Q&A

Several questions arose during lectures some of which deserve more attention. Here we provide a little more information, including references.

Lecture 1

Is any other term that can be included in the QCD Lagrangian?

By dimensional counting (less or equal four), there is only one possibility:

where $\tilde G$ is the dual field tensor. This term violates parity $P$ and time reversal $T$, but since both are not symmetries of the Standard Model (violated by weak interactions) it should be included. The problem is that one would then expect, from naturalness argument to have $\theta$ of order one. Experimental bounds coming mainly from the limits on the neutron electric dipole moment gives

$

\theta

<10{-10}$. This gives the so-called "strong CP problem". The Peccei-Quinn mechanism (​Phys.Rev.Lett. 38 (1977), 1440) is a famous attempt to solve this problem by introducing a dynamical field, which gives rise to the axion. See the PDG section on ​axion searches for an up-to-date report on axion searches.

The parton distribution functions are non-perturbative quantities. Is there any solid lattice result?

The most recent update on these attempts I was able to find is of 2002,(​hep-ph/0206050). In practice I am not aware of any result competitive with the most common global fits from CTEQ, MRST, NNPDF,...

In a MC approach we always start from the high $Q^{2$ interaction and then apply forward (time-like) evolution to connect it with the final state and backward (space-like) evolution to connect it with the initial state. Why don't we start from the initial state and go all the way to the final one?}

The main reason is just efficiency. Consider for example Higgs production from gg or Drell-Yan. If I start a forward shower from the incoming protons I will only very very rarely hit the right $Q^{2$ (of order of the boson masses) in correspondence with the right x's ($x_1 x_2 S=M}2$).

Lecture 2

What are the key experimental facts which lead to the building of SU(2) x U(1) model?

There are several : the properties (energy and angular distributions) of the muon decay $\mu^{- \to e}- \bar \nu_e \nu_\mu$, Beta decay, and pion decays $\pi^{- \to l}- \bar \nu_l$. A concise list and discussion can be found, for instance, in the older version of the lectures on the SM by A. Pich (​hep-ph/9412274).

Consider the hypercharge assignments. What is the role of anomalies? How does the Inclusion of a right-handed neutrino (Dirac or a Majorana) change this picture?

Hypercharge assignments in the SM are built ad hoc to reproduce the EM charge. The final pattern seems arbitrary. However, chiral anomaly cancellation shows that this is not the case. Anomaly cancellation relates lepton and quark doublet charge assignments in a non trivial way

i.e. it related the number of colors to the electric charge, leading to quantization of the electric charge. In Grand-Unified-Theories ( such as SU(5) and SO(10) ) hypercharge assignments are determined by the matter multiplet representation and predicted.

It's kind of interesting to note that if a neutrino right is added to the SM, charge quantization is "lost", unless this is a Majorana neutrino. See, for instance, Babu and Mohapatra (​Phys. Rev. D41:271,1990).

Neutrino masses are described by the Standard Model or not?

Neutrino masses can be accommodated in the Standard Model, but I prefer to use the definition of Standard Model without any right-handed neutrino. If you do so, then you can consider neutrino masses as our first solid indication of physics beyond the Standard Model. This is nice for many reasons. My preferred one is as follows. Considering the Standard Model as an effective field theory, one can start including the effects of new physics as described by higher dimensional operators. The largest effects should be coming from the lower dimensional operators. Now it turns out that you can write dozens of operators of dimension 6 and beyond. However, there is only one operator of dimension 5, of the type (schematically) $( L \phi) (\phi L)/M$, that describes Majorana neutrino masses. Isn't that great?

What happens to the Veltman equation that describes the 1-loop corrections to the Higgs mass at higher orders?

More to come. In the meantime you can read what Gian Giudice says in ​[arXiv:0801.2562], pag. 14.

You have shown that in MSSM the Higgs mass term can become negative in the evolution to low scales, due to the top loop effects. How much fine tuning does this need?

A brief discussion on this mechanism can be found in the famous ​SUSY lectures by S. Martin, pag. 64, and more details in ​hep-ph/0206136.

-- Main.FabioMaltoni - 04 Sep 2008