The three-loop single mass polarized pure singlet operator matrix element

Two – Loop Matrix Element of the Current – Current Operator in the Decay B → X s γ

We evaluate the important two–loop matrix element 〈sγ|Q2|b〉 of the operator (c̄γPLb) (s̄γμPLb) contributing to the inclusive radiative decay B → Xsγ. The calculation is performed in the NDR scheme, by means of asymptotic expansions method. The result is given as a series in z ≡ m2c/m2b up to O(z6). We confirm the result of Greub, Hurth and Wyler obtained by a different method up to O(z3). Higher–...

The Three - Loop Splitting Functions in QCD : The Singlet Case

We compute the next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of the unpolarized flavour-singlet parton densities in perturbative QCD. The exact expressions are presented in both Mellin-N and Bjorken-x space. We also provide accurate parametrizations for practical applications. Our results agree with all partial results available in the lit...

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra to...

Bottom quark mass and |Vcb | matrix element

Spatial operator factorization and inversion of the manipulator mass matrix

’bo new recursive factorizations are developed of the mass matrix for fixed-base and mobile-base manipulators. First, the mass matrix M is shown to have the factorization M = H$M$* H’. This is referred to here as the Newton-Euler factorization because it is closely related to the recursive Newton-Euler equations of motion. This factorization may be the simplest way to show the equivalence of re...