Snowmass Theory Frontier Eﬀective Field Theory Topical Group Summary October 10 2022

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Snowmass Theory Frontier

Eﬀective Field Theory Topical Group Summary

October 10, 2022

Matthew Baumgart, Fady Bishara, Tomas Brauner, Joachim Brod, Giovanni Cabass, Timothy

Cohen, Nathaniel Craig, Claudia de Rham, Patrick Draper∗, A. Liam Fitzpatrick, Martin

Gorbahn, Sean Hartnoll, Mikhail Ivanov, Pavel Kovtun, Sandipan Kundu, Matthew Lewandowski,

Hong Liu, Xiaochuan Lu, Mark Mezei, Mehrdad Mirbabayi, Ulserik Moldanazarova, Alberto

Nicolis, Riccardo Penco, Walter Goldberger, Matthew Reece, Nicholas L. Rodd, Ira Rothstein†,

Shu-Heng Shao, Will Shepherd, Marko Simonovic, Mikhail Solon, Dam Thanh Son, Robert

Szafron, Andrew Tolley, Zhengkang Zhang, Shuang-Yong Zhou, Jure Zupan

∗pdraper@illinois.edu, †izr@andrew.cmu.edu

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2021)

arXiv:2210.03199v1 [hep-ph] 6 Oct 2022

I. Introduction and Executive Summary

Quantum ﬁeld theory is the fundamental mathematical structure describing the world. Not sur-

prisingly, its power and generality leads to overwhelming mathematical challenges in its application

to the real world, i.e., in non-idealized situations. A primary source of complexity arises from the

fact that typical physical systems depend upon physics arising from hierarchically distinct length

scales. However, given the local nature of physical laws, we may disentangle these scales in a way

that reduce the computational complexity for any given prediction. This procedure involves ﬁnding

the proper action to capture the physics at a particular length scale. These actions are constrained

by the symmetry breaking pattern which ﬁxes the number of unknown parameters that either need

to be ﬁt from experiment or calculated using the knowledge of the short distance theory. Finding a

systematic expansion within which to design these actions is the art of eﬀective ﬁeld theory (EFT).

EFTs were ﬁrst utilized in a modern sense in describing pion physics and later the weak inter-

actions, though much of the physical insight, including the use of the renormalization group, came

from the realm of critical phenomena. While the EFT approach may be said to have been champi-

oned by the HEP community, it is has been utilized to great success in many ﬁelds and sub-ﬁelds of

physics, as described in various contributions to these proceedings. Here we summarize the recent

process and future opportunities reviewed in detail in the whitepapers [1–8].

Dark matter detection relies on EFTs for both direct and indirect measurements in various

contexts, including systematizing the low energy interactions with nuclei and re-summing large logs

in cosmic annihilation processes [3]. In cosmology, EFTs have been utilized to great success to

study Large Scale Structure (LSS) and inﬂation [1]. In particular, EFT calculations have led to

state-of-the-art predictions for cosmological parameters from the LSS data that compete with those

from the cosmic microwave background. In models of inﬂation, EFT techniques have been used to

place novel bounds on non-Gaussianities.

The ubiquitous nature of EFTs has lead to inter-disciplinary cross pollination. Condensed

Matter Physics (CMT) is another natural setting for EFT methods, where they has been utilized to

shed light on various systems, including out of equilibrium phenomena, hydrodynamics, and (non)

Fermi liquids [7]. Recently there has been a strong inter-disciplinary movement leveraging EFTs to

understand new exotic states of matter called “fractons." EFTs have also played an important role

in the nascent ﬁeld of gravitational wave astronomy, with the development of an EFT to predict

the signatures of binary inspirals [8]. Scattering amplitudes techniques can be used within this

EFT to streamline-higher order calculations, much like in the case of QCD, and using these ideas,

state-of-the-art calculations have been performed by people within the HEP community. Given the

relative newness of this ﬁeld and the wealth of new data, EFTs will play an important role in future

theoretical eﬀorts.

EFTs also continue to play a central role in accelerator physics. Soft-Collinear Eﬀective Theory

(SCET) has greatly improved our understand of factorization in high energy scattering, which

is a necessary ingredient for any theoretical prediction in order to disentangle the physics of the

proton from the high energy scattering process of interest. Moreover, SCET is utilized to sum large

logarithms which lead to poorly-behaved perturbative series. Its value has lead SCET to become

its own sub-ﬁeld, with dedicated yearly conferences.

