International Journal of Modern Physics A

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda chain, discrete NLS model) and continuum integrable models (NLS, sine–Gordon models and affine Toda field theories) are also discussed.

Hadronic form factors for the rare weak transitions Λ_b → Λ^(*) are calculated using a nonrelativistic quark model. The form factors are extracted in two ways. An analytic extraction using single-component wave functions (SCA) with the quark current being reduced to its nonrelativistic Pauli form is employed in the first method. In the second method, the form factors are extracted numerically using the full quark model wave function (MCN) with the full relativistic form of the quark current. Although there are differences between the two sets of form factors, both sets satisfy the relationships expected from the heavy quark effective theory (HQET). Differential decay rates, branching ratios (BRs) and forward–backward asymmetries (FBAs) are calculated for the dileptonic decays Λ_b → Λ^(*) ℓ⁺ ℓ^-, for transitions to both ground state and excited daughter baryons. Inclusion of the long distance contributions from charmonium resonances significantly enhances the decay rates. In the MCN model the Λ(1600) mode is the dominant mode in the μ channel when charmonium resonances are considered; the Λ(1520) mode is also found to have a comparable BR to that of the ground state in the μ channel.

Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short-distance physics is characterized by a nontrivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross-section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross-sections display a threshold, are suppressed in the Planckian, and reproduce the semiclassical result in the deep trans-Planckian region. Further implications are discussed.

It is an intriguing question how local time can be introduced in the emergent picture of space–time. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rank-three tensor model with first class constraints in Hamilton formalism is presented. In the limit of usual continuous spaces, the algebra of constraints reproduces that of general relativity in Hamilton formalism. While the momentum constraints can be realized rather easily by the symmetry of the tensor models, the form of the Hamiltonian constraints is strongly limited by the condition of the closure of the whole constraint algebra. Thus the Hamiltonian constraints have been determined on the assumption that they are local and at most cubic in canonical variables. The form of the Hamiltonian constraints has similarity with the Hamiltonian in the c < 1 string field theory, but it seems impossible to realize such a constraint algebras in the framework of vector or matrix models. Instead these models are rather useful as matter theories coupled with the tensor model. In this sense, a three-index tensor is the minimum-rank dynamical variable necessary to describe gravity in terms of tensor models.

The oblique parameters S, T and U and their higher-order extensions (V, W and X) are observables that combine electroweak precision data to quantify deviation from the Standard Model. These parameters were calculated at one loop in the basis-independent CP-violating Two-Higgs Doublet Model (2HDM). The scalar parameter space of the 2HDM was randomly sampled within limits imposed by unitarity and found to produce values of the oblique parameters within experimental bounds, with the exception of T. The experimental limits on T were used to predict information about the mass of the charged Higgs boson and the difference in mass between the charged Higgs boson and the heaviest neutral Higgs boson. In particular, it was found that the 2HDM predicts -600 GeV < m_H^± - m₃ < 100 GeV, with values of m_H^± > 250 GeV being preferred. The mass scale of the new physics (M_NP) produced by random sampling was consistently fairly high, with the average of the scalar masses falling between 400 and 800 GeV for , although the model can be tuned to produce a light neutral Higgs mass (~120 GeV). Hence, the values produced for V, W and X fell well within 0.01 of zero, confirming the robustness of the linear expansion approximation. Taking the CP-conserving limit of the model was found to not significantly affect the values generated for the oblique parameters.

The structure of the D_s1(2460) meson has not yet been exactly known in the quark model. Considering the D_s1 meson as a conventional meson, we investigate the strong form factors and coupling constants g_Ds1D*K and in the framework of the three point QCD sum rules. Any future experimental measurement on these form factors as well as coupling constants g_Ds1D*K and and their comparison with the obtained results in the present work can give considerable information about the structure of this meson.