The proton laid bare

What a proton is depends on how you look at it, or rather on how hard you hit it. A century after Rutherford’s discovery, our picture of this ubiquitous particle is coming into focus.

Glorious complexity

Every student of physics learns that the nucleus was discovered by firing alpha particles at atoms. The results of this famous experiment by Rutherford in 1911 indicated the existence of a hard-scattering core of positive charge, and, within a few years, led to his discovery of the proton (see Rutherford, transmutation and the proton). Decades later, similar experiments with electrons revealed point-like scattering centres inside the proton itself. Today we know these to be quarks, antiquarks and gluons, but the glorious complexity of the proton is often swept under the carpet. Undergraduate physicists are more often introduced to quarks as objects with flavour quantum numbers that build up mesons and baryons in bound states of twos and threes. Indeed, in the 1960s, many people regarded quarks simply as a useful book-keeping device to classify the many new “elementary” particles that had been discovered in cosmic rays and bubble-chamber experiments. Few people were aware of the inelastic-scattering experiments at SLAC with 20 GeV electrons, which were beginning to reveal a much richer picture of the proton.

The results of these experiments in the 1960s and early 1970s were remarkable. Elastic scattering by the point-like electrons revealed the spatial distribution of the proton’s charge, and cross sections had to be modified by form-factors as a result. These varied strongly depending on how hard the proton was struck – a hardness called the scale of the process, Q2, defined by the negative squared four-momentum transfer between incoming and outgoing electrons. At high enough scales the proton broke up, a phenomenon that can be quantified by x, a kinematic variable related to the inelasticity of the interaction. Both the scale and the inelasticity could be determined from the dynamics of the outgoing electron. Physicists anticipated a complicated dependence on both variables. Studies of scattering at ever higher and lower scales continue to bear fruit to this day.

A surprise at SLAC

The big surprise from the SLAC experiments was that the cross section did not depend strongly on Q2, a phenomenon called “scaling”. The only explanation for scaling was that the electrons were scattering from point-like centres within the proton. Feynman worked out the formalism to understand this by picturing the electron as hitting a point-like “parton” inside the proton. With elegant simplicity, he deduced that the partons each carried a fraction x of the proton’s longitudinal momentum.

Gell-Mann and Zweig had proposed the existence of quarks in 1964, but at first it was by no means obvious that they were partons. The SLAC experiments established that the scattering centres had spin ½ as required by the quark model, but there were two problems. On the one hand there appeared to be not only three, but many scattering centres. On the other, Feynman’s formalism required the partons to be “free” and independent of each other, yet they could hardly be independent if they remained confined in the proton.

Painting a picture

The picture became even more interesting in the late 1970s and 1980s when scattering experiments started to use neutrinos and antineutrinos as probes. Since neutrinos and antineutrinos have a definite handedness, or helicity, such that their spin is aligned against their direction of motion for neutrinos and with it for antineutrinos, their weak interaction with quarks and antiquarks gives different angular distributions. This showed that there must be antiquarks as well as quarks within the proton. In fact, it led to a picture in which the flavour properties of the proton are governed by three valence quarks immersed in a sea of quark–antiquark pairs. But this is not all: the same experiments indicated that the total momentum carried by the valence quarks and the sea still amounts to only around half of that of the proton. This missing momentum was termed an energy crisis, and was solved by the existence of gluons with spin 1, which bind the quarks together and confine them inside the proton.

In fact, the SLAC experiments had been lucky to be making measurements in the kinematic region where scaling holds almost perfectly – where the cross section is independent of Q2. The quark–parton model had to be extended, and became the field theory of quantum chromodynamics (QCD), in which the gluons are field carriers, just like photons in quantum electrodynamics (QED). Formulated in 1973, QCD has a much richer structure than QED. There are eight kinds of gluons that are characterised in terms of a new quantum number called colour, which is carried by both quarks and the gluons themselves, in contrast to QED, where the field carrier is uncharged. The gluon can thus interact with itself as well as with quarks.

Fig. 1.

From the 1980s onwards, a series of experiments probed increasingly deeply into the proton. Deep-inelastic-scattering experiments using neutrino and muon beams were performed at CERN and Fermilab, before the HERA electron–proton collider at DESY made definitive measurements from 1992 to 2007 (figure 1). The aim was to test the predictions of QCD as much as to investigate the structure of the proton, the goal being not just to list the constituents of the proton, but also to understand the forces between them.

Meanwhile, the EMC experiment at CERN had unearthed a mystery concerning the origin of the proton’s spin (see The proton spin crisis), while elsewhere, entirely different experiments were placing increasingly tough limits on the proton’s lifetime (see The pursuit of proton decay).

