An Effective Field Theory Look at Deep Inelastic Scattering

This talk discusses the effective field theory view of deep inelastic scattering. In such an approach, the standard factorization formula of a hard coefficient multiplied by a parton distribution function arises from matching of QCD onto an effective field theory. The DGLAP equations can then be viewed as the standard renormalization group equations that determines the cut-off dependence of the non-local operator whose forward matrix element is the parton distribution function. As an example, the non-singlet quark splitting functions is derived directly from the renormalization properties of the non-local operator itself. This approach, although discussed in the literature, does not appear to be well known to the larger high energy community. In this talk we give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters

Reconstructing parton densities at large fractional momenta

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results.Comment: 12 pages, 7 double-panel figures in pdf, RevTeX4-

Matching NLO QCD with parton shower in Monte Carlo scheme - the KrkNLO method

A new method of including the complete NLO QCD corrections to hard processes in the LO parton-shower Monte Carlo (PSMC) is presented. This method, called KrkNLO, requires the use of parton distribution functions in a dedicated Monte Carlo factorization scheme, which is also discussed in this paper. In the future, it may simplify introduction of the NNLO corrections to hard processes and the NLO corrections to PSMC. Details of the method and numerical examples of its practical implementation, as well as comparisons with other calculations, such as MCFM, MC@NLO, POWHEG, for single $Z/\gamma^*$-boson production at the LHC, are presented.Comment: 50 pages, 14 figures. Version published in JHEP: added a comparison of krkNLO results and the fixed-order NNLO result from the DYNNLO program and addressed several points raised by the refere

Recent results from HERA and their impact for LHC

Recent measurements of inclusive and semi-inclusive deep inelastic scattering in electron-proton collisions at HERA are reviewed. These measurements are used to determine the parton distribution functions (PDFs) of the proton, a necessary input to theory predictions for hadron colliders. An introduction to the PDF determination with an emphasis on HERA PDFs is presented. Theory predictions based on HERAPDF are compared to a selection of recent LHC and Tevatron measurements. The impact of jet and charm production measurements on the PDFs is discussed.Comment: Presented at the 2011 Hadron Collider Physics symposium (HCP-2011), Paris, France, November 14-18 2011, 6 pages, 13 figure

Charm Production in Deep Inelastic Scattering from Threshold to High $Q^{2}

Charm final states in deep inelastic scattering constitute $\sim 25$ of the inclusive cross-section at small $x$ as measured at HERA. These data can reveal important information on the charm and gluon structure of the nucleon if they are interpreted in a consistent perturbative QCD framework which is valid over the entire energy range from threshold to the high energy limit. We describe in detail how this can be carried out order-by-order in PQCD in the generalized \msbar formalism of Collins (generally known as the ACOT approach), and demonstrate the inherent smooth transition from the 3-flavor to the 4-flavor scheme in a complete order $\alpha_s$ calculation, using a Monte Carlo implementation of this formalism. This calculation is accurate to the same order as the conventional NLO $F_2$ calculation in the limit $\frac{Q}{m_c} >> 1$. It includes the resummed large logarithm contributions of the 3-flavor scheme (generally known in this context as the fixed-flavor-number or FFN scheme) to all orders of $\alpha_s\ln(m_c^2/Q^2)$. For the inclusive structure function, comparison with recent HERA data and the existing FFN calculation reveals that the relatively simple order-$\alpha_s$ (NLO) 4-flavor ($m_c \neq 0$) calculation can, in practice, be extended to rather low energy scales, yielding good agreement with data over the full measured $Q^2$ range. The Monte Carlo implementation also allows the calculation of differential distributions with relevant kinematic cuts. Comparisons with available HERA data show qualitative agreement; however, they also indicate the need to extend the calculation to the next order to obtain better description of the differential distributions.Comment: 22 pages (LATEX), 8 figures (EPS); A few clarifying changes made; version published in JHE

Charm quark and D^* cross sections in deeply inelastic scattering at DESY HERA

A next-to-leading order Monte Carlo program for the calculation of heavy quark cross sections in deeply inelastic scattering is described. Concentrating on charm quark and D^*(2010) production at HERA, several distributions are presented and their variation with respect to charm quark mass, parton distribution set, and renormalization-factorization scale is studied.Comment: 15 pages including 8 figures. Uses Latex, Revtex, and psfig. References added - others updated. Several sentences/words added for clarity. Results/conclusions unchanged. To appear in Phys. Rev.

A parton picture of de Sitter space during slow-roll inflation

It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical field equations plus a stochastic source term. I argue that--when quantum-mechanical loop corrections are taken into account--the separate-universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular, the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected. Matches version published in JCA