The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

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Foundations of Perturbative QCD

Relativistic dynamics on a null plane

Since the discovery of the first charmed meson in 1976, many open-charm and open-bottom hadrons were observed. In 2003 two narrow charm-strange states $D_{s0}^*(2317)$ and $D_{s1}(2460)$ were discovered by the BaBar and CLEO Collaborations, respectively. After that, more excited heavy hadrons were reported. In this work, we review the experimental and theoretical progress in this field.

A review of the open charm and open bottom systems

Since the discovery of the first charmed meson in 1976, many open-charm and open-bottom hadrons were observed. In 2003 two narrow charm-strange states [Formula: see text] and D s1(2460) were discovered by the BaBar and CLEO Collaborations, respectively. After that, more excited heavy hadrons were reported. In this work, we review the experimental and theoretical progress in this field.

With the aim of generating new constraints on the OZI suppressed couplings of chiral perturbation theory a set of six equations of the Roy and Steiner type for the S- and P-waves of the $\pi K$ scattering amplitudes is derived. The range of validity and the multiplicity of the solutions are discussed. Precise numerical solutions are obtained in the range $E\lesssim 1$ GeV which make use as input, for the first time, of the most accurate experimental data available at $E\gtrsim 1$ GeV for both $\pi K\to\pi K$ and $\pi\pi\to K\overline{K}$ amplitudes. Our main result is the determination of a narrow allowed region for the two S-wave scattering lengths. Present experimental data below 1 GeV are found to be in generally poor agreement with our results. A set of threshold expansion parameters, as well as sub-threshold parameters are computed. For the latter, a matching with the SU(3) chiral expansion at NLO is performed.

A new analysis of pi K scattering from Roy and Steiner type equations

Veneziano's model and nonet scheme for 1− and 2+ mesons

It is pointed out that for the null-plane quantization a paradox arises in connection with Haag's theorem. A prescription is proposed to overcome this difficulty.

Null-plane quantization and Haag's theorem

Discussions are given of possible solutions for the Finite Energy Sum Rules (FESR), applied to baryon-antibaryon scattering, with or without assuming resonances in exotic channels Exotic resonances, assuming they exist, are classified, as a result of factorization, according to 36-plet, 18-plet, 18-plet and nonet It is then shown that these mesons are required to obey an equal spacing mass formula and nonet-like couplings, which are direct extensions of the ideal nonet scheme for 1- and 2+ mesons When there are no resonances in exotic channels, the idea of duality between ordinary meson resonances is not applicable to baryon-antibaryon scattering However, by extending the concept of the duality, it is possible to find a solution of the FESR \"fVe construct an explicit formula with such extended duality, where Regge cuts as well as Regge poles appear in the amplitude in question

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Dualities in Baryon-Antibaryon Scattering

The high-energy behavior of scattering amplitudes is investigated by analyzing the contribution from a certain class of Mandelstam branch points in the complex angular momentum plane. We denote symbolically, for example, by $\mathrm{nP}$ the branch point generated by $n$-Pomeranchon exchange. It is shown that the totality of the contributions from the branch points of the type $X+nP$ ($n=1,2,\ensuremath{\cdots}$) gives an oscillatory behavior to scattering amplitudes at high energies, and that it results in a simple modification of the one-Regge-pole ($X$) contribution in the impact-parameter formalism. For the branch points of the type $\mathrm{nX}$ ($n=2,3,\ensuremath{\cdots}$; $X\ensuremath{\ne}P$), the concept of an effective trajectory is introduced. High-energy proton-proton scattering at 90\ifmmode^\circ\else\textdegree\fi{} is explained by the effective trajectory generated by the branch points of the type $(n\ensuremath{-}m){P}^{\ensuremath{'}}+m\ensuremath{\omega}$ ($n=2,3,\ensuremath{\cdots}$; $m=0,\ensuremath{\cdots},n$).

Haruichi Yabuki

Papers

Veneziano's model and nonet scheme for 1− and 2+ mesons

Null-plane quantization and Haag's theorem

Dualities in Baryon-Antibaryon Scattering

Branch Points in the Complex Angular Momentum Plane and High-Energy Behavior of Scattering Amplitudes

Relativistic wave equation for the harmonically confined quark-antiquark system