1202.4944 (Nikolai Kivel)

Factorizing the hard and soft spectator scattering contributions for the
nucleon form factor F_1 at large Q^2    [PDF]

Nikolai Kivel

We investigate the soft spectator scattering contribution for the FF $F_{1}$.
We focus our attention on factorization of the hard-collinear scale $\sim
Q\Lambda$ corresponding to transition from SCET-I to SCET-II. We compute the
leading order jet functions and find that the convolution integrals over the
soft fractions are logarithmically divergent. This divergency is the
consequence of the boost invariance and does not depend on the model of the
soft correlation function describing the soft spectator quarks. Using as
example a two-loop diagram we demonstrated that such a divergency corresponds
to the overlap of the soft and collinear regions. As a result one obtains large
logarithm $\ln Q/\Lambda$ which must be included in the correct factorization
formalism. We conclude that a consistent description of the factorization for
$F_{1}$ implies the end-point collinear divergencies in the hard and soft
spectator contributions, i.e. convolution integrals with respect to collinear
fractions are not well-defined. Such scenario can only be realized when the
twist-3 nucleon distribution amplitude has non-vanishing end-point behavior at
a certain low normalization point. Such behavior leads to the violation of the
collinear factorization for the hard spectator scattering contribution. We also
discuss the physical subtraction scheme for SCET-I factorization which can be
used for systematical analysis of the hadronic processes in the range of
moderate values of $Q^{2}\sim 5-20$ GeV$^{2}$ where the hard collinear scale
$\sim Q\Lambda$ is still not large.

View original: http://arxiv.org/abs/1202.4944