After 17 Months: PRD Publication

We published a paper based on my Bachelor’s thesis – submitted in July 2011 at Humboldt University. You can read it on arXiv or PRD.

What did we do?
We analysed the efficiency of new analytical expressions for tree-level amplitudes in massless QCD. To give an idea what this means, you have to read the last sentence backwards (almost word for word):

  • QCD
    QCD stands for Quantum Chromo Dynamics and is a quantum field theory to describe the fundamental particles of matter, namely quarks and their interaction through gluons. Protons and Neutrons (in the nucleus of every atom) are built from quarks. Understanding QCD is crucial to understand the behavior of matter on high energies, for example in high energy experiment at the Large Hadron Collider (LHC) at CERN.
  • Massless
    Quarks are not massless (otherwise we would not feel gravity). However, on high energies the mass is negligible compared to the high-energy in their momentum: a bullet shot with a canon will still fall down, but as approximation for a few meters we can assume that it follows almost a straight line. In the same way, we can neglect mass if a particle is accelerated to a very high speed and momentum.
  • Amplitudes
    For many experiments in high-energy physics we want to know how likely it is that accelerated particles scatter and produce new particles. This can be answered by calculating a probability distribution which depends on the absolute value of a complex quantity called scattering amplitude. Roughly speaking, a (scattering) amplitude is the function that allows us to calculate the probability of a scattering event to happen and it depends on the properties of the particles involved.
  • Tree-level
    Calculating scattering amplitudes is difficult: Even with computer there is no way to calculate scattering amplitudes to arbitrary precision. Instead we have to use a perturbation series of very complicated expressions. Feynman found a way to represent these complicated expressions by simple diagrams called Feynman diagrams and the perturbation series
  • Analytical exprressions
    Calculation of such amplitudes is mainly done through a numerical recursion that repeats certain steps a number of times to get a numerical result. In contrast to this, an analytical expression is one formula describing how you get a numerical value by just applying certain operations (like addition, multiplication, squareroots etc.) and is mathematically speaking a function with explicit form. In our case, we have such analytical expressions for the tree-level amplitudes, even though they are very long and complicated.
  • Efficiency
    In order to predict certain outcomes of a scattering experiment one needs to predict probabilities by calculating the amplitudes for different possible processes. Because even on tree-level (leading order) one finds a huge number of possible processes one has to evaluate thousands and millions of amplitudes which makes efficiency very important: the less time one evaluation of an amplitude takes the more realistic is it to make certain predictions. Our whole analysis has the goal to compare the efficiency of just evaluating our analytical expressions with one commonly used numerical procedures (called Berends-Giele) that use a recursion to approximate the value. Furthermore, we compared the precision of the different approaches.

What did we get?
As expected before, our implementation of the analytical formulae (the main work of my bachelor thesis) is faster for the first two orders (MHV and NMHV). The third order (NNMHV) that I implemented, as well, becomes slower than the Berends-Giele approach as the number of involved particles increases. I did not implement higher orders because it was clear that higher orders will be slower than Berends-Giele. Finally, the accuracy of the analytical formulae was a bit higher than using the Berends-Giele scheme.

Busy Break – Busy 2013

German Christmas Candies

German Christmas Candies

I decided to return to Europe for the two weeks of winter break to see my girlfriend and to celebrate Christmas in Germany. Furthermore, I wanted to realize a long dream: to celebrate New Year in Berlin!

In the following list you see a short order of events:

  1. Flight: Dakar-Madrid and Madrid-Paris (22.12/23.12)
  2. Trainride: Paris-Mannheim (24.12)
  3. Christmas in Freinsheim (24.12-29.12)
  4. Visiting Cologne, Essen and Hagen (29.12-31.12)
  5. New Year in Berlin (31.12-3.1)
  6. Flight: Berlin-Paris (3.1)
  7. Relaxing in Paris (3.1-5.1)
  8. Flight: Paris-Madrid and Madrid-Dakar (5.1)

Over the break I did not do much work and focused on enjoying a good time. However, during the last week I was ill which enabled me to do at least some computer work. On the weekend when I felt better we had some meetings to discuss the progress of different projects.

Concretely, I am currently involved in the following activities for 2013:

  1. Preparation: Summer School in Quantum Information Theory
    Together with Robert Jonsson I will teach a course on quantum information theory at the beginning of August: the school is offered for talented highschool students (German: Deutsche Schülerakademie) I am very excited about this opportunity.
  2. Writing: Lecture Notes on Shape Dynamics
    I started to write some lecture notes on my current research that I would like to finish soon. You find the current version on the course page of my Sunday lectures.
  3. Production: AIMS Movie
    We still have to film some student interviews, some intro animations and a conversation with Neil Turok, founder of AIMS. Morgan, Pavel and I are optimistic to finish a version within the next month.
  4. Launch: African Opportunity Network
    Yannick, Pavel and I were working hard to launch the official website for the African Opportunity Network.
  5. Lobbying: PSI Alumni Conference 2014
    The PSI Alumni Committee is thinking about lobbying for a re-union of four generations of PSI in the form of an scientific conference at Perimeter Institute in 2014.
  6. Preparation: Internship at Global Public Policy Institute in Berlin
    At the end of April I will begin an internship at GPPi in Berlin and I try to start reading about public policy and relevant stakeholders to get grasp on this unknown field.
  7. Research: Perturbative approach to Shape Dynamics
    With Tim Koslowski I am continuing a collaboration from my Master’s thesis and I am spending the remaining time beside my tutor job and other activities on tricky calculations involving tons of Poisson brackets.

I am very excited what else 2013 will bring. My plans reach until the 17th of August when Robert’s and my summer school on quantum information ends – what I will do next or where I will hopefully begin my PhD is open. Stay tuned…