We introduce photon and gluon propagators in which the scalar polarization component is subtracted systematically by making use of the BRST invariance of the off-shell vector boson created from physical on-shell states. The propagator has the light-cone gauge form, where the spacial component of the gauge vector points along the negative of the off-shell vector boson momentum. We call the gauge as parton-shower gauge, since in collinear configurations the absolute value squared of each Feynman amplitude reproduces all the singular behaviors of the corresponding parton shower in this gauge. We introduce new HELAS codes that can be used to calculate the tree-level helicity amplitudes of arbitrary QED and QCD processes by using MadGraph. The absence of subtle gauge cancellation among Feynman amplitudes allows numerical codes to evaluate singular behaviors accurately, and helps us gaining physical insights on interference patterns.
We present an antenna-shower formalism that includes helicity dependence for massless partons. The formalism applies to both traditional (global) showers and to sector-based variants. We combine the shower with VINCIA's multiplicative approach to matrix-element matching, generalized to operate on each helicity configuration separately. The result is a substantial gain in computational speed for high parton multiplicities. We present an implementation of both sector and global showers, with min and max variations, and helicity-dependent tree-level matching applied for vector bosons or Higgs dec…
We present the theory of QED x QCD resummation and its interplay with shower/matrix element matching in precision LHC physics scenarios. We illustrate the theory using single heavy gauge boson production at hadron colliders.
We discuss the elements of QED X QCD exponentiation and its interplay with shower/ME matching and IR-improved DGLAP theory in precision LHC physics scenarios. Applications to single heavy gauge boson production at hadron colliders are illustrated.
An improved QED Parton Shower algorithm to calculate photonic radiative corrections to QED processes at flavour factories is described. We consider the possibility of performing photon generation in order to take into account also the effects due to interference between initial and final state radiation. Comparisons with exact order $α$ results are shown and commented.
We present a complete set of helicity-dependent 2->3 antenna functions for QCD initial- and final- state radiation. The functions are implemented in the Vincia shower Monte Carlo framework and are used to generate showers for hadron-collider processes in which helicities are explicitly sampled (and conserved) at each step of the evolution. Although not capturing the full effects of spin correlations, the explicit helicity sampling does permit a significantly faster evaluation of fixed-order matrix-element corrections. A further speed increase is achieved via the implementation of a new fast li…
We present the recent developments in exact amplitude-based resummation methods for non-Abelian gauge theories as they relate to precision LHC physics. We discuss QEDXQCD exponentiation, shower/ME matching, IR-improved DGLAP-CS theory and implications, as developed by one of us (BFLW), for a UV finite theory of quantum general relativity.
We calculate all the four-photon helicity amplitudes at the one-loop level in a massive theory using multiple-cut methods. The amplitudes are derived in scalar QED, QED and $\textrm{QED}^{\caln =1}$ theories. We will see the origin of rational terms. We extend the calculation to the simplest six-photon helicity amplitude where all photons have the same helicity.
We report on a high-precision calculation of the Bhabha process in QED, of interest for precise luminosity determination of low-energy electron-positron colliders. The calculation is based on the matching of exact next-to-leading order corrections with a Parton Shower algorithm. The structure of the algorithm (implemented in an improved version of the event generator BABAYAGA) is illustrated, with a discussion on the resulting theoretical uncertainty, of the order of 0.1 %.
We develop an event generator, NLL-QEDPS, based on the QED shower including the next-to-leading logarithm correction in the e^+e^- annihilation. The shower model is the Monte Carlo technique to solve the renormalization group equation so that they can calculate contributions of alpha^m log^n(S/m_e^2) for any m and n systematically. Here alpha is the QED coupling, m_e is the mass of electron and S is the square of the total energy in the e^+e^- system. While the previous QEDPS is limited to the leading logarithm approximation which includes only contributions of (alpha log(S/m_e^2))^n, the mode…
We summarize the recent progress in a new approach to precision LHC physics based on the IR-improved DGLAP-CS theory as it relates to a new MC friendly exponentiated scheme for precision calculation of higher order corrections to LHC physics in which IR singularities from both QED and QCD are canceled to all orders in αand in α_s simultaneously in the presence of rigorous shower/ME matching. We present the first MC data comparing the implied new showers themselves with the standard ones using the HERWIG6.5 MC event generator as a test case at LHC energies.
