## Periodic Reporting for period 1 - HIGGS-BSM-EFT (Higgs and Beyond the Standard ModelEffective Field Theory, systematic developments.)

Reporting period: 2015-04-01 to 2017-03-31

The focus of this work was to systematically develop the Standard Model of particle physics as an effective field theory and to use this formalism to study the famous Higgs boson and related experimental signals. By developing this general theoretical framework (i.e. an effective field theory) to include quantum mechanical corrections, deviations in Higgs properties can be systematically studied at high precision in a model independent manner. Further understanding the nature of the Higgs boson is of fundamental importance to understanding the origin of mass that makes up the particles of the Standard Model of particle physics. Using the growing Large Hadron Collider data set, Higgs properties will be determined with an order of magnitude improvement in experimental precision in the coming years. Resolving more precisely the properties of the Higgs boson experimentally is expected to offer significant evidence for the effects of new particles and interactions, involved in stabilising the Higgs mass against quantum corrections. This can expand our knowledge about the fundamental nature of reality encoded in the Standard Model of particle physics. The calculations of this project allow these properties to be interpreted in a consistent theoretical framework with such higher precision measurements. Calculations of the most important quantum corrections to Higgs production and decay processes in the general effective field theory of the Standard Model were undertaken with the resources of this grant, building upon past contributions in this area by the experienced researcher. Phenomenological analyses to refine our knowledge of the Higgs boson in this general effective field theory framework were also further developed. All of these efforts have developed further the theoretical framework that describes the most fundamental interactions while allowing the current leading model of particle physics to break down at higher energies, and in more precise measurements.

Being fundamental research, the implications for society are long-term. Through training and education of young researchers we prepare them for the future roles in society. In my own research, as EU Marie Curie Fellow, I have co-supervised two PhD students on the topic of this project, and I have also co-supervised two MSc students during this time. Two of these students have moved on to valuable positions in private industry and the third has continued to PhD-studies Oxford University. This is a great example of how the pursuit of fundamental research eventually can be of great benefit to society as a whole. I would also note that three of the four students were female which helps to address the gender imbalance in theoretical particle physics.

The overall objectives of this project are to establish a systematic and complete characterisation of extensions of the Standard Model of particle physics to use in studying data from the Large Hadron Collider, in particular with a view towards its Run II, which is ongoing. At the end of my two-year period I have made very substantial progress towards this overall objective.

Being fundamental research, the implications for society are long-term. Through training and education of young researchers we prepare them for the future roles in society. In my own research, as EU Marie Curie Fellow, I have co-supervised two PhD students on the topic of this project, and I have also co-supervised two MSc students during this time. Two of these students have moved on to valuable positions in private industry and the third has continued to PhD-studies Oxford University. This is a great example of how the pursuit of fundamental research eventually can be of great benefit to society as a whole. I would also note that three of the four students were female which helps to address the gender imbalance in theoretical particle physics.

The overall objectives of this project are to establish a systematic and complete characterisation of extensions of the Standard Model of particle physics to use in studying data from the Large Hadron Collider, in particular with a view towards its Run II, which is ongoing. At the end of my two-year period I have made very substantial progress towards this overall objective.

The work performed lead to results reported in a series of papers explained here.

The global fit papers are https://arxiv.org/abs/1502.02570 https://arxiv.org/abs/1508.05060 https://arxiv.org/abs/1606.06693. In these works, a global fit to experimental data was developed in the Standard Model effective field theory framework. We incorporated electroweak precision data, low energy data, and data from detectors that operated at the particle accelerators known by their acronyms: PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II. We demonstrated how previously neglected corrections due to quantum mechanics and even higher order terms in the effective field theory expansion introduce a theoretical error into global fits of this form, and how reducing such errors requires further development of this theoretical formalism. These considerations relax bounds compared to a naive leading order analysis, and show that constraints that rise above the percent level are subject to substantial theoretical uncertainties.

