School and Workshop on pQCD@West Lake

From March 26 to March 30, 2018, School and Workshop on pQCD@West Lake was held at the Shao Yifu ScienceBuilding, Yuquan Campus, Zhejiang University. The conference was hosted by the Department of Physics of Zhejiang University and Zhejiang Institute of Modern Physics. More than 90 professors and students from various universities at home and abroad attended the meeting.

At 9:00 am on March 26, the meeting officially began. Prof. Kai Wang, the vice dean of the Department of Physics, introduced the basic situation of the Department of Physics to both foreign and Chinese professors and students in order to promote interest in and understanding of the Department of Physics, Zhejiang University. After the introduction given by Prof. Wang, Prof. Kirill Melnikov from the Karlsruhe Institute of Technology (KIT) introduced the importance, the current status and the prospects of perturbative quantum chromodynamics(pQCD). Prof. Melnikov pointed out that the Large Hadron Collider (LHC) is still producing important data and the accuracy of experiments at the LHC is continuously improving. This gives theoretical physicists access to more accurate experimental results which can be used to test their theories. Afterward, Prof. Melnikov analyzed the complexity of calculations required in pQCD and discussed many possible physical and mathematical breakthroughs that may be surrounding this research. 

The conference focused on three topics within the scope of QCD and high energy collider physics:  resummation, infrared subtraction, and parton showers. Fixed-order calculations in perturbative QCD is usually performed according to perturbative expansions on small increments, and as long as these increments are small enough, the calculation of the first few orders can obtain sufficient precision. However, when the problem is of many scales, these small increments are multiplied by large logarithms, which makes the new amount too large causing the required precision to be lost. At this point, resummation is needed. The result of the corresponding fixed-order calculation is re-summed to all orders. This resummation algorithm was introduced by Prof. Pier F. Monni at CERN. Prof. Monni first introduced the necessity of resummation, and then used an example to explore how to apply it to collider observables. After applying resummation, it was shown that the theoretical calculations were in good agreement with CERN experiments, verifying the accuracy of resummation technique. Prof. Monni pointed out that although the idea of resummation is simple, different observables require different analyses, which is one of the difficulties in resummation. After Prof. Monni’s introduction to resummation, there was a lively discussion between professors and students.

Next, the workshop focused on infared subtraction in QCD. One of the difficulties in QCD calculations is that divergences will often appear in the calculation of Feynman integrals. To get the final result, one needs to regulate the divergence with regulators. The general approach is to calculate the integral directly after the introduction of the regulator, and the obtained result will contain a finite part and a divergent part. This direct calculation method is straightforward but is very complicated at high loop level. Infrared subtraction attempts to separate the divergent part from the finite part at the integrand level, so that Monte Carlo techniques can be used to calculate the finite part. The remaining part, which contains the divergence, still needs to be calculated analytically. However, this part is much simpler compared with a complete analytical calculation. The study of infrared subtraction was introduced by Prof. Raoul Rontsch from the Karlsruhe Institute of Technology. He first introduced the origins of infrared divergences and the benefits of infrared subtraction methods. Prof. Rontsch then introduced infrared subtraction at both the one loop and two loop levels. He pointed out that at the one loop level, the method of infrared subtraction has been put on rigorous theoretical grounding. Although different kinds of subtraction schemes have been applied to infrared subtraction, none of them work especially well and all are still in development. The professors and students discussed about the existing subtraction schemes and current developments in this area of research.

Finally, the workshop reported on parton showers in QCD. The necessity of parton showers mainly lies in the following two items: firstly, when the number of initial states and final states of particles is large enough, one cannot get the physical results from direct calculation due to the underlying complexity; secondly, when the energy is very low, the QCD coupling constant becomes very large and there is no method to perform the perturbative calculations. The approximate image of parton showers is that when the energy is high, the coupling constant is very small, at this time, there are only a few partons in a physical process which can be calculated perturbatively. As the energy decreases, the coupling constant becomes large, and some of the particles radiate out lots of other particles. These radiated particles also radiate a lot of new particles. Just like a shower, the particles move in different directions. This is the origin of the name “parton shower”. This part is difficult to calculate directly, and one can only resort to parton shower methods which works according to the evolution of parton distribution functions and statistical methods. Parton showers methods were introduced by Prof. Stefan Hoche of Stanford University, one of the authors of the famous parton shower software, Sherpa. After introducing the basics of parton showers, Prof. Hoche lectured about two major concepts of parton showers -- the event generator and the jet algorithm. He pointed out that most of the parton shower software today only considers the leading power of the parton shower, if one needs to obtain more accurate results, one must also consider the correction of the next-leading power. After the introduction on parton showers, the professors and students engaged in an in-depth discussion on this correction of the next-leading power for parton methods.

In addition to the above three topics, the conference also invited domestic experts to give short reports to discuss QCD and high-energy collider physics. These public reports were held in Lecture Hall 117 of the Shao Yifu Science Building. Lance Dixon, a professor from Stanford University, gave a report titled “Hunting the Elusive Higgs Boson and the Origin of Mass”. More than 250 guests participated in the report, including more than 90 professors and students attending the seminar, as well as undergraduate and graduate students from various colleges of Zhejiang University.

In the afternoon of March 30^th, Prof. Lance Dixon gave a report titled Outlook for Perturbative QCD at Colliders as a closing ceremony. Prof. Dixon first briefly summarized the seminars given at the workshop and lectured on the outlook and future for QCD and high-energy collider physics. He pointed out that numerical methods in the future will be more numerical and the analytical methods in the future will be more analytical. In the future, computer resources will become cheaper, and one can use powerful computers to calculate results that are not currently possible, and at the same time utilizing machine learning to help with these calculations. With regards to the portions of QCD where analytical methods are possible, the combination of mathematics and mathematical physics will be continuously developing, creating more powerful analytical tools to solve these problems, and it will also be possible to use QCD's toy model N = 4 supersymmetric Yang–Mills theory to study QCD. At the end of this final report, there was a warm round of applause concluding the workshop.