Exclusive differential spectra in color-singlet processes at hadron colliders are benchmark observables that have been studied to high precision in theory and experiment. We present an effective-theory framework utilizing soft-collinear effective theory to incorporate massive (bottom) quark effects into resummed differential distributions, accounting for both heavy-quark initiated primary contributions to the hard scattering process as well as secondary effects from gluons splitting into heavy-quark pairs. To be specific, we focus on the Drell-Yan process and consider the vector-boson transverse momentum, q T , and beam thrust, T , as examples of exclusive observables. The theoretical description depends on the hierarchy between the hard, mass, and the q T (or T ) scales, ranging from the decoupling limit q T m to the massless limit m q T . The phenomenologically relevant intermediate regime m ∼ q T requires in particular quark-mass dependent beam and soft functions. We calculate all ingredients for the description of primary and secondary mass effects required at NNLL resummation order (combining NNLL evolution with NNLO boundary conditions) for q T and T in all relevant hierarchies. For the q T distribution the rapidity divergences are different from the massless case and we discuss features of the resulting rapidity evolution. Our results will allow for a detailed investigation of quark-mass effects in the ratio of W and Z boson spectra at small q T , which is important for the precision measurement of the W -boson mass at the LHC.

We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

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Conventionally, factorized scattering in two dimensions is argued to be a consequence of the conservation of local higher charges. However, integrability may well be realized via nonlocal charges, while higher local charges are not known. Here we address the question of whether a nonlocal Yangian symmetry implies factorized scattering of the Smatrix. We explicitly study the constraints on three-particle scattering processes of particles transforming in the fundamental representations of su(N ), u(1|1), and the centrally extended su(2|2) underlying the dynamic scattering and hexagon form factors in AdS/CFT. These considerations shed light on the role of the Yangian as an axiomatic input for the bootstrap program for integrable theories.

We consider the spectrum of anomalous dimensions in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory and its $$ \mathcal{N} $$ N = 1 super-conformal Leigh-Strassler deformations. The two-loop truncation of the integrable $$ \mathcal{N} $$ N = 4 dilatation operator in the SU(2) sector, which is a next-to-nearest-neighbour deformation of the XXX spin chain, is not strictly integrable at finite coupling and we show that it indeed has Wigner-Dyson level statistics. However, we find that it is only weakly chaotic in the sense that the cross-over to chaotic dynamics is slower than for generic chaotic systems.For the Leigh-Strassler deformed theory with generic parameters, we show that the one-loop dilatation operator in the SU(3) sector is chaotic, with a spectrum that is well described by GUE Random Matrix Theory. For the imaginary-β deformation, the statistics are GOE and the transition from the integrable limit is that of a generic system. This provides a weak-coupling analogue of the chaotic dynamics seen for classical strings in the dual background.We further study the spin chains in the semi-classical limit described by generalised Landau-Lifshitz models, which are also known to describe large-angular-momentum string solutions in the dual theory. We show that for the higher-derivative theory following from the two-loop $$ \mathcal{N} $$ N = 4 SU(2) spin chain, the maximal Lyapunov exponent is close to zero, consistent with the absence of chaotic dynamics. For the imaginary-β SU(3) theory, the resulting Landau-Lifshitz model has classically chaotic dynamics at finite values of the deformation parameter.