Overview of Non-Relativistic QCD

An overview of recent theoretical progress on Non-Relativistic QCD and related effective theories is provided.Comment: Plenary talk at the 4th International Conference on Quarks and Nuclear Physics (QNP06), 5-10 June 2006, Madrid, Spain; 6 pages, 1 figure, EPJ style. References added. Journal versio

Incompressible States in Double Quantum Dots

Incompressible (magic) states of vertically coupled quantum dots submitted to strong magnetic fields such that only the lowest Landau level is relevant are studied within an exact diagonalization calculation for N=3, 5 and 6, electrons. We find that the sequences of total angular momentum M for which incompressible states exists depend on the interplay between the inter-dot hopping parameter \Delta_t and the inter-dot distance d. For d of the order of the magnetic length and for all values of \Delta_t, we conclude that, in contrast to previous claims, the incompressible states appear at magic values of M which do not differ from those obtained for a single dot, namely M=N(N-1)/2+jN where j is a positive integer number. For large inter-dot distance and simultaneously small inter-dot hopping parameter, new sequences of magic values of $M$ are observed. These new sequences can be easily understood in terms of a transition regime towards a system of two decoupled single dots. However, important differences in the nature of the incompressible ground states are found with respect to those of a single dot.Comment: 23 pages, 11 figures; discussion improved, references added, journal versio

Renormalizing the Lippmann-Schwinger equation for the one pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.Comment: 26 pages, 1 figure; extended version with references adde

Effective Field Theory with Dibaryon Fields: Nucleon-Nucleon amplitudes at NNLO

We calculate the nucleon-nucleon scattering amplitudes in the 1S0 and 3S1-3D1 channels at next-to-next to leading order starting from a recently proposed non-relativistic chiral effective theory, which includes dibaryon fields as fundamental degrees of freedom. We restrict ourselves to center of mass energies (E) smaller than the pion mass (m_pi), and further divide the calculation into two relative momentum (p) regions, a high energy one p ~ m_pi >> delta m_i, \delta m_i being the dibaryon residual masses, and low energy one p ~ delta m_i. We first match to a lower energy effective theory in which we calculate the amplitudes in the high energy region. We further match this effective theory to the so called pionless effective theory in the low energy region, and carry out the calculations in the latter. Dimensional regularization and minimal subtraction scheme are used throughout. For 1S0 channel a good description of the phase shift data is obtained for E < 50 MeV. For the 3S1-3D1 channel, the 3S1 phase shift data is only well described up to E < 20 MeV.Comment: 25 pages, 21 figures. Journal versio

Radiative decays and the nature of heavy quarkonia

We argue that the photon spectra in radiative decays of various heavy quarkonium states provide important information on their nature. If two of these states are in the strong coupling regime, we are able to produce a parameter-free model independent formula, which holds at next-to-leading order and includes both direct and fragmentation contributions. When the formula is checked against recent CLEO data it favors Upsilon (2S) and Upsilon (3S) in the strong coupling regime and disfavors Upsilon (1S) in it.Comment: 5 pages, 3 figures. Clarifications introduced, including extra curve in plots. Journal versio

Combining constructive and equational geometric constraint solving techniques

In the past few years, there has been a strong trend towards developing parametric, computer aided design systems based on geometric constraint solving. An efective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropiate techniques toachieve the expected functional capabilities. This work reports on a hybrid method which combines two geometric constraint solving techniques: Constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.Postprint (published version

Semi-inclusive radiative decays of Upsilon 1S

We discuss in detail the photon spectrum of radiative Upsilon 1S decays taking into account a number of results that have recently appeared in the literature. In particular, we show how to consistently combine expressions which are valid in the upper end-point region, where NRQCD factorization breaks down, with those of the central region, where NRQCD factorization holds. An excellent description of data is achieved, but theoretical errors are large.Comment: 18 pages, 7 figures. Minor modifications. References added and corrected. Journal versio