There's been some new developments since 2 weeks ago when LHCb came out with the evidence of CP violation in the charm meson sector. Recall that LHCb studied the D-meson decay to π+π- and K+K- meson pairs. The observable of interest was the asymmetry of D- and anti-D-meson decay rates to these final states, A(π+π-) and A(K+K-). A non-zero value of any of these two asymmetries signals CP violation (particle and anti-particle decay rates to the same CP eigenstate being different). LHCb found that the difference ΔA = A(K+K-) - A(π+π-) is (-0.82±0.24)%, which means that, with large confidence, at least one of these asymmetries is non-zero.

The most pressing question is whether the LHCb result implies new physics? Experts emphatically agree that the answer is definitely maybe. From the existing literature one can learn that "...CP violation from new physics must be playing a role if an asymmetry is observed with present experimental sensitivities O(1%)", and "...observation of CP violation in the decay of D mesons will not necessarily be a signal of new physics...". Now, a paper from last week makes a reassessment of the Standard Model predictions and clarifies the LHCb result may or may not signal new physics.

The problem is that we are lacking reliable methods to compute processes involving D mesons. Normally, when dealing with heavy flavored mesons, one employs an effective theory where the heavy Standard Model and possibly new physics particles have been integrated out, leaving effective 4-quark interactions. This allows one to compute observables at the leading order in the expansion in powers of (1 GeV/m_quark), the former being the typical scale for QCD effects, and the latter the suppression scale of higher-dimensional operators. That is a decent expansion parameter for bottom quarks, but not so much for charm quarks. Now, ignoring that convergence issue and taking the leading order predictions at face value one arrives at the estimate ΔA∼0.1%, well below the value measured by LHCb. The new paper by Brod et al. attempts to estimate the contribution of the higher order operators to the asymmetry, using some guidance from other experimental data on D-mesons. For example, one finds that the branching fraction for D0 → K0 K0bar, which receives contributions only at next-to-leading order in 1/mc, is about five times smaller than the branching fraction of D0 → K+ K-, which received leading order contributions. That means that the respective amplitudes differ only by a factor of two, which in turn proves that the higher order 1/mc contributions can be significant. Taking that into account, the paper concludes that the Standard Model can account for |ΔA| as large as 0.4%, uncomfortably close to the LHCb measurement.

Another last week paper takes a less pessimistic approach. It simply assumes that the asymmetry measured by LHCb is dominated by new physics and attempts to understand constraints on the underlying model. In the language of effective theory, to explain the LHCb result one needs to include a ΔC =1 four-quark operator (with 1 charm and 3 light quarks, [sbar Γ c][ubar Γ s]). There are many possibilities differing by the structure of Lorentz and color indices that lead to the same observable asymmetry. The scale suppressing this higher dimensional operator should be of order 10 TeV to match to the LHCb result. This is actually a very small suppression. From non-observation of CP violation in D meson mixing we know that the scale suppressing generic ΔC=2 4-quark operators (with 2 charm and 2 light quarks) must be close to 10 000 TeV. On the other hand, once a ΔC=1 operator is present, ΔC=2 ones will necessarily be generated by loop corrections. This means that a random new physics model explaining the LHCb result will be in conflict with the data on D-meson mixing. However, the paper by Isidori et al. concludes that a subset of the ΔC=1 operators explaining the LHCb asymmetry is consistent with all other experimental data. In particular, the ΔC=1 operators involving only right-handed quarks are not excluded by the data on D-meson mixing and on direct CP violation in kaon decays (ε'/ε in the flavor jargon).

Finally, a small experimental update. CDF posted on arXiv a new paper that is similar to the earlier public note but contains one bonus track. The known result is the separate CP asymmetries D-meson decays to pions and kaons:

A(K+K-) = -0.24 ± 0.24 A(π+π-) = 0.22 ± 0.26

The bonus is that they did the subtraction and also present the difference of the asymmetries:
ΔA = -0.46 ± 0.33

which can be directly compared to the LHCb result. The CDF asymmetry difference is perfectly consistent with the LHCb one, and it's also consistent with zero. This is a hint that the true asymmetry difference is probably at a lower end of the range suggested by the LHCb measurement, and therefore closer to the Standard Model prediction. One more point for the Standard Model, but the game is not over yet.
## 11 comments:

I think it will come down to one's definition of New Physics. If we one day compute it using SM ideas, but with new twistor techniques, is that New Physics or not? I would say yes, but it's debatable.

For the sake of debating, I'd say No, and here is perhaps part of the problem: a research topic on new techiques is probably less glamourous that on new particles; a hard task with less reward.

Of course, you can always try the AdS/CFT-QFT trick: perhaps they going to be, at the end, a calculational technique, but they sell themselves as based in NP, so they get some of the NP glamour.

What does take a knock is first-order old physics (FOOP). The search for power-series solutions goes back to Gustav Mie and p-adic arithmetic, but got under way as a trend with chaos theory, so for many observers this is non-linear or fractal physics.

Well, the CP-violating operators almost certainly have purely numerical coefficients much smaller than one in front of them - like the CKM-matrix angle - so the real mass scale responsible for this stuff may be much smaller than 10 TeV, right?

Right, you can explain the result with new light particles, at 1 TeV or below, and it's perhaps much more natural this way. 10 TeV would be the scale of completely generic CP-violating new physics. I quoted that number mainly to compare to the suppression scale in D-meson mixing, which is much larger.

hi Jester,

Just a quick botanical comment: the (1 GeV/m_quark) counting rule for the expansion mainly applies to quarks exchanged in the Delta F=2 box diagram. Those are up-type for B and K mixing, and down-type for D mixing. After using unitarity to eliminate the lightest quark, one gets the standard Delta F=2 dimension six operators entering B_B and B_K by assuming that both 1 GeV/m_t and 1 GeV/m_c are small. As you mention, the latter one is tricky --- what with sizeable NLO OPE corrections to the mixing, especially if external momenta are O(m_K) and not O(m_B).

In the case of D mixing, unfortunately, there's an s quark in the box: game over. Working with the full (Delta F=1)^2 structure is mandatory, and computations of low-energy QCD contributions are hence much tougher.

What? No Higgs rumours? What's wrong with you, man, continue like this and you'll start writing about science in a while.

Hello. I'm here for the Higgs rumors. Should I wait on this couch over here?

I've been waiting for half an hour at this cashier and still no service? What part of the sentence I want my Higgs rumor and I want it now don't you understand?

Okay, that does it, I wanna talk to the manager.

Sorry, could not post the rumors earlier without putting my agents in danger. You know what they do to experimentalists caught spying for theorists :-)

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