A parton shower method for the photonic radiative correction is applied to the single W-boson production processes. The energy scale for the evolution of the parton shower is determined so that the correct soft-photon emission is reproduced. Photon spectra radiated from the partons are compared with those from the exact matrix elements, and show a good agreement. Possible errors due to a inappropriate energy-scale selection or due to the ambiguity of energy scale determination are also discussed, particularly for the measurements on triple gauge-couplings.
Parton showers are crucial components of high-energy physics calculations. Improving their modelling of QCD is an active research area since shower approximations are stumbling blocks for precision event generators. Naively, the interference between sub-dominant Standard-Model interactions and QCD can be of similar size to subleading QCD corrections. This article assesses the impact of QCD/QED interference effects in parton showers, by developing a sophisticated shower including QED, QCD at fixed color, and employing complete tree-level matrix element corrections for individual $N_C=3$ color c…
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 simila…
Inclusion of the QED higher order radiative corrections in the two-photon process, e+e- -> e+e- mu+mu-, is examined by means of the structure function and the parton shower. Results are compared with the exact $O(α)$ calculations and give a good agreement. These two methods should be universally applicable to any other non-annihilation processes like the single-W productions in the e+e- collisions. In this case, however, the energy scale for the evolution by the renormalization-group equation should be chosen properly depending on the dominant diagrams for the given process. A method to find t…
As continuation of our previous paper we further develop our new method for calculating helicity amplitudes of jet-like QED processes described by tree diagrams, applying it to lepton pair production. This method consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices. New vertices are introduced for the pair production case, and previous bremsstrahlung vertices are generalized to include virtual photons inside the considered jet. We present a diagrammatic approach that allows to write down in an efficient way the leading helicity …
KKMChh adapts the CEEX (Coherent Exclusive Exponentiation) formalism of the Monte Carlo Program KKMC for Z boson production and decay to hadron scattering. Amplitude-level soft photon exponentiation of initial and final state radiation, together with initial-final interference, is matched to a perturbative calculation to second order next-to-leading logarithm, and electroweak corrections to the hard process are included via DIZET. The first release of KKMChh included complete initial state radiation calculated with current quark masses. This version assumes idealized pure-QCD PDFs with negligi…
Inelastic QED processes, the cross sections of which do not drop with increasing energy, play an important role at high-energy colliders. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles $m/E \lesssim θ\ll 1$, which yields the dominant contribution to their total cross sections. A new effective method is presented and applied to QED processes with emission of real photons to calculate the helicity amplitudes of these processes. Its basic idea is similar to the well-known equivalen…
The emission of W and Z gauge boson is included in a traditional QCD + QED shower. The unitarity of the shower algorithm links the real radiation of the weak gauge bosons to the negative weak virtual corrections. The shower evolution process leads to a competition between QCD, QED and weak radiation, and allows for W and Z boson production inside jets. Various effects on LHC physics are studied, both at low and high transverse momenta, and effects at higher-energy hadron colliders are outlined.
The generator QEDPS, a parton shower model in QED, developed by the present authors has been improved. By a careful study on the shower algorithm it was found that some finite contributions have been missed in the original version. They are small, but cannot be neglected when the contribution of the soft photons is dominant. A method is presented to correct these finite pieces and then a new generator, improved QEDPS, is proposed, which is able to make more precise prediction for the processes observed in e+e- annihilation as far as the initial radiation is concerned.
We present an implementation of the full electroweak $H+2~\text{jets}$ production process at hadron colliders in the framework of the $\tt{POWHEG~BOX}$, a public tool for the matching of fixed-order perturbative calculations with parton shower generators. Our implementation allows for the simultaneous description of vector-boson fusion and Higgsstrahlung contributions. NLO-QCD and electroweak corrections are taken into account and matched to QCD and QED showers, respectively. The size of the fixed-order QCD and electroweak corrections is found to be moderate, but dependent on the considered se…
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…
The interpretation of measurements of high-energy particle collisions relies heavily on the performance of full event generators. By far the largest amount of time to predict the kinematics of multi-particle final states is dedicated to the calculation of the hard process and the subsequent parton shower step. With the continuous improvement of quantum devices, dedicated algorithms are needed to exploit the potential quantum computers can provide. We propose general and extendable algorithms for quantum gate computers to facilitate calculations of helicity amplitudes and the parton shower proc…
Vacuum birefringence is governed by the amplitude for a photon to flip helicity or polarisation state in an external field. Here we calculate the flip and non-flip amplitudes in arbitrary plane wave backgrounds, along with the induced spacetime-dependent refractive indices of the vacuum. We compare the behaviour of the amplitudes in the low energy and high energy regimes, and analyse the impact of pulse shape and energy. We also provide the first lightfront-QED derivation of the coefficients in the Heisenberg-Euler effective action.
