When I get asked what I do, I usually give a top-down answer. If you are signed up for more and more, keep clicking!
I work at the Helmholtz Institute for Radiation and Nuclear Physics (HISKP) in the group of PD Dr. Bastian Kubis and Prof. Dr. Christoph Hanhart.
What we do:
Our group works in phenomenological particle physics, which is a bridge between theoretical and experimental particle physics. We focus on precision tests of the Standard Model, specifically, when it comes to the strong interaction (see the next section).
Why we do it:
Fundamental research is very important for our understanding of nature, which—on its own—is directly correlated with technological advancement. Today we have computers, mobile phones, internet, etc. and we can afford to take them for granted, owing to research that laid the groundwork decades and centuries ago. In the 1920s quantum mechanics was the strangest and one of the least tangible subfield of physics. Nowadays, mere hundred years after, we use all our accumulated knowledge to build quantum computers.
Our group works with hadrons (see the next section). Most of them are very exotic. We don't know how to put them in computers, mobile phones, or cameras (yet!), but we study their properties very closely and the hope is that one day in the not-so-distant future, we will be taking them for granted as well.
We work with hadrons, which are composite particles. You might know some of the elementary particles, like electrons, photons, etc. Hadrons are (oversimplification coming) states made up from quarks and gluons, held together by the strong interaction. There are hundreds of them known to mankind, documented by the Particle Data Group. Famous examples are:
- Baryons, such as
- Protons (made up using 2 up quarks and 1 down quark),
- Neutrons (1 up quark and 2 down quarks),
- etc...
- Mesons, such as
- Pions (up and down quarks),
- Kaons (strange quarks),
- etc...
I work with mesons, especially, with pions, which are the lightest of them. My focus is to study the connection of pions with the electromagnetic current (=a fancy name for a photon). This inevitably means that I am interested in electrons/positrons as well, since most pions we study are produced in electron-positron collisions.
We use dispersion relations and here is why. What we care about are two basic principles: unitarity and analyticity.
Unitarity is connected with something called "probability conservation". This may sound complicated, but it really means a simple thing. In quantum mechanics, we work with an object called a "wavefunction". The wavefunction (squared) gives a probability distribution. The requirement for any probability distribution is that the area below the curve is equal to 1. In simple terms, this means that the total probability is 1 (or 100%). By time, the wavefunction of a physical state changes. But the resulting wavefunction must also produce a probability distribution. A mathematician's way of saying this is that time evolution must be a unitary operation ("unit" = 1), otherwise (as sloppier physicists usually say) "probability is not conserved".
When we say analyticity, we mean the properties of the scattering amplitude as a function on the complex energy plane. The reason why we care if this function is analytic is that this ensures a very important principle - causality, that is the future should not affect the past. Strictly speaking, scattering matrix is not analytic, but meromorphic, which means that certain singularities are allowed, but there is always a physical reason behind them. For instance, branch cuts are associated with the production of particles, poles with resonances, etc. When we compare our models with the experimental data, we only have access to the absolute value of the scattering matrix in isolated regions of the complex plane. The information about the rest of the plane comes from analyticity.
If we are dealing with a meromorphic (analytic up to singularities) function, we can use the Cauchy's integral formula to analytically continue the function from the real axis to the whole complex plane, integrating over the singularities. This is the essence of dispersion relations.