*The Standard Model of Particle Physics is our most experimentally verified theory of nature having its final test in 2012 with the discovery of the Higgs Boson. With this, many thought we wouldn’t see any new physics beyond the Standard Model and that it was complete, but as Adam Koberinski writes, the Higgs discovery was not a verification but rather a falsification of the effective field theory framework in which the Standard Model subsides.*

When the Higgs boson was discovered and confirmed in the early 2010s, a decades-long quest to empirically confirm every aspect of the Standard Model of particle physics came to a close. Along with this triumph came disappointment — there was no further evidence for any proposed theories of physics beyond the Standard Model. Despite the major success, certain theoretical problems remain unresolved, and the way forward is no longer clear.

The Standard Model of particle physics crystallized in the mid-1970s, and describes the elementary physics of all terrestrially known types of matter. It describes three of the four fundamental physical forces: the strong nuclear force, the weak nuclear force, and the electromagnetic force. Only gravity, and gravitational mass-energy like dark matter and dark energy, fall outside its scope. When first proposed, the Standard Model predicted the existence of several elementary particles that had yet to be discovered. Over the next several decades, these missing pieces were found in particle accelerators reaching higher and higher energies, culminating with the Higgs boson in 2012.

Experimentally, then, the Standard Model seems to be a stunning success — all and only the particles that it predicts have been found. So why has the failure to discover new physics at CERN’s Large Hadron Collider caused a crisis among particle physicists? One answer is simple: we are still searching for evidence in favour of one of several candidate theories of quantum gravity, and we are running out of the most obvious places to look. But that answer is not the full story. It turns out that new physics near the Higgs mass scale was required in order for the Standard Model to remain theoretically consistent. Understanding the scope of the crisis requires digging a little deeper into the theoretical framework underlying the Standard Model.

The Standard Model is constructed within the framework of quantum field theory, which merges quantum physics with the relativistic spacetime structure discovered by Einstein. Quantum field theory is a *framework *in the sense that it provides a scaffolding of concepts, constraints, and mathematical formalism within which to construct particular theories. The theory of quantum electrodynamics, for example, is a particular quantum field theory of electromagnetic interactions.

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Regularization involves putting limits into the theory to render the infinite quantities finite ... Renormalization is the process of altering the theory so that it makes predictions that do not depend on the particular value of regulator limit, and that therefore remain finite even after these limits have been removed.

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Most realistic quantum field theories have several mathematical ambiguities, and before these are addressed, the theory will spit out infinities as predictions for probabilities of experimental outcomes. Resolving the ambiguities to yield finite predictions is done via the steps of *regularization *and *renormalization*. Regularization involves putting limits into the theory to render the infinite quantities finite. For example, one form of regularization involves truncating an infinite sum of terms after some large but finite number. Renormalization, on the other hand, is the process of altering the theory so that it makes predictions that do not depend on the particular value of regulator limit, and that therefore *remain *finite even after these limits have been removed. Renormalization is a tricky process, and it can’t always be done. Only a small set of possible quantum field theories, called *renormalizable , *can be consistently renormalized to yield a finite theory. In the early days of quantum field theory, physicists unsurprisingly required any proposed theory to be renormalizable. Since the limits put in to regularize a theory had no physical justification, any good theory should make predictions that do not depend on the choice of arbitrary limits.

However, advances in understanding renormalization led to a change in perspective. The development of the renormalization group led to a reinterpretation of the whole of quantum field theory, and a Nobel Prize for its founder Kenneth Wilson. One important aspect of this new development is the understanding of how quantum field theories change when probed at different energy scales. The electromagnetic force, for example, gets stronger when particles are collided at higher energies. Another key insight is that full renormalization is not strictly necessary. As long as quantities do not depend *too sensitively *on the exact value of the limits chosen, the theory can still make sensible predictions.

