There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

The Pythia program can be used to generate high-energy-physics ''events'', i.e. sets of outgoing particles produced in the interactions between two incoming particles. The objective is to provide as accurate as possible a representation of event properties in a wide range of reactions, within and beyond the Standard Model, with emphasis on those where strong interactions play a role, directly or indirectly, and therefore multihadronic final states are produced. The physics is then not understood well enough to give an exact description; instead the program has to be based on a combination of analytical results and various QCD-based models. This physics input is summarized here, for areas such as hard subprocesses, initial- and final-state parton showers, underlying events and beam remnants, fragmentation and decays, and much more. Furthermore, extensive information is provided on all program elements: subroutines and functions, switches and parameters, and particle and process data. This should allow the user to tailor the generation task to the topics of interest.

/pdf/pythia-6-4-physics-and-manual-3dvwmijpnq.pdf

PYTHIA 6.4 Physics and Manual

We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

/pdf/the-automated-computation-of-tree-level-and-next-to-leading-4etm0g6w46.pdf

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

http://risa.stanford.edu/teaching/362/particledarkmatter.pdf

Particle dark matter: Evidence, candidates and constraints

We examine some problems associated with the low-momentum behavior of gauge theories and other renormalizable field theories. Our main interest is in the infrared structure of unbroken non-Abelian gauge theories and how this is affected by the presence of other heavy fields coupled to the massless gauge fields. It is shown in the context of a simple model of gauge mesons coupled to massive fermions that the heavy fields decouple at low momenta except for their contribution to renormalization effects. This result is used to discuss the mass-shell structure of the fermion propagator. The decoupling theorem is then stated for a general renormalizable theory and applied to some interesting examples. One is a more general gauge theory which makes use of the Higgs mechanism and attempts to unify the elementary particle forces. Another is the connection of the linear and nonlinear $\ensuremath{\sigma}$ models in the limit ${m}_{\ensuremath{\sigma}}\ensuremath{\rightarrow}\ensuremath{\infty}$.

Infrared Singularities and Massive Fields

The effects of new, heavy quarks are examined in a colored quark-gluon model. The e+e- total cross section scales for energies far above any quark mass. However, it is much greater than the scaling prediction in a domain about the nominal two-heavy-quark threshold, despite σe+e- being a weak-coupling problem above 2 GeV. We expect spikes at the low end of this domain and a broad enhancement at the upper end.

/pdf/heavy-quarks-and-e-e-annihilation-3uosinzvth.pdf

Heavy Quarks and e+ e− Annihilation

We demonstrate that for sufficiently high temperature $T$ the behavior of any four-dimensional gauge theory with small coupling constant $\ensuremath{\alpha}$, at distances beyond the electrical Debye screening length ${\ensuremath{\xi}}_{D}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\alpha}}T}$, is determined precisely by the corresponding three-dimensional theory. This is the magnetic sector of the original theory, and in the non-Abelian case it is a Yang-Mills theory like three-dimensional quantum chromodynamics (QC${\mathrm{D}}_{3}$). We study QC${\mathrm{D}}_{3}$ in the loop expansion, which is only valid for distances $\ensuremath{\ll}\frac{1}{\ensuremath{\alpha}T}$, in both covariant and Coulomb gauges. At a finite order in the loop expansion, the presence of logarithmic infrared divergences signals the appearance of new operators in the operator-product expansion. For example, in a covariant gauge, the gauge self-energy develops infrared divergences at two-loop order associated with the operator ${\overline{A}}^{2}$. Infrared divergences in the Wilson loop are also considered and shown to cancel below the order at which gauge-invariant local operators can appear in the operator-product expansion. The infrared structure of QC${\mathrm{D}}_{3}$ at distances $\ensuremath{\gtrsim}\frac{1}{\ensuremath{\alpha}T}$ cannot be directly probed in the loop expansion, however. We present a simpler model which is calculable in this infrared limit, and which might serve as a prototype for QC${\mathrm{D}}_{3}$. The model is massless scalar QE${\mathrm{D}}_{3}$, which with $N$ charged scalars is soluble in a $\frac{1}{N}$ expansion as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Using the $\frac{1}{N}$ expansion, we demonstrate that infrared softening occurs: the long-range behavior of the photon propagator in massless scalar QE${\mathrm{D}}_{3}$ is less singular than that of free fields. Infrared softening might also occur in QC${\mathrm{D}}_{3}$, although it cannot be demonstrated to finite order in the loop expansion. The implications of an assumed infrared softening in QC${\mathrm{D}}_{3}$ for the magnetic sector of Yang-Mills theories at high temperatures are also discussed. In particular, we consider the possibility that, if the softening is sufficiently great, there is screening of hot non-Abelian magnetic fields and possible confinement of primordial magnetic monopoles.

High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics

The effects of new, heavy quarks are examined in a colored quark-gluon model. The ${e}^{+}{e}^{\ensuremath{-}}$ total cross section scales for energies far above any quark mass. However, it is much greater than the scaling prediction in a domain about the nominal two-heavy-quark threshold, despite ${\ensuremath{\sigma}}_{{e}^{+}{e}^{\ensuremath{-}}}$ being a weak-coupling problem above 2 GeV. We expect spikes at the low end of this domain and a broad enhancement at the upper end.

/pdf/orthocharmonium-and-e-e-annihilation-rm9fb2qm8g.pdf

Orthocharmonium and e+ e- Annihilation

A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale \ensuremath{\alpha}\ensuremath{\equiv}N ${e}^{2}$ of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order \ensuremath{\alpha}, so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to \ensuremath{\alpha}. Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.

Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED

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