# New Horizons in Quantum Field Theory, Particle Physics and String Phenomenology

Lead Research Organisation:
University of Liverpool

Department Name: Mathematical Sciences

### Abstract

Theoretical investigations of the Standard Model have underpinned experimental discoveries and have been instrumental in shaping our current knowledge of the nature of matter and its interactions. At a time when the standard model (SM) has finally been completed by the discovery of the Higgs boson, deep and profound mysteries remain in our understanding of the Universe. The existence of dark matter necessitates new physics beyond the SM, and crucial issues concerning dark energy and the unification of gravity with the other forces remain unaddressed. Meanwhile, the mathematical structures that underlie quantum field theory are far from fully explored; and there are important open questions about the dynamics of matter within the SM, especially in extreme environments.

The Theoretical Physics group in Liverpool is contributing to searches for New Physics from three complementary directions. (i) We carry out perturbative calculations within the standard model to an unprecedented precision. This is essential if deviations of observables from their SM predictions, occurring due to new physics, are to be detected in accelerator experiments. Concurrently, we are using our theoretical expertise to explore promising extensions of the Standard Model and to inform the development of experiments that are well placed to discover new physics. (ii) These efforts are complemented by large scale computer based calculations. This non-perturbative approach is essential for unlocking certain inputs for standard model theory predictions, which are beyond the reach of perturbation theory. The current lack of precision in these inputs limits the usefulness of experimental observations. Our simulations are state-of-the-art and are now including electro-magnetic corrections (QED) to the theory of strong interactions QCD. (iii) We determine the fingerprints that Beyond the Standard Model (BSM) physics could produce in experimental data and observations. Such work includes the use of astrophysical and cosmological data, e.g. from dark energy surveys and gravitational waves, and it leads to constraints that complement laboratory based searches. This is accompanied by rigorous studies in string theory. In addition to progressing towards an understanding of quantum gravity, our work in this direction informs and inspires BSM model building.

We also explore terra incognita within the Standard Model itself: we will study the phases of strongly interacting matter in particular at finite densities, and we will embark on the study of real-time dynamics in quantum field theory using first principle computer simulations. A key challenge is to understand how quarks and gluons form hadrons, the basic building blocks of matter. The standard explanation for forming hadrons out of a heavy ion collision fireball invokes a local thermal equilibrium, which might or might not be justified. A distinctive alternative to explain observations is a genuine quantum effect called entanglement, which we will endeavour to explore.

The Theoretical Physics group in Liverpool is contributing to searches for New Physics from three complementary directions. (i) We carry out perturbative calculations within the standard model to an unprecedented precision. This is essential if deviations of observables from their SM predictions, occurring due to new physics, are to be detected in accelerator experiments. Concurrently, we are using our theoretical expertise to explore promising extensions of the Standard Model and to inform the development of experiments that are well placed to discover new physics. (ii) These efforts are complemented by large scale computer based calculations. This non-perturbative approach is essential for unlocking certain inputs for standard model theory predictions, which are beyond the reach of perturbation theory. The current lack of precision in these inputs limits the usefulness of experimental observations. Our simulations are state-of-the-art and are now including electro-magnetic corrections (QED) to the theory of strong interactions QCD. (iii) We determine the fingerprints that Beyond the Standard Model (BSM) physics could produce in experimental data and observations. Such work includes the use of astrophysical and cosmological data, e.g. from dark energy surveys and gravitational waves, and it leads to constraints that complement laboratory based searches. This is accompanied by rigorous studies in string theory. In addition to progressing towards an understanding of quantum gravity, our work in this direction informs and inspires BSM model building.

We also explore terra incognita within the Standard Model itself: we will study the phases of strongly interacting matter in particular at finite densities, and we will embark on the study of real-time dynamics in quantum field theory using first principle computer simulations. A key challenge is to understand how quarks and gluons form hadrons, the basic building blocks of matter. The standard explanation for forming hadrons out of a heavy ion collision fireball invokes a local thermal equilibrium, which might or might not be justified. A distinctive alternative to explain observations is a genuine quantum effect called entanglement, which we will endeavour to explore.

