Is there new LHC data on coupling constant running?

  • #1


Gold Member

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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Answers and Replies

  • #2
Answering my own question a bit with further research (some not from the LHC and still quite slim pickings although I don't know how comprehensive my searches were and if they missed papers which they could easily have done):

The SM running of the strong coupling constant is confirmed from about 7 GeV to 1100 GeV in three overlapping recent studies. None of the recent studies confirm the running of the weak force coupling constant. The running of the fine structure constant is confirmed in the recent studies only up to a little less than 1 GeV (although older studies have confirmed its running at considerably higher energies).

arXiv:1801.09007 [pdf, other] hep-ex This confirms that there is a hadronic contribution to the running of the fine structure constant at low energies with 5 sigma as predicted in QED, but is not a comprehensive comparison of theory to experiment at high energies. Instead it is a high precision confirmation at very low energies.
Recent results from KLOE-2
Authors: Wojciech Krzemien
Abstract: The most recent results from the KLOE experiment are presented, covering: the measurement of the running fine-structure constant alpha_em,the Dalitz plot measurement of eta to pi+pi-pi0, the search of a U boson, tests of discrete symmetries and quantum coherence. The KLOE-2 Collaboration will take data until mid 2018 aiming to collect 5 inversed fb increasing the data set, in order to produce new precision measurements and continue studies of fundamental symmetries and New Physics.
Submitted 26 January, 2018; originally announced January 2018.
Comments: 6 pages, 4 figures. talk presented at Particles and Nuclei International Conference 2017 (PANIC 2017)

arXiv:1709.07251 [pdf, other] hep-ex "the running of the strong coupling is confirmed in the accessible range of approximately 7 to 90 GeV."
Determination of the strong coupling constant αs(MZ) in next-to-next-to-leading order QCD using H1 jet cross section measurements
Authors: H1 collaboration, V. Andreev, A. Baghdasaryan, K. Begzsuren, A. Belousov, V. Bertone, A. Bolz, V. Boudry, G. Brandt, V. Brisson, D. Britzger, A. Buniatyan, A. Bylinkin, L. Bystritskaya, A. J. Campbell, K. B. Cantun Avila, K. Cerny, V. Chekelian, J. G. Contreras, J. Cvach, J. Currie, J. B. Dainton, K. Daum, C. Diaconu, M. Dobre , et al. (123 additional authors not shown)
Abstract: The strong coupling constant αs(MZ) is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic ep scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of αs(MZ) at the Z-boson mass mZ are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be αs(MZ)=0.1157(20)exp(29)th. Complementary, \asmz\ is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value αs(MZ)=0.1142(28)totobtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations.
Submitted 21 September, 2017; originally announced September 2017.
Comments: 45 pages, 17 figures
Report number: DESY17-137

arXiv:1709.01171 [pdf, other] hep-ex This is from the LHC and pertains to the running of a coupling constant but isn't a complete measurement of the running of the coupling constant, only one contribution to it.
Measurement of the e+e−→π+π−π0π0 cross section using initial-state radiation at BaBar
Authors: The BaBar Collaboration
Abstract: The process e+e−→π+π−2π0γ is investigated by means of the initial-state radiation technique, where a photon is emitted from the incoming electron or positron. Using 454.3fb−1 of data collected around a center-of-mass energy of s√=10.58GeV by the BaBar experiment at SLAC, approximately 150000 signal events are obtained. The corresponding non-radiative cross section is measured with a relative uncertainty of 3.6% in the energy region around 1.5GeV, surpassing all existing measurements in precision. Using this new result, the channel's contribution to the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is calculated as (gπ+π−2π0μ−2)/2=(17.9±0.1stat±0.6syst)×10−10 in the energy range 0.85GeV<ECM<1.8GeV. In the same energy range, the impact on the running of the fine structure constant at the Z0-pole is determined as Δαπ+π−2π0(M2Z)=(4.44±0.02stat±0.14syst)×10−4. Furthermore, intermediate resonances are studied and especially the cross section of the process e+e−→ωπ0→π+π−2π0 is measured.
Submitted 26 October, 2017; v1 submitted 4 September, 2017; originally announced September 2017.
Comments: Version accepted by PRD. 19 pages, 21 figures
Report number: SLAC-PUB-17147
Journal ref: Phys. Rev. D 96, 092009 (2017)

