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 is

3.5 sigma away from the Standard Model prediction which is approximately zero!

Here is an explanation in a slightly more human language:

- 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. - 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).
- 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 called 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. - 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.

## 29 comments:

Yes, yes, yes! You should not assume that ALL theorists were not expecting such a thing ...

I have been predicting for some time that the CKM phases will differ from standard ones, but NOT beta_s, as observed.

Kea, you don't even understand what the measurement is.

Excellent report! Thank You. You just gave a proof that blogging can be ultrafast, ultraprecise and yet obey quite a few rules.

According to Your question.. Little higgs (arxiv:0904.1545v3)?

Speak for yourself, Jester.

I wonder how tightly the running of the strong force coupling constant in that equation is determined at that energy level?

If the strong force coupling constant fell off at higher energies more slowly than expected (the standard expectation is proportional to 1/ln(E^2/(strong force decay width)^2)) and this wasn't too tightly constrained by other experiments, wouldn't it be possible to explain the excess in the CP violation without introducing another CP violating phase in the CKM matrix? For example, what if the running of the strong force coupling constant was really proportional to the SM term minus (k/ln(E^2)/(strong force decay width)^2)^3 for a suitable constant k (perhaps the full expression would be some sort of infinite series with terms of alternating signs).

I would think that D-meson decays at LHCb should start to be at energy levels that are starting to exceed well calibrated runnings of the strong force coupling constant from Tevatron, et al. And, tweaking the beta function of running of the the strong force coupling constant would seem like a more subtle tweak than the addition of a new CP violating phase parameter if it would work.

Anon, yes I know this one, but doesn't it rather predict large CP violation in *mixing*?

Couldn't this effect be due to the existence of a fourth generation of quarks?

I agree with Jester. 0904.1545 is about CP violation in D0 - D0bar mixing predicted by the Littlest Higgs with T-parity. I doubt that LHT dynamics can generate significant CP violation in a decay, that occurs at the tree level in the SM and is only singly Cabibbo-suppressed...

IIRC, this SM4 paper from this past June also offers a theoretical fix.

0904.1545 has only 3 lines about the D decays to KK and pi-pi. They say the effect would be driven by the mixing phase (as far as I understand, the indirect contribution cancels out in the asymmetry difference).

This paper does a good job discussing the effect of a fourth generation on D0-D0 mixing:

http://arxiv.org/abs/1004.4565

There is an old paper that predicts SM asymmetries in these channels to be more than an order of magnitude smaller. This asymmetry is notoriously difficult to predict. I usually quote 0.1% as an upper bound for SM predictions in individual channels. WHat they see is close to it, but it's also bigger. Who knows...

Quite amusing that 0904.1545 seems to have taken inspiration for the title from hep-ph/0703204, with the appropriate replacement MSSM -> LHT.

All these papers focus on CPV in mixing though.

most importantly, you beat your fellow bloggers with this news ;)

I was lucky to be at ground zero

Jester, LHCb check that the indirect contribution cancels, as you say, but the point is that the same

theoretical parameterscan be responsible for both CP types.where is matti pitkanen's TGD explanation? ;-)

Ptrslv2 and anyone interested can find a more detailed

summary about direct CP breaking in TGD Universe at my blog.

P. I'll kick your ass for provocation.

oh great. what an excellent opportunity for lattice QCD.

Thank you for such a clearly worded explanation. It's been a long time since my undergraduate degree ;)

Jester, now that you have revealed your phobia of flavor physics some previously puzzling things become more understandable..

But I'm curious about the psychological effect of this episode on you. Does it make your more or less inclined to continue to ignore the existence of previous indications of new flavor physics discussed e.g. here and here?

Jester, were you at the LHCb workshop, where this new measurement was apparently first unveiled?

Anon-1, no I wasn't there. Anon-2, I don't ignore these papers, and I won't be shocked if those hints will be upgraded to evidence one day. But, regardless, I have an impression there is some cherry picking there.

Jester, sorry for being a pedantic smart ass: "analyzing the full data set will shrink the error by at least Sqrt[2]" should be ...by at most Sqrt[2]. Adding stat and sys errors quadratically I get an expected significance of about 4.5 sigma. Just short of the magic 3.5*Sqrt[2]=5.

Well, whether you get 4.8 or 5.2 sigma is subject to statistical fluctuations as well.

If the effect is real and as large as the presented value, the analysis of the full 2011 dataset should get somewhere close to 5 sigma and 2012 data will surpass this without problems.

There is a SM explanation of this: it was written in 1989; see Phys Lett B 222(1989)501. In it we (yes, this is self-serving, I am a co-author) discuss D0 -> K+K- and D0 -> Pi+pi- and state that in the absence of large SU(3) breaking one should expect large CP violation in these modes! Alas, we were cowards and followed this statement with a caveat that "This is of course very unlikely; the preferred explanation ... is that SU(3) violating effects are large in this decay."

The article by M. Golden and B. Grinstein cited by ben-hqet appears to be this one.

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