The dipole formalism provides a powerful framework from which parton showers can be constructed. In a recent paper, we proposed a dipole shower with improved colour accuracy and in this paper we show how it can be further improved. After an explicit check at $\mathcal{O}(α_{\mathrm{s}}^{2})$ we confirm that our original shower performs as it was designed to, i.e. inheriting its handling of angular-ordered radiation from a coherent branching algorithm. We also show how other dipole shower algorithms fail to achieve this. Nevertheless, there is an $\mathcal{O}(α_{\mathrm{s}}^{2})$ topology where it differs at sub-leading $N_{\mathrm{c}}$ from a coherent branching algorithm. This erroneous topology can contribute a leading logarithm to some observables and corresponds to emissions that are ordered in $k_t$ but not angle. We propose a simple, computationally efficient way to correct this and assign colour factors in accordance with the coherence properties of QCD to all orders in $α_{\mathrm{s}}$.
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…
A parton-shower model for hadronic collisions based on the emission properties of QCD dipoles is proposed. This proposal therefore extends the well-known radiation pattern of pure final-state colour dipoles to QCD initial-state radiation, both of which are treated perturbatively. Corresponding dipole splitting functions are derived and the kinematics of all dipole splittings is discussed. Application to hadron production in electron-positron annihilation, to Drell-Yan lepton-pair and QCD jet production yields encouraging results.
We argue that the increase of the ratio baryon/meson due to the presence of strong colour fields and percolation in ultra-high energy hadronic collisions, helps to explain some of the global features of ultra-high energy cosmic ray cascades at E>10^18 eV and, in particular the observed excess in the number of muons with respect to current models of hadronic interactions. A reasonable agreement with the small value and slope of the average depth of shower maximum Xmax vs shower energy -- as seen in data collected at the Pierre Auger Observatory -- can be obtained with a fast increase of the p-A…
We present an algorithm to rearrange the colour chains of dipole showers in the shower process according to the colour amplitudes of a simple matrix element. We implement the procedure in the dipole shower of Herwig and show comparisons to data.
We analyse the dependence of the peak position of the thrust distribution on the cutoff value in the Nagy-Soper dipole shower. We compare the outcome of the parton shower simulations to a relation of the dependence from an analytic computation, derived within soft-collinear effective theory. We show that the result of the parton shower simulations and the analytic computation are in good agreement.
In this publication the implementation of a new parton shower model based on the Catani-Seymour dipole factorisation, as first suggested by Z. Nagy and D. E. Soper, is discussed. First results obtained with the new algorithm are compared with experimental data.
We present an implementation of a parton shower algorithm for hadron colliders and electron-positron colliders based on the dipole factorisation formulae. The algorithm treats initial-state partons on equal footing with final-state partons. We implemented the algorithm for massless and massive partons.
A new parton shower algorithm has been presented with the claim of providing soft-gluon resummation at `full colour' (arXiv:2001.11492). In this paper we show that the algorithm does not succeed in this goal. We show that full colour accuracy requires the Sudakov factors to be defined at amplitude level and that the simple parton-shower unitarity argument employed in arXiv:2001.11492 is not sufficient.
It has been argued recently that parton showers based on colour dipoles conflict with collinear factorization and do not lead to the correct DGLAP equation. We show that this conclusion is based on an inappropriate assumption, namely the choice of the gluon energy as evolution variable. We further show numerically that Monte Carlo programs based on dipole showers with "infrared sensible" evolution variables reproduce the DGLAP equation both in asymptotic form as well as in comparison to the leading behaviour of second-order QCD matrix elements.
We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a r…
We report on the implementation of a coherent dipole shower algorithm along with an automated implementation for dipole subtraction and for performing POWHEG- and MC@NLO-type matching to next-to-leading order (NLO) calculations. Both programs are implemented as add-on modules to the event generator Herwig++. A preliminary tune of parameters to data acquired at LEP, HERA and Drell-Yan pair production at the Tevatron has been performed, and we find an overall very good description which is slightly improved by the NLO matching.
