ar X iv : h ep - p h / 06 03 10 3 v 1 1 4 M ar 2 00 6 Regge Trajectories and Renormalization Group Vladimir
نویسنده
چکیده
On the basis of the RG invariance we show, in particular, that the Regge trajectory intercept cannot be calculated as a function of the coupling constant. Since the early days of the complex angular momentum approach [1] to obtaining the high-energy asymptotic behaviour of the scattering amplitude [2] numerous attempts were undertaken to calculate the leading j-plane sin-gularities (poles, cuts...) and their t-dependence in the course of the asymp-totic summation of some " leading " terms in the perturbative expansions (see e.g. [3]). Last 30 years are marked by widely spread hopes that the problem can find its solution in the framework of the study of some QCD-motivated Bethe-Salpeter-type equations [4] the kernel of which is a trunkated series in the QCD coupling, α s. During some quite a long time the result obtained in Ref.[4] that the leading singularity is of the form j 0 = 1 + 12 π ln2 · α s with α s assumed to be O(10 −1), was considered, in particular, as an explanation of the fast rise of the structure functions at small x observed at HERA. Eight years ago it was obtained in Refs [5] that the further term, proportional to α 2 s , had an unexpetedly large and negative coefficient which invalidated the use of this value of j 0 for explanation of the HERA data: j 0 ≈ 1 + 12ln2 π α s [1 − 20 α s π ]. (1)
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