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ohwilleke
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Question
Has the LHC released any papers or reports on the observed running of any of the three Standard Model coupling constants with energy scale from either Run-1 or Run-2 data (or both data sets)?
Last time I looked I couldn't find any data
As of January 2014, I had not locate any papers on this topic from any of the LHC experiments, but I don't have access to great resources to look for this kind of paper other than scanning arXiv hep experiment preprints as they come out on a daily basis occasionally missing a few days or not perhaps not recognizing a relevant paper from the title and abstract alone.
Also, if there are no such papers or reports, and there is a good reason why they don't exist, that would also be helpful to know.
Why Is This About BSM Physics?
Running Coupling Constants in the SM v. BSM theories
One of the generic differences between the Standard Model and almost all beyond the Standard Model theories including supersymmetry and other grand unified theories is that the Standard Model coupling constants for the three Standard Model forces (at a layman's level usually called electromagnetism, the weak force and the strong force although with electroweak unification the terminology for the first two isn't necessarily perfect) run with energy scale pursuant to different beta functions.
In other words, many BSM theories predict that the value of the three coupling constants measured at the highest available LHC energies will be somewhat different from the SM predictions for the values of those coupling constants.
For example:
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, 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).
So, if you can make a measurement of the values at the strong force coupling constant's strength at these energy scales with 2% at 730 GeV and 4% precision at 1460 GeV, you can distinguish these two hypotheses. Also, even if you don't have enough precision to distinguish between the SM and the MSSM, you can still rule out of a lot of BSM theories with more of a difference between the SM prediction and the BSM prediction.
(The link to the source I used for these numbers in January of 2014 has gone dead on me, but please don't get overly wrapped up in their accuracy which are model dependent anyway in the BSM example, for purposes of this background portion of the post they are provided simply to provide a concrete numerical example of what I am talking about for people who can understand that better than when I am speaking in generalities.)
Similar discrepancies should exist in the "fine structure constant" (i.e. the electromagnetic coupling constant) which should get a little stronger in the MSSM than it is in the SM, for example, and in the weak force or SU(2) coupling constant (which gets weaker at higher energies in the SM, but stronger at higher energies in the MSSM, for example).
The Standard Model predictions for coupling constant beta functions (which describe the running of each respective coupling constant) have been confirmed for the strong force at low energies as far back as 2000, and for the EM force as recently as 2011 (at BES).
There was a good chance discussed before the LHC data was available, that LHC data would have made it possible to greatly extent the range of previous experimental tests of coupling constant running with energy scales. (The ability to discriminate between the SM and competing hypotheses depends both upon the magnitude of the expected difference and the margins of error in the measurements and predictions.)
The much higher energies of the LHC should be more than sufficient to greatly expand the energy scale ranges at which this is measured and to constrain significantly the amount by which beta functions in BSM theories can deviate from the SM prediction, particularly now that a lot of Run-2 data has been collected at higher energies. But, I've been surprised to see any reports about whether this is the case.
These are great global tests for BSM physics that are relatively easy to apply to particular proposed BSM theories
The running of the coupling constants measured physically is a very attractive thing to measure because, a bit like muon g-2, the running of the coupling constants is a measure that is globally sensitive to many aspects over the overall particle physics model you are using, and it is relatively easy to calculate (in theory at least) the predicted running of the coupling constants in any given BSM theory because the beta functions of the SM and of BSM models are determined entirely from theory and don't have to be experimentally measured.
In other words, given a particular set of experimentally measured values of the three coupling constants at the Z boson mass which is about 90 GeV, for example, which is known to considerable accuracy, you can calculate precisely what the value of those coupling constants will be at any given higher energy scale (e.g. 2 TeV), without further experimental input for both the SM and for any particular BSM model you care to test.
For example, if your BSM model predicts that the weak force coupling constant gets stronger at higher energies, contrary to the SM prediction that it gets weaker at higher energies, you can, without immense difficulty determine what the value should be in the SM at 2 TeV and what the value should be in your BSM model at 2 TeV, and then compare those predictions to the LHC measured value at 2 TeV with whatever error bars go into the respective predictions (due to theory impression from truncating infinite series in the beta function and due to the 100% correlated low energy measured values of those coupling constants), and into your new experimental measurement.
If the data is consistent with the SM at 2 sigma, and excludes the BSM model at 2 sigma, the BSM theory in question is usually considered to be excluded. And, by combining data on all three beta functions and using Baysean or Monte Carlo statistical methods, you can even make some pretty reliable guesses with slightly weaker tensions in some individual coupling constant beta function measurements.
A high energy measurement from the LHC would allow one greatly narrow the parameter space of possible BSM models that are consistent with measurement in a very generic and robust way for a lot of theories of ongoing theoretical interest.
This is because it is very hard to add new particles or forces to the SM in a quite broad mass range without producing significant changes to the running of one or more of these coupling constants at the energy scales that the LHC can measure, so a lack of a discrepancy can rule out a wide swath of theories that add new particles or forces in this quite broad mass range.
Because this is so useful, I'd greatly appreciate any information on LHC papers or reports so far that measure this. Analysis of the impact of the new data on BSM theories would also be great, but I'd be happy simply to locate LHC data even without this analysis.
My understanding is that experimental measurements of beta functions aren't very informative, however, if all new particles in the BSM theory are even moderately higher than the highest energy scale at which the LHC can measure these quantities directly. So, if all of your BSM particles are, for example, 20 TeV or more in mass, the LHC wouldn't be able to see the changes in the beta functions that the new particles cause (because the impact at low energies would be so modest).
So, for example, the LHC could use this as an additional way to rule out a lot of the parameter space of electroweak scale supersymmetry theories that direct searches for supersymmetric sparticles does not rule out.
