CERN Courier January/February 2013 CERN Courier January/February 2013 QCD QCD experimental results on electron and neutrino deep-inelastic scat- received much attention recently as a means of constructing uni- tering gave strong evidence that charged partons are spin 1/2 par- fi ed and renormalizable theories of the weak and electromagnetic A watershed: the ticles [13] and that they have baryon number 1/3 [14], i.e. that charged interactions. In this note we report an investigation of the ultravio- partons are quarks. let (UV) asymptotic behaviour of such theories. We have found Quantum fi eld theory and the renormalization group: Martinus that they possess the remarkable feature, perhaps unique among Veltman and Gerardus ’t Hooft [15] brought powerful new tools to renormalizable theories, of asymptotically approaching free-fi eld the study of perturbative renormalization theory, leading to a more theory. Such asymptotically free theories will exhibit, for matrix emergence of QCD rigorous, quantitative formulation of gauge theories of electroweak elements between on-mass-shell states, Bjorken scaling. We there- interactions. Kenneth Wilson introduced a wealth of new ideas, fore suggest that one should look to a non-Abelian gauge theory conveniently though rather obscurely referred to as the renormali- of the strong interactions to provide the explanation for Bjorken zation group, into the study of quantum fi eld theory beyond the scaling, which has so far eluded fi eld-theoretic understanding.” limits of perturbation theory. He used these ideas with great suc- Thus the tension between scaling and quantum field theory David Gross and Frank Wilczek look cess to study critical phenomena. Neither of those developments might be resolved but only within a special, limited class of theo- related directly to the strong interaction problem but they formed ries. The paper surveys those possibilities and concludes: “One back at how QCD began to emerge in its an important intellectual background and inspiration. They particularly appealing model is based on three triplets of fermi- showed that the possibilities for quantum fi eld theory to describe ons, with Gell-Mann’s SU(3)xSU(3) as a global symmetry and an current form 40 years ago. physical behaviour were considerably richer than previously appre- SU(3) “colour” gauge group to provide the strong interactions. That ciated. Wilson [16] also sketched how his renormalization-group is, the generators of the strong-interaction gauge group commute ideas might be used to study short-distance behaviour, with spe- with ordinary SU(3)xSU(3) currents and mix quarks with the same In a recent article, Harald Fritzsch shared his perspective on the cifi c reference to problems in the strong interaction. isospin and hypercharge but different “colour”. In such a model history of the understanding of the strong interaction (CERN Cou- These various clues appeared to be mutually exclusive, or at least the vector mesons are neutral and the structure of the operator rier October 2012 p21). Here, we’d like to supplement that view. in considerable tension. The parton model is based on neglect of product expansion of electromagnetic or weak currents is (assum- Our focus is narrower but also sharper. We will discuss a brief interference terms whose existence, however, is required by basic ing the strong coupling constant but dramatic period during 1973–1974, when the modern theory principles of quantum mechanics. Attempts to identify partons is in the domain of attraction of the strong interaction – quantum chromodynamics, or QCD – with dynamical quarks [17] were partially successful but ascribed a of the origin!) essentially that emerged, essentially in its current form. While we were active par- David Gross and Frank Wilczek, when they received the Nobel much more intricate structure to protons than was postulated in the The confi nement of the free quark model (up to ticipants in that drama, we have not relied solely on memory but prize in 2004. (Image credit: D Gross.) simplistic quark models and unambiguously required additional, of quarks calculable logarithmic correc- have carefully reviewed the contemporary literature. non-quark constituents. The confi nement of quarks contradicted contradicted all tions).