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Spin-parity analysis of the X(3872) June 9, 2006

Posted by dorigo in news, physics, science.

A few days ago, Michael Schmitt made the following comment here:

I have a suggestion for your blog: after the collaboration meeting is over,why don't you tell us the most interesting result you heard about -especially if it surprised you – and also make a prediction about what will the most interesting result coming out by the end of the year. Of course, you need to respect the rules about revealing unblessed results…

Ok, the collaboration meeting ends today, and I have a pretty clear idea of the most intruguing new measurement (new to me of course – I cannot follow everything that is done by my 700 CDF colleagues: that's the reason for following a collaboration meeting!) I heard about during this week. It is a good-old "angular distributions" kind of measurement, quite carefully carried out to investigate the properties of the X(3872) particle. The talk was given by our Karlsruhe collaborator Michael Feindt, and I owe him for some of the pictures and plots I am posting here.   The X was discovered at the e+ e- B factory BELLE in 2003, and was very shortly thereafter confirmed by CDF (who actually determined we had it in our dataset since quite a few years before, darn), D0 and BaBar. It is a funny little resonance, that can be observed in our data by selecting J/psi –> mu mu decays and associating to the J/psi a pair of charged pion tracks. Its characteristics are unknown as of yet, but its mass is unreasonably close to the sum of masses of two neutral charmed mesons, a D and a D*. This may indicate that the X is actually a sort of "molecular state" of those two particles. The graph above shows the peak in the invariant mass distribution of J/psi-pi-pi combinations, the X(3872) signal. About 2200 events sit on top of a large combinatioral background due to random associations of tracks. The more mundane explanation of the X is that it is a charmonium state, that is a bound state of a charm-anticharm pair. Charm quarks have a mass of about 1.5 GeV, and if they rotate around each other with sufficient angular momentum, the rest mass of the system may well be of the order of that of the X. However, the charmonium hypothesis has some shortcomings: other decay modes of the X are not observed as they should, and the observed one is not the one that should be preferred by a ccbar state at that mass. Also, the X lives quite long before decaying, a fact indicated by its narrowness (the longer an oscillation lives, the better determined its oscillation frequency is: the same goes with elementary particles, whose "oscillation frequency" is their mass). The two above explanations (molecule of D mesons or simple charmonium state), along with other hypotheses, can be discriminated by studying angular distributions in the particle decay. That is, when the X produces the J/psi and the two pions, it not only provides the decay products with momentum – in measure related to the difference between its own mass and the mass of the projectiles – but also with angular momentum, and the resulting relative motion of the projectiles tell us a lot about the quantum numbers of the X. The picture above shows the definition of the three angles one can experimentally measure from the decay products. They carry information on the spin-parity quantum numbers of the X. The measurement of the angular distributions in the decay of the X mesons observed by CDF is difficult, because the signal sits on top of a large, irreducible background (see first plot above). However, a careful statistical analysis can extract the distributions we need to fit. As the figure above shows, the data (black points) are divided in 12 bins as a function of the three angles describing the decay. Some of the possible spin-parity assignments are clearly incompatible with the data. Two possible spin-parity assignments of the X(3872) are equally probable: in particular, the X may be indeed a molecular bound state of two neutral D mesons (state J^(PC)=1^(++), that is a spin-one positive parity and charge conjugation state), or a charmonium state 2^(-+). Both are compatible with the data, with chisquared probabilities of 28% and 26%, respectively. Other explanations are ruled out by the analysis. More data will discriminate the two hypotheses. Also, it will be very important to search for this particle in other decay modes, and possibly search for a similar bound state decaying to a Upsilon and two pions – but there, things are experimetally even harder… Time will tell!


1. Michael Schmitt - June 11, 2006

Ciao Tommaso,

this is a very nice explanation of a relatively difficult analysis. And I agree this is quite interesting and relevant for non-perturbative QCD. We have a professor here at Northwestern who knows a lot about the charm system to we have often discussed whether these meson “molecules” really might exist, or not. It seems like the experts have a wide range of opinions, which helps make this area of investigation more fun! Certainly it is not as cut-and-dried as things like electroweak symmetry breaking…

warm regards,

2. dorigo - June 11, 2006

That is right, there is a lot to learn in low energy QCD and things such as the X may be places where real discoveries are made. If – as Belle first claimed without too much emphasis nor investigation, and as CDF data seem to favor – the X is a 1++ state, a whole new chapter opens in the understanding of “not-so-elementary” particles. Complex objects, that is. Just imagine, a whole new Mendelejev table to fill up !

3. Collider Blog » Tommaso’s Tips - June 11, 2006

[…] First, he described with wonderful clarity and simplicity the analysis of the angular decay distributions of the X(3872). This is a very nice result coming from CDF which helps identify the nature of this peculiar object. See his post for the discussion, to which I would add that this kind of physics is rich and interesting, if not the most popular in HEP. However, if you want really to know what’s going on, you need to pay attention – if new particles are found at the LHC then the same kinds of analyses will be needed to identify them. Also, I agree that it is slightly embarassing that CDF had a nice signal in the data but did not spot this until after Belle did. We are not being vigilant enough, perhaps… […]

4. Alexey Petrov - June 14, 2006

Hmm.. I thought Belle’s angular analysis was only consistent with 1++ quantum numbers, which is good for molecular interpretation. Is there a reason for CDF to leave 2-+ as a viable interpretation? Is that because Belle has all X’s come from B-decays and CDF doing inclusive analysis?

5. dorigo - June 14, 2006

Hello Alexey,

yes, Belle is consistent with the 1++ hypothesis, but AFAIK has not done a full-fledged test, which would be even easier with the polarized state of the produced X in B decays.

The reason why a 2-+ case has been considered by CDF is that it is the most obvious thing to do with a potential ccbar bound state. And the data do not disprove that spin-parity assignment yet. However, I do believe in the explanation of the molecular D -D* state, it fits the bill and the charmonium hypothesis is instead contradictory.

The matter will be settled in a few months, I think.


6. Joachim - July 4, 2006

Hi Alexey,

Belle only considered angular distributions of 0++, 1++ and 2++, since only those fit into the description of a decay via a rho (e.g. C=+1) and in addition having a relative angular momentum of JPsi and rho L=0 (kicking 2-+, 1-+ and 0-+) which can be accessed by the the mass spectrum of the PiPi system.
While this is clearly favored, also by CDF data, others (e.g. L=1) are not ruled out. This analysis takes all sensible JPC assumptions, without the knowledge of other experiments (e.g. also JP-) states were tested, which is in the meantime ruled out by Babar’s and Belle’s X->JPsi gamma.


PS: great post Tommaso! 🙂
PPS: in my opinion data also favors 1++, but there is still quite a way to go to prove that (it’s different to say that England sucks in penalties from proving that they will lose every time 🙂 )

7. dorigo - July 4, 2006

Hi Joachim,
And yes, probability and certainty are two different things… And as far as penalties go, tonight Italy meets Germany and… Well, Italy is not better than England for penalty kicks! I hope the game ends sooner!

8. A new precise measurement of the X particle « A Quantum Diaries Survivor - August 14, 2008

[…] by dorigo in news, physics, science. Tags: BaBar, charmonium, X(3872) trackback Remember the X(3872) ? It is a new neutral particle decaying into a J/Psi meson and a pair of pions, which was […]

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