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From a boson to the standard model Higgs: a case study in confirmation and model dynamics

  • S.I.: Reasoning in Physics
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Abstract

Our paper studies the anatomy of the discovery of the Higgs boson at the Large Hadron Collider and its influence on the broader model landscape of particle physics. We investigate the phases of this discovery, which led to a crucial reconfiguration of the model landscape of elementary particle physics and eventually to a confirmation of the standard model (SM). A keyword search of preprints covering the electroweak symmetry breaking (EWSB) sector of particle physics, along with an examination of physicists own understanding of the discovery as documented in semiannual conferences, has allowed us an empirical investigation of its model dynamics. From our analyses we draw two main philosophical lessons concerning the nature of scientific reasoning in a complex experimental and theoretical environment. For one, from a confirmation standpoint, some SM alternatives could be considered even more confirmed by the Higgs discovery than the SM. Nevertheless, the SM largely remains the commonly accepted account of EWSB. We present criteria for comparing degrees of confirmation and expose some limits of a purely logical approach to understanding the Higgs discovery as a victory for the SM. Second, we understand the persistence of SM alternatives in the face of disfavourable evidence by borrowing the Lakatosian concept of a research programme, where the core idea behind a group of models survives, while other aspects adapt to incoming data. In order to apply this framework to the model landscape of EWSB, we must introduce a new category of research programme, the model-group, and we test its viability using the example of composite Higgs models.

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Notes

  1. A \(\hbox {Z}^*\) is an off-shell Z boson with a significantly different mass from the default one.

  2. In contrast to a ‘global significance’, this does not account for the look-elsewhere effect.

  3. See Franklin (2013) for the criteria particle physicists use to claim ‘evidence’ versus ‘observation’ or ‘exclusion.’

  4. This parameter space is considerably smaller than that of the SM, which makes it a bolder and more precise prediction, though small increases of the limit are possible (for example, the Higgs mass would increase logarithmically if supersymmetric particles were significantly heavier than 1 TeV). These bolder predictions have interesting implications for the confirmation of these hypotheses, which we will discuss further in Sect. 4.1.2.

  5. The construction of a linear \(e^+e^-\) collider (ILC) is being considered and could lead to an improvement of the coupling measurements by some factor of 10, but it is unclear when it would become operational.

  6. These groups include the ones we discussed in the previous section, as well as the SM itself.

  7. Because there is no single keyword term for the SM Higgs, it has been estimated using keywords for experimental results and measurements on the Higgs boson doublet which do not feature supersymmetry, dark matter, or charged or composite Higgses (see “Appendix A”).

  8. This is distinct from a non-technical understanding of what it means to confirm a hypothesis, which brings with it a sense of finality or certainty. This is perhaps why physicists are hesitant to use the word ‘confirm’ even though it is appropriate in the philosophy of science.

  9. For a more in-depth discussion of ad-hocness and the SM Higgs, see Friederich et al. (2014). They argue that the most crucial characteristic of an ad hoc hypothesis, a lack of experimental evidence, is no longer obeyed now that Higgs boson has been discovered.

  10. We cannot be certain that the particle is indeed elementary, but we will follow the views of physicists and tentatively accept the confirmation of the SMHH.

  11. There are other scalar particles, but these are not elementary particles like the SM Higgs boson.

  12. The importance is also reflected in the press release quoted in Sect. 2.4. It is interesting to note that the measurement of the \(J^P\) = \(0^+\) quantum numbers were performed by discriminating against different spin-parities. However, this was not performed in view of alternative models.

  13. Though this is not really considered a show stopper for SMHH confirmation.

  14. This paradox arises out of two principles: Nicod’s Rule, which states that \(Ra \wedge Ba\) confirms \(\forall x \left( Rx \rightarrow Bx\right) \), and the Equivalence Rule, that confirmation of a hypothesis confirms logically equivalent hypotheses. So, because \(H_1\): All ravens are black and \(H_2\): All non-black things are non-ravens are equivalent there is no way to formally distinguish between these types of evidence.

  15. To be more precise: it predicts four neutral electroweak spin-\(\frac{1}{2}\) particles which can mix into four ’neutralino’ states.

  16. In a frequently used quip, proponents of SUSY claim that half of its particles have already been discovered.

  17. Significantly tighter constraints have been derived from precision measurements, implying a probability of a 125 GeV Higgs to be at the 0.2 level. For the sake of the argument we will not use this in the following.

  18. There exists a small (logarithmic) dependence of this bound on the masses of the SUSY particles. Even if more Higgs multiplets exist, the bound would only rise to 150 GeV.

  19. Besides, DM candidates are also predicted in other BSM models, so understanding DM better may not bolster MSSM’s confirmation.

  20. The experimental sensitivity of a model with certain parameters qualifies the expected exclusion of a predicted signal, conventionally given at 95% confidence. It is obtained by simulating the SM both with and without the model in question, accounting for the proper luminosity, background processes, and detector effects. The expected yield from assuming the SM alone is calculated, then the upper limit of that yield at 95% confidence is determined. This yield is then compared with that of another simulation which incorporates the model, including the respective statistical and systematic uncertainties. If the latter is above the former, the model is considered open to exclusion and the experiment is considered to have the sensitivity to do so. Conversely, one can use this procedure to calculate the probability of discovering a signal, which is conventionally assumed to require a \(5\sigma \) significance above the pure SM expectation (see, e.g., Cranmer 2015).

  21. Johansson and Matsubara (2011) assess string theory using a Lakaotosian framework, for instance.

  22. A quick note: though we borrow the apparatus of research programmes from Lakatos, we do not commit ourselves to the rest of his philosophy.

  23. Progressiveness requires an expansion of the empirical content of a research programme, largely in the form of novel, risky predictions.

