Abstract:
The main focus of this PhD thesis is on final state physics at particle colliders. In particular,
two different inclusive final state observables are considered: hadronic jets and identified hadrons originating
from a fragmentation process. Said inclusive final states may also be combined into a novel class of semi-inclusive observables:
in-jet fragmentation processes. All of these final states are of major importance in the era of high energy particle colliders like the
famous Large Hadron Collider (LHC).
In this thesis we work within the framework of perturbative Quantum Chromodynamics (pQCD)
and present analytical next-to-leading order (NLO) calculations for final state hadronic jets and, for the first time,
for observed hadrons inside fully reconstructed jets in an inclusive setup.
Afterwards, we utilize this calculation to perform a global extraction of $D^{*}$-meson fragmentation functions including recent
$D^{*}$-in-jet data from the ATLAS collaboration. Finally, we explore two closely related topics: photon-in-jet production
and fragmentation functions beyond fixed order accuracy.\\
To be more precise, we start by presenting a NLO calculation for
the inclusive production of jets at hadron colliders. The calculation of the partonic cross sections is performed
analytically within the so-called narrow jet approximation, where the jet is assumed to be rather collimated.
In said calculation we address two novelties: the formulation of jet cross sections in a convenient form
using appropriate jet functions and the first NLO implementation of a newly proposed jet algorithm which is based on
maximizing an appropriate function of the jet's energy and momentum.
The formulation of jet cross sections in terms of jet functions has been established in the framework of
soft collinear effective theory (SCET) for electron-positron annihilation and for exclusive jet production.
We present a consistent formulation within the standard framework of pQCD for inclusive jet production
in hadronic collisions.
The so obtained structure not only facilitates the implementation of new jet algorithms, but also allows
for an interesting physical interpretation in close analogy to inclusive hadron production.
After having established the formulation of jet cross sections in terms of jet functions, we study the production
of identified hadrons inside jets. Again, we use the narrow jet approximation to formulate
the partonic cross sections analytically in terms of suitable
sets of semi-inclusive jet functions. The first set describes the formation of the jet and the second set parametrizes
the formation of a specific parton inside the jet. Said parton eventually undergoes the complicated and not yet completely
understood process of hadronization to form the observed final state hadron.
In the factorized pQCD framework, hadronization is parametrized by non-perturbative
functions, so-called fragmentation functions. We demonstrate the importance of this process for studies of fragmentation
functions. At leading order (LO) the cross section directly probes the fragmentation functions in a similar way
as single-inclusive annihilation (SIA) does. Moreover, due to the hadronic initial state, the process gives valuable constraints
on the elusive gluon-to-hadron fragmentation function.
Recently, first data for observed hadrons inside jets were presented by the ATLAS collaboration. These $D^{*}$-in-jet
data are not well described with the $D^{*}$-fragmentation functions available in literature. Thus, we perform
a global NLO analysis of $D^{*}$-fragmentation functions, including data for single-inclusive hadron production in electron-positron
annihilation and hadronic collisions, and, for the first time, hadron-in-jet data. We find a consistent set of fragmentation
functions which yields a satisfying description of all the available data. This extraction is possible due to the analytical calculation
of the hadron-in-jet cross section which is a prerequisite for an efficient numerical implementation.
Moreover, we present results for two topics which are closely related to the work described above.
Motivated by the success of in-jet fragmentation in the extraction of parton-to-hadron fragmentation functions,
we extend the framework to photon-in jet production
and present the NLO calculation necessary to include this process into future extractions of parton-to-photon fragmentation
functions. We make use of the same techniques developed for the hadron-in-jet calculation and present analytical
expressions in terms of (photonic) jet functions within the narrow jet approximation.
Finally, we study fragmentation functions beyond fixed order accuracy by including small-$z$ resummations.
These resummations account for the singular behavior of the time-like evolution kernels and the coefficient
functions by summing up the divergent terms to all orders in perturbation theory.
Since the corresponding resummed expressions are not available for other processes,
we restrict our analysis to SIA. While the inclusion of such resummations is
needed for a reasonable formulation of integrated observables, we find that for phenomenological studies of differential observables
in the kinematical regimes accessible by today's experiments already next-to-next-to-leading order (NNLO)
results yield a satisfying description of data. The resummed expressions only show negligible differences compared to NNLO ones well within the experimental uncertainties.
