Dynamical NNLO parton distributions

Utilizing recent DIS measurements (\sigma_r, F_{2,3,L}) and data on hadronic dilepton production we determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2 < 1 GeV^2). These are compared with `standard' NNLO distributions generated from positive input distributions at some fixed and higher resolution scale (Q_0^2 > 1 GeV^2). Although the NNLO corrections imply in both approaches an improved value of \chi^2, typically \chi^2_{NNLO} \simeq 0.9 \chi^2_{NLO}, present DIS data are still not sufficiently accurate to distinguish between NLO results and the minute NNLO effects of a few percent, despite of the fact that the dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both are, as expected, smaller than those of their `standard' counterparts. The dynamical predictions for F_L(x,Q^2) become perturbatively stable already at Q^2 = 2-3 GeV^2 where precision measurements could even delineate NNLO effects in the very small-x region. This is in contrast to the common `standard' approach but NNLO/NLO differences are here less distinguishable due to the much larger 1\sigma uncertainty bands. Within the dynamical approach we obtain \alpha_s(M_Z^2)=0.1124 \pm 0.0020, whereas the somewhat less constrained `standard' fit gives \alpha_s(M_Z^2)=0.1158 \pm 0.0035.Comment: 44 pages, 15 figures; minor changes, footnote adde

First O(αs3)O(\alpha_s^3) heavy flavor contributions to deeply inelastic scattering

In the asymptotic limit $Q^2 \gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In this way, one can calculate all but the power corrections in $(m^2/Q^2)^k, k > 0$. The heavy flavor operator matrix elements are known to ${\sf NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the ${\sf NNLO}$ anomalous dimensions \cite{LARIN,MVVandim} are obtained as well.Comment: 6 pages, Contribution to the Proceedings of "Loops and Legs in Quantum Field Theory", 2008, Sondershausen, Germany, and DIS 2008, London, U

The uses of Connes and Kreimer's algebraic formulation of renormalization theory

We show how, modulo the distinction between the antipode and the "twisted" or "renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes the proofs of equivalence of the (corrected) Dyson-Salam, Bogoliubov-Parasiuk-Hepp and Zimmermann procedures for renormalizing Feynman amplitudes. We discuss the outlook for a parallel simplification of computations in quantum field theory, stemming from the same algebraic approach.Comment: 15 pages, Latex. Minor changes, typos fixed, 2 references adde

The massless higher-loop two-point function

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends only on the topology of $G$, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless 2-loop 2-point function is expressible in terms of multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We find that the coefficients in the Taylor expansion of planar graphs in this range evaluate to multiple zeta values, but the non-planar graphs with crossing number 1 may evaluate to multiple sums with $6^\mathrm{th}$ roots of unity. Our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite graph $K_{3,4}$ at one edge

b-Initiated processes at the LHC: a reappraisal

Several key processes at the LHC in the standard model and beyond that involve $b$ quarks, such as single-top, Higgs, and weak vector boson associated production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In the former, $b$ quarks appear only in the final state and are typically considered massive. In 5-flavor schemes, calculations include $b$ quarks in the initial state, are simpler and allow the resummation of possibly large initial state logarithms of the type $\log \frac{{\cal Q}^2}{m_b^2}$ into the $b$ parton distribution function (PDF), ${\cal Q}$ being the typical scale of the hard process. In this work we critically reconsider the rationale for using 5-flavor improved schemes at the LHC. Our motivation stems from the observation that the effects of initial state logs are rarely very large in hadron collisions: 4-flavor computations are pertubatively well behaved and a substantial agreement between predictions in the two schemes is found. We identify two distinct reasons that explain this behaviour, i.e., the resummation of the initial state logarithms into the $b$-PDF is relevant only at large Bjorken $x$ and the possibly large ratios ${\cal Q}^2/m_b^2$'s are always accompanied by universal phase space suppression factors. Our study paves the way to using both schemes for the same process so to exploit their complementary advantages for different observables, such as employing a 5-flavor scheme to accurately predict the total cross section at NNLO and the corresponding 4-flavor computation at NLO for fully exclusive studies.Comment: Fixed typo in Eq. (A.10) and few typos in Eq. (C.2) and (C.3

On the singular behaviour of scattering amplitudes in quantum field theory

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences