• 01 TRIUMF Theory Department
  • 02 Theory Science Highlights
  • 03 Nuclear Theory at TRIUMF
  • 04 Particle Theory at TRIUMF

01 TRIUMF Theory Department

TRIUMF’s Theory Department is unique in Canada as a theoretical team embedded in a world-leading rare isotope laboratory. This context provides a synergistic interface between theorists whose original work is informed by leading-edge experimental technologies and results, and in turn whose independent research guides and inspires experimental approaches.  

The Theory Department specializes in two areas: nuclear theory and particle theory. 

TRIUMF’s nuclear theorists are leaders in building a first-principles understanding of nuclear structure and reactions using computational modeling with the world’s largest supercomputers. This involves developing and applying first-principle, or ab initio, methods to explain how the interaction of quarks and gluons produce the observed structure and properties of atomic nuclei. These ab initio methods are at the scientific forefront in using computational mathematics to model complex systems, including rare isotopes. In the past decade, TRIUMF nuclear theorists have contributed to extending ab initio techniques to larger, more complex nuclei up to an atomic mass 100. 

TRIUMF’s particle theorists are pushing the scientific frontiers in the search for new beyond-Standard Model (SM) physics and proposing ways to test beyond-SM theories in existing or future experimental facilities. This includes direct and indirect searches for dark matter (DM), searches for new particles in high energy colliders, and new tests of neutrino characteristics. With big-data particle physics experiments the volume of data itself can be a limiting factor to discovery and TRIUMF’s particle theorists are providing direction to narrow in on the most potentially fruitful avenues for research. 

The Theory Department’s five core staff lead a diverse research program that involves, at any one time, more than a dozen additional team members from across Canada and around the world. In 2018, this included five postdoctoral researchers from the United States, Italy, Australia and Israel; four graduate students from TRIUMF member universities, and four undergraduate co-op students.  

The Theory Department is also a hub for the Canadian and international subatomic physics theory communities. This includes hosting annual workshops on “Progress in Ab Initio Techniques in Nuclear Physics” and new topics in particle physics. Similarly, the Theory Department contributes to linking TRIUMF, through partnerships and collaborations, to a range of major national and international institutions, including the Institute for Particle Physics and the Perimeter Institute in Canada, CERN in Europe, U.S. Department of Energy national laboratories including Lawrence Livermore and Oak Ridge, and the Japan Proton Accelerator Research Complex (J-PARC). 

02 Theory Science Highlights

Tin-100: A gateway to ab initio calculations in heavy nuclei

Tin-100: A gateway to ab initio calculations in heavy nuclei: For many years Tin-100 (100Sn) has stood as a distant milestone of first-principles calculations of atomic nuclei, a gateway to modeling nuclei in the heavy-mass region above atomic mass 100. 100Sn is the heaviest self-conjugate nucleus, it exhibits the largest known β-decay strength, and is close to the proton dripline. As reported in Physical Review Letters (2017), TRIUMF nuclear theorists linked the structure of nuclei around 100Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers, to nucleon-nucleon and three-nucleon forces constrained only by data of few-nucleon systems. The results provide the first ab initio prediction that 100Sn is indeed doubly magic, paving the way for ab initio calculations to the heaviest nuclei.            

Extending first principles of nuclear structure to all open-shell nuclei

Extending first principles of nuclear structure to all open-shell nuclei: The breadth of first-principles nuclear structure calculations in medium- and heavy-mass nuclei has largely been limited to closed-shell and neighboring nuclei or spherical even-even systems. As reported in Physical Review Letters (2017), TRIUMF nuclear theorists developed a new approach for calculating virtually any property of the atomic nucleus. It generalizes the ideas of the nuclear shell model to capture the effects of three-nucleon forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1% level. This approach then effectively extends the reach of ab initio nuclear structure calculations to essentially all medium- and many heavy-mass nuclei.    

Vacuum stability and the MSSM Higgs mass

Vacuum stability and the MSSM Higgs mass: Supersymmetry is a leading candidate for beyond-Standard Model physics. A crucial requirement for supersymmetry to be realized is that it does not lead to the catastrophic destruction of the universe, which can occur if the theory contains new lowest-energy vacuum states that are deeper than the one that we live in. As reported in the Journal of High Energy Physics (2014), TRIUMF theorists investigated the implications of this vacuum stability condition on the minimal supersymmetric extension of the Standard Model (MSSM) by studying the vacuum structure of the theory as well as the quantum transition rates between vacuum states. A close connection was found between the stability of the Universe, the observed mass of the Higgs boson, and the properties of the supersymmetric partner particles of the top quarks which are currently being searched for with CERN's Large Hadron Collider.

Dark matter from a new dark strong force

Dark matter from a new dark strong force: Most of the matter in the Universe seems to be a new form that gives off very little light, called dark matter (DM).  While the evidence for DM is very strong, very little is known about what it is made of.  As reported in Physical Review D, TRIUMF theorists showed that DM can arise from a new strong force that interacts only very feebly with regular matter. In this realization, DM consists of glueballs consisting of a conglomeration of the mediators of the new force. Implications of glueball dark matter and decays on the formation of light elements in the early Universe, the cosmic microwave background radiation, and astronomical gamma rays seen today were also studied.

Searching for new dark forces at lower-energy experiments

Searching for new dark forces at lower-energy experiments: New forces may exist beyond those described by the Standard Model. The characteristic energy of a new force can be much smaller than that of the weak force provided it interacts only very feebly with regular matter. One of the most promising ways to discover such new dark forces is in lower-energy beam dump experiments in which a very intense beam is directed at a material target. As reported in the Journal of High Energy Physics (2014), TRIUMF theorists investigated new ways to apply existing beam dump experiments (usually designed for other scientific objectives) to look for dark forces and new particles associated with them. They also connected theories of dark forces with limits from cosmology and direct searches for dark matter.    

Neutron-skin as a portal to neutron star properties

Neutron-skin as a portal to neutron star properties: With the new era opened up by the LIGO and VIRGO observation of neutron-star mergers, multi-messenger astronomy will provide us with new ways to constrain the equation of states of neutron-rich matter. Stronger constraints will be obtained by combining such future data with observations on finite nuclei. Indeed, neutron-rich nuclei provide a portal to study neutron-rich matter, in that they form a neutron-skin around their surface which is directly related to the equation of state of nuclear matter. As reported in Nature (2016), TRIUMF theorists and international collaborators provided the first ab initio computation of calcium-48 (48Ca), a nucleus with 20 protons and 28 neutrons. It was predicted that a neutron-skin is formed, though much smaller than previously thought, calling for new experimental investigations.  

Solar fusion and Big Bang nucleosynthesis from ab initio theory

Solar fusion and Big Bang nucleosynthesis from ab initio theory: The 3He(α,γ)7Be and 3H(α,γ)7Li radiative-capture processes hold great astrophysical significance. Their reaction rates between ∼20 and 500 keV are essential to calculate the primordial 7Li abundance in the universe. In addition, standard solar model predictions for the fraction of pp-chain branches resulting in 7Be versus 8B neutrinos depend critically on the 3He(α,γ)7Be astrophysical S factor at about 20 keV. These capture cross sections are strongly suppressed at such low energies and thus hard to measure in a laboratory. As reported in Physics Letters B (2016), TRIUMF nuclear theorists investigated these reactions ab initio using a chiral nucleon–nucleon interaction. Our calculated 3He(α,γ)7Be cross sections agree reasonably with the higher-energy experimental data including those measured at TRIUMF while the 3H(α,γ)7Li ones are overestimated. Our low-energy predictions help reduce uncertainty of nuclear data evaluations for astrophysics.

Understanding the phenomenon of parity inversion in beryllium-11

Understanding the phenomenon of parity inversion in beryllium-11: It has been known since 1960s that the spectrum of beryllium-11 (11Be) has peculiar features, namely, its weakly bound ground state has positive parity contrary to the standard shell model picture. Yet, a first-principles explanation of this phenomenon has been lacking. As reported in Physical Review Letters (2016), TRIUMF nuclear theorists investigated this nucleus ab initio and demonstrated that the inclusion of continuum effects is crucial for a description of the 11Be system. The results showed that the spectrum is extremely sensitive to the details of the nuclear two- and three-nucleon interactions and constitutes an important benchmark for future forces. In particular, the parity inversion of the bound states could be achieved only by a nuclear force that provides accurate predictions of nuclear radii and matter saturation properties.    

Unified ab initio approach to bound and unbound states

Unified ab initio approach to bound and unbound states: Theoretical understanding of weakly bound and unbound atomic nuclei produced and investigated at TRIUMF and other rare isotope facilities requires quantum mechanical description that includes continuum effects, in other words, the nuclear bound and unbound states must be treated on the same footing. As reported in Physical Review Letters C (2013), TRIUMF nuclear theorists achieved such a description by introducing a novel ab initio approach called no-core shell model with continuum capable of predicting properties of exotic nuclei from basic interactions between nucleons. As the first demonstration of this approach we calculated the properties of resonances of the unbound exotic 7He nucleus that was subject of several experimental investigations contradicting each other especially in properties of a low-lying ½- resonance. Our results clearly discriminated among three experiments agreeing with only one of them.       

