# 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.

### Organisations

### Publications

Aalbers J
(2022)

*A next-generation liquid xenon observatory for dark matter and neutrino physics*in Journal of Physics G: Nuclear and Particle Physics
Abi B
(2021)

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

*Z'-mediated Majorana dark matter: suppressed direct-detection rate and complementarity of LHC searches*in Journal of High Energy Physics
Amoroso S
(2021)

*Longitudinal Z-boson polarization and the Higgs boson production cross section at the Large Hadron Collider*in Physics Letters BDescription | Experimental Particle Physics Consolidated Grant 2019 |

Amount | £7,175,122 (GBP) |

Funding ID | ST/S000879/1 |

Organisation | Science and Technologies Facilities Council (STFC) |

Sector | Public |

Country | United Kingdom |

Start | 09/2019 |

End | 09/2023 |

Description | Maths Research Associates 2021 Liverpool |

Amount | £300,000 (GBP) |

Funding ID | EP/W522399/1 |

Organisation | Engineering and Physical Sciences Research Council (EPSRC) |

Sector | Public |

Country | United Kingdom |

Start | 03/2021 |

End | 12/2023 |

Description | New Frontiers of Lattice Field Theory |

Amount | £755,227 (GBP) |

Funding ID | MR/S015418/1 |

Organisation | Medical Research Council (MRC) |

Sector | Public |

Country | United Kingdom |

Start | 04/2019 |

End | 04/2023 |

Description | Quantum Sensing for the Hidden Sector (QSHS) |

Amount | £218,968 (GBP) |

Funding ID | ST/T006145/1 |

Organisation | Science and Technologies Facilities Council (STFC) |

Sector | Public |

Country | United Kingdom |

Start | 01/2021 |

End | 06/2023 |

Title | Dataset for "Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors" |

Description | Decoding File Names: Consider the file name f8l24t48b48m00889_S0.csv. We will break down the meaning of the various pieces of the filename "f8" means 8 Dirac flavors. "l24t48" means 243×48 lattice. "b48" means beta=4.8, related to the inverse bare gauge coupling. "m00889" means fermion mass m=0.00889. "S" means flavor-singlet scalar meson. Other options are "P" for flavor non-singlet pseudoscalar meson and "C" for flavor non-singlet scalar meson. "0" an integer from 0 to 4 proportional to the squared length of the spatial momentum vector of the correlation function. Columns of the CSV files: Each line of the CSV file should contain 41 entries, separated by commas. Refer to the Eq. (8) which defines model A in the accompanying paper to understand the physical interpretation of these parameters. Model number: 1 is model A, 2 is model B, 3 is model C. nmax: the number of non-oscillating states in the fit. jmax: the number of oscillating states in the fit. tmin: the minimum t value used in the fit. tmax: the maximum t value used in the fit. 2 of the fit. \(\log\ p\left(\left.M\right|D\right)\): log of model probability used in Bayesian model averaging. fit value for c0 (model A) or \(\overline{c}_0\) (model B). fit error for c0 (model A) or \(\overline{c}_0\) (model B). fit value for c1. fit error for c1. fit value for c2. fit error for c2. fit value for c3. fit error for c3. fit value for c4. fit error for c4. fit value for \(c_1^\prime\). fit error for \(c_1^\prime\) fit value for \(c_2^\prime\). fit error for \(c_2^\prime\). fit value for \(c_3^\prime\). fit error for \(c_3^\prime\). fit value for \(c_4^\prime\). fit error for \(c_4^\prime\). fit value for \(\log(E_2 - E_1)\). fit error for \(\log(E_2-E_1)\). fit value for \(\log(E_3-E_2)\). fit error for \(\log(E_3-E_2)\). fit value for \(\log(E_4-E_3)\). fit error for \(\log(E_4-E_3)\). fit value for \(\log(E_2^\prime - E_1^\prime)\). fit error for \(\log(E_2^\prime - E_1^\prime)\). fit value for \(\log(E_3^\prime - E_2^\prime)\). fit error for \(\log(E_3^\prime - E_2^\prime)\). fit value for \(\log(E_4^\prime - E_3^\prime)\). fit error for \(\log(E_4^\prime - E_3^\prime)\). fit value for \(\log(E_1)\). fit error for \(\log(E_1)\). fit value for \(\log(E_1^\prime)\). fit error for \(\log(E_1^\prime)\). |

Type Of Material | Database/Collection of data |

Year Produced | 2023 |

Provided To Others? | Yes |

Impact | We made this dataset public to enable independent scrutiny, reproduction, and extension of our research. It has been viewed 142 times and downloaded 492 times as of 12 March 2024. Its open publication makes a leading contribution to the growth and establishment of open science in lattice field theory research, both in the UK and around the world. |

URL | https://zenodo.org/record/8007954 |

Title | Non-perturbative phase structure of the bosonic BMN matrix model --- data release |

Description | This HDF5 file collects data and analysis results for non-perturbative lattice calculations investigating the phase structure of the bosonic part of the Berenstein--Maldacena--Nastase matrix model. See the README for further information. |

Type Of Material | Database/Collection of data |

Year Produced | 2022 |

Provided To Others? | Yes |

Impact | We made this dataset public to enable independent scrutiny, reproduction, and extension of our research. It has been viewed 231 times and downloaded 54 times as of 12 March 2024. Its open publication makes a leading contribution to the growth and establishment of open science in lattice field theory research, both in the UK and around the world. |

URL | https://zenodo.org/doi/10.5281/zenodo.6462432 |

Title | Phase diagram of two-dimensional SU(N) super-Yang--Mills theory with four supercharges --- data release |

Description | This HDF5 file collects data and analysis results for non-perturbative lattice field theory calculations investigating two-dimensional supersymmetric SU(N) Yang--Mills theory with four supercharges. See the README for further information. |

Type Of Material | Database/Collection of data |

Year Produced | 2023 |

Provided To Others? | Yes |

Impact | We made this dataset public to enable independent scrutiny, reproduction, and extension of our research. It has been viewed 120 times and downloaded 56 times as of 12 March 2024. Its open publication makes a leading contribution to the growth and establishment of open science in lattice field theory research, both in the UK and around the world. |

URL | https://zenodo.org/doi/10.5281/zenodo.10083864 |

Description | UKLFT Annual Meeting 26/27 May 2022, Liverpool |

Form Of Engagement Activity | Participation in an activity, workshop or similar |

Part Of Official Scheme? | No |

Geographic Reach | National |

Primary Audience | Postgraduate students |

Results and Impact | Organisation and hosting of the annual UK Lattice Field Theory meeting in May 2022 in Liverpool, a two day event for academics, postdoctoral researchers and postgraduate students working in the field of lattice field theory in the UK. This Virtual Centre activity is supported by STFC as part of the STFC Consolidated Grant in Theoretical Physics. |

Year(s) Of Engagement Activity | 2022 |

URL | http://generic.wordpress.soton.ac.uk/uklft/ |