Has the LHC released any papers or reports on the observed running of any of the three Standard Model coupling constants with energy scale from either Run-1 or Run-2 data (or both data sets)?
Last time I looked I couldn't find any data
As of January 2014, I had not locate any papers on this topic from any of the LHC experiments, but I don't have access to great resources to look for this kind of paper other than scanning arXiv hep experiment preprints as they come out on a daily basis occasionally missing a few days or not perhaps not recognizing a relevant paper from the title and abstract alone.
Also, if there are no such papers or reports, and there is a good reason why they don't exist, that would also be helpful to know.
Why Is This About BSM Physics?
Running Coupling Constants in the SM v. BSM theories
One of the generic differences between the Standard Model and almost all beyond the Standard Model theories including supersymmetry and other grand unified theories is that the Standard Model coupling constants for the three Standard Model forces (at a layman's level usually called electromagnetism, the weak force and the strong force although with electroweak unification the terminology for the first two isn't necessarily perfect) run with energy scale pursuant to different beta functions.
In other words, many BSM theories predict that the value of the three coupling constants measured at the highest available LHC energies will be somewhat different from the SM predictions for the values of those coupling constants.
For example:
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, 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).
So, if you can make a measurement of the values at the strong force coupling constant's strength at these energy scales with 2% at 730 GeV and 4% precision at 1460 GeV, you can distinguish these two hypotheses. Also, even if you don't have enough precision to distinguish between the SM and the MSSM, you can still rule out of a lot of BSM theories with more of a difference between the SM prediction and the BSM prediction.
(The link to the source I used for these numbers in January of 2014 has gone dead on me, but please don't get overly wrapped up in their accuracy which are model dependent anyway in the BSM example, for purposes of this background portion of the post they are provided simply to provide a concrete numerical example of what I am talking about for people who can understand that better than when I am speaking in generalities.)
Similar discrepancies should exist in the "fine structure constant" (i.e. the electromagnetic coupling constant) which should get a little stronger in the MSSM than it is in the SM, for example, and in the weak force or SU(2) coupling constant (which gets weaker at higher energies in the SM, but stronger at higher energies in the MSSM, for example).
The Standard Model predictions for coupling constant beta functions (which describe the running of each respective coupling constant) have been confirmed for the strong force at low energies as far back as 2000, and for the EM force as recently as 2011 (at BES).
There was a good chance discussed before the LHC data was available, that LHC data would have made it possible to greatly extent the range of previous experimental tests of coupling constant running with energy scales. (The ability to discriminate between the SM and competing hypotheses depends both upon the magnitude of the expected difference and the margins of error in the measurements and predictions.)
The much higher energies of the LHC should be more than sufficient to greatly expand the energy scale ranges at which this is measured and to constrain significantly the amount by which beta functions in BSM theories can deviate from the SM prediction, particularly now that a lot of Run-2 data has been collected at higher energies. But, I've been surprised to see any reports about whether this is the case.
These are great global tests for BSM physics that are relatively easy to apply to particular proposed BSM theories
The running of the coupling constants measured physically is a very attractive thing to measure because, a bit like muon g-2, the running of the coupling constants is a measure that is globally sensitive to many aspects over the overall particle physics model you are using, and it is relatively easy to calculate (in theory at least) the predicted running of the coupling constants in any given BSM theory because the beta functions of the SM and of BSM models are determined entirely from theory and don't have to be experimentally measured.
In other words, given a particular set of experimentally measured values of the three coupling constants at the Z boson mass which is about 90 GeV, for example, which is known to considerable accuracy, you can calculate precisely what the value of those coupling constants will be at any given higher energy scale (e.g. 2 TeV), without further experimental input for both the SM and for any particular BSM model you care to test.
For example, if your BSM model predicts that the weak force coupling constant gets stronger at higher energies, contrary to the SM prediction that it gets weaker at higher energies, you can, without immense difficulty determine what the value should be in the SM at 2 TeV and what the value should be in your BSM model at 2 TeV, and then compare those predictions to the LHC measured value at 2 TeV with whatever error bars go into the respective predictions (due to theory impression from truncating infinite series in the beta function and due to the 100% correlated low energy measured values of those coupling constants), and into your new experimental measurement.
If the data is consistent with the SM at 2 sigma, and excludes the BSM model at 2 sigma, the BSM theory in question is usually considered to be excluded. And, by combining data on all three beta functions and using Baysean or Monte Carlo statistical methods, you can even make some pretty reliable guesses with slightly weaker tensions in some individual coupling constant beta function measurements.
A high energy measurement from the LHC would allow one greatly narrow the parameter space of possible BSM models that are consistent with measurement in a very generic and robust way for a lot of theories of ongoing theoretical interest.
This is because it is very hard to add new particles or forces to the SM in a quite broad mass range without producing significant changes to the running of one or more of these coupling constants at the energy scales that the LHC can measure, so a lack of a discrepancy can rule out a wide swath of theories that add new particles or forces in this quite broad mass range.
Because this is so useful, I'd greatly appreciate any information on LHC papers or reports so far that measure this. Analysis of the impact of the new data on BSM theories would also be great, but I'd be happy simply to locate LHC data even without this analysis.
My understanding is that experimental measurements of beta functions aren't very informative, however, if all new particles in the BSM theory are even moderately higher than the highest energy scale at which the LHC can measure these quantities directly. So, if all of your BSM particles are, for example, 20 TeV or more in mass, the LHC wouldn't be able to see the changes in the beta functions that the new particles cause (because the impact at low energies would be so modest).
So, for example, the LHC could use this as an additional way to rule out a lot of the parameter space of electroweak scale supersymmetry theories that direct searches for supersymmetric sparticles does not rule out.
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