A novel strong coupling expansion of the QCD Hamiltonian

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in \lambda = g^{-2/3} can be obtained. The free part is the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and the interaction terms proportional to \lambda^n contain n discretised spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order \lambda^2 for the case of SU(2) Yang-Mills theory.Comment: Talk given at the 6th International Workshop on "Critical Point and Onset of Deconfinement (CPOD)", Dubna, Russia, 23-29 August 201

Time reparameterization in Bianchi type I spinor cosmology

The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presentedComment: 16 pages, no figures, to appear in Annals of Physic

Unconstrained SU(2) Yang-Mills Quantum Mechanics with Theta Angle

The unconstrained classical system equivalent to spatially homogeneous SU(2) Yang-Mills theory with theta angle is obtained and canonically quantized. The Schr\"odinger eigenvalue problem is solved approximately for the low lying states using variational calculation. The properties of the groundstate are discussed, in particular its electric and magnetic properties, and the value of the "gluon condensate" is calculated. Furthermore it is shown that the energy spectrum of SU(2) Yang-Mills quantum mechanics is independent of the theta angle. Explicit evaluation of the Witten formula for the topological susceptibility gives strong support for the consistency of the variational results obtained.Comment: 20 pages REVTEX, no figures, one reference added, final version to appear in Phys. Rev.

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

Hamiltonian reduction of SU(2) Dirac-Yang-Mills mechanics

The SU(2) gauge invariant Dirac-Yang-Mills mechanics of spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is obtained using the gaugeless method of Hamiltonian reduction. The latter includes the Abelianization of the first class constraints, putting the second class constraints into the canonical form and performing a canonical transformation to a set of adapted coordinates such that a subset of the new canonical pairs coincides with the second class constraints and part of the new momenta is equal to the Abelian constraints. In the adapted basis the pure gauge degrees of freedom automatically drop out from the consideration after projection of the model onto the constraint shell. Apart from the elimination of these ignorable degrees of freedom a further Hamiltonian reduction is achieved due to the three dimensional group of rigid symmetry possessed by the system.Comment: 25 pages Revtex, no figure

Search for resonances in the mass spectrum of muon pairs produced in association with b quark jets in proton-proton collisions at root 8 and 13 TeV

A search for resonances in the mass range 12-70 GeV produced in association with a b quark jet and a second jet, and decaying to a muon pair, is reported. The analysis is based on data from proton-proton collisions at center-of-mass energies of 8 and 13 TeV, collected with the CMS detector at the LHC and corresponding to integrated luminosities of 19.7 and 35.9 fb(-1), respectively. The search is carried out in two mutually exclusive event categories. Events in the first category are required to have a b quark jet in the central region (|| 2.4) and at least one jet in the forward region (|| > 2.4). Events in the second category are required to have two jets in the central region, at least one of which is identified as a b quark jet, no jets in the forward region, and low missing transverse momentum. An excess of events above the background near a dimuon mass of 28 GeV is observed in the 8 TeV data, corresponding to local significances of 4.2 and 2.9 standard deviations for the first and second event categories, respectively. A similar analysis conducted with the 13 TeV data results in a mild excess over the background in the first event category corresponding to a local significance of 2.0 standard deviations, while the second category results in a 1.4 standard deviation deficit. The fiducial cross section measurements and 95% confidence level upper limits on those for a resonance consistent with the 8 TeV excess are provided at both collision energies