arXiv subjects

G. Grunberg

Publications and source records attributed to G. Grunberg.

9 recordsLinked to original sources

arXiv2009

On threshold resummation beyond leading 1-x order

We check against exact finite order three-loop results for the non-singlet F_2 and F_3 structure functions the validity of a class of momentum space ansaetze for threshold resummation at the next-to-leading order in 1-x, which generalize results previously obtained in the large-β_0 limit. We find that the ansaetze do not work exactly, pointing towards an obstruction to threshold resummation at this order, but still yield correct results at the leading logarithmic level for each color structures, as well as at the next-to-next-to-leading logarithmic level for the specific C_F^3 color factor. A universality of the leading logarithm contributions to the physical evolution kernels of F_2 and F_3 at the next-to-leading order in 1-x is observed.

hep-ph↗

arXiv2007

Constant terms in threshold resummation and the quark form factor

We verify to order alpha_s^4 two previously conjectured relations, valid in four dimensions, between constant terms in threshold resummation (for Deep Inelastic Scattering and the Drell-Yan process) and the second logarithmic derivative of the massless quark form factor. The same relations are checked to all orders in the large beta_0 limit; as a byproduct a dispersive representation of the form factor is obtained. These relations allow to compute in a symmetrical way the three-loop resummation coefficients B_3 and D_3 in terms of the three-loop contributions to the virtual diagonal splitting function and to the quark form factor, confirming results obtained in the literature.

hep-ph↗

arXiv1998

On power corrections in the dispersive approach

Power corrections in QCD (both conventional and unconventional ones arising from the ultraviolet region) are discussed within the infrared finite coupling-dispersive approach. It is shown how power corrections in Minkowskian quantities can be derived from the corresponding ones in associated Euclidean quantities through analyticity, allowing a parametrization in term of the Euclidean coupling and a renormalon-free perturbative expansion. It is argued that one should in general expect coefficients functions computed in the true non-perturbative vacuum to differ from the standard perturbative ones, even without assuming new physics. A phenomenology of $1/Q^2$ terms arising from eventual new physics of ultraviolet origin is also set-up. Models for non-perturbative contributions to the (universal) QCD coupling are suggested. Issues of renormalization scheme dependence are commented upon.

hep-ph↗

arXiv1997

Power corrections from short distances

It is argued that power contributions of short distance origin naturally arise in the infrared finite coupling approach. A phenomenology of $1/Q^2$ power corrections is sketched.

hep-ph↗

arXiv1997

1/Q^2 terms and Landau singularity

Standard power-behaved contributions in QCD arising from non-perturbative effects at low scale can be described, as shown by Dokshitzer, Marchesini and Webber, with the notion of an infrared regular effective coupling. In their approach, a non-perturbative contribution to the coupling, essentially restricted to low scales, parametrizes the non-perturbative power corrections. I argue that their framework naturally allows for another type of power contributions, arising from short distances (hence unrelated to renormalons and the operator product expansion) which appear in the process of removing the Landau singularity present in perturbation theory. A natural definition of an infrared finite perturbative coupling is suggested within the dispersive method. Implications for the tau hadronic width, where $O(1/Q^2)$ contributions can be generated, are pointed out.

hep-ph↗

arXiv1997

Power corrections and Landau singularity

In the dispersive approach of Dokshitzer, Marchesini and Webber, standard power-behaved contributions of infrared origin are described with the notion of an infrared regular QCD coupling. I argue that their framework suggests the existence of non-standard contributions, arising from short distances (hence unrelated to renormalons and the operator product expansion), which appear in the process of removing the Landau singularity of the perturbative coupling. A natural definition of an infrared finite perturbative coupling is suggested within the dispersive method. Implications for the tau hadronic width and the lattice determination of the gluon condensate, where $O(1/Q^2)$ contributions can be generated, are pointed out.

hep-ph↗

arXiv1996

Fixed points and power corrections

The connection between renormalons and power corrections is discussed in the case the effective coupling constant has an infrared fixed point of perturbative origin.

hep-ph↗

arXiv1996

Nucleon spin structure,topological susceptibility and the $η^\prime$ singlet axial vector coupling

The observed small value of the first moment of the polarized nucleon spin structure function $g_1$ may be interpreted, in the Veneziano--Shore approach, as a suppression of the first moment $χ^\prime(0)$ of the QCD topological susceptibility. I give an extension of the Witten--Veneziano argument for the $U(1)$ problem, which yields the $O(1/N)$ correction to the $N = \infty$ relation $χ^\prime(0)/F^2_0 = 1$ (where $F_0$ is the $η^\prime$ axial vector coupling).The correction, although negative, seems too small to account for the data. I further argue that the $(η,η^\prime)\rightarrowγγ$ and $J/ψ\rightarrow (η, η^\prime)γ$ decays indicate an enhancement rather than a suppression of $F_0$. A substantial gluon-like contribution in $\langle 0\vert\partial^μj^{(0)}_{μ_5} \vertγγ\rangle \vert_{q^2=0}$,which could parallel a similar one in the corresponding nucleon matrix element,is suggested.

hep-ph↗

arXiv1995

Renormalons and fixed points

The connection between renormalons and power corrections is investigated for the typical infrared renormalon integral assuming the effective coupling constant has an infrared fixed point of an entirely perturbative origin. It is shown that even then the full answer differs from the Borel sum by a power correction. A comparaison with the analogue results when the fixed point is generated by the explicit addition of non perturbative power suppressed terms is given.

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