Richness out of smallness a Possible Staged Blueprint on Future Colliders Meng Lu1Qiang Li2yZhengyun You1zand Ce Zhang2x 1. School of Physics Sun Yat-Sen University Guangzhou 510275 China and

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Richness out of smallness: a Possible Staged Blueprint on Future Colliders

Meng Lu∗1,∗Qiang Li∗2,†Zhengyun You1,‡and Ce Zhang2§

1. School of Physics, Sun Yat-Sen University, Guangzhou 510275, China and

2. State Key Laboratory of Nuclear Physics and Technology,

School of Physics, Peking University, Beijing, 100871, China

Novel collision methods and rich phenomena are crucial to keeping high-energy collision physics

more robust and attractive. In this document, we present a staged blueprint for future high-energy

colliders: from neutrino-neutrino collision, neutrino-lepton collision to electron-muon and muon-

muon collisions. Neutrino beam from TeV scale muons is a good candidate to enrich high-energy

collision programs and can serve as a practical step toward a high-energy muon collider, which

still requires tens of years of R&D. Neutrinos-neutrinos collision provides a promising way to probe

heavy Majorana neutrinos and eﬀective neutrino mass; neutrino and antineutrino annihilation into

Z boson has a huge cross-section at 10K pb level; leptons-neutrinos collision beneﬁts W boson mass

precision measurements. With only a minimal amount of integrated luminosity, one can envision

the “Richness out of smallness”. This document summarizes the current status and the roadmap

towards the muon-muon collider with less challenging techniques required through intermediate

facilities, where a wide variety of physics goals could be achieved. A (preparatory) laboratory on

novel colliders could attract vast international interests and collaborations.

I. INTRODUCTION

The discovery of the Higgs boson at the LHC in 2012 [1] symbolizes that particle physics is entering a key period.

On one hand, direct searches for new physics beyond the Standard Model (BSM, such as supersymmetry and extra

dimensions) through the Higgs portal receive intense attention. On the other hand, rich progress has been made

on heavy ﬂavor and electroweak measurements from the LHC and other experiments, which deepens the scope of

precision tests on the SM, and stimulates indirect searches for BSM with the eﬀective ﬁeld method in a bottom-up

approach [2].

Recent years have witnessed several signiﬁcant anomalies or hints of possible new physics BSM. First, the LHCb

Collaboration, in a test of lepton ﬂavor universality using B→Kll, reports a measurement that deviates by 3.1 standard

deviations from the SM prediction [14]. Second, the latest result from the Muon g−2 Experiment at Fermilab has

pushed the world average of the muon anomalous magnetic moment measurements to 4.2 standard deviations away

from the SM prediction [15]. Most recently, the CDF II collaboration has reported a measurement of the W gauge

boson mass [18], MCDF

W= 80.433 ±0.009 GeV, which is 7.2 standard deviations away from the SM prediction of

MSM

W= 80.357 ±0.006 GeV [19]. Numerous theoretical studies attempt to accommodate these anomalies, which may

or may not require a modiﬁcation of the SM.

In the next stage, the LHC will enter the HL-LHC phase after 2025-2027 [3–5], and will collect in total around 3000

fb−1of data in a period of 10 years, which can help deepen our understanding of fundamental physics. In addition,

HEP communities have had intense discussions on the target and strategy for future colliders (see e.g. [6, 7]). Various

options include, electron-positron collider at the collision energy from 250 GeV to 3 TeV [8–12], hadron collider at

100 TeV scale, and TeV scale muon colliders [13], etc. These future colliders are aiming at precision measurement

of Higgs properties and searching for new physics at higher energy scales. The International Linear Collider (ILC)

costs around 10B dollars; the 100 km double-ring circular electron-positron collider (CEPC) and the Future Circular

Collider (FCC) cost less but are space-consuming due to energy loss from synchrotron radiation.

Muons suﬀer less synchrotron energy loss by 8 orders of magnitude than electrons and positrons, which leads to the

fact that a TeV scale muon collider can be kept as small as O(km) in circumference. muon collider has a much cleaner

environment and larger eﬀective center of mass energy with respect to the collision energy than the hadron collider.

It is also sensitive directly to muon-related new physics. Recently, due to the LHCb lepton ﬂavor universality and

Fermilab muon g−2 anomalies, interest in muon colliders has revived [16].

It is generally believed that a muon collider still needs decades of research and challenging development, especially,

on how to achieve high quality (intensity and emittance) beam and mitigate the beam-induced background (BIB)

∗meng.lu@cern.ch

†qliphy0@pku.edu.cn

‡youzhy5@mail.sysu.edu.cn

§ce.zhang@pku.edu.cn

arXiv:2210.06690v1 [hep-ph] 13 Oct 2022

eﬀects from muon decays. Muon beams are usually achieved in proton or positron interactions on target, which have

both pros and cons on beam cooling or intensity. BIB is crucial in the physics program at a muon collider [17], for

which usually a nozzle or a timing detector is introduced to mitigate such eﬀect.