### Planned Impact

Here, we discuss our Impact activities in the reporting period, complementing our

Pathways to Impact document, which summarises our strategy and approach to generating non-academic Impact.

Activities to incentivise industrial collaborations:

A research collaboration day with the School of Engineering January 2019 to spark collaborations in research areas with high Impact potential. This has already led to collaborative teams forming.

Week long "Allotey workshop" with ODA seed funds in May 2018: The African Institute of Mathematical Sciences (AIMS) is a pan-African network of centres of excellence. Over a week in May, the chairs of the AIMS excellence centres and scientists from UoL gave overview talks (covering topics including stochastic methods, relativity and cosmology), scoped common grounds for funded future collaborations and agreed on workpackages for African based Impact cases and GCRF funding applications.

Outreach activities are a key element of our Impact activities. Selected impact activities over the reporting period are:

Annual Barkla Lecture: The group has organised this well-publicised open lecture series by an eminent scientist since 2006. Previous speakers include the Nobel laureates Wilczek, Veltman and 't Hooft. The series is highly popular, attracting colleagues and students across Faculties and outside UoL, Alumni and members of the public. Speakers were Katherine Freese, Director of the Nordic Institute for Theoretical Physics (Nov 2015), Dame Susan Jocelyn Bell Burnell (Feb 2017) and Sir Roger Penrose (Nov 2018). Sir Roger Penrose talked about ``Hawking Points'' and we had to restrict access to 350 attendees despite much higher demand.

Talk by Parameswaran at the "Women in STEM" event at Merchant Taylors' Girls' School, Crosby, in April 2016.

Talk at the "Marie Curie's 150th birth anniversary celebration" for school children, with UoL, CERN and LMU Munich, 7th November 2017.

Participation in the `Big Bang Days' at the Liverpool Convention Centre in June 2016/7/8.

Featured article in Gizmodo around the work on g-2 (Teubner and Keshavarzi) leading to an invited short article in Nature Physics.

Talk to Alumni and the public, Wonders beyond everyday life experience, in the series Science in the Snug, Liverpool, 5 October 2017.

Public evening talk around quantum physics at the De Morgan House, LMS, London, 7 November 2017.

Talk on String Theory to secondary school students at Carmel College and during the STEM week in Liverpool.

Internships for local sixth form students introducing university level mathematics and encouraging participation in higher level education.

We contribute to the activities of the Outreach Team of the Department of Mathematical Sciences including giving interactive talks to the monthly UoL Maths Club for local school and college students and contributing to workshops covering exciting topics in particle physics and cosmology. During the academic year 2017-2018, the Maths Outreach Team interacted with 8,200 pupils on 81 school visits. Over 60% of the schools were in areas having young peoples' Higher-Education participation rates within HEFCE's two lowest classification bands.

Pathways to Impact document, which summarises our strategy and approach to generating non-academic Impact.

Activities to incentivise industrial collaborations:

A research collaboration day with the School of Engineering January 2019 to spark collaborations in research areas with high Impact potential. This has already led to collaborative teams forming.

Week long "Allotey workshop" with ODA seed funds in May 2018: The African Institute of Mathematical Sciences (AIMS) is a pan-African network of centres of excellence. Over a week in May, the chairs of the AIMS excellence centres and scientists from UoL gave overview talks (covering topics including stochastic methods, relativity and cosmology), scoped common grounds for funded future collaborations and agreed on workpackages for African based Impact cases and GCRF funding applications.

Outreach activities are a key element of our Impact activities. Selected impact activities over the reporting period are:

Annual Barkla Lecture: The group has organised this well-publicised open lecture series by an eminent scientist since 2006. Previous speakers include the Nobel laureates Wilczek, Veltman and 't Hooft. The series is highly popular, attracting colleagues and students across Faculties and outside UoL, Alumni and members of the public. Speakers were Katherine Freese, Director of the Nordic Institute for Theoretical Physics (Nov 2015), Dame Susan Jocelyn Bell Burnell (Feb 2017) and Sir Roger Penrose (Nov 2018). Sir Roger Penrose talked about ``Hawking Points'' and we had to restrict access to 350 attendees despite much higher demand.

Talk by Parameswaran at the "Women in STEM" event at Merchant Taylors' Girls' School, Crosby, in April 2016.

