Policing the legume-Rhizobium symbiosis: a critical test of partner choice

In legume-Rhizobium symbioses, specialised soil bacteria fix atmospheric nitrogen in return for carbon. However, ineffective strains can arise, making discrimination essential. Discrimination can occur via partner choice, where legumes prevent ineffective strains from entering, or via sanctioning, where plants provide fewer resources. Several studies have inferred that legumes exercise partner choice, but the rhizobia compared were not otherwise isogenic. To test when and how plants discriminate ineffective strains we developed sets of fixing and non-fixing strains that differed only in the expression of nifH - essential for nitrogen fixation - and could be visualised using marker genes. We show that the plant is unable to select against the non-fixing strain at the point of entry, but that non-fixing nodules are sanctioned. We also used the technique to characterise mixed nodules (containing both a fixing and a non-fixing strain), whose frequency could be predicted using a simple diffusion model. We discuss that sanctioning is likely to evolve in preference to partner choice in any symbiosis where partner quality cannot be adequately assessed until goods or services are actively exchanged

The real radiation antenna function for S→QQˉqqˉS \to Q {\bar Q} q {\bar q} at NNLO QCD

As a first step towards the application of the antenna subtraction formalism to NNLO QCD reactions with massive quarks, we determine the real radiation antenna function and its integrated counterpart for reactions of the type $S \to Q{\bar Q} q {\bar q}$, where $S$ denotes an uncolored initial state and $Q$, $q$ a massive and massless quark, respectively. We compute the corresponding integrated antenna function in terms of harmonic polylogarithms. As an application and check of our results we calculate the contribution proportional to $\alpha_s^2 e^2_Q N_f$ to the inclusive heavy-quark pair production cross ection in $e^+e^-$ annihilation.Comment: Latex, 32 page

Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours

The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiatior partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction terms, classify all relevant antenna functions and describe their integration over the relevant antenna phase space. For the initial-initial antenna functions with two quark flavours, we derive the phase space master integrals and obtain the integrated antennae