We present a new parton-shower algorithm. Borrowing from the basic ideas of dipole cascades, the evolution variable is judiciously chosen as the transverse momentum in the soft limit. This leads to a very simple analytic structure of the evolution. A weighting algorithm is implemented, that allows to consistently treat potentially negative values of the splitting functions and the parton distributions. We provide two independent, publicly available implementations for the two event generators Pythia and Sherpa.
Parton showers have become a standard component in the description of high-energy collisions. Nowadays most final-state ones are of the dipole character, wherein a pair of partons branches into three, with energy and momentum preserved inside this subsystem. For initial-state showers a dipole picture is also possible and commonly used, but the older global-recoil strategy remains a valid alternative, wherein larger groups of partons share the energy--momentum preservation task. In this article we introduce and implement a dipole picture also for initial-state radiation in PYTHIA, and compare w…
We present a complete formalism for final-state (timelike) dipole-antenna showers including fermion masses, but neglecting polarization and finite-width effects. We make several comparisons of tree-level expansions of this shower algorithm to fixed-order matrix elements for hadronic Z decays, up to and including Z to 6 partons, to which the algorithm can be consistently matched over all of phase space. We also compare to analytical resummations at the NLL level. The shower algorithm has been implemented in the publicly available VINCIA plugin to the PYTHIA 8 event generator, which enables us t…
We derive an improved prescription for the merging of matrix elements with parton showers, extending the CKKW approach. A flavour-dependent phase space separation criterion is proposed. We show that this new method preserves the logarithmic accuracy of the shower, and that the original proposal can be derived from it. One of the main requirements for the method is a truncated shower algorithm. We outline the corresponding Monte Carlo procedures and apply the new prescription to QCD jet production in e+e- collisions and Drell-Yan lepton pair production. Explicit colour information from matrix e…
Colour evolution and parton branching at the amplitude level have become important theoretical frameworks to improve parton showers, and are algorithms in their own right: they complement shower development by resummation algorithms capable of including interference effects and subleading colour contributions at an unprecedented level. I summarize recent development in the field, focusing on soft gluon evolution, hadronization, and the CVolver framework.
We compute the next-to-leading order corrections to soft-gluon radiation differentially in the one-emission phase space. We show that their contribution to the evolution of color dipoles can be obtained in a modified subtraction scheme, such that both one- and two-emission terms are amenable to Monte-Carlo integration. The two-loop cusp anomalous dimension is recovered naturally upon integration over the full phase space. We present two independent implementations of the new algorithm in the two event generators Pythia and Sherpa, and we compare the resulting fully differential simulation to t…
We briefly summarize the equivalence of off-diagonal generalized vector dominance and the colour-dipole approach to deep-inelastic scattering (DIS) in the diffraction region of values of $x \simeq Q^2/W^2 << 1$.
We present an algorithm for improving subsequent parton shower emissions by full SU(3) colour correlations in the framework of a dipole-type shower. As a proof of concept, we present results from the first implementation of such an algorithm for a final state shower.
We confront a very wide body of HERA diffractive electroproduction data with the predictions of the colour dipole model. We focus upon three different parameterisations of the dipole scattering cross-section and find good agreement for all observables. There can be no doubting the success of the dipole scattering approach and more precise observations are needed in order to expose its limitations.
We study the colour connection structure of R-parity violating decays and production cross sections, and construct a Monte Carlo simulation of these processes including colour coherence effects. We then present some results from the implementation of these processes in the HERWIG Monte Carlo event generator. We include the matrix elements for the two-body sfermion and three-body gaugino and gluino decays as well as the two-to-two resonant hard production processes in hadron-hadron collisions.