The analytical result for the six-photon helicity amplitudes in scalar QED is presented. To compute the loop, a recently developed method based on multiple cuts is used. The amplitudes for QED and $QED^{\caln=1}$ are also derived using the supersymmetric decomposition linking the three theories.
Three-loop helicity amplitudes of four-lepton scattering in QED
Higgs Centre for Theoretical Physics, School of Physics and Astronomy The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Department of Mathematical Sciences, University of Liverpool（利物浦大学数学科学系）；Dipartimento di Fisica e Astronomia, Universita di Padova（帕多瓦大学物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
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, includ…
We calculate the complete one-loop quantum corrections to the helicity eigenstate chargino pair production cross sections in polarized electron positron collisions, within the Minimal Supersymmetric Standard Model. We calculate the non-QED corrections using the helicity amplitudes formalism, and Dimensional Regularization to deal with ultraviolet divergences. We calculate QED corrections using the dipole subtraction formalism to extract soft and collinear divergences in Bremsstrahlung, canceling them with the infrared divergences from virtual QED corrections. We show numerical results for the …
In this note we will recall the main tests that document robustness and flexibility of the PHOTOS design. This aspect may be of broader use and may find extensions in future applications, also outside the simple case of purely QED bremsstrahlung in decays. The components of the PHOTOS algorithm will be presented using operator language. The results of some flexibility tests, not documented before, will also be presented.
We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\it all}\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.
We consider parton showers based on radiation from QCD dipoles or `antennae'. These showers are built from 2->3 parton splitting processes. The question then arises of what functions replace the Altarelli-Parisi splitting functions in this approach. We give a detailed answer to this question, applicable to antenna showers in which partons carry definite helicity, and to both initial- and final-state emissions.
We consider $W^\pm Z$ production in hadronic collisions and present high-precision predictions in QCD and electroweak (EW) perturbation theory matched to parton showers. To this end, we match next-to-next-to-leading order QCD corrections to parton showers using the MiNNLO$_{\rm PS}$ method and consistently combine them with next-to-leading order EW corrections matched to parton showers. This is the first time such accuracy in the event generation is achieved for any collider process, and we study in detail the impact of different choices in the combination of QCD and EW corrections as well as …
We have developed a Monte Carlo event generator for non-resonant diphoton ($γγ$) production at hadron collisions in the framework of GR@PPA, which consistently includes additional one-jet production. The jet-matching method developed for initial-state jet production has been extended to the final state in order to regularize the final-state QED divergence in the $qg \rightarrow γγ+ q$ process. A QCD/QED-mixed parton shower (PS) has been developed to complete the matching. The PS has the capability of enforcing hard-photon radiation, and small-$Q^{2}$ photon radiations that are not covered by t…
We present a Monte-Carlo approach to prompt-photon production, where photons and QCD partons are treated democratically. The photon fragmentation function is modelled by an interleaved QCD+QED parton shower. This known technique is improved by including higher-order real-emission matrix elements. To this end, we extend a recently proposed algorithm for merging matrix elements and truncated parton showers. We exemplify the quality of the Monte-Carlo predictions by comparing them to measurements of the photon fragmentation function at LEP and to measurements of prompt photon and diphoton product…
We present a first principles study of chiral plasma instabilities and the onset of chiral turbulence in QED plasmas far from equilibrium. By performing classical-statistical lattice simulations of the microscopic theory, we show that the generation of strong helical magnetic fields from a helicity imbalance in the fermion sector proceeds via three distinct phases. During the initial linear instability regime the helicity imbalance of the fermion sector causes an exponential growth(damping) of magnetic field modes with right(left) handed polarization, for which we extract the characteristic gr…
We use an n-dimensional projection method to calculate helicity amplitudes for photon-photon scattering up to the two-loop level, for massless particles inside the loop. We confirm the recent standard model results found by Bern et al using another calculational method. We further apply the method to N=1 and N=2 supersymmetric QED. As predicted by the supersymmetric Ward identity, two of the independent amplitudes vanish. The remaining amplitude simplifies as the number of supersymmetries increases. For N=2 SUSY QED, only contributions of weight 4 remain.
