Explore the vast range of titles available.

The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for simulation-based parameter estimation problems is presented. The matrix formalism, termed the Linear Template Fit, calculates the best estimators for the parameters of interest. It combines a linear regression with the method of least squares. The algorithm uses only predictions calculated for a few values of the parameters of interest, which have been made available prior to its execution. The Linear Template Fit is particularly suited for performance-critical applications and parameter estimation problems with computationally intense simulations, which are otherwise often limited in their usability for statistical inference. Equations for error propagation are discussed in detail and are given in closed analytic form. For the solution of problems with a nonlinear dependence on the parameters of interest, the Quadratic Template Fit is introduced. As an example application, a determination of the strong coupling constant from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.

At the proposed electron-proton collider LHeC electroweak interactions can be uniquely studied in a largely unexplored kinematic region of spacelike momentum transfer. We simulate inclusive neutral- and charged-current deep-inelastic lepton proton scattering cross section data at center-of-mass energies of 1.2 and 1.3 TeV, and estimate the uncertainties of Standard Model parameters as well as of parameters describing physics beyond the Standard Model. A precision at sub-percent level is expected for the measurement of the weak neutral-current couplings of the light-quarks to the Z boson, g A / V u / d , improving their present precision by more than an order of magnitude. The weak mixing angle can be determined with a precision of about Δ sin 2 θ W = ± 0.00015 , and its scale dependence can be studied in the range between about 25 and 700 GeV. An indirect determination of the W -boson mass in the on-shell scheme is possible with an experimental uncertainty down to Δ m W = ± 6 MeV . We discuss how measurements in deep-inelastic scattering compare with those in the timelike domain, and which aspects are unique, for instance electroweak parameters in charged-current interactions. We conclude that the LHeC will determine electroweak physics parameters, in the spacelike region, with unprecedented precision leading to thorough tests of the Standard Model and possibly beyond.

Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low x and low \\[Q^2\\]. A resolution of this tension incorporating \\[\\ln (1/x)\\]-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function \\[F_L\\], it also results in a gluon PDF which is steeply rising at low x for low scales, \\[Q^2 \\simeq 2.5\\,\\hbox {GeV}^2\\], contrary to the fixed-order NLO and NNLO gluon PDF.

Inclusive jet cross section measurements from the ATLAS, CDF, CMS, D0, H1, STAR, and ZEUS experiments are explored for determinations of the strong coupling constant \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\]. Various jet cross section data sets are reviewed, their consistency is examined, and the benefit of their simultaneous inclusion in the \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\] determination is demonstrated. Different methods for the statistical analysis of these data are compared and one method is proposed for a coherent treatment of all data sets. While the presented studies are based on next-to-leading order in perturbative quantum chromodynamics (pQCD), they lay the groundwork for determinations of \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\] at next-to-next-to-leading order.

The lepton–proton collisions produced at the HERA collider represent a unique high energy physics data set. A number of years after the end of collisions, the data collected by the H1 experiment, as well as the simulated events and all software needed for reconstruction, simulation and data analysis, were migrated into a preserved operational mode at DESY. A recent modernisation of the H1 software architecture has been performed, which will not only facilitate on going and future data analysis efforts with the new inclusion of modern analysis tools, but also ensure the long-term availability of the H1 data and associated software. The present status of the H1 software stack, the data, simulations and the currently supported computing platforms for data analysis activities are discussed.

We study charm production in charged-current deep-inelastic scattering (DIS) using the xFitter framework. Recent results from the LHC have focused renewed attention on the determination of the strange-quark parton distribution function (PDF), and the DIS charm process provides important complementary constraints on this quantity. We examine the current PDF uncertainty and use LHeC pseudodata to estimate the potential improvement from this proposed facility. As xFitter implements both fixed-flavor- and variable-flavor-number schemes, we can compare the impact of these different theoretical choices; this highlights some interesting aspects of multi-scale calculations. We find that the high-statistics LHeC data covering a wide kinematic range could substantially reduce the strange PDF uncertainty.

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution . It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, α s ( Q 2 ) , that varies with the energy scale Q 2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of α s at low momentum transfers limits perturbative calculations to the high-energy region where Q 2 ≫ Λ QCD 2 ≃ (250 MeV) 2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large N c -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected q q ¯ mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, W ± or Z , is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

Results on the measurements of the hadronic final state in e super(+ or -)p collisions by the H1 and ZEUS experiments at HERA are presented. These are measurements on the production of prompt photons in photoproduction, inclusive jet, dijet and trijet production in deep-inelatic scattering and on the search for QCD instantons. The jet production data is employed for the extraction of the strong coupling constant alpha sub(s)(M sub(Z)).

Results on the measurements of the hadronic final state in e± p collisions by the H1 and ZEUS experiments at HERA are presented. These are measurements on the production of prompt photons in photoproduction, inclusive jet, dijet and trijet production in deep-inelatic scattering and on the search for QCD instantons. The jet production data is employed for the extraction of the strong coupling constant αs(MZ).

The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for simulation-based parameter estimation problems is presented. The matrix formalism, termed the Linear Template Fit, calculates the best estimators for the parameters of interest. It combines a linear regression with the method of least squares. The algorithm uses only predictions calculated for a few values of the parameters of interest, which have been made available prior to its execution. The Linear Template Fit is particularly suited for performance critical applications and parameter estimation problems with computationally intense simulations, which are otherwise often limited in their usability for statistical inference. Equations for error propagation are discussed in detail and are given in closed analytic form. For the solution of problems with a nonlinear dependence on the parameters of interest, the Quadratic Template Fit is introduced. As an example application, a determination of the strong coupling constant from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.