Much like b-quarks, c-quarks can form relatively long-lived mesons (quark-antiquark bound states) with lighter quarks. Since mesons containing a b-quark are called B-mesons, those containing a c-quark are, logically, called D-mesons. Among these are 2 electrically neutral mesons: D0 = charm + anti-up quark, and D0bar = anti-charm + up cbar-u quark. CP symmetry relates particles and anti-particles, in this case it relates D0 and D0bar. Note that D0 and D0bar mix, that is they can turn into one another; this is an important and experimentally established phenomenon which in general may be related to CP violation however in the present story it plays a lesser role .

D-mesons are produced at the LHC with a huge cross-section of a few milibarns. LHCb is especially well equipped to identify and study them. In particular, they can easily tell kaons from pions thanks to their Cherenkov sub-detector.

Here we are interested in D mesons decays to a CP invariant final state f+f- where f = π,K. Thus, the D0 → f+f- and D0bar → f+f- processes are related by a CP transformation, and we can define the CP asymmetry as

If CP was an exact symmetry of the universe, the asymmetries defined above would be zero: the decay probabilities into pions/kaons of D0 and D0bar would be the same. The Standard Model does violate CP, however its contributions are estimated to be very small in this case, as I explain in the following.

If CP was an exact symmetry of the universe, the asymmetries defined above would be zero: the decay probabilities into pions/kaons of D0 and D0bar would be the same. The Standard Model does violate CP, however its contributions are estimated to be very small in this case, as I explain in the following. At the Tevatron and B-factories they measured separate measurements of the asymmetries A _CP (π+π-) and A _CP (K+K-) (obtaining results consistent with zero). LHCb quotes only the difference A_ CP (K+K-) - A _CP (π+π-) because, at a proton-proton collider, the D0 and D0bar mesons are produced at a different rate. That introduces a spurious asymmetry at the detection level which, fortunately, cancels out in the difference. Besides, the mixing contribution to the asymmetry approximately cancels out in the difference as well. Thus, the observable measured by LHCb is sensitive to so-called direct CP violation (as opposed to indirect CP violation that proceeds via meson-antimeson mixing).

(π+π-) and A (K+K-) (obtaining results consistent with zero). LHCb quotes only the difference A_ (K+K-) - A (π+π-) because, at a proton-proton collider, the D0 and D0bar mesons are produced at a different rate. That introduces a spurious asymmetry at the detection level which, fortunately, cancels out in the difference. Besides, the mixing contribution to the asymmetry approximately cancels out in the difference as well. Thus, the observable measured by LHCb is sensitive to so-called CP violation (as opposed to CP violation that proceeds via meson-antimeson mixing). LHCb has collected 1.1 inverse femtobarn (fb-1) of data, 5 times less than ATLAS and CMS, because the LHCb detector cannot handle as large luminosity. The present analysis uses a half of the available data set. The error of the measurement is still dominated by statistics, so analyzing the full data set will shrink the error by at least Sqrt[2].

What does the good old Standard Model has to say about these asymmetries? First of all, any CP asymmetry has to arise from interference between 2 different amplitudes entering with different complex phases. In the Standard Model the 2 dominant amplitudes are:

#1: Tree-level weak decay amplitude. The pictured amplitude involves the CKM matrix elements V_us and V_cs, therefore it is suppressed by one power of Cabibbo angle, the parameter whose approximate value is 0.2.

#2: One-loop amplitude which, for reasons that should be kept secret from children, is calle d the penguin . Again it involves the CKM matrix elements V_us and V_cs, and also a loop suppression factor α_strong/π. However, as is well known, any CP violation in the Standard Model has to involve the 3rd generation quarks, in this case a virtual b-quark in the loop entering via V_cb and V_ub CKM matrix elements.

The corresponding D0 → π+π- amplitudes are of the same order of magnitude.

#1: The pictured amplitude involves the CKM matrix elements V_us and V_cs, therefore it is suppressed by one power of Cabibbo angle, the parameter whose approximate value is 0.2. #2: which, for reasons that should be kept secret from children, is calle d the . Again it involves the CKM matrix elements V_us and V_cs, and also a loop suppression factor α_strong/π. However, as is well known, any CP violation in the Standard Model has to involve the 3rd generation quarks, in this case a virtual b-quark in the loop entering via V_cb and V_ub CKM matrix elements. The corresponding D0 → π+π- amplitudes are of the same order of magnitude. All in all, the direct CP asymmetry in the D0 → π+π- and D0 → K+K- is parametrically proportional to (α_strong/π) (Vcb*Vub)/(Vus*Vcs) which is suppressed by the 4-th power of the Cabibbo angle and a loop factor. This huge suppression factor leads to an estimate of the Standard Model contribution to the CP asymmetry at the level of 0.01-0.1%. On the other hand, LHCb finds a much larger magnitude of the asymmetry, of order 1%.

Is it obviously new physics? Experts are not sure because D-mesons are filthy bastards. With the masses around 2 GeV, they sit precisely in the no man's land between perturbative QCD (valid at energies >> GeV) and low-energy chiral perturbation theory (valid between 100 MeV and 1 GeV). For this reason, making precise Standard Model predictions in the D-meson sector is notoriously difficult. It might well be that the above estimates are too naive, for example the penguin diagram may be enhanced by non-calculable QCD effects by a much-larger-than-expected factor.

And what is it if it indeed is new physics beyond the Standard Model? This was definitely not the most expected place where theorists had expected new physics to show up. Currently there are almost no models on the market that predict CP violation in D0 decays without violating other constraints. I'm aware of one that uses squark-gluino loops to enhance the penguin, let me know about other examples. This gap will surely be filled in the coming weeks, and I will provide an update once new interesting examples are out.

It finally happened: we have the first official claim of new physics at the LHC. Amusingly, it comes not from ATLAS or CMS, but from LHCb, a smaller collaboration focused on studying processes with hadrons formed by b- and c-quarks. Physics of heavy quark flavors is a subject for botanists and, if I only could, I would never mention it on this blog. Indeed, a mere thought of the humongous number of b- and c-hadrons and of their possible decay chains gives me migraines. Moreover, all this physics is customarily wrapped up in a cryptic notation such that only the chosen few can decipher the message. Unfortunately, one cannot completely ignore flavor physics because it may be sensitive to new particles beyond the Standard Model, even very heavy ones. This is especially true for CP-violating observables because, compared to small Standard Model contributions, new physics contributions may easily stand out.So, the news of the day is that LHCb observed direct CP violation in neutral D-meson decays. More precisely, using 0.58 fb-1 of data they measured the difference of time-integrated CP asymmetries of D→ π+π- and D→ K+K- decays. The result is3.5 sigma away from the Standard Model prediction which is approximately zero!Here is an explanation in a slightly more human language:So, is this new physics or the Standard Model? The LHCb result is definitely exciting, but the jury is still out. This time we need not only more data, but also a more inspired approach to understand the Standard Model predictions. Let's see what theorists will make of it. The only certain thing is that it's the first evidence of CP violation in the charm sector. For more insight see also Sean Tommaso . Thanks to Diego for enlightenment.