs jump out of its error bounds, right?

[sigmoid10]

The top quark mass itself was much, much more uncertain back then. The original paper referred to a mass with an error of 2.4GeV[1], while the latest direct measurements give an uncertainty of 0.3GeV[2]. That's an order of magnitude improvement thanks to new data collected by the LHC over the last decade. Also bear in mind that these uncertainties are given as standard deviations. Almost a third of all statistical measurements will fall outside one standard deviation, while less than 0.3% will exceed three standard deviations. Anything less than two standard deviations is usually considered not statistically significant in most scientific fields. The new value is not surprising at all in that light.

[1] https://pdg.lbl.gov/2008/tables/rpp2008-sum-quarks.pdf

[2] https://pdg.lbl.gov/2022/tables/rpp2022-sum-quarks.pdf

[bjornsing]

Thanks again. But in my mind that doesn’t really explain the Higgs mass prediction/estimate going from 126 +/- 2.2 GeV to 130 GeV… The reason you have that +/- 2.2 GeV is (among other things) that the mass of the top quark mass is uncertain, right? So how could a new measurement of the top quark mass make the prediction for the Higgs mass jump so far (unless the new top quark mass was wildly unexpected)?

[sigmoid10]

I think you misunderstand the way the Higgs mass is calculated here. This is a highly non-linear relationship that is extremely sensitive to the top quark mass. In fact the second most massive quark would only contribute a fraction of one thousandth to the result (which is why it was ignored in the paper).

Consider this toy example: The mass m is calculated from some parameter like m~=b^4 and that parameter b was measured b=2.0±0.1. Using Gaussian error propagation, m would be 16±3.2. Now update the measurement of b just slightly to b=2.1±0.05. That 5% change in b changes the result to m=19.45±1.85 -> more than 20%, and with just one standard deviation of difference in b. The relationship is not linear.

[bjornsing]

That’s a clarifying example. But note that what happened with the Higgs mass was significantly more extreme than your example. All I’m saying is that I found that surprising. But you’re right, it could potentially be an extreme non-linearity that caused the surprise.