Lattice QCD and QCD Sum Rule determination of the decay constants of eta_c, J/psi and hc states

We compute the decay constants of the lowest ccbar-states with quantum numbers J(PC)=0(-+) [eta_c], 1(--) [J/psi], and 1(+-) [hc] by using lattice QCD and QCD sum rules. We consider the coupling of J/psi to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched (Nf=2) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate of eta_c --> gamma gamma decay, and to comment on the factorization in B --> X K decays, with X being either eta_c or J/psi.Comment: 25 pages (published version

Quasimomentum distribution and expansion of an anyonic gas

We point out that the momentum distribution is not a proper observable for a system of anyons in two-dimensions. In view of anyons as Wilczek's composite charged flux-tubes, this is a consequence of the fact that the orthogonal components of the kinetic momentum operator do not commute at the position of a flux tube, and thus cannot be diagonalized in the same basis. As a substitute for the momentum distribution of an anyonic (spatially localized) state, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. This definition is identical with the standard one when the statistical parameter approaches that for bosons or fermions. Exact examples of expansion dynamics, which underpin our proposal, and observables that can be used to measure anyonic statistics, are shown.Comment: are welcom

Direct numerical calculation of one-loop Feynman diagrams

U ovom je doktorskom radu izložena nova, potpuno numerička metoda izračuna jednopetljenih Feynmanovih amplituda. Metoda se temelji na dvjema postojećim metodama za numerički izračun jednopetljenih Feynmanovih dijagrama. U jednoj se od tih metoda numerička stabilnost postiže deformacijom integracijske krivulje u kompleksnu ravninu, dok se u drugoj metodi integrabilni singulariteti regula- riziraju Feynmanovim ∈ parametrom, te se fizikalna vrijednost dijagrama dobije ekstrapolacijom ∈ → 0. Za razliku od ovih metoda, koje su namijenjene izračunu pojedinih dijagrama, novom se metodom računa kompletna amplituda, dana kao suma dijagrama, odjednom. Nakon što se amplituda rastavi na dva, tzv. UV i IR, doprinosa, UV doprinos se računa deformacijom integracijske krivulje, dok se IR doprinos računa s konačnim ∈, te naknadno ekstrapolira prema ∈ → 0. Računanjem cjelokupne amplitude odjednom, dobiva se na ekonomičnosti i stabilnosti samog računa, te se eliminira potreba za regularizacijom pojedinih dijagrama u slučaju konačnih amplituda. Metoda je implementirana u programskom jeziku Wolfram Mathematica i primjenjena na slučaj raspršenja u skalarnoj teoriji i kvantnoj elektrodinamici.Presented in this thesis is a new, completely numerical approach to one-loop Feynman amplitudes. The method is based upon two existing methods of numerical calculation of one-loop Feynman diagrams. In one of these methods, the numerical integration is performed by a contour deformation into a complex plane, while the other method regularizes the integrable singularities by keeping the Feynman ∈ parameter _nite and then calculates the physical value of the diagram by extrapolation ∈ ! 0. Contrary to these methods, which are designed to calculate individual diagrams, the new method calculates the complete amplitude, given as a sum of diagrams, at once. After separating the amplitude into two contributi- ons, named UV and IR, the UV contribution is integrated via contur deformation, while the IR contribution is calculated using finite ∈ parameter and subsequently extrapolated for the value ∈ ! 0. Calculating the complete amplitude at once is more economical and numerically stable approach and it elliminates the need for diagram regularization whenever the complete amplitude is finite. The method is implemented in the Wolfram Mathematica language and applied to calculation of scattering amplitudes in scalar theory and quantum electrodynamics

Berry phase for a Bose gas on a one-dimensional ring

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(\phi)=g \delta(\phi-\phi_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\Delta q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\Delta q/\hbar \oint \mathbf{A}\cdot d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly-interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems