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Register a new userSeparating perturbative and non-perturbative contributions to the plaquette
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We try to separate the perturbative and non-perturbative contributions to the plaquette of pure SU(3) gauge theory. To do this we look at the large-n asymptotic behaviour of the perturbation series in order to estimate the contribution of the as-yet uncalculated terms in the series. We find no evidence for the previously reported Lambda^2 contribution to the gluon condensate. Attempting to determine the conventional Lambda^4 condensate gives a value of approximately 0.03(2) GeV^4, in reasonable agreement with sum rule estimates, though with very large uncertainties.
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The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with $d leq 5$ will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with $d<5$) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Greens functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the $K-pi$ matrix element are being performed in simulations with 4 dynamical ($N_f = 2+1+1$) twisted mass fermions and the Iwasaki improved gluon action.
We discuss a non-perturbative lattice calculation of the ghost and gluon propagators in the pure Yang-Mills theory in Landau gauge. The ultraviolet behaviour is checked up to NNNLO yielding the value $Lambda^{n_f=0}_{ms}=269(5)^{+12}_{-9}text{MeV}$, and we show that lattice Green functions satisfy the complete Schwinger-Dyson equation for the ghost propagator for all considered momenta. The study of the above propagators at small momenta showed that the infrared divergence of the ghost propagator is enhanced, whereas the gluon propagator seem to remain finite and non-zero. The result for the ghost propagator is consistent with the analysis of the Slavnov-Taylor identity, whereas, according to this analysis, the gluon propagator should diverge in the infrared, a result at odds with other approaches.
The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.
We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ($simeq 270$MeV) of $Lambda_{ms}$ than the one obtained from the propagators separately($simeq 320$MeV). This argues in favour of significant non-perturbative $sim 1/q^2$ power corrections in the ghost and gluon propagators. We check the self-consistency of the method.
In the present paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach up to ${cal O}(alpha_s^4)$-level still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $alpha_s$-running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $Q^2$-region, the effective momentum of the process is small and to have a reliable prediction, we adopt four low-energy $alpha_s$ models to do the analysis. Our predictions show that even though the high-twist terms are generally power suppressed in high $Q^2$-region, they shall have sizable contributions in low and intermediate $Q^2$ domain. By using the more accurate scheme-and-scale independent pQCD prediction, we present a novel fit of the non-perturbative high-twist contributions by comparing with the JLab data.
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