In a parallel series of papers the one loop corrections to important Standard model processes were developed. In https://arxiv.org/abs/1505.02646 and https://arxiv.org/abs/1507.03568 we calculated the one loop corrections to the decay of the Higgs boson to two photons in the Standard Model Effective Field Theory. This is a critical experimental signal of the properties of the Higgs boson, that is expected to be measured with increase precision in the near future at the Large Hadron Collider. We showed how to overcome many technical challenges related to these calculations. In particular we showed how a modified gauge fixing procedure is required to perform these calculations. This calculation was developed to the first example of this form in the literature of a full one loop correction due to the local dimension six operators interfering with the Standard Model, which was reported in the prestigious journal Physical Review Letters. These results showed that for the most precise measurements of Standard Model processes it is clearly required to incorporate one loop corrections of this form in the effective field theory. This lead to a further paper, https://arxiv.org/abs/1611.09879 where we calculated one loop corrections to the decay of the Z boson in the large top Yukawa and Higgs self coupling limit.

These results have been highly cited in the literature, and lead to two prominent invited talks at the international conferences Moriond 2016 and 2017 in order to disseminate the results.

The global fit papers are https://arxiv.org/abs/1502.02570 https://arxiv.org/abs/1508.05060 https://arxiv.org/abs/1606.06693. In these works, a global fit to experimental data was developed in the Standard Model effective field theory framework. We incorporated electroweak precision data, low energy data, and data from detectors that operated at the particle accelerators known by their acronyms: PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II. We demonstrated how previously neglected corrections due to quantum mechanics and even higher order terms in the effective field theory expansion introduce a theoretical error into global fits of this form, and how reducing such errors requires further development of this theoretical formalism. These considerations relax bounds compared to a naive leading order analysis, and show that constraints that rise above the percent level are subject to substantial theoretical uncertainties.

In a parallel series of papers the one loop corrections to important Standard model processes were developed. In https://arxiv.org/abs/1505.02646 and https://arxiv.org/abs/1507.03568 we calculated the one loop corrections to the decay of the Higgs boson to two photons in the Standard Model Effective Field Theory. This is a critical experimental signal of the properties of the Higgs boson, that is expected to be measured with increase precision in the near future at the Large Hadron Collider. We showed how to overcome many technical challenges related to these calculations. In particular we showed how a modified gauge fixing procedure is required to perform these calculations. This calculation was developed to the first example of this form in the literature of a full one loop correction due to the local dimension six operators interfering with the Standard Model, which was reported in the prestigious journal Physical Review Letters. These results showed that for the most precise measurements of Standard Model processes it is clearly required to incorporate one loop corrections of this form in the effective field theory. This lead to a further paper, https://arxiv.org/abs/1611.09879 where we calculated one loop corrections to the decay of the Z boson in the large top Yukawa and Higgs self coupling limit.

These results have been highly cited in the literature, and lead to two prominent invited talks at the international conferences Moriond 2016 and 2017 in order to disseminate the results.

The conclusions of the action are the development of the most extensive global fit to the Standard Model Effective field theory in the world. As we measure the properties of the Higgs boson at the Large Hadron Collider, we could find deviations in the properties of this state that could point to a new theory of fundamental interactions. We can only properly understand these deviations if we have a consistent theoretical framework that allows a consistent interpretation of deviations. This requires the development of a general effective field theory extension of the Standard Model, which is the task that this project advanced.

The expected impact of these results on society is long term. These works are aimed at a fundamental advance of our knowledge of the most fundamental theory in physics. Finding deviations in the properties of the Standard Model can lead to profound technological advancements in the long term based on a deeper understanding of a new fundamental theory of physics. This can occur in a manner that is similar to how our understanding of the theory of electromagnetism in the 1800's lead to profound technological change in the last century. Similarly, the development of quantum mechanics in the pursuit of fundamental physics understanding in the last century is currently leading to a revolution in quantum devices. If an advance in our understanding of the most fundamental interactions using these theoretical developments will lead to such long term socio-economic impacts on society is currently unknown. But history argues that such a profoundly beneficial long term return on investment for society as a whole is reasonable to expect.

The expected impact of these results on society is long term. These works are aimed at a fundamental advance of our knowledge of the most fundamental theory in physics. Finding deviations in the properties of the Standard Model can lead to profound technological advancements in the long term based on a deeper understanding of a new fundamental theory of physics. This can occur in a manner that is similar to how our understanding of the theory of electromagnetism in the 1800's lead to profound technological change in the last century. Similarly, the development of quantum mechanics in the pursuit of fundamental physics understanding in the last century is currently leading to a revolution in quantum devices. If an advance in our understanding of the most fundamental interactions using these theoretical developments will lead to such long term socio-economic impacts on society is currently unknown. But history argues that such a profoundly beneficial long term return on investment for society as a whole is reasonable to expect.