Relativistic and Binding Energy Corrections to Direct Photon Production In Upsilon Decay

A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.Comment: 13 pages, LateX, One figure (to be published in Phys. Rev. D, Sept. 1, 1996

Soft-Collinear Factorization in Effective Field Theory

The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The leading order Lagrangian is derived using power counting and gauge invariance in the effective theory. Several species of gluons are required, and softer gluons appear as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in B->D pi, and the soft-collinear convolution for the B->Xs gamma spectrum.Comment: 32 pages, 11 figs, journal versio

Breit Hamiltonian and QED Effects for Spinless Particles

We describe a simplified derivation for the relativistic corrections of order $\alpha^4$ for a bound system consisting of two spinless particles. We devote special attention to pionium, the bound system of two oppositely charged pions. The leading quantum electrodynamic (QED) correction to the energy levels is of the order of $\alpha^3$ and due to electronic vacuum polarization. We analyze further corrections due to the self-energy of the pions, and due to recoil effects, and we give a complete result for the scalar-QED leading logarithmic corrections which are due to virtual loops involving only the scalar constituent particles (the pions); these corrections are of order $\alpha^5 \ln \alpha$ for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press

NRQED and Next-to-Leading Hyperfine Splitting in Positronium

We compute the next-to-leading, O(m alpha^5), contribution to the hyperfine splitting in positronium within the framework of NRQED. When applied to the ground state, our calculation reproduces known results, providing a further test of NRQED techniques. Besides providing a very simple method of calculation of the standard result, we also obtain new expressions for excited states of positronium with negligible additional effort. Our calculation requires the complete next-to-leading matching of the lowest-dimension NRQED four-fermi couplings, which we publish here for the first time.Comment: 24 pages, plain TeX, 6 figures included using eps

Effective field theories for QED bound states: extending Nonrelativistic QED to study retardation effects

Nonrelativistic QED bound states are difficult to study because of the presence of at least three widely different scales: the masses, three-momenta ($p_i$) and kinetic energies ($K_i$) of the constituents. Nonrelativistic QED (NRQED), an effective field theory developed by Caswell and Lepage, simplifies greatly bound state calculations by eliminating the masses as dynamical scales. As we demonstrate, NRQED diagrams involving only photons of energy $E_\gamma \simeq p_i$ contribute, in any calculation, to a unique order in $\alpha$. This is not the case, however, for diagrams involving photons with energies $E_\gamma \simeq K_i$ (``retardation effects"), for which no simple counting counting rules can be given. We present a new effective field theory in which the contribution of those ultra-soft photons can be isolated order by order in $\alpha$. This is effectively accomplished by performing a multipole expansion of the NRQED vertices.Comment: 39 pages, 9 Postscript figures, uses Rev.tex V3.0 and epsf.te

Current Closure in the Auroral Ionosphere: Results from the Auroral Current and Electrodynamics Structure Rocket Mission

The Auroral Current and Electrodynamics Structure (ACES) mission consisted of two sounding rockets launched nearly simultaneously from Poker Flat Research Range, AK on January 29, 2009 into a dynamic multiple-arc aurora. The ACES rocket mission was designed to observe electrodynamic and plasma parameters above and within the current closure region of the auroral ionosphere. Two well instrumented payloads were flown along very similar magnetic field footprints, at different altitudes, with small temporal separation between both payloads. The higher altitude payload (apogee 360 km), obtained in-situ measurements of electrodynamic and plasma parameters above the current closure region to determine the input signature. The low altitude payload (apogee 130 km), made similar observations within the current closure region. Results are presented comparing observations of the electric fields, magnetic components, and the differential electron energy flux at magnetic footpoints common to both payloads. In situ data is compared to the ground based all-sky imager data, which presents the evolution of the auroral event as the payloads traversed through magnetically similar regions. Current measurements derived from the magnetometers on the high altitude payload observed upward and downward field-aligned currents. The effect of collisions with the neutral atmosphere is investigated to determine it is a significant mechanism to explain discrepancies in the low energy electron flux. The high altitude payload also observed time-dispersed arrivals in the electron flux and perturbations in the electric and magnetic field components, which are indicative of Alfven waves

Invariant vector fields and the prolongation method for supersymmetric quantum systems

The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method. Generators of supersymmetries are then introduced so that we get Lie superalgebras of symmetries and supersymmetries. This approach does not require the introduction of Grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry. The Jaynes-Cummings model and supersymmetric generalizations are then studied. We show how it is closely related to the preceding models. Lie algebras of symmetries and supersymmetries are also obtained.Comment: 37 pages, 7 table

Renormalization group analysis of the QCD quark potential to order v^2

A one-loop renormalization group analysis of the order v^2 relativistic corrections to the static QCD potential is presented. The velocity renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv^2) terms. The results are compared to previous calculations in the literature.Comment: 13 pages. important change: running of soft Lagrangian include

Order alpha^3 ln(1/alpha) Corrections to Positronium Decays

The logarithmically enhanced alpha^3 ln(1/alpha) corrections to the para- and orthopositronium decay widths are calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics.In the case of parapositronium, the correction is negative, approximately doubles the effect of the leading logarithmic alpha^3 ln^2(1/alpha) one, and is comparable to the nonlogarithmic O(alpha^2) one. As for orthopositronium, the correction is positive and almost cancels the alpha^3 ln^2(1/alpha) one. The uncertainties in the theoretical predictions for the decay widths are reduced.Comment: 10 pages (Latex); missing term added, corrected coefficient B_p used, numerical results insignificantly change

Renormalization group scaling in nonrelativistic QCD

We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed in which a subtraction velocity nu is used rather than a subtraction scale mu. We derive a novel renormalization group equation in velocity space which can be used to sum logarithms of v in the effective theory. We apply our method to several examples. In particular we show that our formulation correctly reproduces the two-loop anomalous dimension of the heavy quark production current near threshold.Comment: (27 pages, revtex