# Conference Amplitudes 2015!

It’s conference season! I’m hanging out in very warm Zurich with the biggest names in my field – scattering amplitudes. Sure it’s good fun to be outside the office. But there’s serious work going on too! Research conferences are a vital forum for the exchange of ideas. Inspiration and collaboration flow far more easily in person than via email or telephone. I’ll be blogging the highlights throughout the week.

Monday | Morning Session

To kick-off we have some real physics from the Large Hadron Collider! Professor Nigel Glover‘s research provides a vital bridge between theory and experiment. Most physicists in this room are almost mathematicians, focussed on developing techniques rather than computing realistic quantities. Yet the motivation for this quest lie with serious experiments, like the LHC.

We’re currently entering an era where the theoretical uncertainty trumps experimental error. With the latest upgrade at CERN, particle smashers will reach unprecedented accuracy. This leaves us amplitudes theorists with a large task. In fact, the experimentalists regularly draw up a wishlist to keep us honest! According to Nigel, the challenge is to make our predictions twice as good within ten years.

At first glance, this 2x challenge doesn’t seem too hard! After all Moore’s Law guarantees us a doubling of computing power in the next few years. But the scale of the problem is so large that more computing power won’t solve it! We need new techniques to get to NNLO – that is, corrections that are multiplied by $\alpha_s^2$ the square of the strong coupling. (Of course, we must also take into account electroweak effects but we’ll concentrate on the strong force for now).

Nigel helpfully broke down the problem into three components. Firstly we must compute the missing higher order terms in the amplitude. The start of the art is lacking at present! Next we need better control of our input parameters. Finally we need to improve our model of how protons break apart when you smash them together in beams.

My research helps in a small part with the final problem. At present I’m finishing up a paper on subleading soft loop corrections, revealing some new structure and developing a couple of new ideas. The hope is that one day someone will use this to better eliminate some irritating low energy effects which can spoil the theoretical prediction.

In May, I was lucky enough to meet Bell Labs president Dr. Marcus Weldon in Murray Hill, New Jersey. He spoke about his vision for a 10x leap forward in every one of their technologies within a decade. This kind of game changing goal requires lateral thinking and truly new ideas.

We face exactly the same challenge in the world of scattering amplitudes. The fact that we’re aiming for only a 2x improvement is by no means a lack of ambition. Rather it underlines that problem that doubling our predictive power entails far more than a 10x increase in complexity of calculations using current techniques.

I’ve talked a lot about accuracy so far, but notice that I haven’t mentioned precision. Nigel was at pains to distinguish the two, courtesy of this amusing cartoon.

Why is this so important? Well, many people believe that NNLO calculations will reduce the renormalization scale uncertainty in theoretical predictions. This is a big plus point! Many checks on known NNLO results (such as W boson production processes) confirm this hunch. This means the predictions are much more precise. But it doesn’t guarantee accuracy!

To hit the bullseye there’s still much work to be done. This week we’ll be sharpening our mathematical tools, ready to do battle with the complexities of the universe. And with that in mind – it’s time to get back to the next seminar. Stay tuned for further updates!

Update | Monday Evening

Only time for the briefest of bulletins, following a productive and enjoyable evening on the roof of the ETH main building. Fantastic to chat again to Tomek Lukowski (on ambitwistor strings), Scott Davies (on supergravity 4-loop calculations and soft theorems) and Philipp Haehnal (on the twistor approach to conformal gravity). Equally enlightening to meet many others, not least our gracious hosts from ETH Zurich.

My favourite moment of the day came in Xuan Chen’s seminar, where he discussed a simple yet powerful method to check the numerical stability of precision QCD calculations. It’s well known that these should factorize in appropriate kinematic regions, well described by imaginatively named antenna functions. By painstakingly verifying this factorization in a number of cases Xuan detected and remedied an important inaccuracy in a Higgs to 4 jet result.

Of course it was a pleasure to hear my second supervisor, Professor Gabriele Travaglini speak about his latest papers on the dilatation operator. The rederivation of known integrability results using amplitudes opens up an enticing new avenue for those intrepid explorers who yearn to solve $\mathcal{N}=4$ super-Yang-Mills!

Finally Dr. Simon Badger‘s update on the Edinburgh group’s work was intriguing. One challenge for NNLO computations is to understand 2-loop corrections in QCD. The team have taken an important step towards this by analysing 5-point scattering of right-handed particles. In principle this is a deterministic procedure: draw some pictures and compute.

But to get a compact formula requires some ingenuity. First you need appropriate integral reduction to identify appropriate master integrals. Then you must apply KK and BCJ relations to weed out the dead wood that’s cluttering up the formula unnecessarily. Trouble is, both of these procedures aren’t uniquely defined – so intelligent guesswork is the order of the day!

That’s quite enough for now – time for some sleep in the balmy temperatures of central Europe.