arXiv:1707.03248 [pdf, other] hep-ex The money chart is on page 4 and shows that the running of the charm quark mass is consistent with the SM prediction from 3 GeV to 145 GeV given quite wide error bars in the measurements.
Recent investigations of QCD at HERA
Authors: Matthew Wing
Abstract: The latest results from the H1 and ZEUS collaborations which challenge the QCD description of high energy ep collisions are presented. Data from HERA continue to provide precision measurements and are compared to the latest theoretical predictions. Measurements of new processes are also presented as well as investigation of regions where perturbative QCD fails to describe the data. Four themes are presented here. Measurements of hard QCD processes, prompt photon and jet production, are used to compare to the latest theoretical predictions and, in the case of jet production, used to make high-precision extractions of the strong coupling constant up to next-next-to-leading order in QCD. All H1 and ZEUS charm and beauty cross sections in deep inelastic scattering have been combined and used to extract heavy-quark masses, including the running of the charm-quark mass with the scale of the process. Factorisation in diffraction has been investigated in charm production in deep inelastic scattering and prompt photon production in diffractive photoproduction has been measured for the first time. Finally, the inclusive data on deep inelastic scattering is presented in various forms in order to allow investigation of the underlying mechanism at very low photon virtuality Q2and low Bjorken x.
Submitted 17 July, 2017; v1 submitted 11 July, 2017; originally announced July 2017.
Comments: 11 pages, 9 figures. submitted to the proceedings of the "DIS2017" Workshop, Birmingham, UK. Updated with some additional references

This paper seems to be the only clear fit to my original question which is a bit disappointing. Pages 15-24 are relevant and the money chart is at page 23 of the pdf file showing agreement with the SM to 1.1 TeV and if anything a trend towards observations a bit on the low side relative to the SM prediction but within 1 sigma below it, past 140 GeV, rather than higher than the SM prediction by about 7-8% as predicted in the MSSM. The conclusion states that the uncertainties in the money chart are about 4%, so the MSSM is rejected at about 3 sigma, if my numbers in the question for which my citation link went bad are accurate.
arXiv:1707.02562 [pdf, other] hep-ex
Determination of the strong coupling constant αs from transverse energy-energy correlations in multijet events at s√=8 TeV using the ATLAS detector
Authors: ATLAS Collaboration
Abstract: Measurements of transverse energy-energy correlations and their associated asymmetries in multi-jet events using the ATLAS detector at the LHC are presented. The data used correspond to s√=8 TeV proton-proton collisions with an integrated luminosity of 20.2 fb−1. The results are presented in bins of the scalar sum of the transverse momenta of the two leading jets, unfolded to the particle level and compared to the predictions from Monte Carlo simulations. A comparison with next-to-leading-order perturbative QCD is also performed, showing excellent agreement within the uncertainties. From this comparison, the value of the strong coupling constant is extracted for different energy regimes, thus testing the running of αs(μ) predicted in QCD up to scales over 1 TeV. A global fit to the transverse energy-energy correlation distributions yields αs(mZ)=0.1162±0.0011 (exp.)+0.0084−0.0070 (theo.), while a global fit to the asymmetry distributions yields a value of αs(mZ)=0.1196±0.0013 (exp.)+0.0075−0.0045 (theo.).
Submitted 22 January, 2018; v1 submitted 9 July, 2017; originally announced July 2017.
Comments: 32 pages plus author list (49 pages total), 11 figures, 13 tables, published in Eur. Phys. J. C, All figures including auxiliary figures are available at
Report number: CERN-EP-2017-093
Journal ref: Eur. Phys. J. 77 (2017) 872

