by Vincenzo Barone and Enrico Predazzi, Springer Verlag 2002, ISBN 3540421076, €74.95 plus local VAT.
Diffraction has played a fundamental role in physics for centuries, beginning with the realization of the wave nature of light. Given the wave-particle duality of quantum mechanics (QM), diffraction continued to be an important concept in non-relativistic QM scattering, and later in the study of elementary particle scattering using relativistic S-matrix theory.
For some decades after 1950, a vast experimental and theoretical effort went into the study of high-energy elastic and diffractive scattering of elementary particles, culminating in the largely unexpected discovery that cross-sections grow with energy. Being essentially non-perturbative processes, theory could not provide a really detailed description of elastic and diffractive scattering, but it did introduce a new idea that is truly fundamental. This new idea was the concept of complex angular momentum in non-relativistic QM (now a vital component in any serious book on QM) and its connection with the behaviour of relativistic scattering amplitudes at high energy. This led to the theory of Regge poles, which enjoyed enormous success in correlating the data on many reactions, though it also experienced some failures. Terms like Regge pole, pomeron and reggeon became household words. (A non-physicist spouse, upon being introduced to Tulio Regge at a party in the 1960s, is reported to have said: “Ah, Mr Pole, I have heard so much about you.”)
The discovery of the partonic structure of hadrons and the advent of quantum chromodynamics (QCD) led to a dramatic change in the thrust of experimental high-energy physics, away from the study of elastic and diffractive scattering. Because of its property of asymptotic freedom, QCD was able to predict interesting correlations between experimental data in certain kinematical regions characterized by a hard scale. Consequently, a huge effort has gone into the study of such deep inelastic reactions.
But history, according to the Italian philosopher Vico, is supposed to be cyclical. So we should not be surprised to learn that there is a connection between certain aspects of deep inelastic reactions and Regge concepts, and that the relatively new field of hard diffraction opens up the possibility of a bridge between Regge theory and QCD (leading, one hopes, to an understanding of Regge theory in the language of QCD).
Unfortunately, the concepts and language of Regge theory have largely fallen into disuse, so that several generations of young physicists, whose education had a lacuna in this field, now find themselves working on experiments in which such concepts are of importance. It is for these lost generations, and, of course, for the present generation of elementary particle physicists that this volume will be of great value. It manages to succinctly introduce all the important ideas in the Regge theory of diffraction (now referred to as soft diffraction) and attempts to connect these to the recent developments in hard diffraction and its interpretation in the framework of QCD.
There are three main sections to this book. The first offers a rapid but clear survey of scattering theory in both classical wave optics and non-relativistic QM. It also includes a discussion of the eikonal approximation, which plays a major role in later chapters, when attempting to understand the high-energy behaviour of very complex QCD Feynman diagrams. A chapter on relativistic kinematics introduces the concepts of rapidity and rapidity gaps, the latter being the current focus of intense experimental study in lepton-hadron deep inelastic scattering (DIS).
The second part of the book surveys concisely the old soft diffraction from the “golden age” of Regge theory. Here the emphasis is on those aspects of theory and experiment that are directly relevant to the present-day resurgence of interest in diffraction – i.e. to the diffractive aspects of hard interactions. The essential ideas of dispersion relations, Muller’s generalization of the optical theorem to inclusive reactions and the key, rigorous theorems on permissible growth with energy of cross-sections are presented. Also discussed is the Pomeranchuk theorem relating particle-particle to particle-antiparticle asymptotic cross-section growth, but, surprisingly, no attention is drawn to the optics-diffraction motivation for the key assumption in the proof of this “theorem”.
The reasons for introducing complex angular momentum, crucial in the development of Regge theory, are simply and convincingly explained, and there follows an intelligible treatment of diffractive dissociation, the triple Regge limit (relevant to contemporary experiments), and how Regge theory can emerge from a field theoretic point of view. The latter is one of the most challenging issues in the study of perturbative QCD.
This section ends with a chapter devoted to the phenomenology of soft diffraction, summarizing cross-section growth, diffraction peaks and diffractive dissociation. The successful description of the energy behaviour of cross-sections in terms of Regge poles and the soft pomeron (that has an intercept of approximately 1.08) is emphasized. Included is a brief mention of the odderon, the intriguing object that seems to emerge from QCD and would be responsible for the breaking of the Pomeranchuk theorem, giving rise to a difference asymptotically between particle-particle and particle-antiparticle reactions.
The third section, about half of the book, is addressed to the relatively new subject of hard diffraction, which is currently under intense experimental study at DESY’s HERA collider and Fermilab’s Tevatron, and will be pursued at Brookhaven’s RHIC and the LHC at CERN. This is a difficult subject. The theoretical approaches involve very complex and subtle calculations requiring the summation of an infinite series of Feynman graphs. The phenomenology is difficult to describe. The kinematic specification and experimental isolation of the class of events one wants to study is highly non-trivial and technically complex.
This final section begins with the theory of the BKFL equation, a perturbative treatment of generalized two-gluon exchange – summed to all orders in leading logarithmic approximation (LLA) – in parton-parton scattering. This leads to the conclusion that the gluon itself “reggeises”, i.e. it behaves as a Regge pole and, perhaps more dramatically, that a pomeron-like object – the hard pomeron – emerges to control the high-energy behaviour of parton-parton scattering with an intercept of about 1.5. Perturbation theory breaks down in the range of small momentum transfer where the soft pomeron is operative, so it is not clear whether there is any incompatibility with the hard QCD pomeron. Unfortunately, studies going beyond the LLA appear to change the intercept appreciably and the full story remains untold.
After this challenging chapter we are offered a gentle introduction to lepton-hadron DIS and then led to the intriguing question of the behaviour of the structure functions at very small Bjorken-x. Here the soft pomeron, the QCD hard pomeron and the small-x behaviour of the DGLAP evolution equations confront each other. The theoretical aspects seem, unavoidably, to be complicated.
The last two chapters are devoted to the new field of hard diffraction, first the phenomenological aspects, mainly in DIS, where the topology of rapidity gaps, the concept of diffractive structure functions and parton densities, and the partonic structure of the pomeron are explained. There is also a brief description of single and double diffraction in hadron-hadron collisions. In the final chapter the BFKL version of the hard pomeron and the colour dipole picture of a highly virtual photon are used to derive theoretical predictions for various hard diffractive reactions. Many processes of current interest are covered: jets in diffractive DIS, diffractive production of open charm and vector mesons, nuclear shadowing, colour transparency and the cross-section for g* g * scattering.
High-Energy Particle Diffraction offers a comprehensive survey of the theoretical and experimental sides of one of the major areas of study in current elementary particle physics. It provides essential background information for younger physicists who were not taught about soft physics and Regge theory, and for those who were it is a helpful bridge to the newer area of hard diffraction. This book is not easy going. Some of the theoretical approaches are inherently very complex and, despite the efforts of the authors, remain an intellectual challenge. This is somewhat exacerbated by a large number of typographical errors, which will hopefully be rectified in the second edition.
