The Standard Theory of Particle Physics

The following sections are included:

• Contents
• Preface

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field theoretical model to be renormalizable were established, there were two other developments that quickly accelerated acceptance of this approach: first the Brout-Englert-Higgs mechanism, and then asymptotic freedom. Together, these gave us a complete understanding of the perturbative sector of the theory, enough to give us a detailed picture of what is now usually called the Standard Model. Crucial for this understanding were the strong indications and encouragements provided by numerous experimental findings. Subsequently, non-perturbative features of the quantum field theories were addressed, and the first proposals for completely unified quantum field theories were launched. Since the use of continuous symmetries of all sorts, together with other topics of advanced mathematics, were recognised to be of crucial importance, many new predictions were pointed out, such as the Higgs particle, supersymmetry, and baryon number violation. There are still many challenges ahead.

The following sections are included:

• Introduction
• Prehistory
• Thirty Years of Unconcern, Thirty Years of Doubt
• Gauge Theories
• Fighting the Infinities
• The Standard Model
• Beyond the Standard Model

This article first describes the parton model which was the precursor of the QCD description of hard scattering processes. After the discovery of QCD and asymptotic freedom, the first successful applications were to Deep Inelastic lepton-hadron scattering. The subsequent application of QCD to processes with two initial state hadrons required the understanding and proof of factorization. To take the fledgling theory and turn it into the robust calculational engine it has become today, required a number of technical and conceptual developments which will be described. Prospects for higher loop calculations are also reviewed.

The test of the electroweak corrections has played a major role in providing evidence for the gauge and the Higgs sectors of the Standard Model. At the same time the consideration of the electroweak corrections has given significant indirect information on the masses of the top and the Higgs boson before their discoveries and important orientation/constraints on the searches for new physics, still highly valuable in the present situation. The progression of these contributions is reviewed.

I review the the application of the lattice formulation of QCD and large-scale numerical simulations to the evaluation of non-perturbative hadronic effects in Standard Model Phenomenology. I present an introduction to the elements of the calculations and discuss the limitations both in the range of quantities which can be studied and in the precision of the results. I focus particularly on the extraction of the QCD parameters, i.e. the quark masses and the strong coupling constant, and on important quantities in flavour physics. Lattice QCD is playing a central role in quantifying the hadronic effects necessary for the development of precision flavour physics and its use in exploring the limits of the Standard Model and in searches for inconsistencies which would signal the presence of new physics.

The strong coupling constant is one of the fundamental parameters of the Standard Theory of particle physics. In this review I will briefly summarise the theoretical framework, within which the strong coupling constant is defined and how it is connected to measurable observables. Then I will give an historical overview of its experimental determinations and discuss the current status and world average value. Among the many different techniques used to determine this coupling constant in the context of quantum chromodynamics, I will focus in particular on a number of measurements carried out at the Large Electron-Positron Collider (LEP) and the Large Hadron Collider (LHC) at CERN.

Precision tests of the Standard Theory require theoretical predictions taking into account higher-order quantum corrections. Among these vacuum polarisation plays a predominant role. Vacuum polarisation originates from creation and annihilation of virtual particle–antiparticle states. Leptonic vacuum polarisation can be computed from quantum electrodynamics. Hadronic vacuum polarisation cannot because of the non-perturbative nature of QCD at low energy. The problem is remedied by establishing dispersion relations involving experimental data on the cross section for e⁺ e⁻ annihilation into hadrons. This chapter sets the theoretical and experimental scene and reviews the progress achieved in the last decades thanks to more precise and complete data sets. Among the various applications of hadronic vacuum polarisation calculations, two are emphasised: the contribution to the anomalous magnetic moment of the muon, and the running of the fine structure constant α to the Z mass scale. They are fundamental ingredients to high precision tests of the Standard Theory.

The Standard Theory can fit any number of fermion families, as long as the number of leptons and quark families are the same. At the time of the conception of LEP, the number of such families was unknown, and it was feared that the Z resonance would be washed out by decaying into so many families of neutrinos! It took only a few weeks in the fall of 1989 to determine that the number is three. The next six years (from 1990 to 1995) were largely devoted to the accurate determination of the Z line shape, with a precision that outperformed the most optimistic expectations by a factor of 10. The tale of these measurements is a bona fide mystery novel, the precession of electrons being strangely perturbed by natural phenomena, such as tides, rain, hydroelectric power, fast trains, not to mention vertical electrostatic separators. The number hidden in the loops of this treasure hunt was 179, the first estimate of the mass of the top quark; then, once that was found, where predicted, the next number was close to zero: the logarithm of Higgs mass divided by that of the Z. Twenty years later, the quality of these measurements remains, but what they tell us is different: it is no longer about unknown parameters of the Standard Theory, it is about what lies beyond it. This is so acutely relevant, that CERN has launched the design study of a powerful Z, W, H and top factory.

