Abstract
We examine physicists’ charge of ad hocness against the Higgs mechanism in the standard model of elementary particle physics. We argue that even though this charge never rested on a clear-cut and well-entrenched definition of “ad hoc”, it is based on conceptual and methodological assumptions and principles that are well-founded elements of the scientific practice of high-energy particle physics. We further evaluate the implications of the recent discovery of a Higgs-like particle at the CERN’s Large Hadron Collider for the charge of ad hocness against the Higgs mechanism.
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Notes
On July 4, 2012, ATLAS and CMS, the two largest experimental collaborations at CERN, announced the observation of a new particle whose properties, as measured up to now, agree well with those of a Higgs boson to be expected from the SMHM; see (ATLAS Collaboration 2012) and (CMS Collaboration 2012). Meanwhile, more data have been collected and analyzed, and the “observation” has been upgraded to a “discovery”; see (ATLAS Collaboration 2013) and (CMS Collaboration 2013).
These considerations are enforced by noting that from a gauge-independent perspective, local gauge symmetry is never broken and the Higgs field, as a gauge-dependent variable, has zero expectation value under all conditions. See (Elitzur 1975) for an important result on this matter and (Friederich 2013, Sects. 5, 6) for a more detailed discussion of the ramifications of this and other results that is aimed at philosophers.
Even though the values of parameters used in the SMHM are theoretically unconstrained and therefore arbitrary, they appear by no means random. For example, the so-called CKM matrix which relates the three quark generations in the SM, is approximately diagonal, even though its elements are not in any way determined by the theory and could therefore be arbitrary. Other oddities are the enormous spread of the charged-fermion masses, spanning six orders of magnitude, with the largest one (the top-quark mass) being suspiciously close to the Higgs field’s vacuum expectation value.
See (Karaca 2010), Chapter 6, for a more detailed overview of philosophical accounts of ad hoc hypotheses.
The fact that the neutrino and the trans-Uranian planet hypotheses were independently “confirmed” in the past and, as a result of this, no charge of “ad hocness” is raised against them any more seems to vindicate the general consensus on ad hoc hypotheses indicated by Leplin’s condition of justification.
In 1979 S. Glashow shared the Nobel prize with S. Weinberg and A. Salam “for their contributions to the theory of the unified weak and electromagnetic interactions between elementary particles” (http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/).
See (Karaca 2010), Chapter 7, for the original statement of the claim that the SMHM is not strictly speaking ad hoc on any account according to which ad hocness requires that a conflict be removed between an established theory and incoming empirical data. Rather, Karaca argues that the SMHM is an ad hoc hypothesis that was proposed to solve a conceptual problem, namely, the problem of how to account for the non-zero masses of vector bosons while preserving the gauge invariance of the theory.
Whether Weinberg himself considered his theory a modification of Glashow’s seems difficult to decide. His only reference to Glashow’s model is in a footnote, where he characterizes it as “similar to [his own model]; the chief difference is that Glashow introduces symmetry-breaking terms into the Lagrangian, and therefore gets less definite predictions.” (Weinberg 1967, p. 1266)
The failure of renormalizability in Glashow’s theory may have been the chief reason why it was not recognized earlier as an important contribution. According to the Science Citation Index (Glashow 1961) was cited only once per year between 1961 and 1967. In fact, even Weinberg’s paper was cited less than five times in the three years between its publication and ’t Hooft’s proof of renormalizability (’t Hooft 1971). For a historical comparison of Glashow’s and Weinberg’s theories, see (Karaca 2013).
To arrive at the SM from the starting point of the SM0 is conceptually more straightforward than to arrive at the SM from the starting point of Glashow’s theory, which, however, is closer to the actual historical course of events. Thus, whether one prefers to conceive of the SM as an ad hoc modification of Glashow’s theory or of the SM0 depends, respectively, on whether one prefers a historical perspective or one of rational reconstruction. (We would like to thank an anonymous referee for proposing this distinction.)
The latest results can be accessed from the following URLs (retrieved on February 17, 2014) for the ATLAS and CMS experiments, respectively: https://twiki.cern.ch/twiki/bin/view/AtlasPublic/WebHome#Physics_papers; https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResults.
The idea alluded to here is that considerations involving the string theory landscape may help dispelling the naturalness problem by integrating the SM in a multiverse scenario, where anthropic arguments may be used to explain away the perceived fine tuning of fundamental parameters as an unproblematic observation-selection effect. See (Donoghue 2007) for details.
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Acknowledgments
This research is part of the project “An Ontological and Epistemological Analysis of the Higgs-mechanism,” funded by the Deutsche Forschungsgemeinschaft (DFG, contract HA 2990/4-1), within the research collaboration “The Epistemology of the Large Hadron Collider (LHC)” at the University of Wuppertal: http://www.lhc-epistemologie.uni-wuppertal.de. The authors would like to thank two anonymous referees, as well as audiences at conferences and seminars in Ankara, Dresden, Tel Aviv and Wuppertal, for thoughtful comments and suggestions.
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Friederich, S., Harlander, R. & Karaca, K. Philosophical perspectives on ad hoc hypotheses and the Higgs mechanism. Synthese 191, 3897–3917 (2014). https://doi.org/10.1007/s11229-014-0504-4
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DOI: https://doi.org/10.1007/s11229-014-0504-4