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

Quarks in the Skyrme-'t Hooft-Witten Model

The three-flavor Skyrme-'t Hooft-Witten model is interpreted in terms of a quark-like substructure, leading to a new model of explicitly confined color-free ``quarks'' reminiscent of Gell-Mann's original pre-color quarks, but with unexpected and significant differences.Comment: Latex, 6 pages, no figure

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

Heavy meson semileptonic differential decay rate in two dimensions in the large Nc

We study QCD in 1+1 dimensions in the large $N_c$ limit using light-front Hamiltonian perturbation theory in the $1/N_c$ expansion. We use this formalism to exactly compute hadronic transition matrix elements for arbitrary currents at leading order in $1/N_c$. We compute the semileptonic differential decay rate of a heavy meson, $d\Gamma/dx$, and its moments, $M_N$, using the hadronic matrix elements obtained previously. We put some emphasis in trying to understand parity invariance. We also study with special care the kinematic region where the operator product expansion ($1/N \sim 1-x \sim 1$) or non-local effective field theories ($1/N \sim 1-x \sim \Lambda_{QCD}/m_Q$) can be applied. We then compare with the results obtained using an effective field theory approach based on perturbative factorization, with the focus to better understand quark-hadron duality. At the end of the day, using effective field theories, we have been able to obtain expressions for the moments with relative accuracy of $O(\Lambda_{QCD}^2/m_Q^2)$ in the kinematic region where the operator product expansion can be applied, and with relative accuracy of $O(\Lambda_{QCD}/m_Q)$ in the kinematic region where non-local effective field theories can be applied. These expressions agree, within this precision, with those obtained from the hadronic result using the layer-function approximation plus Euler-McLaurin expansion. Very good numerical agreement for the moments is obtained between the exact result and the result using effective field theories.Comment: 52 pages, 30 figures, references added, small modifications, some discussion of the four dimensional case changed, journal versio

Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.Comment: 14 pages, 1 figure; references added and typographical errors corrected; to appear in Phys. Rev.

Chiral Perturbation Theory with tensor sources

We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \bar{\psi}\sigma_{\mu\nu}\psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p^2). With this choice, we build the even-parity effective Lagrangian up to the p^6-order (NLO). While there are only 4 new terms at the p^4-order, at p^6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p^8-order (NNLO).Comment: 23 pages, one figure; typos corrected, one paragraph added, new section added, references added, published versio

Enhanced Nonperturbative Effects in Z Decays to Hadrons

We use soft collinear effective field theory (SCET) to study nonperturbative strong interaction effects in Z decays to hadronic final states that are enhanced in corners of phase space. These occur, for example, in the jet energy distribution for two jet events near E_J=M_Z/2, the thrust distribution near unity and the jet invariant mass distribution near zero. The extent to which such nonperturbative effects for different observables are related is discussed.Comment: 17 pages. Paper reorganized, and more discussion and results include

1/N Expansion for Exotic Baryons

The 1/N expansion for exotic baryons is developed, and applied to the masses, meson couplings and decay widths. Masses and widths of the 27 and 35 pentaquark states in the same tower as the Theta+ are related by spin-flavor symmetry. The 27 and 35 states can decay within the pentaquark tower, as well as to normal baryons, and so have larger decay widths than the lightest pentaquark Theta. The 1/N expansion also is applied to baryon exotics containing a single heavy antiquark. The decay widths of heavy pentaquarks via pion emission, and to normal baryons plus heavy D^(*),B^(*) mesons are studied, and relations following from large-N spin-flavor symmetry and from heavy quark symmetry are derived.Comment: Major additions: plots of widths and branching ratios, discussion of strong decays of heavy pentaquarks, including consequences of heavy quark symmetr

Power Counting in the Soft-Collinear Effective Theory

We describe in some detail the derivation of a power counting formula for the soft-collinear effective theory (SCET). This formula constrains which operators are required to correctly describe the infrared at any order in the Lambda_QCD/Q expansion (lambda expansion). The result assigns a unique lambda-dimension to graphs in SCET solely from vertices, is gauge independent, and can be applied independent of the process. For processes with an OPE the lambda-dimension has a correspondence with dynamical twist.Comment: 12 pages, 1 fig, journal versio