*” This was the fi rst clear At the end of 1972 there was no fundamental theory of the strong Quarks and colour: A large body of strong-interaction phenom- all previous experience in phenomenology. Furthermore, such formulation of the theory that interaction – and no consensus on how to construct one. Proposals enology, including the particle spectrum and magnetic moments, behaviour could not be obtained within per turbative quantum fi eld previous we know today as QCD. The based on S-matrix philosophy, dual-resonance models, phenom- had been organized using the idea that mesons and baryons are theory. There were numerous technical challenges in combining experience in footnote indicated by * refers to enological quark models, current algebras, ideas about “partons” composite particles made from combinations of a small number of re-scaling transformations, as used in the renormalization group, phenomenology. additional work, which became and chiral dynamics – the logical descendant of Hideki Yukawa’s more fundamental constituents: quarks. This approach, which had with gauge symmetry. the core of our two subsequent original pion-exchange idea – created a voluminous and rapidly its roots in the ideas of Murray Gell-Mann [6] and George Zweig [7], But the most concrete, quantitative tension, and the one whose papers [3, 4]. growing literature. None of those competing ideas, however, is reviewed in a nice book by J J J Kokkedee [8]. For the model to resolution ultimately broke the whole subject open, was the tension David Politzer’s paper [2] contains calculations of the renormali- offered a framework in which uniquely defi ned calculations lead- work, the quarks were required to have bizarre properties – quali- between the scaling behaviour observed experimentally at SLAC zation group coeffi cients for non-Abelian gauge theories with fer- ing to sharp, testable predictions could be carried out. It seemed tatively different from the proper ties of any known par ticles. Their and the basic principles of quantum fi eld theory. Several workers mions, broadly along the same lines as in our fi rst paper quoted possible that strong-interaction physics would evolve along the electric charges had to be fractional. They had to have an extra [18] expanded Wilson’s somewhat sketchy indications into a precise above [1]. It does not refer to the problem of understanding scaling in lines of nuclear physics: one would gradually accumulate insight internal “colour” degree of freedom [9,10]. Above all, they had to be mapping between calculable properties of quantum fi eld theories the hadronic strong interaction. (The reference to “strong interac- experimentally, and acquire command of an ever-larger range of confi ned. Extensive experimental searches for individual quarks and observable aspects of inclusive cross-sections. Specifi cally, tions” in the title is generic.) Politzer emphasized the importance phenomena through models and rules of thumb. An overarching gave negative results. Within the model quark–antiquark pairs this work made it clear that the scaling behaviour observed at of the converse of asymptotic freedom – that is, that the effective theory worthy to stand beside Maxwell’s electrodynamics or Ein- made mesons, while quark–quark–quark triplets made baryons; SLAC could be obtained only in quantum fi eld theories with very coupling grows at long distances. He remarks that this could lead stein’s general relativity was no more than a dream – and not a single quarks had to be much heavier than mesons and baryons – if, small anomalous dimensions. (Strict scaling, which is equivalent to surprises regarding the particle content of asymptotically free widely shared one. indeed, they existed at all. to vanishing anomalous dimensions, cannot occur in a non-trivial – theories and support dynamical symmetry breaking. Although Within less than two years the situation had transformed radi- Scaling and partons: The famous electroproduction experi- interacting – quantum fi eld theory[19] .) A few realized that approxi- we arrived at our results independently, we and Politzer learnt of cally. We had arrived at a very specifi c candidate theory of the ments at SLAC revealed, beginning in the late 1960s, that inclusive mate scaling could be achieved in an interacting quantum theory, each other’s work before publication, compared results, requested strong interaction, one based on precise, beautiful equations. And cross-sections did not exhibit the “soft” or “form factor” behaviour if the effective interaction approached zero at short distances. simultaneous publication and referred to one another. The paper we had specifi c, quantitative proposals for testing it. The theoreti- familiar in exclusive and purely hadronic processes (as explored up Anthony Zee called such fi eld theories “stagnant”(they are essen- by Howard Georgi and Politzer [5] adopts QCD without comment cal works [1–5] that were central to this transformation can be identi- to that time). Richard Feynman [11] interpreted these experiments tially what we now call asymptotically free theories) and he [20], and independently derives predictions for deviations from scaling fi ed, we think, with considerable precision. as indicating the existence of more