Soft spectator scattering in the nucleon form factors at large Q2 within the soft collinear effective theory approach

The proton form factors at large momentum transfer are dominated by two contributions which are associated with the hard and soft rescattering, respectively. Motivated by a very active experimental form factor program at intermediate values of momentum transfers, Q(2) similar to 5-15 GeV2, where an understanding in terms of only a hard rescattering mechanism cannot yet be expected, we investigate in this work the soft rescattering contribution using soft collinear effective theory (SCET). Within such a description, the form factor is characterized, besides the hard scale Q(2), by a hard-collinear scale Q Lambda, which arises due to the presence of soft spectators, with virtuality Lambda(2) (Lambda similar to 0.5 GeV), such that Q(2) >> Q Lambda >> Lambda(2). We show that in this case a two-step factorization can be successfully carried out using the SCET approach. In a first step (SCETI), we perform the leading-order matching of the QCD electromagnetic current onto the relevant SCETI operators and perform a resummation of large logarithms using renormalization group equations. We then discuss the further matching onto a SCETII framework, and propose the factorization formula (accurate to leading logarithmic approximation) for the Dirac form factor, accounting for both hard and soft contributions. We also present a qualitative discussion of the phenomenological consequences of this new framework.