The flavour projection of staggered fermions and the quarter-root trick

It is shown that the flavour projection of staggered fermions can be written as a projection between the fields on four separate, but parallel, lattices, where the fields on each are modified forms of the standard staggered fermion field. Because the staggered Dirac operator acts equally on each lattice, it respects this flavour projection. We show that the system can be gauged in the usual fashion and that this does not interfere with flavour projection. We also consider the path integral, showing that, prior to flavour projection, it evaluates to the same form on each lattice and that this form is equal to that used in the quarter-root trick. The flavour projection leaves a path integral for a single flavour of field on each lattice.Comment: 8 pages, including title pag

Fabrication and characterization of hot- pressed tantalum carbide

Microstructure and chemistry of hot pressed powder compacts of tantalum carbid

Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors

The hard-scattering contributions to heavy-to-light form factors at large recoil are studied systematically in soft-collinear effective theory (SCET). Large logarithms arising from multiple energy scales are resummed by matching QCD onto SCET in two stages via an intermediate effective theory. Anomalous dimensions in the intermediate theory are computed, and their form is shown to be constrained by conformal symmetry. Renormalization-group evolution equations are solved to give a complete leading-order analysis of the hard-scattering contributions, in which all single and double logarithms are resummed. In two cases, spin-symmetry relations for the soft-overlap contributions to form factors are shown not to be broken at any order in perturbation theory by hard-scattering corrections. One-loop matching calculations in the two effective theories are performed in sample cases, for which the relative importance of renormalization-group evolution and matching corrections is investigated. The asymptotic behavior of Sudakov logarithms appearing in the coefficient functions of the soft-overlap and hard-scattering contributions to form factors is analyzed.Comment: 50 pages, 10 figures; minor corrections, version to appear in JHE

Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension

We present a factorization formula for the production of pairs of heavy coloured particles in hadronic collisions at the production threshold, which forms the basis for the resummation of soft gluons and Coulomb gluons. We construct a basis in colour space that diagonalizes the soft function appearing in the factorization formula to all orders in perturbation theory. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.Comment: 36 pages, LaTeX, 2 figures. v2 matches published version (improved discussion of NNLL resummation, note added on work by Ferroglia et al.

Infrared regulators and SCETII

We consider matching from SCETI, which includes ultrasoft and collinear particles, onto SCETII with soft and collinear particles at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. We give a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in SCETII are sufficient to reproduce all the infrared divergences of SCETI. We explain the relationship between IR regulators and an additional mode proposed for SCETII.Comment: 9 pages. Added discussion about relationship between IR regulators and messenger mode

Direct photon production with effective field theory

The production of hard photons in hadronic collisions is studied using Soft-Collinear Effective Theory (SCET). This is the first application of SCET to a physical, observable cross section involving energetic partons in more than two directions. A factorization formula is derived which involves a non-trivial interplay of the angular dependence in the hard and soft functions, both quark and gluon jet functions, and multiple partonic channels. The relevant hard, jet and soft functions are computed to one loop and their anomalous dimensions are determined to three loops. The final resummed inclusive direct photon distribution is valid to next-to-next-to-leading logarithmic order (NNLL), one order beyond previous work. The result is improved by including non-logarithmic terms and photon isolation cuts through matching, and compared to Tevatron data and to fixed order results at the Tevatron and the LHC. The resummed cross section has a significantly smaller theoretical uncertainty than the next-to-leading fixed-order result, particularly at high transverse momentum.Comment: 42 pages, 9 figures; v2: references added, minor changes; v3: typos; v4: typos, corrections in (16), (47), (72

Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet

We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case both the microscopic and the effective theory can be solved analytically. In this way the low-energy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The low-energy behavior at half-filling as well as in the single- and two-hole sectors is described exactly by the systematic low-energy effective field theory. In particular, for weakly bound two-hole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic low-energy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.Comment: 34 pages, 1 figur

The relativistic self-energy in nuclear dynamics

It is a well known fact that Dirac phenomenology of nuclear forces predicts the existence of large scalar and vector mean fields in matter. To analyse the relativistic self-energy in a model independent way, modern high precision nucleon-nucleon ($NN$) potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. It allows further to calculate the relativistic self-energy in nuclear matter in Hartree-Fock approximation. Independent of the choice of the nucleon-nucleon interaction large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. In the framework of chiral EFT these fields are dominantly generated by contact terms which occur at next-to-leading order in the chiral expansion. Consistent with Dirac phenomenology the corresponding low energy constants which generate the large fields are closely connected to the spin-orbit interaction in $NN$ scattering. The connection to QCD sum rules is discussed as well.Comment: 49 pages, 13 figure