arXiv:1705.08793 [pdf, ps, other]
Measurement of the running of the fine structure constant below 1 GeV with the KLOE detector (not LHC but still notable).
Authors: V. De Leo
Abstract: The precision measurement of the dσ(e+e−→μ+μ−γ)/ds√ cross section with the photon emitted in the initial state with the KLOE detector has been used to measure the running of the QED coupling constant α(s) in the energy range 0.6 <s√<0.975 GeV in the time-like region. We were able to achieve a significance of the hadronic contribution to the running of α(s) of more than 5σ with a clear contribution of the ρ−ω resonances to the photon propagator. The real and imaginary part of the shift Δα to the running has been extracted and a fit of the real part allowed us to measure the branching fraction BR(ω→μ+μ−) = (6.6±1.4stat±1.7syst )⋅10−5.
Submitted 24 May, 2017; originally announced May 2017.
Comments: 5 pages, 3 figures, Rencontres de Moriond, QCD and High Energy Interactions 2017

arXiv:1609.06631 [pdf, other] hep-ex
Measurement of the running of the fine structure constant below 1 GeV with the KLOE Detector
Authors: The KLOE-2 Collaboration, :, A. Anastasi, D. Babusci, G. Bencivenni, M. Berlowski, C. Bloise, F. Bossi, P. Branchini, A. Budano,L. Caldeira Balkeståhl, B. Cao, F. Ceradini, P. Ciambrone, F. Curciarello, E. Czerwiński, G. D'Agostini, E. Dané, V. De Leo, E. De Lucia, A. De Santis, P. De Simone, A. Di Cicco, A. Di Domenico, R. Di Salvo , et al. (42 additional authors not shown)
Abstract: We have measured the running of the effective QED coupling constant α(s) in the time-like region 0.6<s√<0.975GeV with the KLOE detector at DAΦNE using the Initial State Radiation process e+e−→μ+μ−γ. It represents the first measurement of the running of α(s) in this energy region. Our results show a more than 5σ significance of the hadronic contribution to the running of α(s), which is the strongest direct evidence both in time- and space-like regions achieved in a single measurement. By using the e+e−→π+π− cross section measured by KLOE, the real and imaginary part of the shift Δα(s) has been extracted. By a fit of the real part of Δα(s) and assuming the lepton universality the branching ratio BR(ω→μ+μ−)=(6.6±1.4stat±1.7syst)⋅10−5 has been determined.
Submitted 10 April, 2017; v1 submitted 21 September, 2016; originally announced September 2016.
Comments: 19 pages, 8 figures, version accepted for publication in Phys. Lett. B

arXiv:1406.4709 [pdf, ps, other] hep-ex
Measurement of Multijet Production in ep Collisions at High Q^2 and Determination of the Strong Coupling alpha_s
Authors: H1 Collaboration
Abstract: Inclusive jet, dijet and trijet differential cross sections are measured in neutral current deep-inelastic scattering for exchanged boson virtualities 150 < Q^2 < 15000 GeV^2 using the H1 detector at HERA. The data were taken in the years 2003 to 2007 and correspond to an integrated luminosity of 351 pb^{-1}. Double differential Jet cross sections are obtained using a regularised unfolding procedure. They are presented as a function of Q^2 and the transverse momentum of the jet, P_T^jet, and as a function of Q^2 and the proton's longitudinal momentum fraction, Xi, carried by the parton participating in the hard interaction. In addition normalised double differential jet cross sections are measured as the ratio of the jet cross sections to the inclusive neutral current cross sections in the respective Q^2 bins of the jet measurements. Compared to earlier work, the measurements benefit from an improved reconstruction and calibration of the hadronic final state. The cross sections are compared to perturbative QCD calculations in next-to-leading order and are used to determine the running coupling and the value of the strong coupling constant as alpha_s(M_Z) = 0.1165 (8)_exp (38)_{pdf,theo}.
Submitted 6 October, 2014; v1 submitted 18 June, 2014; originally announced June 2014.
Comments: 84 Pages, 22 figure, 40 tables, submitted to EPJC
Report number: DESY-14-089