Using the renormalization group scaling transformations, theories with a regulator in the form of an upper limit energy scale can still be used to make predictions, as long as one restricts oneself to energies well below the upper limit cutoff, where those predictions are not sensitive to the exact value of the cutoff. The cutoff itself is now reinterpreted as containing physical information — it marks an energy scale beyond which the theory no longer applies. These theories came to be known as *effective field theories*, to indicate their limited domain of applicability. Renormalizable theories are special simply because they contain only terms that are unchanged in the limit where the energy that the theory is probed becomes negligible compared to the cutoff energy. Thus, the space of effective field theories is much larger than that of renormalizable theories, but contains the renormalizable theories as a subset.

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Effective field theories heed the words of the great German philosopher Ludwig Wittgenstein: “whereof one cannot speak, thereof one must remain silent”.

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Some physicists and philosophers of science have taken this effective field theory perspective to be a great conceptual advance in science. After all, every theory we have ever come up with so far has only been applicable within some restricted domain of phenomena; we have never had a so-called ‘theory of everything’. By making this domain restriction explicit, some claim that this endows our best quantum field theories with a degree of humility that all scientific theories should possess. After all, the theories don’t just make incorrect predictions outside their restricted domain; they cease to give any meaningful predictions at all. Effective field theories heed the words of the great German philosopher Ludwig Wittgenstein: “where of one cannot speak, thereof one must remain silent”.

Rather than making bold (but incorrect) claims about highly energetic phenomena, effective field theories stop working, indicating the need for a new theory. If we treat our best theories in particle physics as effective field theories, then we should expect them to begin to break down at sufficiently high energies, depending on their exact form. By trying to find this breakdown scale, we can find where we expect our best theories to fail, and where new physics should occur.

The Standard Model is a collection of renormalizable quantum field theories, and marks the state-of-the-art of our knowledge of matter. But this new perspective allows us to treat it as an effective field theory, of which the renormalizable terms are only a part. If we had some way to place a restrictive upper bound on the Standard Model’s cutoff energy, then we would have a hint at where we expect it to fail, and for new physics to appear. Luckily, there is one free parameter within the Standard Model that was expected to depend very sensitively on the value of this cutoff: the mass of the Higgs boson.

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It seemed like there were two possible options ... First, the Higgs boson really is a fundamental scalar ... [or] Second, the Standard Model is wrong

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The Higgs boson is a unique particle in the Standard Model, as it is the only fundamental scalar particle. This means that it has zero intrinsic spin, and that its mass scales proportionally to the cutoff under the renormalization group scaling transformations. Other fundamental particles gain their mass through interaction with the Higgs boson, but the Higgs itself is unique in that it needs a mass term that is put in by brute force. This unique scaling behaviour for the Higgs was one of the features of the Standard Model that physicists were most excited about testing when the Large Hadron Collider started running. It seemed like there were two possible options, both pointing to the discovery of new fundamental physics. First, the Higgs boson *really is *a fundamental scalar, in which case its mass is roughly at the energy scale that we expect new physics to occur. Finding the Higgs boson would then mean that we should also find something not predicted by the Standard Model nearby. Second, the Standard Model is wrong, and the Higgs is not a fundamental scalar. Either it has spin, or is a composite of more fundamental particles. In this case, we learn new physics about the Higgs boson and make changes to the Standard Model. Either way, the expectation was that we would discover something new when we found the Higgs boson at the Large Hadron Collider.

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If the Higgs boson’s mass doesn’t scale with the cutoff for the Standard Model, then it seems that something has gone wrong with our understanding of effective field theory and the way the Standard Model fits into it.

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What happened instead, however, was that we found the Higgs boson, it turned out to be a fundamental scalar particle (as far as we can tell so far), and no hints of the breakdown of the Standard Model have been found. Not only is this disappointing for those hoping to find new physics, it contradicts the effective field theory framework within which the Standard Model is situated. If the Higgs boson’s mass doesn’t scale with the cutoff for the Standard Model, then it seems that something has gone wrong with our understanding of effective field theory and the way the Standard Model fits into it.

