Electroweak Splitting Functions and High Energy Showering

Abstract

We derive the electroweak (EW) collinear splitting functions for the Standard Model, including the massive fermions, gauge bosons and the Higgs boson. We first present the splitting functions in the limit of unbroken SU(2)xU(1) and discuss their general features in the collinear and soft-collinear regimes. We then systematically incorporate EW symmetry breaking (EWSB), which leads to the emergence of additional "ultra-collinear" splitting phenomena and naive violations of the Goldstone-boson Equivalence Theorem. We suggest a particularly convenient choice of non-covariant gauge (dubbed "Goldstone Equivalence Gauge") that disentangles the effects of Goldstone bosons and gauge fields in the presence of EWSB, and allows trivial book-keeping of leading power corrections in the VEV. We implement a comprehensive, practical EW showering scheme based on these splitting functions using a Sudakov evolution formalism. Novel features in the implementation include a complete accounting of ultra-collinear effects, matching between shower and decay, kinematic back-reaction corrections in multi-stage showers, and mixed-state evolution of neutral bosons (gamma/Z/h) using density-matrices. We employ the EW showering formalism to study a number of important physical processes at O(1-10 TeV) energies. They include (a) electroweak partons in the initial state as the basis for vector-boson-fusion; (b) the emergence of "weak jets" such as those initiated by transverse gauge bosons, with individual splitting probabilities as large as O(30%); (c) EW showers initiated by top quarks, including Higgs bosons in the final state; (d) the occurrence of O(1) interference effects within EW showers involving the neutral bosons; and (e) EW corrections to new physics processes, as illustrated by production of a heavy vector boson (W') and the subsequent showering of its decay products.

67 pages, 12 figures; v2, published in JHEP, some expanded discussions and other minor revisions

References in corpus (25)

• PYTHIA 6.4 Physics and Manual
• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Event generation with SHERPA 1.1
• Herwig++ Physics and Manual
• Weak Corrections are Relevant for Dark Matter Indirect Detection
• Physics Opportunities of a 100 TeV Proton-Proton Collider
• The Bulk RS KK-gluon at the LHC
• Parton showers with quantum interference
• Top pair invariant mass distribution: a window on new physics
• Heavy Majorana Neutrinos from $W\gamma$ Fusion at Hadron Colliders
• Electroweak corrections to hadronic production of W bosons at large transverse momenta
• Electroweak Sudakov Corrections using Effective Field Theory
• Weak Boson Emission in Hadron Collider Processes
• Heavy Dark Matter Annihilation from Effective Field Theory
• Soft Collinear Effective Theory for Heavy WIMP Annihilation
• The "Top Priority" at the LHC
• Electroweak corrections to large transverse momentum production of W bosons at the LHC
• Weak corrections to four-parton processes
• Top-Quark Initiated Processes at High-Energy Hadron Colliders
• Electroweak Sudakov Logarithms and Real Gauge-Boson Radiation in the TeV Region
• Non-cancellation of electroweak logarithms in high-energy scattering
• Semi-Inclusive Wino and Higgsino Annihilation to LL'
• Electroweak corrections to W-boson hadroproduction at finite transverse momentum
• Unbroken $SU(2)$ at a 100 TeV collider
• Resummation of electroweak Sudakov logarithms for real radiation

Cited by in corpus (70)

