Periodic Reporting for period 1 - EWMassHiggs (Massive QCD-Electroweak Corrections to Higgs Production Through Gluon Fusion at NNLO)
Période du rapport: 2022-09-01 au 2024-08-31
In order to understand the composition of the universe and the properties of matter within it, we consider its smallest building blocks, such as electrons, photons and quarks, and try to understand how they interact with each other. After the Higgs boson has recently been discovered, its properties are of particular interest to the scientific community, as it is the key ingredient to the mechanism which gives all other particles their mass. This property could also be a gateway to understanding dark matter, which we have so far only observed through the influence of its mass on light rays travelling through the universe and which appears to be invisible otherwise.
To learn about the properties of particles, we formulate a mathematical model of their interactions (like the Standard Model) and calculate the probabilities of producing a certain particle in collision experiments such as the one taking place at the Large Hadron Collider (LHC) at CERN. By comparing the calculated probabilities to the measured ones, we can infer whether our model represents the laws of nature or not. Mathematically, we encode these probabilities in so-called scattering amplitudes. These can generally not be calculated exactly, but we have to approximate them using a technique called perturbation theory, where we consider ever-more 'perturbations' of the underlying process. With each additional perturbation, our result becomes more accurate, while the calculation becomes more and more complicated.
In this project, we consider the calculation of scattering amplitudes as functions of the masses of the Z- and W-bosons, the Higgs boson as well as the top quark, which constitute the heavy particles of the Standard Model. Generally, calculations become much more difficult, when keeping track of the masses of particles, and we often encounter new mathematical functions which are not yet well understood. The goal of this project is to understand the mathematical properties of these functions in order to enable the calculation of scattering amplitudes to very high orders in perturbation theory, resulting in very precise theoretical predictions for collider experiments. In particular, we consider the production of a Higgs boson at the Large Hadron Collider, which is an important ingredient to understanding the properties of the Higgs boson and potentially to illuminating the hidden features of dark matter.
To learn about the properties of particles, we formulate a mathematical model of their interactions (like the Standard Model) and calculate the probabilities of producing a certain particle in collision experiments such as the one taking place at the Large Hadron Collider (LHC) at CERN. By comparing the calculated probabilities to the measured ones, we can infer whether our model represents the laws of nature or not. Mathematically, we encode these probabilities in so-called scattering amplitudes. These can generally not be calculated exactly, but we have to approximate them using a technique called perturbation theory, where we consider ever-more 'perturbations' of the underlying process. With each additional perturbation, our result becomes more accurate, while the calculation becomes more and more complicated.
In this project, we consider the calculation of scattering amplitudes as functions of the masses of the Z- and W-bosons, the Higgs boson as well as the top quark, which constitute the heavy particles of the Standard Model. Generally, calculations become much more difficult, when keeping track of the masses of particles, and we often encounter new mathematical functions which are not yet well understood. The goal of this project is to understand the mathematical properties of these functions in order to enable the calculation of scattering amplitudes to very high orders in perturbation theory, resulting in very precise theoretical predictions for collider experiments. In particular, we consider the production of a Higgs boson at the Large Hadron Collider, which is an important ingredient to understanding the properties of the Higgs boson and potentially to illuminating the hidden features of dark matter.
Since the start of the project, we have made progress both in the calculation of scattering amplitudes to high orders in perturbation theory and have furthermore identified a mechanism which can lead to the simplification of the apparent function spaces appearing in certain scattering amplitude calculations.
We have calculated so-called master integrals (i.e. a set of needed Feynman integrals which suffices to express scattering amplitudes to a given process) for the production of a top-quark pair in association with another hadron in quantum chromo dynamics (QCD) at the LHC. This process is of great importance, as it is very sensitive to the mass of the top quark, which has not yet been determined to sufficiently high precision. The integrals we computed are key ingredients in calculating highly relevant scattering amplitudes both for the scattering process considered here as well as other scattering processes to be calculated in the future or by other researchers. The results have been published in open-access journals and have been provided, for immediate use by other colleagues, in machine-readable format.
