BFKL resummation effects in gamma* gamma* to rho rho Page: 3 of 23
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there now exists high quality data from HERA , and the BFKL calculations reproduce
the measured differential cross sections for longitudinal p meson production and for J/p
production very well, while the Born level calculations do not work so well [9-11]. At the
same time the cross section for transversely polarized p mesons is not well understood .
In a recent paper , the scattering amplitude of the process (1) was calculated in
the Born approximation and the feasibility of a dedicated experiment was proved. The
production amplitude decreases dramatically with t so that its magnitude at t = tmn
dictates the rate of the reaction. In this paper, we report on a calculation of BFKL effects
in the leading order approximation at t = tmin. We find that the leading logarithmic (LL)
BFKL resummation greatly enhances the cross section, as previously observed in other
reactions [8,12-14]. In addition, we estimate next-to-leading logarithmic (NLL) effects by
the use of the BLM scale fixing prescription  supplemented by the resummation scheme
of Refs. [16-18]. We show that there is still a substantial increase in the cross section
compared to fixed-order calculations, but smaller than the LL calculation. It would be
interesting to compare our estimates with the ones based on the recently available NLL
impact factor for the process y* -> V of Ref.  and the NLL BFKL kernel .
2 Leading order BFKL forward amplitude
2.1 General expression
In the BFKL framework, the amplitude of the process (1) can be expressed through the
inverse Mellin transform with respect to the squared center-of-mass energy s as
A(s, t) = is j 1 fW(r2) ,(2)
where t - tmin - -r2, (r is considered as Euclidean, as is any two-dimensional vector in
the following), and Y is the rapidity variable, Y = ln(s/so). The minimum momentum
transfer is here given by tmin ~-s Q2Q2/s . In the particular case where r2 = 0, the
BFKL Green's function can be easily obtained in momentum space . In this case, the
impact representation for f,(0) reads
fL(0) = 2 j d32 d e'2 (k)- ) )7(k') d, (3)
where the integration over angles has been performed. The functions tab are the impact
factors describing the coupling of the BFKL pomeron to vertex 1 or 2, and a, b are color
indices. The function w(v) is the BFKL characteristic function which is defined by 
c(v)= Osx(v), (4)
with as - asNc/fr and
x(v) = 2v(1) - C + iv - - iv , (x) = F'(x)/F(x). (5)
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Enberg, R.; Pire, B.; Szymanowski, L. & Wallon, S. BFKL resummation effects in gamma* gamma* to rho rho, article, August 11, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc892501/m1/3/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.