At the LHC, a core component of the search for new physics involves treating the Standard Model

as an eﬀective theory (SMEFT) and looking for signatures associated with its higher dimensional

operators. There has been considerable progress in constraining the values of the Wilson coeﬃcients

which capture the unknown UV physics of interest and systematizing calculational procedures [5,6].

The SMEFT formalism will continue to be a staple of experimental analyses.

The examples above highlight the critical role of EFTs in the direct comparison of theory with

observation across a huge range of physical systems. Thinking critically about the self-consistency of

our EFT descriptions of nature has also played an essential role in establishing the “big" questions

that physics should seek to answer. The major naturalness puzzles – the electroweak hierarchy

problem, the strong CP problem, and the cosmological constant problem – are strongly suggestive

of new dynamics and principles, and they continue to drive creative new theoretical approaches and

experimental designs in tandem [4]. At the same time, more formal studies of EFT have resulted

in new methods to constrain consistent low energy theories [2,9], exploiting basic principles both of

QFT and of quantum gravity. These approaches have lead to testable predictions about the possible

forms new physics can take.

EFTs have become an essential tool in many areas of physics and are continually being developed.

Given that the scientiﬁc output of any experiment is bounded by the accuracy of the theoretical

predictions, it is not an understatement to say that EFTs play a vital role in any scientiﬁc program.

The HEP community has leaned heavily on this formalism and the need for further developments

in this ﬁeld is driven by experimental exigencies. Meanwhile more formal EFT research continues

to provide new tools for attacking some of the deepest questions in the ﬁeld.

II. Dark Matter

It is diﬃcult to overstate the scientiﬁc importance of the dark matter problem. This is evidenced

by the tremendous amount of resources presently being focussed to ﬁnd the solution. The list of

experiments, both large and small, dedicated to this problem is an increasing function of time. The

reason for the challenging nature of DM detection is not diﬃcult to discern given its name. The

design of an appropriate experiment involves some speculation as to the dark matter abundance

and interaction rate, and this relies heavily on the theoretical input which quantiﬁes the reach of

an experiment in the space of DM parameters.

EFT has played in increasingly important role in both direct and indirect dark matter detec-

tion [3]. In case of the former, for heavy DM candidates (MMW), the cross section for DM

to interact with nuclei can be described a heavy particle eﬀective theory which is derivative of the

heavy-quark eﬀective theory (HQET). In the heavy mass limit spin-independent WIMP-nucleon

scattering cross sections become universal for given WIMP electroweak quantum numbers. More-

over, the EFT analysis revealed that the generic amplitude involved cancellations which suppress

the cross section orders of magnitude below naive estimates. Furthermore, working within the EFT,

one is able to systematically include the eﬀects of QCD corrections. When the mediator mass is

larger than the momentum exchanges one can then write down as set of operators where by the DM

has contact interactions with nucleons, leading to a reduced operator basis which can be scanned

by experiment.

The nature of the relevant EFT changes when considering indirect detection, as now the physics

involves a semi-inclusive annihilation process. If the DM is charged under SU(2)L⊗U(1)Y(or

another force with light mediators), then it is subject to a long-range potential (when MDM mW)

which can boost its annihilation rate via a so-called “Sommerfeld enhancement". Moreover, when

calculating the gamma ray spectrum from annihilation, the hierarchy of scales leads to large (double)

logarithms that may necessitate resummation. Thus the EFT in this case is richer as it must be

able to systematically describe both the Coulombic infra-red singularities as well as the soft and

collinear singularities which arise due to gauge boson emission. Since the DM velocity is smaller for

the signal events then in the early universe freeze-out, Coulombic corrections are more enhanced in

the former case.

To resum the Coulombically enhanced terms, which form a power series in the ratio mDM /mW,

one may lean upon NRQCD (Non-Relativistic QCD), the EFT developed to describe quarkonia in

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SnowmassTheoryFrontierEectiveFieldTheoryTopicalGroupSummaryOctober10,2022MatthewBaumgart,FadyBishara,TomasBrauner,JoachimBrod,GiovanniCabass,TimothyCohen,NathanielCraig,ClaudiadeRham,PatrickDraper,A.LiamFitzpatrick,MartinGorbahn,SeanHartnoll,MikhailIvanov,PavelKovtun,SandipanKundu,MatthewLewandows...

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Snowmass Theory Frontier Eﬀective Field Theory Topical Group Summary October 10 2022

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