FINITE VOLUME FEYNMAN INTEGRALS IN TIME-MOMENTUM REPRESENTATION
(2020) FYTK02 20201Theoretical Particle Physics - Undergoing reorganization
- Abstract
- Finite-volume corrections to the Lattice Quantum Chromo Dynamics (LQCD) calculation of the hadronic vacuum polarization are here considered to one loop, for the simplified case of one and two propagators of equal mass. Simplifications in the calculations are sought for by comparing computations in momentum space, time-momentum space and position space. The derivation of the finite-volume corrections in momentum space and time-momentum space is revisited. We introduce a derivation of the finite-volume corrections in position space. We conclude that the fastest method is to derive the computations in time-momentum space and manually removing the infinite-volume term.
- Popular Abstract
- The agreement between theory and experiments is fundamental in physics. When we measure things, an error is always present. Think, for example, when measuring a length with a ruler, how we can’t get rid of the resolution error, no matter how close we make the notches. We can imagine the error as a small bar attached on both sides of the measured value, meaning that the true value could be a number anywhere on the small bars. To test a theory, we need to compare the value predicted by the theory (that can also have an error) to the measured value. We say the two values agree if their error bars touch. What calls for physicists’ attention is the thrilling case of when theoretical and experimental values don’t agree. It could indeed mean two... (More)
- The agreement between theory and experiments is fundamental in physics. When we measure things, an error is always present. Think, for example, when measuring a length with a ruler, how we can’t get rid of the resolution error, no matter how close we make the notches. We can imagine the error as a small bar attached on both sides of the measured value, meaning that the true value could be a number anywhere on the small bars. To test a theory, we need to compare the value predicted by the theory (that can also have an error) to the measured value. We say the two values agree if their error bars touch. What calls for physicists’ attention is the thrilling case of when theoretical and experimental values don’t agree. It could indeed mean two things, of which one is less thrilling: either that the theory is flawed and new unknown physics is hiding in this disagreement, or simply that we underestimated the size of the error bars. The best way to check whether new physics lays behind this disagreement is to aim to improve the accuracy of both theoretical and experimental values.
Our project, in the long run, aims to contribute to the understanding of one long-standing discrepancy between theory and experiment that endures in particle physics. Particle physics is a frontier branch of physics that studies the smallest, irreducible particles that make up matter and how they interact. The theory describing particle physics is the Standard Model (SM), which is the theory here being challenged. In the disagreement we are addressing, a contribution to the theoretical value is problematic to evaluate. This contribution arises from what is known as vacuum polarization. That is, vacuum is not simply empty space, but it contains particles of very brief existence, that are cyclically created and annihilate in pairs. No, no science fiction.
The difficulty in the computations arises when these pairs of particles are quarks, a type of irreducible particle in the SM. This happens because it is not possible to make predictions using the SM for quarks at low energies, the range of our interest. The best tool so far to evaluate the quark contribution to our theoretical value is a numerical approach, but this approach needs the aid of corrections of reasonable size. These corrections can mostly be carried out analytically and are the core of our project. Our goal is to be able to calculate them in a way that requires fewer numerical approximations. Meanwhile, at Fermilab, a particle physics laboratory in the United States, an experiment is running with the aim of reducing the error on the experimental value.
In summary, the end goal is to check why in particle physics this one measurement does not agree with the value predicted by the theory. Is this disagreement evidence of new physics behind the Standard model? Improving the accuracy on theoretical and experimental values could either settle the discrepancy or set the basis for the discovery of new physics. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9025562
- author
- Giacomozzi, Anna LU
- supervisor
- organization
- course
- FYTK02 20201
- year
- 2020
- type
- M2 - Bachelor Degree
- subject
- language
- English
- id
- 9025562
- date added to LUP
- 2020-08-18 14:41:31
- date last changed
- 2020-08-18 14:41:31
@misc{9025562,
abstract = {{Finite-volume corrections to the Lattice Quantum Chromo Dynamics (LQCD) calculation of the hadronic vacuum polarization are here considered to one loop, for the simplified case of one and two propagators of equal mass. Simplifications in the calculations are sought for by comparing computations in momentum space, time-momentum space and position space. The derivation of the finite-volume corrections in momentum space and time-momentum space is revisited. We introduce a derivation of the finite-volume corrections in position space. We conclude that the fastest method is to derive the computations in time-momentum space and manually removing the infinite-volume term.}},
author = {{Giacomozzi, Anna}},
language = {{eng}},
note = {{Student Paper}},
title = {{FINITE VOLUME FEYNMAN INTEGRALS IN TIME-MOMENTUM REPRESENTATION}},
year = {{2020}},
}