The initial-state radiation of soft colour dipoles produced together with a single QCD Pomeron exchange (BFKL) in onium-onium scattering is calculated in the framework of Mueller's approach. The resulting dipole production grows with increasing energy and reveals an unexpected feature of a power-law tail at appreciably large transverse distances from the collision axis, this phenomenon being related to the scale-invariant structure of dipole-dipole correlations.
We formulate PanScales parton showers for hadron collisions so as to achieve next-to-leading logarithmic (NLL) accuracy across a broad set of observables. We do so specifically for colour singlet production. Relative to the existing PanScales final-state showers, the main new question is that of how to redistribute momentum imbalances from initial-state branching across the remainder of the event. We presents tests of the showers at fixed order, including the treatment of full colour for soft-collinear emissions and of spin correlations in both the soft and collinear domains. We also include c…
We employ values of the colour dipole cross section extracted from electroproduction and photoproduction data to show that gluon saturation effects are not required by the current HERA data but will become important in the THERA energy region.
We use data on the deep inelastic structure function F_2 in order to constrain the cross-section for scattering a colour dipole off a proton. The data seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r < r_s(x) where r_s(x) decreases monotonically as x decreases. Subsequent predicitions for the diffractive structure function F_2^{D(3)} also hint at saturation, although the data are not really sufficiently accurate.
The initial-state radiation of soft colour dipoles produced in the central region of onium-onium scattering via single QCD Pomeron exchange (BFKL) is calculated in the framework of Mueller's dipole approach. The resulting dipole production has a two-component structure. One is constant with energy while the other grows and possesses a power-law tail at appreciably large transverse distances from the collision axis. It may be related to the growth of the gluon distribution at small Bjorken-$x.$
We explain why it is possible to formulate a wide variety of high energy (small-x) photon-proton processes in terms of a universal dipole cross section and compare and contrast various parameterizations of this function that exist in the literature.
We carry out extensive tests of the next-to-leading logarithmic (NLL) accuracy of the PanScales parton showers, as introduced recently for colour-singlet production in hadron collisions. The tests include comparisons to (semi-)analytic NLL calculations of a wide range of hadron-collider observables: the colour-singlet boson transverse momentum distribution; global and non-global hadronic energy flow variables related to jet vetoes and analogues of jettiness distributions; (sub)jet multiplicities; and observables sensitive to the DGLAP evolution of the incoming momentum fractions. In the tests,…
We show that a forward jet with large transverse momentum in an onium-onium collision is a hard probe which can be effectively characterized by a colour- dipole distribution at the time of the interaction. The dipole distribution is computed, and compared to its counterpart for a virtual photon in the initial state. We find that while in the photon case, the tail of large sizes is exponentially cut-off, it contributes sizeably in the forward-jet case, which signs the sensitivity of observables based on such events to the infrared region. Moreover, a direct probabilistic interpretation of the d…
In this paper we outline a new parton shower algorithm based on the Catani-Seymour dipole factorization. Our motivation is to have an algorithm which can naturally cooperate with the NLO calculations.
The colour dipole multiplicity distribution is analysed for the wave function of a heavy onium state at small $x$. Numerical results for the average multiplicity and the effect of cutoffs on its power growth are presented. Then, the full multiplicity distribution is analysed: the second multiplicity moment is derived and the tail of the distribution is shown to behave as $\exp(-\log^2 n)$. These results are confirmed by a Monte Carlo simulation which also gives the fluctuations in the spatial density of dipoles.
An analysis of Deeply Virtual Compton Scattering (DVCS) is made within the colour dipole model. We compare and contrast two models for the dipole cross-section which have been successful in describing structure function data. Both models agree with the available cross section data on DVCS from HERA. We give predictions for various azimuthal angle asymmetries in HERA kinematics and for the DVCS cross section in the THERA region.