arXiv:1207.4957 [pdf, ps, other] hep-ex This is a lagging Tevatron result.
Measurement of angular correlations of jets at sqrt(s)=1.96 TeV and determination of the strong coupling at high momentum transfers
Authors: D0 Collaboration
Abstract: We present a measurement of the average value of a new observable at hadron colliders that is sensitive to QCD dynamics and to the strong coupling constant, while being only weakly sensitive to parton distribution functions. The observable measures the angular correlations of jets and is defined as the number of neighboring jets above a given transverse momentum threshold which accompany a given jet within a given distance Delta-R in the plane of rapidity and azimuthal angle. The ensemble average over all jets in an inclusive jet sample is measured and the results are presented as a function of transverse momentum of the inclusive jets, in different regions of Delta-R and for different transverse momentum requirements for the neighboring jets. The measurement is based on a data set corresponding to an integrated luminosity of 0.7 fb-1 collected with the D0 detector at the Fermilab Tevatron Collider in pp-bar collisions at sqrt(s)=1.96 The results are well described by a perturbative QCD calculation in next-to-leading order in the strong coupling constant, corrected for non-perturbative effects. From these results, we extract the strong coupling and test the QCD predictions for its running over a range of momentum transfers of 50-400 GeV.
Submitted 3 December, 2012; v1 submitted 20 July, 2012; originally announced July 2012.
Comments: 10 pages, 3 figures, 3 tables; v2 as published in Phys. Lett. B
Report number: FERMILAB-PUB-12-397-E
Journal ref: Phys.Lett. B 718 (2012) 56-63

This paper discussed what LHC should be able to see not what it actually did see.
arXiv:1202.2641 [pdf, other] hep-ex
QCD and low-x physics at a Large Hadron electron Collider
Authors: Paul Laycock
Abstract: The Large Hadron electron Collider (LHeC) is a proposed facility which will exploit the new world of energy and intensity offered by the LHC for electron-proton scattering, through the addition of a new electron accelerator. This contribution, which is derived from the draft CERN-ECFA-NuPECC Conceptual Design report (due for release in 2012), addresses the expected impact of the LHeC precision and extended kinematic range for low Bjorken-x and diffractive physics, and detailed simulation studies and prospects for high precision QCD and electroweak fits. Numerous observables which are sensitive to the expected low-x saturation of the parton densities are explored. These include the inclusive electron-proton scattering cross section and the related structure functions F2 and FL, as well as exclusive processes such as deeply-virtual Compton scattering and quasi-elastic heavy vector meson production and diffractive virtual photon dissociation. With a hundred times the luminosity that was achieved at HERA, salient expectations for the LHeC include the complete determination of all light and heavy quark parton distributions for the first time, the high precision extraction of the gluon density, the determination of the strong coupling constant to per-mil accuracy and the precision study of the running of the electroweak mixing angle.
Submitted 13 February, 2012; originally announced February 2012.
Comments: The 2011 Europhysics Conference on High Energy Physics-HEP 2011

arXiv:1106.2991 [pdf, ps, other] hep-ex
Recent BES measurements and the hadronic contribution to the QED vacuum polarization
Authors: H. Burkhardt, B. Pietrzyk
Abstract: We have updated our evaluation of the hadronic contribution to the running of the QED fine structure constant using the recent precise measurements of the e+e- annihilation at the center-of-mass (c.m.s.) energy region between 2.6 and 3.65 GeV performed by the BES collaboration. In the low energy region, around the rho resonance, we include the recent measurements from the BABAR, CDM-2, KLOE and SND collaborations. We obtain Delta alpha (5)_had (s) = 0.02750 +/- 0.00033 at s = m_Z^2.
Submitted 15 June, 2011; originally announced June 2011.
Comments: 3 pages, 1 figure
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