  24. We are agnostic on the status of the SM as a model or a theory. Even before the Higgs boson discovery many physicists were calling it a theory and that belief has only increased [see Iliopoulos (2014), who suggests referring to it as the “Standard Theory”]. Because our reading of Lakatos labels it a research programme either way, the status of the SM is irrelevant to our argument.

  25. As they put it, this “autonomy is the result of two components (1) the fact that models function in a way that is partially independent of theory and (2) in many cases they are constructed with a minimal reliance on high level theory” (Morgan and Morrison 1999, 43).

  26. Indeed, Lakatos uses examples, like the Bohr atom, which seem more like models than theories. Meanwhile, the work being done in, say, SUSY has many of the characteristics Lakatos ascribes to theories.

  27. An earlier classification of models around core ideas appears in Borrelli (2012), where she utilizes the notion of “theoretical cores” from Morrison (2007). However, we feel that the framework of research programmes provides a clearer picture for understanding the model landscape of particle physics.

  28. The boundaries of a model-group can be somewhat porous, as physicists and ideas often move from one to another. Elements are cross pollinated between research programmes. This, however, does not contradict the Lakatosian framework we are using, since it allows for such exchanges as long as each research programme as a whole remains intact.

  29. Our account is not meant to explain why physicists choose to work within a particular research programme. As discussed in the literature (see, e.g., Mättig and Stöltzner 2019), the reasons include epistemic and pragmatic virtues.

  30. We will reserve a more detailed discussion of EFTs and OPEs for another occasion.

  31. See Laudan (1978).

  32. The naturalness problem arises from the significant differences in scale between various SM parameters. Solving it has long driven model builders in particle physics (see e.g. Giudice 2013).

  33. In defending the motivations to pursue any BSM programme, Peskin claims

    In seeking an explanation for electroweak symmetry breaking, we could just write down the minimal Lagrangian available. However, for me, it is much more attractive to look for a theory in which electroweak symmetry breaking emerges from a definite physical idea. If the idea is a profound one, it will naturally lead to new phenomena that we can discover in experiments (Peskin 1997, 65).

  34. See, e.g., Arkani-Hamed et al. (2002) and Agashe et al. (2005).

  35. See, e.g., the discussions in Redi and Tesi (2012) and Marzocca et al. (2012).

  36. Fermion mass generation was another problem for TC models.

  37. Using the search terms: ‘find c Nucl Phys B365 259 and d 1991->2011 and (k “Higgs model: composite” or k “Higgs particle: composite”)’ and ‘find c Nucl Phys B365 259 and d 2012->2017 and (k “Higgs model: composite” or k “Higgs particle: composite”)’.

  38. There were attempts to explain the strange di-photon channel findings using CH models. Chala (2013), for example, provides a CH model that incorporates the excess and also provides a DM candidate.

  39. Though, we also find that within our time frame their numbers have begun steadily decreasing.

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Acknowledgements

Our paper was written with the support of the German Research Foundation (DFG) and is part of the Research Unit “The Epistemology of the Large Hadron Collider” (FOR 2063). We are indebted to Radin Dardashti, Robert Harlander, and the rest of the research unit for their many helpful comments throughout the writing process. For detailed comments, we would also like to thank the participants of the “Reasoning in Physics” workshop organized by the Center for Advanced Studies at LMU München and our helpful anonymous reviewers.

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  1. Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 12, 53115, Bonn, Germany

    Cristin Chall, Martin King & Peter Mättig

  2. Philosophy Department, University of South Carolina, 901 Sumter St, Columbia, SC, 29210, USA

    Michael Stöltzner

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Appendix

Appendix

1.1 Search terms

The following is a list of the search terms that were used in calls to the INSPIRE system for the model-groups.

Composite Higgs models find k “technicolor” or k “Higgs model: composite” or k “Higgs particle: composite” or k “Higgs particle: Goldstone particle” or k “pNGB” or k “top: condensation” or k “little Higgs model” or (k “dynamical symmetry breaking” and k “Higgs*”) and not (k “supersymmetry*” or k “minimal supersymmetric standard model”)

SUSY-extended models find k “minimal supersymmetric standard model” or k “MSSM” or k “supersymm*” and k “Higgs*”

Non-SUSY-extended models find k “2HDM” or “Higgs particle: doublet: 2” or “Higgs particle: triplet” or “Higgs particle: doublet: 3” or “Higgs particle: charged particle” and not (k “supersymmetry*” or k “minimal supersymmetric standard model”)

Extra dimensional models find k “Higgsless” or k “Higgsless model” or (k “Randall-Sundrum model” and k “Higgs*”) or (k “dilaton” and k “Higgs*”) or (k “radion” and k “Higgs*”) or (k “warped” and k “Higgs*”) or (k “holography” and k “Higgs*”) or (k “higher-dimensional” and k “Higgs*”)

Model independent find k “effective field theory” or k “operator product expansion” or k “decay: exotic” or k “Higgs particle: invisible decay” and k “Higgs*”

Standard model Higgs find (k “experimental results” or k “precision measurement”) and k “Higgs particle*” or k “coupling: Higgs” or k “Higgs particle: doublet” or k “Higgs particle: width” or k “Higgs particle: production” and not k “technicolor*” and not k “Higgs model: composite” and not k “Higgs particle: composite” and not k “new physics*” and not k “supersymmetry*” and not k “dark matter*” and not k “Higgs particle: charged particle” and not k “minimal supersymmetric standard model”

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Chall, C., King, M., Mättig, P. et al. From a boson to the standard model Higgs: a case study in confirmation and model dynamics. Synthese 198 (Suppl 16), 3779–3811 (2021). https://doi.org/10.1007/s11229-019-02216-7

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