The Effective Vector Boson Approximation in High-Energy Muon Collisions

Abstract

Due to the inclination for forward gauge radiation, lepton colliders beyond a few TeV are effectively electroweak (EW) boson colliders, suggesting the treatment of EW bosons as constituents of high-energy leptons. In the context of a muon collider, we revisit the validity of W and Z parton distribution functions (PDFs) at leading order in 2 → n process. We systematically investigate universal and quasi-universal power-law and logarithmic corrections that arise when deriving (polarized) weak boson PDFs in the collinear limit. We go on to survey a multitude of 2 → n processes at √ s = 2 − 30 TeV via polarized and unpolarized EW boson fusion/scattering. To conduct this study, we report a public implementation of the Effective W/Z and Weizsäcker-Williams Approximations, which we collectively call the Effective Vector Boson Approximation, into the Monte Carlo event generator MadGraph5_aMC@NLO. This implementation lays the groundwork for developing matrix-element matching prescriptions involving EW parton showers and renormalized EW PDFs. To further with this agenda, we give recommendations on using W/Z PDFs.

(New) Physics at a multi-TeV $\mu$ Collider

“…Orange, green and blue line correspond to m H = 125, 300, 700 GeV respectively. The accordance between the full ME computation and the EVA approximation is clearly better for m H > ∼ 300 GeV [5]. Figure 2 (b) shows the cross-section as function of √ s for the various processes…”

“…One of the main feature of this plot is the clear hierarchy of the cross sections and the fact that σ t tt tQCD+EW > ∼ σ t tt tEW , i.e. the cross-section of four tops involving only colorless intermediate states (σ t tt tEW ) is slightly lower than the corresponding process where also gluons are involved (σ t tt tQCD+EW ) [5].…”

“…In this section, we summarize the Effective Vector Boson Approximation (EVA) and its use in evaluating scattering cross sections in many-TeV µ + µ − collisions, in the framework of the Monte Carlo generator M G 5_ MC@NLO [3][4][5]. We focus on muons but the EVA is, in principal, applicable to other colliders.…”

Complementary Signals of Lepton Flavor Violation at a High-Energy Muon Collider

“…Because the colliding objects are second-generation fermions themselves, muon colliders have a particular aptitude for testing physics with generation-specific couplings [37][38][39][40][41][42][43][44][45][46][47][48][49]. Finally, high-energy muons have a large probability to radiate collinear gauge bosons in their collisions [3,[50][51][52][53], and can thus act efficiently as "vector boson colliders", with large rates for VBF processes that can be used both to search for new physics [54][55][56][57][58][59][60][61][62] and to make precision measurements of the electroweak sector [63][64][65][66][67][68][69][70][71][72]. That the muons are color-neutral, and produce far fewer hadronic backgrounds, makes them particularly well-suited for this purpose.…”

Probing New Gauge Forces with a High-Energy Muon Beam Dump

“…Such a muon collider (µC) is a particularly compelling option as it affords a complementary physics program to that of a high-energy hadron collider like the LHC. For example, with a µC we gain access to direct couplings of both electroweak-mediated and secondgeneration processes [7][8][9][10][11][12][13][14][15][16][17]. Additionally, with increased available center-of-mass energy, we can expand our discovery prospects for massive new physics.…”