Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color approximation, which is the leading term in an expansion in powers of $1/N_c^2$, where $N_c = 3$ is the number of colors. We introduce a more general approximation, the LC+ approximation, that includes some of the color suppressed contributions. There is a cost: each generated event comes with a weight. There is a benefit: at each splitting the leading soft$\times$collinear singularity and the leading collinear singularity are treated exactly with respect to color. In addition, an LC+ shower can start from a state of the color density matrix in which the bra state color and the ket state color do not match.
We present the determination of Transverse Momentum Dependent (TMD) parton distributions from Monte Carlo parton showers. We investigate the effective TMD distributions obtained from the PYTHIA8 and HERWIG6 parton showers and compare them to the TMD distributions determined within the Parton Branching method.
Inspecting the power of parton showering the generated events by comparing the events generated in NLO+PS to NLO and NNLO without parton shower in $e^+e^-$ at 91.2 GEV
Standard dipole parton showers are known to yield incorrect subleading-colour contributions to the leading (double) logarithmic terms for a variety of observables. In this work, concentrating on final-state showers, we present two simple, computationally efficient prescriptions to correct this problem, exploiting a Lund-diagram type classification of emission regions. We study the resulting effective multiple-emission matrix elements generated by the shower, and discuss their impact on subleading colour contributions to leading and next-to-leading logarithms (NLL) for a range of observables. I…
When the initial state evolution of a parton shower is organized according to the standard "backward evolution'' prescription, ratios of parton distribution functions appear in the splitting probabilities. The shower thus organized evolves from a hard scale to a soft cutoff scale. At the end of the shower, one expects that only the parton distributions at the soft scale should affect the results. The other effects of the parton distributions should have cancelled. This means that the kernels for parton evolution should be related to the shower splitting functions. If the initial state partons …
The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.
A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the CASCADE package for the full TMD parton shower, final state shower and…
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. Th…
We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximatio…
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 inpu…
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 be…
We propose a new approach for combining next-to-leading order (NLO) and parton shower (PS) calculations so as to obtain three core features: (a) applicability to general showers, as with the MCatNLO and POWHEG methods; (b) positive-weight events, as with the KrkNLO and POWHEG methods; and (c) all showering attributed to the parton shower code, as with the MCatNLO and KrkNLO methods. This is achieved by using multiplicative matching in phase space regions where the shower overestimates the matrix element and accumulative (additive) matching in regions where the shower underestimates the matrix …
We introduce a method for the separation of soft and collinear logarithms in QCD parton evolution at $\mathcal{O}(α_s^2)$ and at leading color. Using an implementation of the technique in the Dire parton shower, we analyze the numerical impact of genuine triple-collinear corrections from quark pair emission in $e^+e^-\to$ hadrons.
We discuss the necessary steps for implementing an angularly ordered (AO) electroweak (EW) parton shower in Herwig 7 multi-purpose event generator. This includes calculating the helicity-dependent quasi-collinear EW branching functions that correspond to the full range of final-state EW parton shower, in addition to the initial-state EW gauge vector boson radiations. The results are successfully embedded in the AO Herwig 7 shower algorithm and have undergone a set of comprehensive and conclusive performance tests. Furthermore, we have used this EW parton shower algorithm, alongside the existin…
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.
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.
I describe MiNNLO$_{\rm PS}$, a novel method to match NNLO QCD computations with Parton Showers, and present a selection of results for color-singlet production at the LHC.