TeV scale muon beams emit bunches of collimated decay products and thus can provide neutrino beams, which

have a great potential for application in high-energy collision programs. With only a small amount of integrated

luminosity, interesting phenomena from neutrino collisions can be observed towards the “Richness out of smallness”.

For example, neutrino and antineutrino annihilate into Z boson with a huge cross-section at 10K pb level. It also opens

doors to many new topics, such as searching for resonances that decay into neutrinos. One can also collide neutrinos

with neutrinos to probe heavy Majorana neutrinos (HMN) and eﬀective neutrino mass. Furthermore, leptons and

neutrinos can collide into W bosons, which can be also observed with a very small amount of integrated luminosity

and beneﬁt W boson mass precision measurements.

Through all these stages, a rich variety of physics goals could be achieved, and may also be useful intermediate

steps as the study of the challenging technologies towards the muon-muon collider by the energy frontier community.

Section II elaborates the physics potentials of these collision schemes. Technical considerations are presented in

Section III. Status and prospects are presented in Section IV. The work is summarized in Section V.

II. PHYSICS POTENTIALS

Neutrinos are among the most abundant and least understood of all particles in the SM that make up our uni-

verse. Observation of neutrino oscillations conﬁrms that at least two types of SM neutrinos have a tiny, but strictly

nonzero, mass. The upper limits on each neutrino mass come from many experiments including cosmology and direct

measurements [19]. For example, the Karlsruhe Tritium Neutrino (KATRIN) experiment [20] ﬁnds an upper limit

m˜νe<0.8 eV at the 90% C.L. for the electron anti-neutrino ˜νe. On the other hand, the direct mass limit on electron

neutrinos and muon neutrinos are relatively much looser [19]. The simplest formalism in which neutrino masses can

arise is through a dimension-5 operator as shown by Weinberg [21], which extends the SM Lagrangian with

L5=C``0

5/ΛΦ·Lc

`L`0·Φ,(1)

where `, `0are the ﬂavors of the leptons, which can be electrons, muons or taus; Λ is the relevant new physics scale;

C``0

5is a ﬂavor-dependent Wilson coeﬃcient; LT

`= (ν`, `) is the left-handed lepton doublet; and Φ is the SM Higgs

doublet with a vacuum expectation value v=√2hΦi ≈ 246 GeV. The Weinberg operator generates the Majorana

neutrino masses as m`` =C``

5v2/Λ = 

PiU2

`imi

, and introduces lepton number violation (LNV).

The ultraviolet (UV) completion of the Weinberg operator can be realised in the context of “see-saw” models [22],

assuming the existence of hypothetical heavy states, for example the HMN in the type-I seesaw model. Searches for

neutrinoless double beta decay in the decays of heavy nuclei have placed strong limit, i.e., m`` <0.08 −0.18 eV at

the 90% C.L. [23].

The physics potential of novel collider schemes is elaborated in a step-by-step manner. We start with using a TeV

scale µ+→e+νe˜νµbeam. Fig. 1 shows the energy distributions of muon decay products from a muon beam with

energy at 1 TeV and 200 GeV. As the decay angle θgoes like θ∼10−4/E(TeV), the muon decay products will be

more collimated with increasing beam energy [24, 25]. With TeV scale µ+→e+νe˜νµand µ−→e−˜νeνµbeams from

two sides, there appears the collisions

νe˜νe→Z→µ+µ−.(2)

Relevant Feynman diagrams for neutrino antineutrino annihilation into Z and SM-like Z’ boson are shown as in

Fig. 2.

To simulate these processes, we implemented the neutrino energy fraction function [24] from 200 GeV muon decay

in MadGraph5 aMC@NLO [26]. The cross section reads 320 pb after requiring the ﬁnal state muon to satisfy

pT>20 GeV and |η|<3.0. As for the same process but with hadronic Z decay, the cross section will be around

5200 pb. Such large cross section can compensate for the luminosity limitation. For example, with a tiny integrated

luminosity of about 10−5fb−1, one can already expect to observe direct neutrino collisions through process. 2 and

further can probe the Zν¯νcouplings [27], or search for possible ν¯νresonance. Figure. 3 shows the outgoing muon

energy distributions for neutrino antineutrino annihilation into Z and SM-like Z’ bosons, with Z’ mass set as 150 GeV

and narrow width.

On the other hand, we can also consider neutrino neutrino collision, which is speciﬁcally sensitive to the Weinberg

operator and Majorana neutrino mass. With 1 TeV µ+→e+νe˜νµbeams from two sides, some of the main physics

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Richnessoutofsmallness:aPossibleStagedBlueprintonFutureCollidersMengLu1,QiangLi2,yZhengyunYou1,zandCeZhang2x1.SchoolofPhysics,SunYat-SenUniversity,Guangzhou510275,Chinaand2.StateKeyLaboratoryofNuclearPhysicsandTechnology,SchoolofPhysics,PekingUniversity,Beijing,100871,ChinaNovelcollisionmethodsan...

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Richness out of smallness a Possible Staged Blueprint on Future Colliders Meng Lu1Qiang Li2yZhengyun You1zand Ce Zhang2x 1. School of Physics Sun Yat-Sen University Guangzhou 510275 China and

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