## Final Report Summary - HIGGSEFT (Higgs precision era at the LHC)

The project HiggsEFT is concerned about understanding and characterising the physical properties of the Higgs boson and its couplings to other elementary particles. The Higgs boson is the ultimate particle discovered in 2012 at the Large Hadron Collider (LHC) experiment at CERN (Geneva). The goal of the project is to develop an Effective Field Theory (EFT) framework to analyse in a model-independent way the experimental data collected at the LHC and to utilise them to discover or put constraints on new physics beyond the standard model. Following the initial objectives, the main results obtained during the four years of the project are the following:

1. The renormalization group flow controlling, as a function of the characteristic energy of a process, the relative size and mixing of a set of operators relevant for Higgs physics and Electroweak Precision Physics has been derived. This set of equations allows for a consistent global fit for both types of data collected at different colliders.

2. The production of the Higgs boson in association with a highly boosted jet was studied as a way to probe the top Yukawa coupling and to distinguish it from a contact interaction between the Higgs and the gluons, an ambiguity the plagues inclusive quantities like the total Higgs production cross-section.

3. A study of the production of the Higgs away from its mass-shell with a subsequent decay into from leptons was performed. This channel has been analysed by the two main LHC collaborations and was used to constrain the Higgs boson width. However, this interpretation requires several assumptions that are specific to a very particular class of models. Alternatively, the data can be used to study the energy dependence of the Higgs couplings and to put stringent bound on contact interactions that exhibit a energy-growing behaviour and are thus particularly relevant in the off-shell regime.

4. A tool that computes all the Higgs branching decay ratios in the presence of new interactions has been developed and made publicly available to the whole community.

5. Simple criteria has been proposed to asses the validity of the effective field theory (EFT) to give an adequate low-energy description of an underlying physics beyond the Standard Model (SM). Starting from the EFT where the SM is extended by higher-dimensional operators, experimental data can be used without further assumptions to measure or set limits on the EFT parameters. The interpretation of these results requires instead a set of broad assumptions (e.g. power counting rules) on the UV dynamics. A practical prescription has been proposed on how experimental results could be reported, so that they admit a maximally broad range of theoretical interpretations. This is especially important for hadron collider experiments where collisions probe a wide range of energy scales.

6. A study of the production of the Higgs boson away from its mass-shell was performed. Inclusive Higgs measurements at the LHC have limited resolution on the gluon fusion loops, being unable to distinguish the long-distance contributions mediated by the top quark from possible short-distance new physics effects. Based an Effective Field Theory approach, a comparaison of several methods to lift this degeneracy was performed, including tth and boosted, off-shell and double Higgs production. Detailed projections to the High-Luminosity LHC and a future hadron collider have been obtained.

7. A comprehensive study of the sensitivity of future colliders in the determination of the various Higgs couplings has been carried out. The impact and complementarity of differential measurements, at different center-of-mass energies and for several beam polarisation configurations, have been studied in a global effective-field-theory framework. A "global determinant parameter" which characterises the overall strengthening of constraints independently of the choice of operator basis has been introduced. The reach of the CEPC, CLIC, FCC-ee, and ILC designs was assessed.

8. The determination of the Higgs self-coupling has been re-assessed. It was proposed to probe this coupling through its radiative corrections to single-Higgs processes. This approach however requires to disentangle these effects from those associated to deviations of other Higgs-couplings to fermions and gauge bosons. We showed that a global fit exploiting only single-Higgs inclusive data suffers from degeneracies that prevent one from extracting robust bounds on each individual coupling. We showed how the inclusion of double-Higgs production via gluon fusion, and the use of differential measurements in the associated single-Higgs production channels WH, ZH and ttH, can help to overcome the deficiencies of a global Higgs-couplings fit.

9. Along a slight different line of research, the potential of probing new light force-carriers, with spin-independent couplings to the electron and the neutron, has been explored using precision isotope shift spectroscopy. In this multidisciplinary collaborations involving high energy particle theorists, experimentalists working with cold atoms, a formalism was developed to interpret linear King plots as bounds on new physics with minimal theory inputs. The focus was on bounding the new physics contributions that can be calculated independently of the Standard Model nuclear effects. The method was applied to existing Ca+ data and we projected its sensitivity to possibly existing new bosons using narrow transitions in other atoms and ions (specifically, Sr and Yb). Future measurements are expected to improve the relative precision by five orders of magnitude, and can potentially lead to an unprecedented sensitivity for bosons within the 10 keV to 10 MeV mass range.

The PI of the project acquired an indisputable expertise in the field, a status demonstrated by the fact that he acted for 3 years as one of the three theory conveners of the LHC Higgs Cross Section working group gathering more than 600 physicists and providing recommendations to the experimentalists. He is also in charge of the report on Higgs physics for the Review of Particle Physics of the Particle Data Group, a unique reference in the community.

In addition, the PI and his group have been involved in the preparation of various documents to establish/clarify/strengthen the physics case of various future collider projects: International Linear Collider, Future Circular Collider with electrons and positrons.

