Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors

In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$. A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\to D^*\ell\,\nu$ receive only small second order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.Comment: (34 pages, REVTEX, two postscript figures available upon request), SLAC-PUB-589

Optimizing nitrogen rates in Camelina sativa

Non-Peer ReviewedCamelina is a new oilseed crop to western Canada with potential applications in cosmetics, human nutrition, and biofuel. Nitrogen recommendations for camelina production in Western Canada aren’t available. Field studies were conducted in 2008 and 2009 for 10 site years at locations in western Canada to determine the effect of nitrogen rate on seed yield. Depending on the experiment, nitrogen rates ranged from 0 to 200 kg ha-1. The join point (N rate at which yields plateau) for camelina were 111 to 116 kg ha-1, which is similar to other Brassica oilseed species

Renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions

We obtain the next-to-next-to-leading-log renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic Hydrogen spectrum where we are able to reproduce some known double logs at O(m\alpha^6). We compare with other formalisms dealing with log resummation available in the literature.Comment: 9 pages, LaTeX. Minor changes, note added, final versio

Ultrasoft Renormalization in Non-Relativistic QCD

For Non-Relativistic QCD the velocity renormalization group correlates the renormalization scales for ultrasoft, potential and soft degrees of freedom. Here we discuss the renormalization of operators by ultrasoft gluons. We show that renormalization of soft vertices can induce new operators, and also present a procedure for correctly subtracting divergences in mixed potential-ultrasoft graphs. Our results affect the running of the spin-independent potentials in QCD. The change for the NNLL t-tbar cross section near threshold is very small, being at the 1% level and essentially independent of the energy. We also discuss implications for analyzing situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig

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

Leptonic μ \mu - and τ \tau -decays: mass effects, polarization effects and O(α) O(\alpha) radiative corrections

We calculate the radiative corrections to the unpolarized and the four polarized spectrum and rate functions in the leptonic decay of a polarized $\mu$ into a polarized electron. The new feature of our calculation is that we keep the mass of the final state electron finite which is mandatory if one wants to investigate the threshold region of the decay. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal and transverse polarization is calculated. We also provide analytical results on the integrated spectrum functions. We analyze the $m_e \to 0$ limit of our general results and investigate the quality of the $m_e \to 0$ approximation. In the $m_e \to 0$ case we discuss in some detail the role of the $O(\alpha)$ anomalous helicity flip contribution of the final electron which survives the $m_e \to 0$ limit. The results presented in this 0203048 also apply to the leptonic decays of polarized $\tau$-leptons for which we provide numerical results.Comment: 39 pages, 11 postscript figures added. Updated version. Four references added. A few text improvements. Final version to appear in Phys.Rev.

Chiral Perturbation Theory for SU(3) Breaking in Heavy Meson Systems

The SU(3) breaking effects due to light quark masses on heavy meson masses, decay constants ($F_{D}, F_{D_{s}}$) and the form factor for semileptonic $\overline{B}\rightarrow D^{(\ast)} l\bar{\nu}_{l}$ transitions are formulated in chiral perturbation theory, using a heavy meson effective Lagrangian and expanding in inverse powers of the heavy meson mass. To leading order in this expansion, the leading chiral logarithms and the required counterterms are determined. At this level, a non-analytic correction to the mass splittings of ${\cal O}(p^3)$ appears, similar the the one found in light baryons. The correction to $F_{D_{s}}/F_{D}$ is roughly estimated to be of the order of $10\%$ and, therefore, experimentally accessible, while the correction to the form factor is likely to be substantially smaller. We explicitly check that the heavy quark symmetry is preserved by the chiral loops.Comment: 21 page

Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum

We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $m\alpha_s \gg \Lambda_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation m\alpha_s^2 \simg \Lambda_{QCD}. When $\Lambda_{QCD} \ll m\alpha_s^2$, this is equivalent to obtain the whole set of $O(m\alpha_s^{(n+4)} \ln^n \alpha_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbative situation $m\alpha_s \sim \Lambda_{QCD}$ are also mentioned.Comment: 16 pages, LaTeX. Minor changes. Final versio

Low Energy Theory for 2 flavors at High Density QCD

We construct the effective Lagrangian describing the low energy excitations for Quantum Chromodynamics with two flavors at high density. The non-linear realization framework is employed to properly construct the low energy effective theory. The light degrees of freedom, as required by 't Hooft anomaly conditions, contain massless fermions which we properly include in the effective Lagrangian. We also provide a discussion of the linearly realized Lagrangian.Comment: 17 pages, RevTeX format, references added. To appear in Phys. Rev.

The QCD heavy-quark potential to order v^2: one loop matching conditions

The one-loop QCD heavy quark potential is computed to order v^2 in the color singlet and octet channels. Several errors in the previous literature are corrected. To be consistent with the velocity power counting, the full dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD one-loop potential are computed by comparing the QCD calculation with that in the effective theory. The graphs in the effective theory are also compared to terms from the hard, soft, potential, and ultrasoft regimes in the threshold expansion. The issue of off-shell versus on-shell matching and gauge dependence is discussed in detail for the 1/(m k) term in the potential. Matching on-shell gives a 1/(m k) potential that is gauge independent and does not vanish for QED.Comment: 28 pages, References added and minor changes to section III, results unchange