arXiv subjects
Publications and source records attributed to Davison E. Soper.
The quark parton model grew out of deeply inelastic scattering experiments. The parton model developed into a full theory, quantum chromodynamics, QCD. This article explains some of the physics issues encountered in connecting the parton model and QCD.
Parton shower evolution is given by a renormalization group equation that reflects the infrared behavior of perturbative QCD including color and spin and including quantum interference. With added approximations, such an evolution equation can provide the basis for a parton shower event generator. To date, splitting functions for parton shower evolution have been derived only to leading order in $\as$. We provide a framework that can provide splitting functions beyond leading order, and in particular at order $\as^2$. This requires a representation of Feynman graphs in which partons are off shell and are characterized by vector or spinor indices instead of on-shell spins.
We explore the features of interpolating gauge for QCD. This gauge, defined by Doust and by Baulieu and Zwanziger, interpolates between Feynman gauge or Lorenz gauge and Coulomb gauge. We argue that it could be useful for defining the splitting functions for a parton shower beyond order $\as$ or for defining the infrared subtraction terms for higher order perturbative calculations.
One can use more than one scale variable to define the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. In an earlier paper, we developed this idea for electron-positron annihilation. Here, we use multiple scale variables for a parton shower with initial state partons. Then we need a more sophisticated analysis because the evolution of parton distribution functions must be coordinated with the parton shower evolution. We make the needed connections more precise than in our earlier work, even for the case of just one scale variable. Then we develop an example with three scale variables, which leads to advantages compared to the usual shower formulation with only one scale variable. We provide results for Drell-Yan muon pair production.
In this brief Snowmass White Paper for the Theory Frontier, we argue that there have been important recent developments in the algorithms used to generate a simulated parton shower and that further progress can be achieved in the coming decade. A much more detailed exposition can be found in a corresponding White Paper of the Energy Frontier.
One can use more than one scale variable to specify the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. Considering $e^+e^-$ annihilation, we use two variables, with shower evolution following a special path in this two dimensional space. In addition, we treat in a special way the part of the splitting function that has a soft emission singularity but no collinear singularity. This leads to certain advantages compared to the usual shower formulation with only one scale variable.
We propose a method to examine how a parton shower sums large logarithms. In this method, one works with an appropriate integral transform of the distribution for the observable of interest. Then, one reformulates the parton shower so as to obtain the transformed distribution as an exponential for which one can compute the terms in the perturbative expansion of the exponent. We apply this general program to the thrust distribution in electron-positron annihilation, using several shower algorithms. Of the approaches that we use, the most generally applicable is to compute some of the perturbative coefficients in the exponent by numerical integration and to test whether they are consistent with next-to-leading-log summation of the thrust logarithms.
In a companion publication, we have explored how to examine the summation of large logarithms in a parton shower. Here, we apply this general program to the thrust distribution in electron-positron annihilation, using several shower algorithms. The method is to work with an appropriate integral transform of the distribution for the observable of interest. Then, we reformulate the parton shower calculation so as to obtain the transformed distribution as an exponential for which we can compute the terms in the perturbative expansion of the exponent.
Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross section data. We review definitions of the PDFs and their relations to high-energy cross sections. We focus on the PDFs in protons, but also discuss PDFs in nuclei. We review in some detail the standard statistical treatment needed to fit the PDFs to data using the Hessian method. We discuss tests that can be used to critically examine whether the assumptions are indeed valid. We also present some ideas of what one can do in the case that the tests indicate that the assumptions fail.
Initial state evolution in parton shower event generators involves parton distribution functions. We examine the probability for the system to evolve from a higher scale to a lower scale without an initial state splitting. A simple argument suggests that this probability, when multiplied by the ratio of the parton distributions at the two scales, should be independent of the parton distribution functions. We call this the PDF property. We examine whether the PDF property actually holds using Pythia and Deductor. We also test a related property for the Deductor shower and discuss the physics behind the results.
A recent Letter has reported that sound waves can carry gravitational mass. I analyze this effect in a Hooke's law solid, considering a wave packet moving in the $z$ direction with an amplitude that is independent of $x$ and $y$. The analysis shows that, at second order in an expansion around small amplitude vibrations, there is a small net motion of material, and thus mass, in the direction opposite to the wave packet propagation. This is a straightforward consequence of Newton's laws.
We study the probability for no jets with transverse momenta above a given cut to be found in the rapidity region between two high pT jets with a large rapidity separation. Our investigation uses the parton shower event generator DEDUCTOR with color beyond the leading-color-plus approximation included perturbatively.
The operator in a parton shower algorithm that represents the imaginary part of virtual Feynman graphs has a non-trivial color structure and is large because it is proportional to a factor of $4π$. In order to improve the treatment of color in a parton shower, it may help to exponentiate this phase operator. We show that it is possible to do so by exponentiating matrices that are no larger than $14\times14$. Using the example of the probability to have a gap in the rapidity interval between two high transverse momentum jets, we test this exponentiation algorithm by comparing to the result of treating the phase operator perturbatively. We find that the exponentiation works, but that the net effect of the exponentiated phase operator is quite small for this problem, so that one can as well use the perturbative approach.
Parton shower event generators typically approximate evolution of QCD color so that only contributions that are leading in the limit of an infinite number of colors are retained. Our parton shower generator, Deductor, has used an "LC+" approximation that is better, but still quite limited. In this paper, we introduce a new scheme for color in which the approximations can be systematically improved. That is, one can choose the theoretical accuracy level, but the accuracy level that is practical is limited by the computer resources available.
We consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to the structure of QCD. We argue that a parton shower with splitting functions proportional to $α_s$ can be viewed not just as a model, but as the lowest order approximation to a shower that is defined at any perturbative order. To support this argument, we present a formulation for a parton shower at order $α_s ^k$ for any $k$. Since some of the input functions needed are specified by their properties but not calculated, this formulation does not provide a useful recipe for an order $α_s ^k$ parton shower algorithm. However, in this formulation we see how the operators that generate the shower are related to operators that specify the infrared singularities of QCD.
We explore jet physics in hadron collisions using the parton shower event generator Deductor. Of particular interest is the one jet inclusive cross section dsigma/dpT for jets of very high pT. Compared to the Born level, the cross section decreases substantially because of pT loss from the jet during showering. We compare to the same effect in Pythia and Dire. The cross section then increases substantially because of the summation of threshold logarithms included in Deductor. We also study the cross section to have a gap with no jets between two hard jets that are widely separated in rapidity. Here we compare Deductor with virtuality based ordering with Deductor with kT ordering and we check whether adding an underlying event and hadronization has a significant effect beyond that found with just a parton shower.
We develop a new method for tagging jets produced by hadronically decaying top quarks. The method is an application of shower deconstruction, a maximum information approach that was previously applied to identifying jets produced by Higgs bosons that decay to bottom quarks. We tag an observed jet as a top jet based on a cut on a calculated variable that is an approximation to the ratio of the likelihood that a top jet would have the structure of the observed jet to the likelihood that a non-top QCD jet would have this structure. We find that the shower deconstruction based tagger can perform better in discriminating boosted top quark jets from QCD jets than other publicly available tagging algorithms.
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in $α_s$ that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.