This is a classic case of theory being falsified by experimental results. But unlike the standard caricature of hypothesis testing given in highschool science classes, this is a case where there are several possible ways to respond. A hypothesis is never tested entirely in isolation, so it is always possible to give up on background or auxiliary assumptions to hold onto the hypothesis. Here are three (reasonable) responses one could take to the current crisis in particle physics, that I outline in a recent paper.

*1. Keep trying for new solutions that retain the effective field theory framework as is. *

Prior to the discovery of the Higgs boson, physicists proposed many different theories going beyond the Standard Model, trying to predict what new physics one would see. The exact value of the Higgs mass is a prediction of many of these new theories, coming from different combinations of parameters in the higher-energy sector of the theory. But these parameters themselves are largely unconstrained until they have been measured. It is possible to “tune” the high-energy parameters in such a way that the contributions cancel out to give a Higgs mass much smaller than we would expect from a generic effective field theory analysis.

Physicists have typically taken “fine-tuning” to be a theoretical vice; explanations relying on parameters that must be carefully selected from a space of possibilities are seen as weaker than those that are insensitive to minor variations in the background conditions. But sometimes the best explanation really is sensitively dependent on the background conditions. One could argue that this is the case for the Higgs mass. Perhaps it really does scale with the cutoff for the Standard Model, but that scaling is hidden due to the cancelling out of parameters in the new theory. While possible, this explanation seems a bit ad hoc, and is not widely favoured. However, it has the virtue of maintaining all of the theoretical background from effective field theory. The downside is that we can no longer use the scaling behaviour to place good estimates on the scale at which new physics might come in; if fine-tuning is permitted, then the estimates are no better than random guesses.

*2. Reinterpret the effective field theory framework without the scaling transformations relating theories.*

An alternative perspective is that the effective field theory framework provides the right mathematical formalism for the Standard Model, but that we have been interpreting it incorrectly. If we revise the way we interpret scaling transformations, then we can eliminate the incorrect prediction that new physics should be present at roughly the Higgs mass scale. We can simply take the scaling to be a formal property of the equations that tells us nothing about other, potentially more fundamental theories. On this view, the scaling transformations are just a formal symmetry of an individual quantum field theory, without implications for new physics.

But this move seems a bit too quick. In other applications of effective field theory, the scaling transformations have reliably been informative of how different theories relate to one another at different energy scales. What is the principled reason motivating rejecting that understanding here, but not elsewhere? Or do we reject that interpretation everywhere, thereby losing some of the appeal of the framework to begin with? At best this seems like a temporary solution applied only to the Standard Model, until we have a better story to tell.

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*3. Look for beyond Standard Model physics outside the effective field theory framework.*

* *While the effective field theory framework has been successful in understanding quantum field theories up to and including the Standard Model, there is no reason to expect it to be a framework universally applicable to all contexts of new physics. On this option, we take the failed prediction seriously, and use it as evidence for the hypothesis that new physics beyond the Standard Model will have to fall outside of the effective field theory framework. Perhaps some key assumptions needed to set up an effective field theory fail to hold at energies where new physics takes place, such that we can no longer use the scaling behaviour of the Standard Model to tell us anything informative about what comes next. This option takes the crisis in particle physics most seriously, and has the virtue of providing a principled reason to keep our understanding of effective field theory unchanged outside the context of beyond Standard Model physics. Like the particular effective field theories with their energy scale cutoffs, the framework itself is limited in scope. What awaits beyond the Standard Model is something new and different from what came before. This further fits with widespread expectations from quantum gravity researchers that radically new ideas are needed to merge quantum theory with gravity.

Option 3 is the best way forward, even if it has the major drawback of leaving the possibilities for new physics almost entirely unconstrained. But even this drawback is also a tantalizing opportunity for creativity in the path forward. The history of science is full of major conceptual breakthroughs, where the only constraint from old theories is to recover most of their empirical successes. If we focus on fixing some of the (admittedly few) outstanding anomalies for the Standard Model, perhaps we will be led in entirely new directions. While the highschool picture of the scientific method may be far too simple, in this case it provides the best guidance. We should take the failed prediction of new physics seriously for our understanding of the Standard Model, and for what new physics lies beyond.

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