Talk at the "Marie Curie's 150th birth anniversary celebration" for school children, with UoL, CERN and LMU Munich, 7th November 2017.

Participation in the `Big Bang Days' at the Liverpool Convention Centre in June 2016/7/8.

Featured article in Gizmodo around the work on g-2 (Teubner and Keshavarzi) leading to an invited short article in Nature Physics.

Talk to Alumni and the public, Wonders beyond everyday life experience, in the series Science in the Snug, Liverpool, 5 October 2017.

Public evening talk around quantum physics at the De Morgan House, LMS, London, 7 November 2017.

Talk on String Theory to secondary school students at Carmel College and during the STEM week in Liverpool.

Internships for local sixth form students introducing university level mathematics and encouraging participation in higher level education.

We contribute to the activities of the Outreach Team of the Department of Mathematical Sciences including giving interactive talks to the monthly UoL Maths Club for local school and college students and contributing to workshops covering exciting topics in particle physics and cosmology. During the academic year 2017-2018, the Maths Outreach Team interacted with 8,200 pupils on 81 school visits. Over 60% of the schools were in areas having young peoples' Higher-Education participation rates within HEFCE's two lowest classification bands.

### Publications

Smith D
(2021)

*Quantum phase transitions on the hexagonal lattice*in International Journal of Modern Physics A
SchÃ¼tte-Engel J
(2021)

*Axion quasiparticles for axion dark matter detection*in Journal of Cosmology and Astroparticle Physics
Gorghetto M
(2021)

*Observing invisible axions with gravitational waves*in Journal of Cosmology and Astroparticle Physics
Bergner G
(2021)

*Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills*in Journal of High Energy Physics
Flett C
(2021)

*Exclusive heavy vector meson electroproduction to NLO in collinear factorisation*in Journal of High Energy Physics
Bishara F
(2021)

*Generic one-loop matching conditions for rare meson decays*in Journal of High Energy Physics
Ray S
(2021)

*Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order*in Physical Review B
Appelquist T
(2022)

*Goldstone boson scattering with a light composite scalar*in Physical Review D
Brower R
(2021)

*Stealth dark matter confinement transition and gravitational waves*in Physical Review D
Flett C
(2022)

*Predictions of exclusive ? photoproduction at the LHC and future colliders*in Physical Review D
Jack I
(2021)

*Anomalous dimensions at large charge for U ( N ) × U ( N ) theory in three and four dimensions*in Physical Review D
Appelquist T
(2021)

*Near-conformal dynamics in a chirally broken system*in Physical Review D
Jack I
(2021)

*Anomalous dimensions at large charge in d = 4 O ( N ) theory*in Physical Review D
Flett C
(2020)

*Very low x gluon density determined by LHCb exclusive J / ? data*in Physical Review D
Barrios N
(2021)

*Two-loop corrections to the QCD propagators within the Curci-Ferrari model*in Physical Review D
Gracey J
(2022)

*Five loop renormalization of the Wess-Zumino model*in Physical Review D
Borinsky M
(2021)

*Five-loop renormalization of ? 3 theory with applications to the Lee-Yang edge singularity and percolation theory*in Physical Review D
Jack I
(2022)

*Scaling dimensions at large charge for cubic ? 3 theory in six dimensions*in Physical Review D
Catterall S
(2020)

*Three-dimensional super-Yang-Mills theory on the lattice and dual black branes*in Physical Review D
Buividovich P
(2021)

*Numerical study of the chiral separation effect in two-color QCD at finite density*in Physical Review D
Buividovich P
(2020)

*Electric conductivity in finite-density S U ( 2 ) lattice gauge theory with dynamical fermions*in Physical Review D
Gracey J
(2021)

*Critical exponent ? at O ( 1 / N 3 ) in the chiral XY model using the large N conformal bootstrap*in Physical Review D
Jack I
(2020)

*Anomalous dimensions for ? n in scale invariant d = 3 theory*in Physical Review D
Abi B
(2021)

*Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm.*in Physical review letters
Hoferichter M
(2022)

*Mixed Leptonic and Hadronic Corrections to the Anomalous Magnetic Moment of the Muon*in Physical Review Letters