First measurement and ab initio calculation of rare excited nucleus' energy loss

First measurement and ab initio calculation of rare excited nucleus' energy loss Using GRIFFIN, researchers confirmed the existence of a very rare case of energy loss from excited scandium-50 (50Sc) nuclei and the TRIUMF theory group produced the first ab initio calculation of this transition rate. Nuclei in hot excited states become more stable by emitting radiation in the form of gamma (γ) rays, high energy photons, that carry away both energy and angular momentum. Usually, the gamma rays carry away one or two units of angular momentum and do not change the parity. As reported in Physical Review C (2017), scientists used the GRIFFIN spectrometer to identify the angular momentum of states in 50Sc using γ-γ angular correlations. The existence was of a transition magnetic octupole was confirmed which carries away three units of angular momentum at once. This decay is so rare that the parent state lives for a full half a second instead of the typical one- trillionth of a second.    

A better view of the strong force

A better view of the strong force: An IRIS experiment discovered that using rare isotopes to scatter protons can reveal subtle, new characteristics of the nuclear strong force which binds protons and neutrons, the building blocks of all matter. The strong force appeared well understood for explaining simple nuclei, such as hydrogen isotopes, but its extension to complex, many body systems has exposed important gaps. Theorists have proposed new models, but many strong force characteristics in these models can only be constrained with experiments. As reported in Physical Review Letters (2017), using the rare isotope carbon-10 (10C), IRIS's researchers showed that the intensity distribution of scattered protons by rare isotope is highly sensitive to different theoretical models of the strong force, providing a key new way to constrain them.  

03 Nuclear Theory at TRIUMF

TRIUMF nuclear theorists use first principle, or ab initio models, to tackle a core question in nuclear theory: how overall nuclear structure emerges from quantum chromodynamics, the SM theory that describes the complex interactions of quarks and gluons. A key strength of TRIUMF’s nuclear theory group lies in its ability to apply a broad toolbox of different computational methods grounded in Chiral Effective Field Theory, which describes nucleon interactions using quantum chromodynamics. 

TRIUMF theorists are extending ab initio techniques to increasingly complex and rare nuclei from exotic light nuclei, to complex medium-sized nuclei. These ab initio insights are helping constrain and guide experiments in extreme nuclear structure at TRIUMF, and beyond, including for astrophysical nuclear reactions, the evolution of shell structure far from stability and for a range of leading-edge physics experiments, including fusion energy. 


Nuclear Theory and Rare Isotopes 

Short-lived, extreme nuclei are the scientific frontier for the discovery of new aspects of nucleon interactions, including in neutron-rich nuclei with halo neutrons, unbound, or unstable, nuclei, and in excited and deformed nuclei.  

The weakly bound and unbound exotic nuclei produced in TRIUMF experiments cannot be understood using traditional nuclear bound-state techniques. As a result, TRIUMF theorists are leaders in developing an ab initio many-body approach, no-core shell model with continuum (NCSMC), which provides a unified description of both bound and unbound nucleon states. This enables theorists to simultaneously investigate both nuclear structure and reactions. The method combines a state-of-the-art technique to incorporate short- and medium-range many-nucleon correlations with a continuous process to incorporate long-range correlations between clusters of nucleons. 

With NCSMC, TRIUMF theorists predict the ground- and excited-state energies of light nuclei, their electromagnetic moments and transitions, resonances and cross-sections. These calculations provide both guidance for experimentalists and a theoretical test and framework for interpreting experimental results. As well, understanding and predicting the formation of shell structure in exotic nuclei is a central challenge for nuclear theory. The Theory Department is refining models and collaborating with TRIUMF experimentalists, including in measurements performed at TRIUMF’s TITAN revealing nuclear binding energies, and the structure of exotic halo nuclei such as 6He and 11Be. 

To better understand extreme nuclei, the Theory Department is pioneering the use of the in-medium similarity renormalization group (IMSRG) approach and coupled-cluster theory that uses only nuclear forces to calculate the energy of nuclei and other observables such as radii and electric dipole polarizability. This has provided the first predictions for the limits of nuclear existence and the evolution of nuclear shell structure in exotic medium-mass isotopes and the first ab initio computation of the neutron-skin thickness in 48Ca, results which will guide experiments at TRIUMF and world-wide.   

The Theory Department is also extending these theoretical tools to address some of the most fundamental questions in nuclear weak physics, including the nature of neutrino masses and mixing angles (through calculations of neutrino scattering and neutrino-less double-beta decay) and the nature of DM, through calculations of DM particle-nucleus scattering cross sections–how likely it is that a DM particle will interact with a particular nucleus. 


High-Performance Computing 

Nuclear structure and reaction modeling are among the most computationally intense research and thus continually pushing the edge of scientific computing. 