A new version of the event generator BABAYAGA is presented, which is based on an original matching of the Parton Shower approach with the complete exact O(alpha) matrix element for the inclusion of the QED radiative corrections to the Bhabha process at flavour factories. The theoretical accuracy of the improved generator is conservatively estimated to be 0.2%, by comparison with independent calculations. The generator is a useful tool for precise luminosity determination at flavour factories, for center of mass energies below 10 GeV.
The PHOTOS Monte Carlo is often used for simulation of QED effects in decay of intermediate particles and resonances. Momenta are generated in such a way that samples of events cover the whole bremsstrahlung phase space. With the help of selection cuts, experimental acceptance can be then taken into account. The program is based on an exact multiphoton phase space. Crude matrix element is obtained by iteration of a universal multidimensional kernel. It ensures exact distribution in the soft photon region. Algorithm is compatible with exclusive exponentiation. To evaluate the program's precisio…
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED X QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize.
We show that, for both scalar and spinor QED, the two-loop Euler-Heisenberg effective Lagrangian for a constant Euclidean self-dual background has an extremely simple closed-form expression in terms of the digamma function. Moreover, the scalar and spinor QED effective Lagrangians are very similar to one another. These results are dramatic simplifications compared to the results for other backgrounds. We apply them to a calculation of the low energy limits of the two-loop massive N-photon `all +' helicity amplitudes. The simplicity of our results can be related to the connection between self-d…
We consider inelastic QED processes, the cross sections of which do not drop with increasing energy. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles m/E <= theta << 1, which yield the dominant contribution to their cross sections. A new effective method is presented to calculate the corresponding helicity amplitudes. Its basic idea consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices for real leptons. The obtained …
In conventional parton showers (including ones based on dipoles/antennae), a given $(\mathrm{Born}+m)$-parton configuration can typically be reached via ${\mathcal O}(m!)$ different "shower histories". In the context of matrix-element-correction and merging procedures, accounting for these histories mandates fairly complex and resource-intensive algorithms. A so far little-explored alternative in the shower context is to divide the branching phase spaces into distinct "sectors", each of which only receives contributions from a single branching kernel. This has a number of consequences includin…
We derive an explicit formula for the low energy limits of the one-loop, on-shell, massive N-photon amplitudes, for arbitrary N and all helicity assignments, in scalar and spinor QED. The two-loop corrections to the same amplitudes are obtained for up to the ten point case. All photon amplitudes with an odd number of `+' helicities are shown to vanish in this limit to all loop orders.
For scattering amplitudes in strong background fields, it is -- at least in principle -- possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds we consider this expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED and QCD. This enables us to obtain multicollinear limits of 1-loop vacuum amplitudes; the resulting helicity configurations are surprisingly restricted, with only the all-plus helicity amplitude surviving. These results are shown to be consistent with well-known vacuum amplitudes. We a…
We compute the leading probability for a gluon to flip helicity state upon traversing a background plane wave gauge field in pure Yang-Mills theory and QCD, with an arbitrary number of colours and flavours. This is a one-loop calculation in perturbative gauge theory around the gluonic plane wave background, which is treated without approximation (i.e., to all orders in the coupling). We introduce a background-dressed version of the spinor helicity formalism and use it to obtain simple formulae for the flip amplitude with pure external gluon polarizations. We also give in-depth examples for gau…
We present the first NLO QCD+EW predictions for Higgs boson production in association with a l nu or l+ l- pair plus zero or one jets at the LHC. Fixed-order NLO QCD+EW calculations are combined with a QCD+QED parton shower using the recently developed resonance-aware method in the POWHEG framework. Moreover, applying the improved MINLO technique to H l nu and H l+ l- production at NLO QCD+EW, we obtain predictions that are NLO accurate for observables with both zero or one resolved jet. This approach permits also to capture higher-order effects associated with the interplay of EW corrections …
The Helicity Structure Functions in the Drell-Yan process are discussed in a framework of Parton Reggeization Approach, which includes the transverse momentum of initial-state partons in a way compatible with QED gauge-invariance. Relationships with conventional Transverse Momentum Dependent Parton Model formalism are clarified.