We have further calculated scattering amplitudes relevant for the production of a Higgs boson at the LHC with dependence on the masses of all heavy particles in the Standard Model. This process is a central part of the project and its calculation constitutes a major challenge, due to the amount of different masses to keep track of, and due to considering the full Standard Model. While the results have been calculated, they are yet to be cross-checked and published, which will be done in the near future.
The function spaces relevant for calculations in theoretical particle physics can often be associated to certain geometric objects. The easiest such object is the Riemann sphere, the surface of a 3-dimensional ball. The function space associated with the Riemann sphere consists of multiple polylogarithms. A slightly more complicated function space which has recently been understood well enough to be used in analytic calculations are the so-called elliptic multiple polylogarithms, which are associated to elliptic curves or tori. Beyond these function spaces, many others, such as hyperelliptic curves of different genera and Calabi-Yau manifolds, have been encountered in calculations, and they usually constitute a bottleneck to analytic calculations. Furthermore, the higher the genus of a hyperelliptic curve, the more complicated the associated function space. In this project, we have investigated and resolved a longstanding discrepancy in genera of hyperelliptic curves associated to certain Feynman integrals. In the corresponding publication, we have also shown that it might often be possible to reduce the genus of hyperelliptic curves appearing in Feynman integral calculations and have provided a computer code to check whether this is the case, which can potentially simplify future calculations in theoretical particle physics.
We have calculated so-called master integrals (i.e. a set of needed Feynman integrals which suffices to express scattering amplitudes to a given process) for the production of a top-quark pair in association with another hadron in quantum chromo dynamics (QCD) at the LHC. This process is of great importance, as it is very sensitive to the mass of the top quark, which has not yet been determined to sufficiently high precision. The integrals we computed are key ingredients in calculating highly relevant scattering amplitudes both for the scattering process considered here as well as other scattering processes to be calculated in the future or by other researchers. The results have been published in open-access journals and have been provided, for immediate use by other colleagues, in machine-readable format.
We have further calculated scattering amplitudes relevant for the production of a Higgs boson at the LHC with dependence on the masses of all heavy particles in the Standard Model. This process is a central part of the project and its calculation constitutes a major challenge, due to the amount of different masses to keep track of, and due to considering the full Standard Model. While the results have been calculated, they are yet to be cross-checked and published, which will be done in the near future.
The function spaces relevant for calculations in theoretical particle physics can often be associated to certain geometric objects. The easiest such object is the Riemann sphere, the surface of a 3-dimensional ball. The function space associated with the Riemann sphere consists of multiple polylogarithms. A slightly more complicated function space which has recently been understood well enough to be used in analytic calculations are the so-called elliptic multiple polylogarithms, which are associated to elliptic curves or tori. Beyond these function spaces, many others, such as hyperelliptic curves of different genera and Calabi-Yau manifolds, have been encountered in calculations, and they usually constitute a bottleneck to analytic calculations. Furthermore, the higher the genus of a hyperelliptic curve, the more complicated the associated function space. In this project, we have investigated and resolved a longstanding discrepancy in genera of hyperelliptic curves associated to certain Feynman integrals. In the corresponding publication, we have also shown that it might often be possible to reduce the genus of hyperelliptic curves appearing in Feynman integral calculations and have provided a computer code to check whether this is the case, which can potentially simplify future calculations in theoretical particle physics.
The treatment of integrals over geometries beyond elliptic curves still constitutes a major challenge in analytic calculations in theoretical particle physics. We have taken a major step towards better understanding how these geometries arise and towards keeping such calculations as simple as possible. We have also calculated Feynman integrals involving the dependence on all heavy particles of the Standard Model, where current state of the art calculations usually only consider the top quark, the heaviest of the Standard Model particles, massive. The results of this project are widely applicable and will be relevant for many future calculations in theoretical particle physics.