Gauge-invariant sub-structures of tree-level double-emission exact QCD spin amplitudes

In this note we discuss possible separations of exact, massive, tree-level spin amplitudes into gauge-invariant parts. We concentrate our attention on processes involving two quarks entering a color-neutral current and, thanks to the QCD interactions, two extra external gluons. We will search for forms compatible with parton-shower languages, without applying approximations or restrictions on phase space regions. Special emphasis will be put on the isolation of parts necessary for the construction of evolution kernels for individual splittings and to some degree for the running coupling constant as well. Our aim is to better understand the environment necessary to optimally match hard matrix elements with parton-shower algorithms. To avoid complications and ambiguities related to regularization schemes, we ignore, at this point, virtual corrections. Our representation is quite universal: any color-neutral current can be used; in particular, our approach is not restricted to vector currents only. This work is partially supported by RTN European Programme, MRTN-CT-2006-035505 (HEPTOOLS, Tools and Precision Calculations for Physics Discoveries at Colliders).     

Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes revisited

We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes.As a key step,we explicitly demonstrate the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules.To achieve this,we introduce specially-defined two-off-shell-line sub-amplitudes and examine their residues at spurious poles.     

Compact QED tree-level amplitudes from dressed BCFW recursion relations

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N²MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.     

Dissolving N = 4 loop amplitudes into QCD tree amplitudes

We use the infrared consistency of one-loop amplitudes in N = 4 Yang-Mills theory to derive a compact analytic formula for a tree-level next-to-next-to-maximal helicity-violating gluon scattering amplitude in QCD, the first such formula known. We argue that the infrared conditions, coupled with recent advances in calculating one-loop box coefficients, can give a new tool for computing tree-level amplitudes in general. Our calculation suggests that many amplitudes have a structure which is even simpler than that revealed so far by current twistor-space constructions.     

Nucleon distribution amplitudes from lattice QCD

We calculate low moments of the leading-twist and next-to-leading-twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS[over ] scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.     

Collinear limits of one-loop helicity amplitudes in QCD

We point out that for QCD subprocesses involving multiple quark pairs, it is useful to investigate the collinear limits of full helicity amplitudes. We study the recently calculated one-loop $0 \to \bar q\bar QQqg$ helicity amplitudes and confirm the results found by Bern, Dixon, Dunbar and Kosower for the loop splitting amplitudes.     

Radiative corrections to QCD amplitudes in quasi-multi-Regge kinematics

Radiative corrections to QCD amplitudes in the quasi-multi-Regge kinematics are interesting, in particular, since the Reggeized form of these amplitudes is used in the derivation of the NLO BFKL. This form is a hypothesis which must be at least carefully checked, if not proved. We calculate the radiative corrections in the one-loop approximation using the s-channel unitarity. Compatibility of the Reggeized form of the amplitudes with the s-channel unitarity requires fulfillment of the set of nonlinear equations for the Reggeon vertices. We show that these equations are satisfied.     

Non-perturbative QCD amplitudes in quenched and eikonal approximations

Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.     

Hadronic quark distribution amplitudes from QCD sum-rule moments

We discuss the reliability of hadronic wave functions (quark distribution amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncertainty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large oscillations of the model function. In particular, the freedom in the moments left by QCD sum rules leads to a nonconverging polynomial expansion. This remains true even if additional constraints on the wave functions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to the true wave function. The differences among the model wave functions persist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by means of such model wave functions are in general very unreliable. As specific examples, we examine the pion and nucleon wave functions and show that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.