In January 2015, the PI moved from IFAE, Barcelona to DESY, Hamburg as a leading scientist to lead the theoretical particle group. He has also been nominated professor of theoretical physics at the Humboldt University in Berlin where he is teaching particle physics.

More information are available at https://particle-physics.desy.de/e282767

1. The renormalization group flow controlling, as a function of the characteristic energy of a process, the relative size and mixing of a set of operators relevant for Higgs physics and Electroweak Precision Physics has been derived. This set of equations allows for a consistent global fit for both types of data collected at different colliders.

2. The production of the Higgs boson in association with a highly boosted jet was studied as a way to probe the top Yukawa coupling and to distinguish it from a contact interaction between the Higgs and the gluons, an ambiguity the plagues inclusive quantities like the total Higgs production cross-section.

3. A study of the production of the Higgs away from its mass-shell with a subsequent decay into from leptons was performed. This channel has been analysed by the two main LHC collaborations and was used to constrain the Higgs boson width. However, this interpretation requires several assumptions that are specific to a very particular class of models. Alternatively, the data can be used to study the energy dependence of the Higgs couplings and to put stringent bound on contact interactions that exhibit a energy-growing behaviour and are thus particularly relevant in the off-shell regime.

4. A tool that computes all the Higgs branching decay ratios in the presence of new interactions has been developed and made publicly available to the whole community.

5. Simple criteria has been proposed to asses the validity of the effective field theory (EFT) to give an adequate low-energy description of an underlying physics beyond the Standard Model (SM). Starting from the EFT where the SM is extended by higher-dimensional operators, experimental data can be used without further assumptions to measure or set limits on the EFT parameters. The interpretation of these results requires instead a set of broad assumptions (e.g. power counting rules) on the UV dynamics. A practical prescription has been proposed on how experimental results could be reported, so that they admit a maximally broad range of theoretical interpretations. This is especially important for hadron collider experiments where collisions probe a wide range of energy scales.

6. A study of the production of the Higgs boson away from its mass-shell was performed. Inclusive Higgs measurements at the LHC have limited resolution on the gluon fusion loops, being unable to distinguish the long-distance contributions mediated by the top quark from possible short-distance new physics effects. Based an Effective Field Theory approach, a comparaison of several methods to lift this degeneracy was performed, including tth and boosted, off-shell and double Higgs production. Detailed projections to the High-Luminosity LHC and a future hadron collider have been obtained.

7. A comprehensive study of the sensitivity of future colliders in the determination of the various Higgs couplings has been carried out. The impact and complementarity of differential measurements, at different center-of-mass energies and for several beam polarisation configurations, have been studied in a global effective-field-theory framework. A "global determinant parameter" which characterises the overall strengthening of constraints independently of the choice of operator basis has been introduced. The reach of the CEPC, CLIC, FCC-ee, and ILC designs was assessed.

8. The determination of the Higgs self-coupling has been re-assessed. It was proposed to probe this coupling through its radiative corrections to single-Higgs processes. This approach however requires to disentangle these effects from those associated to deviations of other Higgs-couplings to fermions and gauge bosons. We showed that a global fit exploiting only single-Higgs inclusive data suffers from degeneracies that prevent one from extracting robust bounds on each individual coupling. We showed how the inclusion of double-Higgs production via gluon fusion, and the use of differential measurements in the associated single-Higgs production channels WH, ZH and ttH, can help to overcome the deficiencies of a global Higgs-couplings fit.

9. Along a slight different line of research, the potential of probing new light force-carriers, with spin-independent couplings to the electron and the neutron, has been explored using precision isotope shift spectroscopy. In this multidisciplinary collaborations involving high energy particle theorists, experimentalists working with cold atoms, a formalism was developed to interpret linear King plots as bounds on new physics with minimal theory inputs. The focus was on bounding the new physics contributions that can be calculated independently of the Standard Model nuclear effects. The method was applied to existing Ca+ data and we projected its sensitivity to possibly existing new bosons using narrow transitions in other atoms and ions (specifically, Sr and Yb). Future measurements are expected to improve the relative precision by five orders of magnitude, and can potentially lead to an unprecedented sensitivity for bosons within the 10 keV to 10 MeV mass range.

The PI of the project acquired an indisputable expertise in the field, a status demonstrated by the fact that he acted for 3 years as one of the three theory conveners of the LHC Higgs Cross Section working group gathering more than 600 physicists and providing recommendations to the experimentalists. He is also in charge of the report on Higgs physics for the Review of Particle Physics of the Particle Data Group, a unique reference in the community.

In addition, the PI and his group have been involved in the preparation of various documents to establish/clarify/strengthen the physics case of various future collider projects: International Linear Collider, Future Circular Collider with electrons and positrons.

In January 2015, the PI moved from IFAE, Barcelona to DESY, Hamburg as a leading scientist to lead the theoretical particle group. He has also been nominated professor of theoretical physics at the Humboldt University in Berlin where he is teaching particle physics.

More information are available at https://particle-physics.desy.de/e282767