We pursue the intriguing possibility that larger-size instantons build up diffractive scattering, with the marked instanton-size scale $<ρ> \approx 0.5$ fm being reflected in the conspicuous ``geometrization'' of soft QCD. As an explicit illustration, the known instanton contribution to DIS is transformed into the intuitive colour dipole picture. With the help of lattice results, the $q \bar{q}$-dipole size r is carefully increased towards hadronic dimensions. Unlike pQCD, one now observes a competition between two crucial length scales: the dipole size r and the size $ρ$ of the background ins…
I report on an analysis of Deeply Virtual Compton Scattering (DVCS) within the dipole model, done in collaboration with M. McDermott and G. Shaw. The two models considered here are distinct in their structure and implications. They both agree with the available cross-section data on DVCS from HERA. Predictions for various asymmetries are also given.
An algorithm is presented in which the Colour-Dipole Cascade Model as implemented in the Ariadne program is corrected to match the fixed order tree-level matrix elements for e+e- -> n jets. The result is a full parton level generator for e+e- annihilation where the generated states are correct on tree-level to fixed order in alpha_S and to all orders with modified leading logarithmic (MLLA) accuracy. In this paper, matrix elements are used up to second order in alpha_S, but the scheme is applicable also for higher orders. An improvement to also include exact virtual corrections to fixed order …
A very wide body of HERA diffractive electroproduction data is confronted with the predictions of the colour dipole model. In doing so we focus upon three different parameterisations of the dipole scattering cross-section, whose parameters are fixed by analysis of DIS structure function data. This analysis strongly suggests the presence of saturation effects, but is not definitive because the conclusion requires the inclusion of data at low-$Q^2$ values. Having fixed the parameters of the models from the DIS structure function data, the resulting dipole cross sections can be used to make genui…
We present a detailed comparison of a variety of predictions for diffractive light vector meson production with the data collected at the HERA collider. All our calculations are performed within a dipole model framework and make use of different models for the meson light-cone wavefunction. There are no free parameters in any of the scenarios we consider. Generally we find good agreement with the data using rather simple Gaussian motivated wavefunctions in conjunction with dipole cross-sections which have been fitted to other data.
Modern parton showers are built using one of two models: dipole showers or angular ordered showers. Both have distinct strengths and weaknesses. Dipole showers correctly account for wide-angle, soft gluon emissions and track the leading flows in QCD colour charge but they are known to mishandle partonic recoil. Angular ordered showers keep better track of partonic recoil and correctly include large amounts of wide-angle, soft physics but azimuthal averaging means they are known to mishandle some correlations. In this paper, we derive both approaches from the same starting point; linking our un…
We evaluate the theoretical uncertainties in next-to-leading order plus parton shower predictions for top quark pair production and decay in hadronic collisions. Our work is carried out using the Herwig 7 event generator and presents an in-depth study of variations in matching schemes with two systematically different shower algorithms, the traditional angular-ordered and alternative dipole shower. We also present all of the required extensions of the Herwig dipole shower algorithm to properly take into account quark mass effects, as well as its ability to perform top quark decays. The predict…
We perform a detailed analysis of next-to-leading order plus parton-shower matching in vector-boson-fusion WW production including leptonic decays. The study is performed in the Herwig 7 framework interfaced to VBFNLO 3, using the angular-ordered and dipole-based parton-shower algorithms combined with the subtractive and multiplicative matching algorithms.
We describe an algorithm for improving subsequent parton shower emissions by full SU(3) color correlations in the framework of a dipole-type shower. As a proof of concept, we present results from the first implementation of such an algorithm for a final state shower. The corrections are found to be small for event shapes and jet rates but can be more significant for tailored observables.
