Hint Of New Physics At LHC – Explaining the LHCb Results
By on November 15th, 2011

The tantalizing possibility of new physics may just be around the corner. The LHCb preliminary results surely hint towards that possibility with the first ever detection of CP violation in the charm quark sector. We reported this big news here and in this editorial piece, we intend to elaborate on what the results mean or might imply in layman’s terms.

The actual news piece, which you should read before reading this:  http://techie-buzz.com/science/lhc-newphysics.html

The LHCb detector

Explaining it simply: topics to cover

We will follow the following sequential treatment of the entire subject:

  • What is CP symmetry and what does its violation mean?
  • What is baryon asymmetry and what does CP violation have anything to do with this?
  • What are the generations of quarks?
  • What decay process are we looking at?
  • What about the Standard Model? What does this predict?
  • What are the experimental results and how might we interpret them?

If you think you know any of the sections, you might skip it. Let’s begin our journey.

1. CP Violation

There are certain symmetries that exist in Nature. Many of the symmetries are continuous symmetries, like the rotational symmetry for a sphere. No matter how small an angle of rotation you give to the sphere, it will still look the same. This is not true for an equilateral triangle, whose rotation angle has to be 600 in order for it to look the same. The first one is a continuous symmetry and the latter a discrete one.

Having known what symmetry means, we can look for symmetries in a quantity called the Lagrangian. A Lagrangian reflects all the possible dynamics of a system, (which are manifested through its derivatives). Symmetries of the Lagrangian can be both continuous and discrete. In the Lagrangian for the electromagnetic field, apart from a lot of continuous symmetries, there is also the symmetry of charges. Namely, if you replace all charges with their opposite (i.e. positive charges with negative and vice-versa), the Lagrangian will still be the same. CP (Charge-Parity) symmetry means that whatever operation you perform, if you replace the particles with the anti-particles (charge’) and then switched their positions or reflect them (parity), then no experiment will be able to tell the difference.

CP violation refers to the breaking of this symmetry. Some experiments can differentiate between the above mentioned configurations and, thus, CP is violated. Most notable violation of CP symmetry is given by the weak interaction. This violation is explicitly put in the Lagrangian, which is otherwise CP invariant.

2. Baryon Asymmetry and CP violation

We see that the Universe, as we know it today, is made up of matter and not anti-matter. If there is nothing to differentiate between matter and anti-matter (the labels of particle and anti-particle are human constructs and nothing physically differentiates them), we couldn’t possibly have had more matter than anti-matter. One of the unsolved mysteries is then this: Why is there so much more matter than anti-matter in the Universe. This is known as Baryon Asymmetry puzzle’.

One of the theoretical ways to resolve this is to look for CP violation (see previous section) signatures. CP violating processes can produce more matter particles and hinder the production of anti-matter particles, treating them on unequal footing as explained above. Even though there are models without CP violation, which predict the Baryon Asymmetry, none of them is as beautiful as the Standard Model with the CP violation plugged in. For this to work for every particle, the Baryon number conservation has to be perturbatively broken. In the Standard Model framework, this is not possible. The mechanism for CP violation generating excess baryons is not understood as of now.

3. Generations of Quarks

There are three generations of quarks in the Standard Model. Later generations of quarks are heavier than earlier generations. The three generations are given below.

The generations of quarks, along with the generation of leptons. (Picture courtesy: CERN)

Most matter is made up of just up and down quarks (the lightest of the lot), given that the proton and neutron are made up of these quarks. The charm quark is a second generation quark and is quite heavy. The heaviest is the top quark, which is so heavy that it cannot exist long enough to form a bound state. We can only identify the top quark by its decay signature.

For our current purposes, only the first two generations of quarks are important. The charm quark, being heavy can decay into strange, anti-strange and up quarks or into down, anti-down and up quarks. The up and down, being the lightest of the lot, doesn’t decay into anything. We shall find out the effect of this decay in the next section.

4. Decay Processes and how the D0 and D0 bar particles decay

We have seen, in the previous section, how the heavy charm quark can decay into lighter particles. Quarks cannot be seen in isolation (due to an effect known as Quark Confinement). The lighter quarks immediately form stable bound states, which can be detected either directly or through their own decay processes.

D0 decay process

The D0 particle is a bound state of a charm quark and an anti-up quark, while the D0bar contains an anti-charm and an up quark. We know how the charm decays (previous section). We are now ready to construct the decay products. The up and anti-strange quarks, from the charm decay, can form a positive Kaon, while the other strange and the up (which did not decay) can now form a negative Kaon. Diagrammatically, it looks like the following. (The diagrams below are known as Feynman Diagrams. Ignore the W-boson in between, if you want.)

Similarly, the decay of the charm to give down quarks, instead of strange quarks, give pion-pion end products.

The D0 bar decay process

The D0bar also gives the same end-products, but through different intermediate channels. Here’s the illustration.

For the more technically oriented, it is worthy to note that the diagrams are just tree-level diagrams. There are higher level diagrams, involving one loop (penguin diagrams) and so on.

5. Standard Model and what it says:

The Standard Model is the backbone of particle physics. This describes the interaction of all known forces, except gravity, and all interactions of all particles with these forces. The Standard Model is flexible enough to allow mixing in the quark sector. The quarks can thus mix’ with each other. This amount of mixing is given as an angle, called the Cabibbo angle. The sine of this angle gives the quantitative measure of the mixing. The angle being zero shows no mixing at all.

The quantity we are interested in measuring is this:

This gives the relative rates of the decay into the lighter particles (pions or kaons). If the Cabibbo angle was zero, this would’ve been zero. The fact that the Cabibbo angle is small, is indicated by the fact that the quantity shown above (ACP) is very small.

6. The LHCb Result!

Finally, we want to pull all the strings together and see what the LHCb results indicate. The LHCb results show that the mixing is much greater than anything expected from the Standard Model. The observed value of ACP is 0.82% +/- 0.22%, which is way greater than the very small, nearly zero value. The results are at 3.5 sigma confidence level. This is an important result, not only because this is the first observed CP violation in the charm sector, but also because of the magnitude.

We don’t know what to make of this result at this moment. Further analysis might actually make this result go away. Even though this is not as exciting as the faster-than-light neutrino results to the general public, this might be far more significant.

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Author: Debjyoti Bardhan Google Profile for Debjyoti Bardhan
Is a science geek, currently pursuing some sort of a degree (called a PhD) in Physics at TIFR, Mumbai. An enthusiastic but useless amateur photographer, his most favourite activity is simply lazing around. He is interested in all things interesting and scientific.

Debjyoti Bardhan has written and can be contacted at debjyoti@techie-buzz.com.
 
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