The impressive progress on the knowledge of lepton and quark electroweak couplings over the LEP and SLC decade is reviewed. The experimental methods for measuring the forward-backward asymmetry of charged-fermion pair-production are described, for different fermion species. The precise measurements of the left–right asymmetry and of tau polarisation at the Z resonance are also reminded. After discussing the determination of the Weinberg electroweak mixing angle, lepton and quark couplings are extracted by combining asymmetry and polarisation measurements with measurements of partial decay widths of the Z boson, performed at LEP in the same years.

The measurement of the W boson mass has been growing in importance as its precision has improved, along with the precision of other electroweak observables and the top quark mass. Over the last decade, the measurement of the W boson mass has been led at hadron colliders. Combined with the precise measurement of the top quark mass at hadron colliders, the W boson mass helped to pin down the mass of the Standard Model Higgs boson through its induced radiative correction on the W boson mass. With the discovery of the Higgs boson and the measurement of its mass, the electroweak sector of the Standard Model is over-constrained. Increasing the precision of the W boson mass probes new physics at the TeV-scale. We summarize an extensive Tevatron (1984–2011) program to measure the W boson mass at the CDF and Dø experiments. We highlight the recent Tevatron measurements and prospects for the final Tevatron measurements.

Ever since the discovery of the top quark at the Tevatron collider in 1995 the measurement of its mass has been a high priority. As one of the fundamental parameters of the Standard Theory of particle physics, the precise value of the top quark mass together with other inputs provides a test for the self-consistency of the theory, and has consequences for the stability of the Higgs field that permeates the Universe. In this review I will briefly summarize the experimental techniques used at the Tevatron and the LHC experiments throughout the years to measure the top quark mass with ever improving accuracy, and highlight the recent progress in combining all measurements in a single world average combination. As experimental measurements became more precise, the question of their theoretical interpretation has become important. The difficulty of relating the measured quantity to the fundamental top mass parameter has inspired alternative measurement methods that extract the top mass in complementary ways. I will discuss the status of those techniques and their results, and present a brief outlook of further improvements in the experimental determination of the top quark mass to be expected at the LHC and beyond.

The last decades have seen tremendous progress in the experimental techniques for measuring key observables of the Standard Theory (ST) as well as in theoretical calculations that has led to highly precise predictions of these observables. Global electroweak fits of the ST compare the precision measurements of electroweak observables from lepton and hadron colliders at CERN and elsewhere with accurate theoretical predictions of the ST calculated at multi-loop level.

For a long time, global fits have been used to assess the validity of the ST and to constrain indirectly (by exploiting contributions from quantum loops) the remaining free ST parameters, like the masses of the top quark and Higgs boson before their direct discovery. With the discovery of the Higgs boson at the Large Hadron Collider (LHC), the electroweak sector of the ST is now complete and all fundamental ST parameters are known. Hence the global fits are a powerful tool to probe the internal consistency of the ST, to predict ST parameters with high precision, and to constrain theories describing physics beyond the ST.

In this chapter we review the global fits of the electroweak sector of the ST from an experimentalist's perspective. We briefly recall the most important achievements from the past (mainly driven by the precise measurements of Z pole observables), discuss the present situation after the accurate measurements of the top quark and Higgs boson masses, and present prospects of the fits as expected from new measurements at the LHC and future lepton colliders.

Since the W^± and Z⁰ discovery, hadron colliders have provided a fertile ground, in which continuously improving measurements and theoretical predictions allow to precisely determine the gauge boson properties, and to probe the dynamics of electroweak and strong interactions. This article will review, from a theoretical perspective, the role played by the study, at hadron colliders, of electroweak boson production properties, from the better understanding of the proton structure, to the discovery and studies of the top quark and of the Higgs, to the searches for new phenomena beyond the Standard Model.

