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Register a new userQuark and gluon form factors to three loops
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We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons to three-loop order within massless perturbative Quantum Chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
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A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general uni-variate first order factorizable systems of differential equations. We also present predictions for the asymptotic structure of these form factors.
Using the instanton picture of the QCD vacuum we compute the nucleon $bar c^Q(t)$ form factor of the quark part of the energy momentum tensor (EMT). This form factor describes the non-conservation of the quark part of EMT and contributes to the quark pressure distribution inside the nucleon. Also it can be interpreted in terms of forces between quark and gluon subsystems inside the nucleon. We show that this form factor is parametrically small in the instanton packing fraction. Numerically we obtain for the nucleon EMT a small value of $bar c^Q(0)simeq 1.4cdot 10^{-2}$ at the low normalisation point of $sim 0.4$ GeV$^2$. This smallness implies interesting physics picture - the forces between quark and gluon mechanical subsystems are smaller than the forces inside each subsystem. The forces from side of gluon subsystem squeeze the quark subsystem - they are compression forces. Additionally, the smallness of $bar c^Q(t)$ might justify Teryaevs equipartition conjecture. We estimate that the contribution of $bar c^Q (t)$ to the pressure distribution inside the nucleon is in the range of 1 -20 % relative to the contribution of the quark $D$-term.
It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exact top quark mass dependence over the full kinematic range. We discuss in detail the renormalization formulae of the individual subsets of the singlet contribution to an axial quark FF with a particular flavor, as well as the renormalization group equations that govern their individual scale dependence. Finally we have extracted the 3-loop Wilson coefficient in the low energy effective Lagrangian, renormalized in a non-$overline{mathrm{MS}}$ scheme and constructed to encode the leading large mass approximation of our exact results for singlet quark FFs. We have also examined the accuracy of the approximation in the low energy region.
Vector and axial form factors in the quark resonance model are analyzed with a combination of theoretical and phenomenological arguments. The new form of form factors is deduced from $Delta$(1232) excitation models and available data. The vector part is shown to agree with the resonant contribution to electron-proton inclusive $F_2$ data. The axial part is obtained by finding a simultaneous fit to ANL and BNL $frac{d sigma}{d Q^2}$ neutrino scattering data. The best fit corresponds to $C_5^A(0)=0.88$ in the Rarita Schwinger formalism.
Nucleon form factors play an especially important role in studying the dynamics of nucleons and explicit structure of the wave functions at arbitrary nucleon velocity. The purpose of the paper is to explain theoretically all four nucleon form factors measured experimentally in the cross section measurements (by the Rosenbluth method), yielding almost equal normalized form factors $G^p_E,G^p_M,G^n_M$, as well as in the polarization transfer experiments, where a strongly decreasing proton electric form factor has been discovered. It is shown, using relativistic hyperspherical formalism, that the nucleon wave functions in the lowest approximation provide almost equal normalized form factors as seen in the Rosenbluth cross sections, but in the higher components they contain a large admixture of the quark orbital momenta, which strongly decreases $G^p_E$ and this effect is possibly detected in the polarization transfer method (not seen in the classical cross section experiments). Moreover, the same admixture of the higher components explains the small positive form factor $G^n_E$. The resulting form factors, $G^p_M(Q),G^p_E(Q),G^n_M(Q)$ are calculated up to $Q^2approx 10$ GeV$^2$, using the standard and the Lorentz contracted wave functions and shown to be in reasonable agreement with experimental data.
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