Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold

We derive non-linear recursion equation for the leading infrared logarithms (LL) in four dimensional sigma-model with fields on an arbitrary Riemann manifold. The derived equation allows one to compute leading infrared logarithms to essentially unlimited loop order in terms of geometric characteristics of the Riemann manifold. We reduce the solution of the SU(oo) principal chiral field in arbitrary number of dimensions in the LL approximation to the solution of very simple recursive equation. This result paves a way to the solution of the model in arbitrary number of dimensions at N-->ooComment: Talk given by MVP at the conference devoted to memory of A.N. Vasilie

Soft spectator scattering in the nucleon form factors at large Q2Q^2 within the SCET 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, $Q^{2}\sim 5-15 \text{GeV}^{2}$, 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 description, the form factor is characterized, besides the hard scale $Q^2$, by a semi-hard scale $Q \Lambda$, which arises due to presence of soft spectators, with virtuality $\Lambda^2$ ($\Lambda \sim 0.5$ GeV), such that $Q^{2}\gg Q\Lambda\gg \Lambda^{2}$. We show that in this case a two-step factorization can be successfully carried out using the SCET approach. In a first step (SCET$_I$), we perform the leading order matching of the QCD electromagnetic current onto the relevant SCET$_I$ operators and perform a resummation of large logarithms using renormalization group equations. We then discuss the further matching onto a SCET$_{II}$ framework, and propose the complete factorization formula 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.Comment: 33 pages, 19 figures; typos corrected, text improved. Version to appear in Phys.Rev.

Radiative corrections to hard spectator scattering in B→ππB\to \pi\pi decays

We present the calculation of the next-to-leading corrections to the tree amplitudes which appear in the description of non-leptonic B-decays in the factorization approach. These corrections, together with radiative corrections to the jet functions, represent the full next-to-leading contributions to the dominant hard spectator scattering term generated by operators $O_{1,2}$ in the decay amplitudes. Using obtained analytical results we estimate $B\to\pi\pi$ branchings fractions in the physical (or BBNS) factorization scheme. We have also found that the imaginary part generated in the hard spectator scattering term is rather large compared to the imaginary part of the vertex contribution.Comment: text is improved and typos are corrected, accepted for publication in JHE

Kinematical twist-3 effects in DVCS as a quark spin rotation

We point out that the kinematical twist-3 contributions to the DVCS amplitude, required to restore electromagnetic gauge invariance of the twist-2 amplitude up to O(t/q^2), can be understood as a spin rotation applied to the twist-2 quark density matrix in the target. This allows for a compact representation of the twist-3 effects, as well as for a simple physical interpretation.Comment: 4 pages, revtex, 3 eps figures included using eps

Hermes and the spin of the proton

HERMES is a second generation experiment to study the spin structure of the nucleon, in which measurements of the spin dependent properties of semi-inclusive deep-inelastic lepton scattering are emphasized. Data have been accumulated for semi-inclusive pion, kaon, and proton double-spin asymmetries, as well as for high-p_T hadron pairs, and single-spin azimuthal asymmetries for pion electroproduction and deep virtual Compton scattering. These results provide information on the flavor decomposition of the polarized quark distributions in the nucleon and a first glimpse of the gluon polarization, while the observation of the azimuthal asymmetries show promise for probing the tensor spin of the nucleon and isolating the total angular momentum carried by the quarks.Comment: LaTeX, 21 page

Resummation of (-B(0) Alpha-s)**N Corrections to the Photon - Meson Transition Form-Factor Gamma* + Gamma ---> Pi0

We have resummed all the (-b_0 alpha_s)^n contributions to the photon-meson transition form factor F_{gamma pi}. To do this, we have used the assumption of `naive nonabelianization' (NNA). Within NNA, a series in (N_f alfa_s)^n is interpreted as a series in (-b_0 alpha_S)^n by means of the restoration of the full first QCD beta-function coefficient -b_0 by hand. We have taken into account corrections to the leading order coefficient function and to the evolution of the distribution function. Due to conformal constraints, it is possible to find the eigenfunctions of the evolution kernel. It turns out that the nondiagonal corrections are small, and neglecting them we obtained a representation for the distribution function with multiplicatively renormalized moments. For a simple shape of the distribution function, which is close to the asymptotic shape, we find that the radiative correction decrease the LO by 30 % and the uncertainty in the resummation lies between 10 % and 2 % for Q^2 between 2 and 10 GeV^2.Comment: 30 pages, LaTeX, 10 figures. New figures and references added. Some changes in the tex

Twist-3 contribution to the γ∗γ→ππ\gamma^*\gamma\to \pi\pi amplitude in the Wandzura-Wilczek approximation

We have calculated the Wandzura-Wilczek contribution to the twist-3 part of $\gamma^*\gamma\to 2\pi$ amplitude. It describes interaction of the longitudinally polarized virtual photon with the real one, and it is suppressed by 1/Q, where $Q^2$ is the virtuality of the $\gamma^*$, as compared to the twist-2 contribution. We have found that, in the Wandzura-Wilczek approximation, factorization applies to the twist-3 amplitude.Comment: 13 pages, 4 figure

DVCS on the nucleon : study of the twist-3 effects

We estimate the size of the twist-3 effects on deeply virtual Compton scattering (DVCS) observables, in the Wandzura-Wilczek approximation. We present results in the valence region for the DVCS cross sections, charge asymmetries and single spin asymmetries, to twist-3 accuracy.Comment: 20 pages, 6 figure

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

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 rapidity logarithm 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 specific end-point behavior which differs from one expected from the evolution of the nucleon distribution amplitude. Such behavior leads to the violation of the collinear factorization for the hard spectator scattering contribution. We suggest that the soft spectator scattering and chiral symmetry breaking provide the mechanism responsible for the violation of collinear factorization in case of form factor $F_{1}$.Comment: 25 pages, 6 figures, text is improved, few typos corrected, one figure added, statement about end-point behavior of the nucleon DA is formulated more accuratel