Wednesday, September 16, 2015

No Surprises In LHC Strong Force Coupling Constant Measurements


In the Standard Model, the strong force coupling constant and the six quark masses are the only experimentally measured parameters of QCD, and the value of the strong force coupling constant is known much less exactly than the electromagnetic coupling constant and the weak force coupling constant.

Like the other two Standard Model forces, the strength of the strong force coupling constant in the Standard Model is a function of the energy scale of the interactions in which it is measured.  Its strength peaks in the general vicinity of the energy scale of the rest mass of the proton and gets weaker at lower and at higher energy scales according to an exactly known formula whose precise terms depend upon the conventions of the renormalization scheme used to define the quark masses, of which there are several versions in widespread use (which are equivalent once operationalized in an experimental setting).  It is customary to quote the value of the strong force coupling constant at its value renormalized to what it would be at the energy scale of the Z boson mass (about 90.1 GeV/c^2).

The New Data

The CMS and ATLAS experiments at the LHC released data today on their measurements of the strong force coupling constant (alpha S) in LHC Run 1, both normalized to strength at the Z boson mass using the running of the strong force coupling constant with energy scale prescribed by the Standard Model, and with raw measurements at energy scales that for the first time exceed 1 TeV.

The New Alpha S Measurements

All of the strong force coupling constant strengths normalized to the Z boson mass are consistent at a one standard deviation level with the Particle Data Group world average is a dimensionless 0.1185(6), although the consistency of the new measurements with the old world average is partially due to the fact that the CMS and ATLAS measurements have much greater margins of errors than the world average.

All but one of the CMS and ATLAS measurements, however, were below the world average and one was identical to the world average with larger error bars, so the LHC data is going to pull down the world average to some value below 0.1185 in coming years, although how much is hard to tell. The Particle Data Group uses a weighted average proportionate to the margin of error in each independent measurement, so the high margin of error LHC measurements may not have all that much weight in the average.

New Measurements Of The Running of Alpha S

The running of the strong force coupling constant as measured by the LHC is also consistent with the Standard Model expectation, which constrains the parameter space of theories such as SUSY in which the running of the strong force coupling constant with higher energy scales differs significantly from the Standard Model expectation. This constraint isn't all that strict yet, however, for two reasons.  First, because the margins of error in these measurements are great.  Second, because these measurements are at energy scales only modestly above those of previous measurements, even though symbolically, breaking the 1 TeV energy scale barrier is a big deal.

How much precision would we need to get more than an interesting hint of SUSY at the LHC?

As I noted previously at this blog in January of 2014 (emphasis and material in the square brackets added):
The strong force coupling constant, which is 0.1184(7) at the Z boson mass, would be about 0.0969 at 730 GeV and about 0.0872 at 1460 GeV, in the Standard Model and the highest energies at which the strong force coupling constant could be measured at the LHC is probably in this vicinity.

In contrast, in the MSSM [i.e. the Minimal Supersymmetric Model], we would expect a strong force coupling constant of about 0.1024 at 730 GeV (about 5.7% stronger) and about 0.0952 at 1460 GeV (about 9% stronger).

Current individual measurements of the strong force coupling constant at energies of about 40 GeV and up (i.e. without global fitting or averaging over multiple experimental measurements at a variety of energy scales), have error bars of plus or minus 5% to 10% of the measured values. But, even a two sigma distinction between the SM prediction and SUSY prediction would require a measurement precision of about twice the percentage difference between the predicted strength under the two models, and a five sigma discovery confidence would require the measurement to be made with 1%-2% precision (with somewhat less precision being tolerable at higher energy scales).
Total uncertainty in the latest measurements is 3.5%-5.5% in one of the measurements, 4.7% in another, 6%-15% in a third (with uncertain in energy scale measurements dominating), 4%-6% in a fourth, and 2.4% in a fifth.  These error bars, in general, are somewhat smaller than anticipated, but are still not small enough to definitively distinguish between the SM and SUSY predictions.

The world average measurement of the strong force coupling constant normalized to the Z boson mass has an uncertainty of less than 0.6%, but that requires aggregating many independent measurements.  This isn't possible when trying to determine the running of the strong force coupling constant at energy scales that only the LHC can reach.

Hints So Far

At a bit over 1 TeV the MSSM expectation for the strong force coupling constant is about 7-8% strong than the Standard Model expectation.  Yet, so far, the high energy measurements of the running of the strong force coupling constant have been weaker than the quite precisely measured world average value of this Standard Model parameter.

This is the opposite of what we would expect if SUSY were an accurate description of Nature.

While the statistical significance of the result isn't great, the LHC data so far favor the SM hypothesis relative to the SUSY hypothesis, although not yet to a statistically significant degree (realistically somewhat less than 2 sigma).  Look elsewhere effects do not apply to the statistical significance of this result to make it even less significant, however, because this is basically a single combined measurement from both experiments and there is no comparable measurement anywhere else at the LHC.

The error bars would have to be about 2.5 times smaller to rule out the MSSM expectation and to greatly constrain SUSY parameter space.  But, only some of the simplifications of SUSY theories present in the MSSM are relevant to determining the terms of the beta function that governs the running of the strong force coupling constant in SUSY theories.  So, this constraint, when and if it is established, will have much broader applicability than many of the other model dependent constraints on SUSY parameter space determined in a model dependent way using the MSSM.

Prospects For LHC Run 2

Measurements of the running of the strong force coupling constant at even higher energies and with smaller margins of error will be one of the most important experimental results to watch at LHC Run 2 because it has the potential to discriminate between SUSY and SM predictions at a lower energy scale that the energy scale at which new particles would be discovered in SUSY theories with the same parameters.  We should almost surely see anomalies in the running of the strong force coupling constant before we definitively discover new particles, because changes in the running of the strong force coupling constant should manifest at lower energy scales.

LHC Run 2 may provide less insight, however, into the absolute value of the strong force coupling constant because even quite small differences between the measured values of the strong force coupling constant at high energies translate into quite big differences in the value of the strong force coupling constant once they are normalized to the Z boson mass according to the Standard Model formula for the running of the strong force coupling constant.  In other words, errors at high energy scales are magnified when measurements are converted to lower energy scale equivalents.

Unless the scientists at CERN can make some breakthroughs in reducing systemic error and in particular in reducing uncertainty in energy scale determinations in QCD events, however, this kind of data is unlikely by itself to produce a breakthrough.  All it can provide are strong hints, and so far, those strong hints favor the Standard Model rather than beyond the Standard Model physics.

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