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Register a new userNon-factorizable contributions to deep inelastic scattering at large x
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Ben D. Pecjak
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We use soft-collinear effective theory (SCET) to study the factorization properties of deep inelastic scattering in the region of phase space where 1-x = O(Lambda_{QCD/Q}). By applying a regions analysis to loop diagrams in the Breit frame, we show that the appropriate version of SCET includes anti-hard-collinear, collinear, and soft-collinear fields. We find that the effects of the soft-collinear fields spoil perturbative factorization even at leading order in the 1/Q expansion.
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In the asymptotic limit $Q^2 gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In this way, one can calculate all but the power corrections in $(m^2/Q^2)^k, k > 0$. The heavy flavor operator matrix elements are known to ${sf NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the ${sf NNLO}$ anomalous dimensions cite{LARIN,MVVandim} are obtained as well.
This contribution covers three recent results on deep-inelastic scattering at HERA: (i) new measurements of the proton longitudinal structure function $F_L$ from H1 and ZEUS experiments, (ii) a dedicated NC cross section measurement from ZEUS in the region of high Bjorken $x$, and (iii) preliminary combination results of all HERA inclusive data published up to now by H1 and ZEUS, taking into account the experimental correlations between measurements.
We derive for deep-inelastic neutrino-proton scattering in the combination nu P - nubar P the perturbative QCD corrections to three loops for the charged current structure functions F_2, F_L and F_3. In leading twist approximation we calculate the first five odd-integer Mellin moments in the case of F_2 and F_L and the first five even-integer moments in the case of F_3. As a new result we obtain the coefficient functions to O(alpha_s^3) while the corresponding anomalous dimensions agree with known results in the literature.
High Q^2 NC and CC cross-sections as measured at HERA can give information on two distinct areas of current interest. Firstly, supposing that all the electroweak parameters are well known, these cross-sections may be used to give information on parton distributions at high x and high Q^2. Secondly, supposing that parton distributions are well known, after evolution in Q^2 from the kinematic regime where they are already measured, these cross-sections can be used to give information on electroweak parameters in a process where the exchanged boson is `spacelike rather than `timelike. WG1 addressed itself to clarifying the limits of our present and possible future knowledge on both these areas.
We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation. Using recent results for the QCD form factor, related anomalous dimensions and Mellin moments of DIS structure functions at four loops we derive the complete soft and collinear contributions to the DIS Wilson coefficients at four loops. For a general $SU(n_c)$ gauge group the results are exact in the large-$n_c$ approximation and for QCD with $n_c=3$ we present precise approximations. We extend the threshold resummation exponent $G^N$ in Mellin-$N$ space to the fifth logarithmic (N$^4$LL) order collecting the terms $alpha_{rm s}^{,3} (alpha_{rm s} ln N)^n$ to all orders in the strong coupling constant $alpha_{rm s}$. We study the numerical effect of the N$^4$LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms. As a byproduct, we derive a numerical result for the complete pole structure of the QCD form factor in the parameter of dimensional regularization $varepsilon$ at four loops.
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