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The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.
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The one-loop NLO radiative corrections to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the unpolarized and different for polarized sum rules, that can be explained as the influence of the finite quark mass effects on NLO QCD corrections. The explicit expression for one-loop NLO QCD contribution to the structure function g_2 is presented.
We investigate a model QCD sum rule for the pion wave function $varphi_{pi}(x)$ based on the non-diagonal correlator whose perturbative spectral density vanishes and $Phi(x,M^2)$, the theoretical side of the sum rule, consists of condensate contributions only. We study the dependence of $Phi(x,M^2)$ on the Borel parameter $M^2$ and observe that $Phi(x,M^2)$ has a humpy form, with the humps becoming more and more pronounced when $M^2$ increases. We demonstrate that this phenomenon reflects just the oscillatory nature of the higher states wave functions, while the lowest state wave function $varphi_{pi}(x)$ extracted from our QCD sum rule analysis,has no humps, is rather narrow and its shape is close to the asymptotic form $varphi_{pi}^{as}(x) = 6x(1-x)$.
We present the most general sum rules reflecting the cancellation of ultraviolet divergences in the Higgs potential in weakly-coupled, natural extensions of the Standard Model. There is a separate sum rule for the cancellation of the quadratic and logarithmic divergences, and their forms depend on whether the divergences are canceled by same-spin or opposite-spin partners. These sum rules can be applied to mass eigenstates and conveniently used for direct collider tests of naturalness. We study in detail the feasibility of testing these sum rules in the top sector at a future $100TeV$ proton collider within two benchmark models, the Little Higgs (LH) and the Maximally Symmetric Composite Higgs (MSCH). We show how the two ingredients of the sum rules, the top partner masses and their Yukawa couplings to the Higgs, can be measured with sufficient accuracy to provide a highly non-trivial quantitative test of the sum rules. In particular, we study observables sensitive to the sign of the top partner Yukawa, which is crucial for verifying the sum rules but is notoriously difficult to measure. We demonstrate that in the benchmark models under study, a statistically significant discrimination between the two possible signs of each Yukawa will be feasible with a 30 ab$^{-1}$ data set at $100TeV$.
Correlations between light neutrino observables are arguably the strongest predictions of lepton avour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a nonzero value of the lightest neutrino mass and to distinct predictions for the e ective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modi cation of the predictions derived from neutrino mass sum rules. We show that, in most cases, the predictions are fairly stable: while small quantitative changes can appear, they are generally rather mild. We therefore establish the predictivity of neutrino mass sum rules on a level far more general than previously known.
We review the calculations of form factors and coupling constants in vertices with charm mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to heavy ion collisions and to B decays. We then present an introduction to the method of QCD sum rules and describe how to work with the three-point function. We give special attention to the procedure employed to extrapolate results obtained in the deep euclidean region to the poles of the particles, located in the time-like region. We present a table of ready-to-use parametrizations of all the form factors, which are relevant for the processes mentioned in the introduction. We discuss the uncertainties in our results. We also give the coupling constants and compare them with estimates obtained with other methods. Finally we apply our results to the calculation of the cross section of the reaction $J/psi + pi rightarrow D + bar{D^*}$.
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