arXiv subjects
Publications and source records attributed to Ronald Kleiss.
We present a pedagogical treatment of the electroweak Higgs mechanism based solely on Feynman diagrams and S-matrix elements, without recourse to (gauge) symmetry arguments. Throughout, the emphasis is on Feynman rules and the Schwinger-Dyson equations; it is pointed out that particular care is needed in the treatment of tadpole diagrams and their symmetry factors.
A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity of this model in the unitary gauge, i.e. employing only physical fields. A new Ward-like identity is used to show that the high-energy behaviour of all amplitudes cannot be more than quadratic; the use of generating functions for all off-shell amplitudes then leads to the unitarity proof.
We present a first implementation of collinear electroweak radiation in the Vincia parton shower. Due to the chiral nature of the electroweak theory, explicit spin dependence in the shower algorithm is required. We thus use the spinor-helicity formalism to compute helicity-dependent branching kernels, taking special care to deal with the gauge relics that may appear in computation that involve longitudinal polarizations of the massive electroweak vector bosons. These kernels are used to construct a shower algorithm that includes all possible collinear final-state electroweak branchings, including those induced by the Yang-Mills triple vector boson coupling and all Higgs couplings, as well as vector boson emissions from the initial state. We incorporate a treatment of features particular to the electroweak theory, such as the effects of bosonic interference and recoiler effects, as well as a preliminary description of the overlap between electroweak branchings and resonance decays. Some qualifying results on electroweak branching spectra at high energies, as well as effects on LHC physics are presented. Possible future improvements are discussed, including treatment of soft and spin effects, as well as issues unique to the electroweak sector.
We present a formalism for a fully coherent QED parton shower. The complete multipole structure of photonic radiation is incorporated in a single branching kernel. The regular on-shell 2 to 3 kinematic picture is kept intact by dividing the radiative phase space into sectors, allowing for a definition of the ordering variable that is similar to QCD antenna showers. A modified version of the Sudakov veto algorithm is discussed that increases performance at the cost of the introduction of weighted events. Due to the absence of a soft singularity, the formalism for photon splitting is very similar to the QCD analogon of gluon splitting. However, since no color structure is available to guide the selection of a spectator, a weighted selection procedure from all available spectators is introduced.
The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by extending the physical phase space to at least 7 spacetime dimensions, which leads to on-shell recursion relations a la BCFW. These lead to a simple proof that all on-shell tree amplitudes obey partial-wave unitarity.
We present a way to analyze the distribution produced by a Monte Carlo algorithm. We perform these analyses on several versions of the Sudakov veto algorithm, adding a cutoff, a second variable and competition between emission channels. The analysis allows us to prove that multiple, seemingly different competition algorithms, including those that are currently implemented in most parton showers, lead to the same result. Finally, we test their performance and show that there are significantly faster alternatives to the commonly used algorithms.
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to the more constrained pMSSM and dMSSM, leading to even more invariants. Extending our search to the two-loop level we find that the number of invariants is considerably reduced.
We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA evaluates the matrix elements in a recursive way by combining off-shell currents. Furthermore, CAMORRA can be used to compute amplitudes involving continuous color and helicity final states.
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect to a scheme invariant quantity. Furthermore, we investigate whether the potentially large logarithms in such an expansion cause inaccuracy and how this can be improved.
We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we determine the complexity as a function of the number of external legs. We describe a method for obtaining the number of topologically inequivalent Feynman graphs containing closed loops, and apply this to one- and two-loop amplitudes. We also compute the number of graphs weighted by their symmetry factors, thus arriving at exact and asymptotic estimates for the average symmetry factor of diagrams. We present results for the asymptotic number of diagrams up to 10 loops, and prove that the average symmetry factor approaches unity as the number of external legs becomes large.
We derive the Feynman rules of the standard model in the axial gauge. After this we prove that the fields $ϕ_W$ and $ϕ_Z$ do not correspond to physical particles. As a consequence, these fields cannot appear as incoming or outgoing lines in Feynman graphs. We then calculate the contribution of these fields in the case of a particular decay mode of the top quark.
If calculated in the standard way, the cross section for the collision of two unstable particles turns out to diverge. This is because this cross section is actually proportional to the size of the colliding beams. The effect is called the "linear beam size effect". We present a way of including this linear beam size effect in the usual Monte Carlo integration procedure. Furthermore we discuss the gauge breaking that this may cause.
We address the problem that the cross section for the collisions of unstable particles diverges, if calculated by standard methods. This problem is considered for beams much smaller than the decay length of the unstable particle, much larger than the decay length and finally also for pancake- shaped beams. We find that in all cases this problem can be solved by taking into account the production/propagation of the unstable particle and/or the width of the incoming wave packets in momentum space.
We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and we compute the mean and variance of this distribution for several theories. We show the distribution's `fine structure', arising from topological sum rules, can be obtained.
We present an enumeration of all possible amplitudes that contribute to an n-jet process in QCD. We estimate the number of amplitudes for large number of jets and determine the actual number of amplitudes to be calculated, which is smaller due to relabelling among (massless) quark flavours.
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit $N\to\infty$. We then examine the circumstances under which this distribution approaches a normal distribution. For large classes of non-uniformity measures, a Law of Many Modes in the spirit of the Central Limit Theorem can be derived.
We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets, and on the other hand uses information on the degree of uniformity of the point set actually used, in the form of a discrepancy or diaphony. A few examples of such discrepancies are given. We derive the distribution of our error estimate in the limit of large number of points. In many cases, Gaussian central limits are obtained. We also present numerical results for the quadratic star-discrepancy for a number of quasi-random sequences.
In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.