Along with a TRIUMF-based computational cluster for initial calculations, TRIUMF nuclear theorists use some of the world’s largest and most advanced supercomputers, providing scientists and students access to world-class computing resources. These high-performance computing facilities include:  Oak Ridge National Laboratory’s TITAN supercomputer and Compute Canada’s Cedar supercomputer at Simon Fraser University, Canada’s most powerful research supercomputer. 

Ab initio atomic and nuclear modeling is also one of the key areas driving the development of quantum computing. TRIUMF nuclear theorists are establishing collaborations with Vancouver’s D-Wave to explore the application of quantum computing to nuclear modeling to solve currently intractable large nuclei physics problems.  


Nuclear Theory and Muonic Atoms

The discovery of the proton-radius puzzle and the subsequent deuteron-radius puzzle catalyzed an on-going discussion about explanations for the difference in the observed radii obtained from muonic atoms and electron-nucleus systems.  Atomic nuclei have an intricate internal structure that must be taken into account when analyzing experimental results. TRIUMF theorists took a leading position in the study of corrections to the structure and the polarizability of nuclei in light muonic atoms. Such results are widely known, and the contribution to the study of the general problem is universally recognized. 

04 Particle Theory at TRIUMF

The global particle physics community is in a dynamic period of work to open the frontier of beyond-SM physics. TRIUMF’s Particle theorists are developing mathematical models of beyond-SM particles and forces and exploring how high-energy physics experimental facilities, from high-energy colliders, ultra-sensitive detectors and TRIUMF’s rare isotope facilities, can be leveraged for innovative beyond-SM searches. The beyond-SM theories address DM, the origin of neutrino masses, sources of the matter-antimatter asymmetry, and solutions to the electroweak hierarchy problem. 


Electroweak Symmetry Breaking and the Higgs 

In the SM, electroweak symmetry breaking, the process through which force carriers achieve mass, is induced by the Higgs field, but still largely unexplored. The Theory Department has extensive expertise in Higgs physics and the ability to predict the rates of Higgs boson production and simulate the signals these processes would generate in collider detectors for both the Higgs of the SM and beyond-SM extensions. These calculations help to guide precise measurements of the Higgs boson, and searches for new Higgs decay channels, at CERN’s Large Hadron Collider (LHC). 

Similarly, the strong sensitivity of the SM electroweak sector to quantum corrections suggests that there are undiscovered particles and forces with masses just above the weak scale, an energy range now being explored by the LHC. The Theory Department has contributed significantly to the development of theories to elucidate the nature of these possible particles and forces, and also applies Monte Carlo simulation tools to model how they would appear in high-energy colliders.  


Dark Matter 

TRIUMF theorists are developing a wide range of innovative theoretical frameworks for both possible dark matter (DM) candidate particles, and experimental approaches for the direct and indirect detection of them. 

The design of DM experiments depends critically on the projected DM particle’s mass and the nature of its predicted interaction with electrons, protons and neutrons. To guide this, TRIUMF theorists are exploring DM theories that produce DM particles over a wide range of masses and have proposed novel DM candidates with a variety of interaction mechanisms with electrons and nucleons.  

For example, TRIUMF theorists are collaborating with both SNOLAB’s DEAP-3600 (targeted at heavier DM candidate particles) and SuperCDMS (focused on lighter DM candidates) collaborations. The Theory Department is providing calculations of the expected signal rates of DM candidates in deep underground direct-search experiments, cosmic-ray telescopes, astrophysical systems and at particle colliders. This is essential for testing whether a DM candidate is consistent with current experimental data and it helps to guide future searches for that candidate. 

TRIUMF theorists are also exploring new ways to explore for DM using experimental facilities designed for other purposes. This includes searches for very light DM particles that could be created in TRIUMF’s new ARIEL high-intensity electron beam, or in the collisions used to produce neutrinos at the T2K experiment. 



The Theory Department is developing models to explain one of the central questions in neutrino and beyond-SM physics: the origin of neutrino masses. 

Similarly, the Theory Department is exploring the experimental implications of these neutrino mass mechanisms. This includes neutrino mass models that could be tested in leading neutrino experiments, such as the T2K collaboration, of which TRIUMF is a key participant, and possible connections between neutrino masses and the top quark that could lead to new signals at the LHC. 


Origin of Matter Asymmetry 

The observable universe contains much more matter than antimatter, something not explained by the SM. TRIUMF theorists are studying mechanisms through which this matter asymmetry could have emerged, including identifying experimental tests that could reveal mechanisms for the matter asymmetry. These potential tests include modified Higgs boson production and decay rates that could be observed at the LHC, neutron-antineutron oscillations that could be found in precision neutron measurements, and possible proton decay signals that could detected by the T2K-related Super-Kamiokande detector.