The Higgs boson was postulated in 1964, and phenomenological studies of its possible production and decays started in the early 1970s, followed by studies of its possible production in e⁺ e⁻, and pp collisions, in particular. Until recently, the most sensitive searches for the Higgs boson were at LEP between 1989 and 2000, which were complemented by searches at the Fermilab Tevatron. Then the LHC experiments ATLAS and CMS entered the hunt, announcing on July 4, 2012 the discovery of a "Higgs-like" particle with a mass of about 125 GeV. This identification has been supported by subsequent measurements of its spin, parity and coupling properties. It was widely anticipated that the Higgs boson would be accompanied by supersymmetry, although other options, like compositeness, were not completely excluded. So far there are no signs of any new physics, and the measured properties of the Higgs boson are consistent with the predictions of the minimal Standard Model. This article reviews some of the key historical developments in Higgs physics over the past half-century.

We present a brief account of the search for the Higgs boson at the three major colliders that have operated over the last three decades: LEP, the Tevatron, and the LHC. The experimental challenges encountered stemmed from the distinct event phenomenology as determined by the colliders energy and the possible values for the Higgs boson mass, and from the capability of these colliders to deliver as much collision data as possible to fully explore the mass spectrum within their reach. Focusing more on the hadron collider searches during the last decade, we discuss how the search for the Higgs boson was advanced through mastering the experimental signatures of standard theory backgrounds, through the comprehensive utilization of the features of the detectors involved in the searches, and by means of advanced data analysis techniques. The search culminated in 2012 with the discovery, by the ATLAS and CMS collaborations, of a Higgs-like particle with mass close to 125 GeV, confirmed more recently to have properties consistent with those expected from the standard theory Higgs boson.

This chapter presents an overview of the measured properties of the Higgs boson discovered in 2012 by the ATLAS and CMS collaborations at the CERN LHC. Searches for deviations from the properties predicted by the standard theory are also summarised. The present status corresponds to the combined analysis of the full Run 1 data sets of collisions collected at centre-of-mass energies of 7 and 8 TeV.

Flavour physics represents one of the most interesting and, at the same time, less understood sector of the Standard Theory. On the one hand, the peculiar pattern of quark and lepton masses, and their mixing angles, may be the clue to some new dynamics occurring at high-energy scales. On the other hand, the strong suppression of flavour-changing neutral-current processes, predicted by the Standard Theory and confirmed by experiments, represents a serious challenge to extend the Theory. This article reviews both these aspects of flavour physics from a theoretical perspective.

In the last 50 years we have seen how an initially ad hoc and not widely accepted theory of the strong and electroweak interactions (Standard Theory: ST) has correctly predicted the entire accelerator based experimental observations with incredible accuracy. Decays of the ST particles (quarks and leptons), which are rare due to some symmetry of the theory, have played an important role in the making of the ST. These rare decays have been powerful tools to search for interactions of the ST particles with new particles which not necessarily have the same symmetries. In this article, I will describe the indirect search for evidence of new physics (NP) using quark and lepton flavour changing neutral decays, which are highly suppressed within the ST and constitute strong probes of potential new flavour structures.

This essay is intended to provide a brief description of the peculiar properties of neutrinos within and beyond the standard theory of weak interactions. The focus is on the flavor oscillations of massive neutrinos, from which one has achieved some striking knowledge about their mass spectrum and flavor mixing pattern. The experimental prospects towards probing the absolute neutrino mass scale, possible Majorana nature and CP-violating effects, will also be addressed.

The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a neutralino, is expected to be stable and a possible candidate for dark matter.

The electroweak breaking requires two doublets, leading to several charged and neutral Brout-Englert-Higgs bosons. This also leads to gauge/Higgs unification by providing extra spin-0 partners for the spin-1 W^± and Z. It offers the possibility to view, up to a mixing angle, the new 125 GeV boson as the spin-0 partner of the Z under two supersymmetry transformations, i.e. as a Z that would be deprived of its spin. Supersymmetry then relates two existing particles of different spins, in spite of their different gauge symmetry properties, through supersymmetry transformations acting on physical fields in a non-polynomial way.

We also discuss how the compactification of extra dimensions, relying on R-parity and other discrete symmetries, may determine both the supersymmetrybreaking and grand-unification scales.

With the Higgs discovery, the full Standard Model (SM) has been experimentally established, and most of its sectors accurately tested. Nevertheless, the SM deeply relies in the presence of the Higgs, a spin-zero field, whose mass term is not expected, on theoretical grounds, to be much smaller than the Planck scale. This problem of naturalness demands a modification of the SM around the weak scale, making the exploration of the TeV-energy regime a top experimental priority. In this chapter we briefly review the most well-motivated scenarios beyond the SM that can accommodate a light Higgs, mainly centering in two ideas: Supersymmetry and compositeness.