Unbinned model-independent measurements with coherent admixtures of multibody neutral DD meson decays

Various studies of Standard Model parameters involve measuring the properties of a coherent admixture of $D^0$ and $\overline{D}^0$ states. A typical example is the determination of the Unitarity Triangle angle $\gamma$ in the decays $B\to DK$, $D\to K_S^0\pi^+\pi^-$. A model-independent approach to perform this measurement is proposed that has superior statistical sensitivity than the well-established method involving binning of the $D\to K_S^0\pi^+\pi^-$ decay phase space. The technique employs Fourier analysis of the complex phase difference between $D^0$ and $\overline{D}^0$ decay amplitudes and can be easily generalised to other similar measurements, such as studies of charm mixing or determination of the angle $\beta$ from $B^0\to D h^0$ decays.Comment: 24 pages, 6 figures; Updated with published versio

The equation of state and the quasiparticle mass in the degenerate Fermi system with an effective interaction

General formulas are derived for the quasiparticle effective mass and the equation of state of the Fermi system with account of the interparticle attraction at long distances and repulsion at short distances. Calculations are carried out of the equation of state and the effective mass of the Fermi system at zero temperature with the use of the modified Morse potential. It is shown that the pair repulsive forces promote a decrease of the effective mass, and the attractive forces promote its increase. With a certain choice of the parameters of the potential the dependence of the pressure on the density has a nonmonotonic character, which enables to describe the coexistence of the liquid and gaseous phases. The influence of three-body interactions on the equation of state and the effective mass is considered. The calculation results are compared with experimental data concerning the quasiparticle effective mass in the liquid $^3$He. Key words: normal Fermi liquid, effective mass, quasiparticle, equation of state, interaction potentialComment: 10 pages, 3 figure

Thermodynamics of the Fermi gas in a nanotube

For the ideal Fermi gas that fills the space inside a cylindrical tube, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. All these quantities are expressed through the introduced standard functions and their derivatives. The radius of the tube is considered as an additional thermodynamic variable. It is shown that at low temperatures in the quasi-one-dimensional case the temperature dependencies of the entropy and heat capacities remain linear. The dependencies of the entropy and heat capacities on the chemical potential have sharp maximums at the points where the filling of a new discrete level begins. The character of dependencies of thermodynamic quantities on the tube radius proves to be qualitatively different in the cases of fixed linear and fixed total density. At the fixed linear density these dependencies are monotonous and at the fixed total density they have an oscillating character. Key words: Fermi particle, nanotube, thermodynamic functions, low-dimensional systems, equation of state, heat capacity, compressibilityComment: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1608.0720