• The Structure of the Proton in the LHC Precision Era
• Electroweak Radiative Corrections for Collider Physics
• Identification of heavy, energetic, hadronically decaying particles using machine-learning techniques
• Direct Detection of Hawking Radiation from Asteroid-Mass Primordial Black Holes
• High Energy Leptonic Collisions and Electroweak Parton Distribution Functions
• Vector boson fusion at multi-TeV muon colliders
• A quantum algorithm for high energy physics simulations
• Friction pressure on relativistic bubble walls
• Fusing Vectors into Scalars at High Energy Lepton Colliders
• Heavy Neutrinos with Dynamic Jet Vetoes: Multilepton Searches at $\sqrt{s}=14,27,$ and $100$ TeV
• Event Generators for High-Energy Physics Experiments
• Quark and Gluon Contents of a Lepton at High Energies
• Hazma: A Python Toolkit for Studying Indirect Detection of Sub-GeV Dark Matter
• The Effective Vector Boson Approximation in High-Energy Muon Collisions
• Automated Predictions from Polarized Matrix Elements
• Resummed Photon Spectra for WIMP Annihilation
• Heavy Neutral Leptons at Muon Colliders
• LePDF: Standard Model PDFs for High-Energy Lepton Colliders
• Electroweak Logarithms in Inclusive Cross Sections
• Learning from Radiation at a Very High Energy Lepton Collider
• Probing New Gauge Forces with a High-Energy Muon Beam Dump
• Vector Boson Scattering Processes: Status and Prospects
• New Physics in $b\to s\mu \mu$: FCC-hh or a Muon Collider?
• One-loop electroweak Sudakov logarithms: a revisitation and automation
• Standard Model Fragmentation Functions at Very High Energies
• Collinear Electroweak Radiation in Antenna Parton Showers
• Polarization Effects in Standard Model Parton Distributions at Very High Energies
• Hunting for Dark Matter and New Physics with GECCO
• Complementary Signals of Lepton Flavor Violation at a High-Energy Muon Collider
• Cosmological Constraints on Dark Scalar
• Goldstone Equivalence and High Energy Electroweak Physics
• Combining initial-state resummation with fixed-order calculations of electroweak corrections
• Multi Higgs production via photon fusion at future multi-TeV muon colliders
• Determining the spin of light primordial black holes with Hawking radiation
• Implementation of Angularly Ordered Electroweak Parton Shower in Herwig 7
• Future Constraints on Primordial Black Holes from XGIS-THESEUS
• Examining the origin of dark matter mass at colliders
• Measurement of Higgs boson self-couplings through $2\to 3$ vector bosons scattering in future muon colliders
• The Muon Smasher's Guide
• QED and QCD helicity amplitudes in parton-shower gauge
• The leptonic di-flavor and di-number violation processes at high energy ${\mu }^{\pm }{\mu }^{\pm }$ colliders
• Z' boson mass reach and model discrimination at muon colliders
• Measuring Higgs Boson Self-couplings with $2\to 3$ VBS Processes
• Pion pair production in $e^{+}{e}^{-}$ annihilation at next-to-leading order matched to Parton Shower
• Electroweak Restoration at the LHC and Beyond: The $Vh$ Channel
• Probing Higgs-muon interactions at a multi-TeV muon collider
• Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories
• Decays of Long-Lived Relics and Their Signatures at IceCube
• $1\leftrightarrow 2$ Processes of a Sterile Neutrino Around Electroweak Scale in the Thermal Plasma
• Probing the Inert Doublet Model via Vector-Boson Fusion at a Muon Collider
• Factorization of Standard Model cross sections at ultra high energy
• Electroweak Scattering at the Muon Shot
• Higgs boson production at ${\mu }^{+}{\mu }^{+}$ colliders
• Matching in $pp\to t\bar{t}W/Z/h+$ jet SMEFT studies
• Precision phenomenology at multi-TeV muon colliders
• Hawking Radiation of Nonrelativistic Scalars: Applications to Pion and Axion Production
• Structures of the Massive Vector Boson Propagators at Finite Temperature Illuminated by the Goldstone Equivalence Gauge
• Top-Tagging at the Energy Frontier
• Radiative return at NLOPS accuracy
• Light Dark Matter Showering under Broken Dark $U(1)$ -- Revisited
• Towards a Fully Automated Differential ${\text{NNLO}}_{\text{EW}}$ Generator for Lepton Colliders
• Hard processes in multi-TeV ion collisions
• Investigating the collinear splitting effects of boosted dark matter at neutrino detectors
• Primordial black holes in Randall-Sundrum: Cosmological signatures
• Physics Beyond the Standard Model with BlackHawk v2.0
• Polarization and kinematic properties of the splitting functions $q\to W^{\pm }+q^{\prime }$ and $q\to Z^0+q$
• ${\mu }^{-}{\mu }^{+}\to {\nu }_{\mu }{\bar{\nu }}_{\mu }t\bar{t}H$ amplitudes in the Feynman-diagram gauge
• Multi-scalar signature of self-interacting dark matter in the NMSSM and beyond
• Coloring mixed QCD/QED evolution
• Weak bosons as partons below 10 TeV partonic center-of-momentum