Quantum considerations

As with all quantum phenomena, what is in a proton depends on how you look at it. A more energetic probe has a smaller wavelength and therefore can reveal smaller structures, but it also injects energy into the system, and this allows the creation of new particles. The question then is whether we regard these particles as having been inside the proton in the first place. At higher scales quarks radiate gluons that then split into quark–antiquark pairs, which again radiate gluons: and the gluons themselves can also radiate gluons. The valence quarks thus lose momentum, distributing it between the sea quarks and gluons – increasingly many, with smaller and smaller amounts of momentum. A proton at rest is therefore very different to a proton, say, circulating in the Large Hadron Collider (LHC) at an energy of 7 TeV.

The deep-inelastic-scattering data from muon, neutrino and electron collisions established that QCD was the correct theory of the strong interaction. Experiments found that the structure functions which describe the scattering cross sections are not completely independent of scale, but depend on it logarithmically – in exactly the way that QCD predicts. This allowed the determination of the strong coupling “constant” αs, in analogy with the fine structure constant of QED, and it is now understood that both parameters vary with the scale of the process. In contrast with QED, the strong-coupling constant varies very quickly, from αs ~1 at low energy to ~0.1 at the energy scale of the mass of the Z boson. Thus the quarks become “asymptotically free” when examined at high energy, but are strongly confined at low energy – an insight leading to the award of the 2004 Nobel Prize in Physics to Gross, Politzer and Wilczek.

Fig. 2.

Once QCD had emerged as the definitive theory, the focus turned to measuring the momentum distributions of the partons, dubbed parton distribution functions (PDFs, figure 2). Several groups work on these determinations using both deep-inelastic-scattering data and related scattering processes, and presently there is agreement between theory and experiment within a few percent across a very wide range of x and Q2 values. However, this is not quite good enough. Today, knowledge of PDFs is increasingly vital for discovery physics at the LHC. Predictions of all cross sections measured at the LHC – whether Standard Model or beyond – need to use input PDFs. After all, when we are colliding protons it is actually the partons inside the proton that are having hard collisions and the rates of these collisions can only be predicted if we know the PDFs in the proton very accurately.

The dominant uncertainty on the direct production of particles predicted by physics beyond the Standard Model now comes from the limited precision of the PDFs of high-x gluons. Indirect searches for new physics are also affected: precision measurements of Standard Model parameters, such as the mass of the W-boson and the weak mixing angle sin2θW, are also limited by the precision of PDFs in the regions where we currently have the best precision.

Strange sightings at the LHC

Standard Model processes at the LHC are now able to contribute to our knowledge of the proton. As well as reducing the uncertainty on PDFs, however, the LHC data have led to a surprise: there seem to be more strange quark–antiquark pairs in the proton than we had thought (CERN Courier April 2017 p11). A recent study of the potential of the High-Luminosity LHC suggests that we can improve the present uncertainty on the gluon PDF by more than a factor of two by studying jet production, direct photon production and top quark–antiquark pair production. Measurements of the W-boson mass or the weak mixing angle will be improved by precision measurements of W and Z-boson production in previously unexplored kinematic regions, and strangeness can be further probed by measurements of these bosons in association with heavy quarks. We also look forward to possible future developments such as a Large Hadron-Electron Collider or a Future Circular Electron Hadron Collider – not least because new kinematic ranges continue to reveal more about the structure of QCD in the high-density regime.

Fig. 3.

In fact the HERA data already give hints that we may be entering a new phase of QCD at very low x, where the gluon density is very large (figure 3). Such large densities could lead to nonlinear effects in which gluons recombine. When the rate of recombination equals the rate of gluon splitting we may get gluon saturation. This state of matter has been described as a colour glass condensate (CGC) and has been further probed in heavy-ion experiments at the LHC and at RHIC at Brookhaven National Laboratory. The higher gluon densities involved in experiments with heavy nuclei enhance the impact of nonlinear gluon interactions. Interpretations of the data are consistent with the CGC but not definitive. A future electron–ion collider, such as that currently proposed in the US (CERN Courier October 2018, p31), will go further, enabling complete tomographic information about the proton and allowing us to directly connect fundamental partonic behaviour to the proton’s “bulk” properties such as its mass, charge and spin. Meanwhile, table-top spectroscopy experiments are shedding new light on a seemingly mundane yet key property of the proton: its radius (see Solving the proton-radius puzzle).

Together with the neutron, the proton constitutes practically all of the mass of the visible matter in the universe. A hundred years on from Rutherford’s discovery, it is clear that much remains to be learnt about the structure of this complex and ubiquitous particle.

Further reading

R Devenish and A Cooper-Sarkar 2004 Deep Inelastic Scattering (Oxford University Press).

J Campbell et al. 2018 The Black Book of Quantum Chromodynamics (Oxford University Press).

About the author

Amanda Cooper-Sarkar, University of Oxford.