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Hard exclusive production of two pions in $γγ$-collisions within the SCET factorization approach

We considered the power corrections to the amplitude describing hard exclusive pion pair production in gamma gamma collisions at large energy and momentum transfer. In order to derive a factorization formula for the subleading power corrections one has to take into account the so-called soft-overlap (or soft) contributions. These terms can be naturally introduced within the SCET framework as a matrix elements of the SCET-I operators. The so-called end-point singularities must cancel in the sum of the hard and soft contributions after matching onto SCET-II. Using the so-called physical subtraction scheme we demonstrated such a cancellation in the case of twist-3 chiral enhanced contributions in the leading logarithmic approximation. As a result we obtained the well defined expression for the subleading power correction which depends only from the two unknown functions. These functions can be associated with the soft-overlap of the outgoing pion state and therefore does not depend on the scattering angle. The angular dependence in this case is defined by the hard subprocess and can be computed in a model independent way. The obtained results were used in the phenomenological analysis of existing data. We showed that using the leading and subleading contributions and considering the unknown functions as a free parameters one can describe consistently the data for $π^{+}π^{-}$ and $π^{0}π^{0}$ production.