# Is it the Higgs? – The role of theory

by Prof. Dr. Robert Harlander / robert.harlander@uni-wuppertal.de

On July 4, 2012 ATLAS and CMS, the two big ones among the four experiments currently running at CERN’s Large Hadron Collider near Geneva, announced the discovery of a new particle. Preliminary measurements of its properties indicated that it might well be the Higgs boson that has been postulated by theoretical physicists for some fifty years. Whether this is, in fact, the case can only be determined by comparison of this particle with precise theoretical calculations. UW has played a decisive role in the ATLAS experiment. This article describes the role of theory in the discovery and measurement of the Higgs boson. Here, too, UW physicists are closely involved.

The standard model of elementary particle physics reduces the structure of matter, out of which we and the entire visible universe are composed, to a clear and well-defined mathematical scheme based on a few fundamental particles. A central element of this model is the so-called Higgs mechanism, without which the theory would only hold for relatively large distances*. Smaller distances would lead to absurd results, in particular to relative frequencies for specific decay or scattering processes that exceed 100%.

(* The diameter of a proton is in this sense ‘large’. In contrast, the standard model has been tested for distances some 10,000 times smaller.)

Superficially, the Higgs mechanism is simply a mathematical device, but as Peter Higgs remarked in his 1964 paper, it postulates the existence of a new electrically neutral particle with spin = 0. The only property of this particle that is not theoretically predetermined is its mass.

Ever since 1967, when the standard model was developed by Steven Weinberg (building on work by Sheldon Glashow), the search has been on for the Higgs boson, and the presentation of direct empirical evidence for this particle is one of the principal tasks of the Large Hadron Collider (LHC). The technological and experimental superlatives surrounding this particle accelerator were presented and discussed by Prof. Dr. Peter Mättig in OUTPUT II/2009 and by Prof. Dr. Wolfgang Wagner and Prof. Dr. Christian Zeitnitz in OUTPUT 5/2011. The present article will outline the theoretical background and developments that have played a role in the search for the Higgs boson.

Fig. 1: The ‘standard model’ of elementary particle physics: the building blocks of matter and the forces that operate between them. Source: DESY

It may today seem rather curious that the standard model was not at first particularly popular. Weinberg’s paper was cited altogether three times in the first three years after its publication. This changed overnight when Gerard ’t Hooft and Martinus Veltman demonstrated the mathematical consistency of the model in 1971. Within a year there were almost 200 citations of Weinberg’s paper – today the figure is 8000. Glashow and Weinberg, together with Abdus Salam (who had developed an analogous model to Weinberg’s), were awarded the Nobel Prize for Physics in 1979, ’t Hooft and Veltman received the Nobel Prize in 1999.The work of ’t Hooft und Veltman was not only pioneering in its results: the theoretical tools they developed remain among the most elegant and most efficient calculational methods in elementary particle physics. They allow the abstract formulations of the standard model to be translated into physical observables. Comparison with the relevant experimental measurements has up to now always been successful; indeed, the standard model has been checked in various contexts to below per mille level.

The calculations are conducted in a systematic approximation procedure in accordance with a mathematical method known as perturbation theory. The roughest approximation, the so-called ‘leading order’ (LO) requires only a simple calculation and is nowadays part of the regular lecture program for any master’s degree in physics. The higher the order of the approximation (NLO = next-to-leading order etc.), the more complex – but also more exact – the calculation. Today almost all the common observables that can be detected at the LHC are known up to NLO, the most important up to NNLO; very few are known to a still higher order.

Why are higher order calculations so important? For one thing, LO or NLO are often too imprecise – an aspect to which we will return later. But a decisive issue is that in principle all the components of the standard model enter into the calculation of every observable. According to quantum theory, interaction involves the exchange of particles. At the lowest order, interactions in electron scattering occur via photon exchange; at higher orders increasingly more and different particles are exchanged between electrons. Theoretical predictions of even simple scattering reactions depend, therefore, on the properties (mass, charge, spin) of all the particles of the standard model.

