未来强子对撞机的高能探索：亮度需求与NP影响

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大规模扩展未来强子对撞机（Future Hadron Colliders, FHCs）的研究旨在探索高能量物理现象，特别是那些超出大型强子对撞机（Large Hadron Collider, LHC）现有能力的新物理（New Physics, NP）。当前的挑战在于，随着质心能量（center-of-mass energy, √s）的提升，为了保持对率限制的NP探测效率（M/√s）不变，所需的综合光度（integrated luminosity）必须按指数级增长，即所谓的"天真缩放"限制。例如，从14 TeV LHC升级到100 TeV的FHC，所需要的光度理论上应增加约50倍，这在实验设计、能源消耗、技术挑战以及财务投入等方面都构成巨大压力。论文作者Thomas G. Rizzo指出，这种光度的增长并非完全按照简单的线性或平方关系，而是受到两个关键因素的影响：一是部分子密度函数（Parton Density Functions, PDFs）的演化，它是描述强子内部结构的基本工具，其变化会改变碰撞事件的概率分布；二是强相互作用的色因子（strong coupling constant, αs）的运行，它决定了粒子之间的相互作用强度。这些效应导致实际的光度需求超过简单线性缩放预期。维持固定NP相对质量范围（即M/√s）的相对亮度增长比例依赖于所考虑的具体NP模型特性。研究者通过构建几种可能的NP场景作为基准示例，探讨了不同的光度需求。如果达不到这些光度目标，将直接影响对新物理的探索能力，可能限制某些信号的检测敏感性，甚至可能导致某些现象难以被观测到。总结来说，大规模扩展FHC是一项复杂的任务，不仅需要突破技术难题，还要精确控制与PDF演化和αs运行相关的物理效应，以确保能有效地揭示超越LHC能量范围的新物理现象。未来的研究和设计工作必须充分考虑这些因素，以优化资源分配和提高发现未知物理的可能性。

Eur. Phys. J. C (2015) 75:161

DOI 10.1140/epjc/s10052-015-3381-1

Regular Article - Theoretical Physics

Mass reach scaling for future hadron colliders

Thomas G. Rizzo

SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA

Received: 29 January 2015 / Accepted: 31 March 2015 / Published online: 24 April 2015

Abstract The primary goal of any future hadron collider

is to discover new physics (NP) associated with a high mass

scale, M, beyond the range of the LHC. In order to maintain

the same relative mass reach for rate-limited NP, M/

√

s,as

√

s increases, Richter recently reminded us that the required

integrated luminosity obtainable at future hadron colliders

(FHC) must grow rapidly, ∼s, in the limit of naive scaling.

This would imply, e.g., a ∼50-fold increase in the required

integrated luminosity when going from the 14 TeV LHC to a

FHC with

√

s = 100 TeV, an increase that would prove quite

challenging on many different fronts. In this paper we point

out, due to the scaling violations associated with the evolu-

tion of the parton density functions (PDFs) and the running

of the strong coupling, α

, that the actual luminosity neces-

sary in order to maintain any ﬁxed value of the relative mass

reach is somewhat greater than this scaling result indicates.

However, the actual values of the required luminosity scal-

ing are found to be dependent upon the detailed nature of the

NP being considered. Here we elucidate this point explicitly

by employing several speciﬁc benchmark examples of pos-

sible NP scenarios and brieﬂy discuss the (relatively weak)

search impact in each case if these luminosity goals are not

met.

1 Introduction and background

There is rising interest in the physics potential of a future

higher energy hadron collider which might begin running

sometime after the high luminosity LHC program is com-

pleted. Such a machine, here generically termed the FHC,

has been discussed in various manifestations at a growing

e-mail: rizzo@slac.stanford.edu

number of workshops.

but generally is expected to oper-

ateinthe

√

s ∼ 100 TeV energy range. The goal of such

a machine will be to explore the unknown, i.e., to search

for new physics (NP), both beyond the standard model (SM)

and beyond the reach of the LHC, that might be kinemati-

cally accessible at these higher collision energies. As such,

its NP search capabilities should be as strong as possible,

and in particular be at least as powerful as those we expect

to be available at the 14 TeV LHC. This NP may take several

forms: it may be relatively light but very weakly coupled to

the SM so that the increased cross sections at a higher energy

collider will allow access. More commonly, we imagine this

NP to manifest as some new, very heavy state(s), simply too

massive to be produced at the 14 TeV LHC; this is the case

we will consider below.

Searches for NP can be quite complex, generally involv-

ing sophisticated experimental analyses in order to extract a

signiﬁcant signal above some SM background. This makes

quantifying the power of a future collider difﬁcult without

a detailed study of a wide range of potential NP physics

scenarios. Depending on what kind of NP one is interested

in various possibilities come to mind. Here, as said above,

we are essentially only interested in NP which is quite heavy.

Perhaps in this case a crude but simple measure of this poten-

tial discovery power is obtainable by employing the value of

the relative mass reach in the case of a rate-limited signal for

associated with a heavy mass scale M, i.e., the value

of the mass reach scaled to the collision energy, M/

√

s.For

example, this would mean that if a new 3.5 TeV state is dis-

See, for example, the several long-term studies and associated

conferences and workshops that have been recently started in both

Europe and China: CERN SFCC Study: https://espace2013.cern.ch/

fcc/Pages/default.aspx, Chinese Study on CEPC-SppC: http://cfhep.

ihep.ac.cn/. There have also been workshops in the US in 2014

on such higher energy hadron colliders, e.g.,: https://indico.fnal.

gov/conferenceDisplay.py?confId=7633 and https://indico.fnal.gov/

conferenceOtherViews.py?view=standard&confId=7864.

In the case of a background-limited signal the required luminosity

would need to grow signiﬁcantly faster with the collision energy ∼s

123

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