Parton Distribution Functions for Precision LHC Phenomenology

Abstract

The main problematics related to the determination of a set of Parton Distribution Functions (PDFs) are presented and, after a brief discussion on different strategies adopted by other groups to address them, the NNPDF methodology is considered. According to this methodology, the fit to extract PDFs from data is performed on a global dataset using the combined implementation of Monte Carlo sampling in the space of data, neural network parametrization, and genetic algorithm minimization. Using these tools the NNPDF collaboration delivers PDF sets which behave in a statistically consistent way and minimize parametrization bias.

Three PDF sets are presented and analyzed: NNPDF2.1 LO, NLO, and NNLO. Heavy quark mass effects are taken into account through the implementation of the FONLL-A GM-VFN scheme for the NNPDF2.1 NLO parton set and using FONLL-C for the NNPDF2.1 NNLO delivery. At LO heavy quark mass effects intervene to a much minor extent. In general, consistency at the one-sigma level is verified among NNPDF releases (with the only exception of LO determination, where theoretical uncertainties are relevant) while rather significant shifts are observed in specific cases in the comparison with results from other groups, especially in the NNLO analysis. Theoretical predictions for a set of LHC observables (inclusive vector boson, top and Higgs production) are computed for benchmarking against results from other groups and against first LHC available measurements. The change in this kind of inclusive cross-sections is found to be rather small when including heavy quark mass effects. The change is instead substantial when looking at observables that directly probe heavy quark distributions. Also, is shown that an estimate of the $\as$ value is possible exploiting the simultaneous dependence of the dataset on PDFs and the \alpha_s value. It is found $\as(M_Z)=0.1191\pm0.0006^{\rm exp}$, with a surprisingly low statistical uncertainty. Studying determinations based on reduced datasets, it is shown that a global dataset is necessary for a reliable determination.

Having determined LO, NLO, and NNLO PDF sets using the very same methodology and the same data, perturbative stability is assessed. Excellent convergence of the perturbative expansion within the kinematic region covered by the experimental data is shown. Moreover, the provided uncertainty on PDFs at LO is found to be only a fraction of the theoretical uncertainty (that is not included). Looking at the NLO fit it can be estimated as dominant in this case. The PDF sets produced by the NNPDF collaboration as well as the ones delivered by other groups only include data's experimental uncertainties. A similar estimate of theoretical uncertainty can be given also for the NLO determination by looking at the following perturbative order (NNLO): in this case the size of theoretical uncertainty is smaller than that of experimental one, thus at NLO and beyond it is reasonable to neglect theoretical uncertainty. The theoretical uncertainty could be evaluated in a more precise way for each single perturbative order determination by varying the renormalization and factorization scale during the PDF fit.

The inclusion of the amazing amount of new data that the LHC is delivering will be the main target in the next years. The NNPDF2.2 PDF set, briefly presented in this thesis, already includes a part of LHC data through the reweighting technique. The presence of this data will be more and more important in parton fits, leading to much better constrained PDFs. Also, new processes will be available at the energies at which the LHC operates, hopefully allowing for a competitive PDFs determination using collider data and allowing the exclusion of the less cleaner fixed-target data and in general of low energy measurements.

La física del Gran Colisionador de Hadrones (GCH), activo al CERN de Ginebra, apoya en la cromodinámica cuántica (QCD) y en general en el modelo estándar. La QCD perturbativa de precisión es posible gracias a la libertad asintótica y también gracias a las propiedades del teorema de factorización. En este trabajo, realizado en el ámbito de la colaboración NNPDF, los efectos debidos a las masas de los quarks pesados son tenidos en cuenta gracias al utilizo del esquema FONLL.

Es utilizada una parametrización de redes neuronales entrenadas con algoritmos genéticos. También se utiliza el método Monte Carlo para generar N_rep réplicas de los datos experimentales y poder así determinar bandas de error para las PDFs que mantienen una interpretación estadística rigurosa.

Se han determinado tres conjuntos: NNPDF2.1 LO, NLO y NNLO. Se ha verificado que en general hay consistencia entre las distribuciones de la colaboración NNPDF dentro de una sigma (excepto para el caso LO). En comparación con los resultados de los demás grupos se han observado diferencias de alguna forma significativas en ciertos casos específicos, sobretodo en el caso NNLO. Comparando los tres conjuntos LO, NLO y NNLO es posible estudiar la estabilidad estadística, siendo los tres determinados según la misma metodología y usando los mismos datos. Se observa una excelente convergencia de la expansión perturbativa en la región cinemática de los datos.

Se han calculado las predicciones para un conjunto de observables del GCH usando las distribuciones partónicas NNPDF2.1 NLO y NNLO. Estas predicciones han sido comparadas entre ellas y también con predicciones obtenidas usando las PDFs de otros grupos. Ha sido posible comparar también estos resultados con los primeros datos de las colaboraciones ATLAS y CMS. Al incluir los efectos debidos a las masas de los quarks pesados se observa una modificación bastante pequeña en estas observables. En cambio, la diferencia es substancial si se mira a observables que sondean directamente las distribuciones partónicas de los quarks pesados. La metodología usada por la colaboración NNPDF ha sido aprovechada también para la determinación de la constante de acoplamiento fuerte alpha_s(M_Z). El valor determinado ha sido alpha_s(M_Z)=0.1191\pm 0.0006 .