We give a detailed account of the recently formulated generalized vector dominance/colour-dipole picture (GVD/CDP) of deep-inelastic scattering at low $x\cong Q^2/W^2$, including photoproduction. The approach, based on $γ^*(q \bar q)$ transitions, $q \bar q$ propagation and diffractive $(q \bar q)p$ scattering via the generic structure of the two-gluon exchange, provides a unique and quantitatively successful theory for the $γ^* p$ total cross section, $σ_{γ^* p} (W^2,Q^2)$, at low $x$. The GVD/CDP is shown to imply the empirical low-$x$ scaling law, $σ_{γ^* p} (W^2,Q^2)=σ_{γ^* p} (η)$ with $η…
We show that the colour glass condensate dipole model of Iancu, Itakura and Munier, improved to include the impact parameter dependence, gives a good fit to the total gamma* p cross section measured at HERA if the anomalous dimension at the saturation scale, gamma_s, is treated as a free parameter. We find that the optimum value of gamma_s = 0.46 is close to the value determined from numerical solution of the Balitsky-Kovchegov equation. The impact parameter dependent saturation scale is generally less than 0.5 GeV^2 in the HERA kinematic regime for the most relevant impact parameters b ~ 2-3 …
We present first results of resumming soft gluon effects in a simulation of high energy collisions beyond the leading-colour approximation. We work to all orders in QCD perturbation theory using a new parton branching algorithm. This amplitude evolution algorithm resembles a parton shower that is able to systematically include colour-suppressed terms. We find that colour suppressed terms can significantly contribute to jet veto cross sections.
We confront the colour glass condensate motivated dipole model parameterization of Iancu, Itakura and Munier with the available HERA data on the diffractive structure function F2D3 and with existing dipole model parameterizations. Reasonably good agreement is found with only two adjustable parameters. We caution against interpreting the success of the model as compelling evidence for low-x perturbative saturation dynamics.
In this review a new method is presented for attaching parton shower algorithms to NLO partonic jet cross sections in electron-positron annihilation. Our method is based on the Catani-Seymour dipole subtraction method and also uses an adaptation of the matching scheme of Catani, Krauss, Kuhn, and Webber.
We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms for…
We outline a new formalism for dipole-type parton showers which maintain exact energy-momentum conservation at each step of the evolution. Particular emphasis is put on the coherence properties, the level at which recoil effects do enter and the role of transverse momentum generation from initial state radiation. The formulated algorithm is shown to correctly incorporate coherence for soft gluon radiation. Furthermore, it is well suited for easing matching to next-to-leading order calculations.
We present the contributions to electric dipole moments (EDMs) induced by the Yukawa couplings of an additional electroweak doublet of colour-octet scalars. The full set of one-loop diagrams and the enhanced higher-order effects from Barr-Zee diagrams are computed for the quark (chromo-)EDM, along with the two-loop contributions to the Weinberg operator. Using the stringent experimental upper limits on the neutron EDM, constraints on the parameter space of this model are derived.
Studying the Infrared Behaviour of Improved Logarithmic Accuracy Parton Showers with Herwig
Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文系）；Institute of Physics, NAWI Graz, University of Graz（格拉茨大学NAWI格拉茨物理研究所）；Particle Physics, Faculty of Physics, University of Vienna（维也纳大学物理学院粒子物理）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）
New coloured scalars in the Manohar-Wise model give sizeable contributions to the Electric Dipole Moment (EDM) of the neutron through one-loop and two-loop diagrams, computed in Reference [1]. Contributions from neutral scalars cancel out for degenerate values of the masses, whose difference is related to the oblique parameters $S$ and $T$. The Manohar-Wise model is able to explain the recent value of the $W$-boson mass published by the CDF collaboration. We show, however, that the case of total degeneracy of masses is strongly disfavoured in this model, whose parameter space is substantially …
A new release of the Monte Carlo event generator Herwig (version 7.1) is now available. This version introduces a number of improvements, notably: multi-jet merging with the dipole shower at LO and NLO QCD; a new model for soft interactions and diffraction; improvements to mass effects and top decays in the dipole shower, as well as a new tune of the hadronisation parameters.
The dipole (Möbius) representation of the colour singlet BFKL kernel in the next-to-leading order is found in supersymmetric Yang--Mills theories. Ambiguities of this form and its conformal properties are discussed.
We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs,…