Fig. 2: A scatter event in the ATLAS detector. The tracks could indicate the decay of a Higgs boson, or be the result of one of the numerous underlying processes.Source: CERN

On this indirect basis, by comparing extremely precise measurement data from LEP (Large Electron-Positron Collider, a predecessor experiment of LHC at CERN) with the at times highly elaborate theoretical calculations, it was possible to limit the mass of the Higgs boson with 95% probability to a value below 160 gigaelectron volts (GeV) – 1 GeV is roughly the mass of a proton. This perfectly matches the mass of the new particle discovered at LHC.What does the search for the Higgs boson at the world’s particle accelerators look like? Put rather simply, what scientists look for is a signal – best of all a peak – in a suitable distribution of data points. For example at the Tevatron, a proton-antiproton accelerator at Fermilab, near Chicago, they were looking mainly for a signal in the energy distribution of the well-known W bosons (actually W boson pairs) that result from collisions. A signal of this sort could be explained by the genesis of some of the W bosons from the decay of a short-lived Higgs boson. The theory enables scientists to predict how many collision reactions must be conducted until the signal is so large that it stands out significantly from the background (i.e. from W pairs that do not result from Higgs decay) – presuming, of course, the Higgs boson actually exists.

The relevant LO prediction was made in 1979 by Ellis, Gaillard, and Nanopoulos. However, working with William B. Kilgore in 2002 we – and shortly after us two other research groups – were able to show by means of an NNLO calculation that in fact only half the expected number of collision reactions was required. This meant that the Tevatron and LHC experiments could yield significant results in the search for the Higgs in only about half the expected time.

The first quantitative results in the Higgs search were published in 2008. These were not direct indications of the Higgs boson – they were exclusion boundaries. Fig. 1 shows an example from March 2009. For a Higgs mass of between 160 and 170 GeV our calculation (in a later form, as refined and updated by other groups) predicted a signal large enough to be detected at the Tevatron. But no such signal was observed, which meant that a Higgs mass in this range could be excluded. In the final two years of its working life, the Tevatron continued to refine these boundaries. The original LO prediction would have called for considerably more data, and hence further months or even years of measurements, to establish exclusion boundaries of this sort.

Fig. 3: Exclusion boundary of Higgs search at the Tevatron. The predicted Higgs signal at the point where the unbroken line drops below 1 is strong enough to stand out from the background. But there is no data record of a signal there. This excludes the existence of a Higgs boson with its relevant mass. In the case of all other masses the predicted signal is too weak to stand out from the background. Source: CDF and D0 Collaboration

http://arvix.org/abs/0903.4001

So is it the Higgs boson? A first crucial test is, as one would expect, a comparison of the size of the signal with the theoretical prediction. It is, in fact, a perfect fit with the spectrum of W and Z bosons; in the photon spectrum both experiments show a slightly higher value, which can, however, still be ascribed to statistical fluctuation. If the LO result had been used instead of the NNLO result, there would have been an estimated discrepancy of three standard deviations between data and theory – which would exclude with far more than 90% certainty that it was the Higgs boson as described in the standard model!

The simple fact that a neutral scalar particle has been found, whose mass is compatible with the predictions for the Higgs boson, is a massive success story for physics. Without this discovery, our understanding of the physical universe and its underlying theories would be open to serious question. In recent years the demand for a consistent and convincing theory on the one hand, and the convergence of precisely measured data with predicted results on the other, has made the existence of such a particle appear increasingly compelling.

Fig. 4: Energy spectrum of photon pairs in the ATLAS experiment. The position of the signal matches the mass of the new particle (126 GeV). The height of the signal is a good match with theoretical predictions. Source: Phys. Lett. B716 (2012) 1-29

http://arxiv.org/abs/1207.7214

The LHC Higgs Cross Section Working Group is composed of more than 100 theoretical and experimental physicists dedicated to working out, discussing and documenting the overall LHC results for the official analysis, as well as their theoretical implications for Higgs physics. Our group is producing key theoretical results, especially predictions for the cross sections of interactions of the dominant processes (Higgs-strahlung, gluon fusion, bottom quark fusion etc.) in the standard model, as well as in other, more far-reaching theories like supersymmetry. Only when a sufficient number of observables have passed the test of comparison between theory and experiment, can we be sure whether or not the new particle is the Higgs boson, or one of several Higgs-like particles, or perhaps something entirely unexpected. One thing is certain, however: we are living in a very exciting era of particle physics.

http://particle.uni-wuppertal.de/harlander/