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I Is there a fine structure constant running anomaly?

  1. Nov 22, 2017 #1


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    The chart above, via Lubos Motl's blog which is standard in any textbook talking about supersymmetry, illustrates the running of the the inverse of the Standard Model (SM) and Minimal Supersymmetric Model (MSSM) coupling constants with energy scale for the electromagnetic force, i.e. U(1), the weak force, i.e. SU(2) and the strong force, i.e. SU(3).

    In the Standard Model the strength of the fine structure constant which is a function of the electromagnetic coupling constant, runs with energy scale. Specifically, it gets stronger at higher energy scales with a logarithmic slope. A low energies is about 1/137. At the Z boson mass it is about 1/125. A higher energies it is stronger.

    The differences between the running of the electromagnetic force coupling constant (aka the fine structure constant) in the Standard Model relative to supersymmetric (SUSY) models are fairly modest over one order of magnitude, but they are still distinct and are similar generically for a large class of SUSY models.

    Generically, the fine structure constant strengthens the electromagnetic force in SUSY models as energy scales increase more rapidly than the fine structure constant does in the Standard Model.

    Because strength of electromagnetic interactions can be measured with a precision approximately 100,000 times as great as the strong force interactions, for example, it seems as if the prospects of being able to distinguish between the Standard Model and supersymmetric models based upon the running of this coupling constant at the LHC is pretty good.

    Even back in 2000, experimenters were able to measure differences in magnitude of the fine structure constant in experiments spanning energies ranges from about 2 GeV^2 to 3434 GeV^2 with a precision equal to about a third of the observed differences in force strength at the different energy levels (which was consistent with the Standard Model prediction).

    The energies at the LHC are five to eight times as great as those made in 2000, and the precision of the measurements at the LHC on a percentage basis are probably at least somewhat improved from those made a decade and a half earlier. The amount by which the fine structure constant should run under SUSY models at peak LHC energies should be on the same order as the amount by which it should run in the Standard Model at energies two and a half to four times as great as those made in 2000.

    By 2011, measurements of the running of the fine structure constants at low GeV scale energies at the BES experiment were far more precise, measuring the differences in coupling strength due to its running with a precision of 1.2% or so. But, the study itself only measured events taking place at energies ranging from 2.6 GeV to 3.65 GeV.

    Naively, it ought to be possible to discriminate experimentally between the running of the fine structure constant in SUSY models and in the Standard Model at something on the order of 3-4 sigma by the time that the LHC's run is complete.

    Naively, if there really is such a discrepancy in the running of the fine structure constant between the Standard Model value and the observed value at the LHC, we ought to have enough data to start seeing some sort of anomaly, even if it wasn't as significant as the anomaly predicted to be discernible when all data has been collected.

    While the slope of the running of the fine structure constant in the Standard Model relative to the logarithm of the energy scale involved is fairly flat, in SUSY models that slope of the running of the fine structure constant are apparently typically kinked, becoming more pronounced at masses ca. 1-2 TeV as the impact of supersymmetric particles somewhat below those masses kick in. For whatever reason, visually at least, in charts showing the predicted running of SUSY gauge coupling constants, this kink appears more pronounced for the electroweak forces than it does, for example, for the strong force.


    Of course, feel free to correct any of my background information if it is based upon a false premise or is inaccurate and that impacts the answer to the questions asked.

    1. Have there been any experimental results since the 2011 paper that I reference (for example, at the LHC) that have identified a statistically significant discrepancy between the measured running of the fine structure constant and the running of the fine structure constant predicted by the Standard Model?

    I haven't seen any news reports or papers or pre-prints on this question, but I easily could have missed on sometime over the last six years. It could be that this result in buried in a paper with multiple results in a particular category that didn't look interesting, or it could be that the literature refers to this kind of experiment using terms different than the ones that I searched for when looking for papers of this kind.

    There have been several papers discussing strong force coupling constant measurements at the LHC, but I haven't seen any for the fine structure constant.

    My guess is that there hasn't been, because if there was, I would think that this would have been big news. But, confirmation and any available references would be nice.

    2. If not, has the running of the fine structure constant at high energies been extended beyond to 3.4 TeV energy scale measured in the data relied upon by the 2011 paper?

    Naively, it seems like the kind of measurement that the LHC experiments should be doing as a matter of course as part of their bread and butter standard set of measurements, so there ought to be some result somewhere on this question at the LHC, but I could be wrong.

    As of 2014, it looked like this was on the "to do" list at the LHC according to a paper here. The paper states that accuracy to the percent level in the 1 TeV-10 TeV energy scale range it seems should be sufficient to distinguish many models including supersymmetric models with reasonably light superpartners from the SM. But, I haven't seen any results from this proposed line of inquiry.

    Maybe this kind of measurement is not considered a high enough priority to make for some reason, or maybe it takes a really long time to analyze the relevant data for some reason.

    I am not very facile at searching the collections of data made available by the respective experiments at their websites.

    3. Does the scale at which a discrepancy arises between the running of the fine structure constant in the Standard Model and the running of the fine structure constant in a SUSY model (or in the alternative the scale at which no discrepancy is observed) naturally and obviously led to a conclusion about the energy scale at which SUSY phenomena, if they exist, arise? In particular, can measuring the running of the fine structure constant at one scale, say for example 6 TeV, tell you anything about the existence or non-existence of new physics at some much higher energy scale, for example, 18 TeV?

    I'm not quite fluid enough with the mathematics of renormalization to have a firm intuition about this question.
    Last edited: Nov 22, 2017
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  3. Nov 22, 2017 #2


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    I had always assumed that the U(1) coupling in the plot is the one of electroweak unification, so "rotated" from the electromagnetic, and then most of the precision goes away, via weinberg angle.
  4. Nov 23, 2017 #3


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    This is true. Above EW symmetry breaking, the it only makes sense to talk of the hypercharge gauge coupling, not the electromagnetic one. Also, below it, the SU(2) symmetry is broken.
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