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A precise measurement of the Bc meson mass *July 27, 2007*

*Posted by dorigo in news, physics, science.*

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The **Bc** meson is a particle composed of a b-quark and a anti-charm quark (charge conjugation applied to the state brings about the antiparticle, made by a anti-b-quark and a charm quark). It is just another meson – a bound state of two quarks – and it would not be so interesting to study, if the mass of the constituents weren’t so large. Indeed, the Bc meson is the first particle containing both b- and c- quarks, and so it does have some entertainment value for particle physicists.

In fact, there are several questions that may receive an answer by studying this particle. Is the decay rate consistent with what one would expect from the current model of these objects ? Is the mass compatible with what one would compute by modeling the state as a almost non-relativistic system composed of a charm quark jiggling around the heavier b-quark ? How about lattice QCD computations for the mass of such a unconventional meson ? Moreover, is the pattern of possible decays following what we predict ? Also, is the overall production rate in agreement with what QCD predicts (this latter question is probably the hardest to answer presently…) ?

The **Bc** was discovered by CDF in 1998, but its decay to a J/psi meson and a single pion had not been seen before. CDF has now performed a very simple search for this final state, by tuning the search criteria on the twin particle **B-,**** **which is much more frequently produced in proton-antiproton collisions. The **B-** is composed of a b-quark and a anti-u quark, and it may decay to a J/psi meson and a Kaon. The kinematics of that decay should be quite similar to the one searched for the **Bc**, so CDF could decide what cuts to apply to particle momenta and other observables beforehand, basing the selection on the well known **B-** signal, and then collect data silently, until the “signal box” was full enough to beg to be opened. By doing things this way, the search has been quite model-independent, and the results much more easy to interpret.

We now have a 8-sigma signal of **Bc –> J/psi pi** decays. You can see the reconstructed invariant mass of the system in the following plot:

As you see, the large dataset of 2.2 inverse femtobarns of proton-antiproton collisions allows for a significant signal to emerge on the exponentially falling background, even if this particle is not very frequently produced -indeed, there are large uncertainties in the theoretical predictions for its production rate – and even if the decay to J/psi and pion is not the most frequent one (I need to check this though… I will update later with some number). The mass of the meson is measured to be **6274.1 +- 3.2 +- 2.6 MeV**, which is smaller but not inconsistent with current estimates from lattice QCD (6304 MeV), which carries some 18-mevish systematics. The ball is now in the lattice QCD field to get a better match with experimental measurements.. In the meantime, CDF will collect more of these interesting events, and improve our understanding of this intriguing particle.

More detail on the recent measurement described above can be found this preprint paper.

## Comments

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Hi Tommaso,

thank your for the link!

I have a stupid question ;-). I remember from your post about Rumsfeld hadrons that the mass of the B_c is very close to the arithmetic mean of the masses of the J/Psi (c-cbar, 3097 MeV) and the Upsilon (b b-bar, 9460 MeV), which yields 6278 MeV. I have for fun checked this “estimate” also using the eta_c (2980 MeV) and the eta_b (9300 MeV), and this mean, 6140 MeV, seems not to work, even taking into account the large error in our knowledge of the mass of the eta_b.

Now, if I remember correctly, the essential difference between the eta_c/eta_b and the J/Psi/Upsilon is the spin, which is 0 for the etas, and 1 for the J/Psi and Uspilon. Thus, one could naively guess that the the B_c should also have spin 1, and not spin 0. Is there anything known about the spin of the B_c, or would this qualify as a prediction 😉 ?

Best, Stefan

Is CDF planning to improve on the measurement of B_c lifetime any time soon? Just curious…

Hi Stefan,

that is correct – one should compare apples to apples. The mass of a meson is usually understood to be the sum of constituents plus a factor due to spin-spin interaction, so called hyperfine splitting – and the latter is different for pseudoscalars or vectors. So in principle, the argument of averaging J/psi and Upsilon mass is flawed, and one should indeed use the etas, but as you note the eta_b mass is not known yet with sufficient accuracy…

Much better is to do what Eichten and Quigg did in 1994 (see hep-ph/9402210) when they used J/psi and Y masses but took the splitting between eta_c and J/psi as a factor to compute the hyperfine splitting effects and extrapolated to the Bc. In any case, the estimates agree with what has been recently measured. The per-mille agreement discussed in the paper I mentioned is probably an accident…

Or is the observed Bc a vector ? I think that seems inconsistent with observations from the final states, in particular its decay to a J/psi and lepton.

Cheers,

T.

Hi Alexei,

sure, they are working on it… I have no estimate for the time frame of a new result though. I will let you know if something comes out.

Cheers,

T.

Hi Tommaso,

so. the B_c is supposed to be a scalar, thank you for that info.

And thanks for the reference to the Eichten/Quigg paper.

Best, stefan

I would like to read research papers or articles related to interaction of B-c meson and Pion in QGP.

What a coincidence! P.B. Burt has a simple mass formula for scalar mesons. See the book below and refereces cited in it:

Mn= (3n+1) m. m =135 Mev— The pion mass.

According to this simple formula, the Bc Meson is a scalar meson with n= 15.

(3*15+1)* 135= 6,210 Mev.

i.e. (6274.1-6210)*100/6274.1 = 1%

P.B. Burt woud have been excited about this but he is no longer with us.

_______________________________________________________________

Info about P.B. Burt:

http://bohr.winthrop.edu/faculty/sebhatu/link_to_webpages/personal/Philip%20B_%20Burt's%20Research%20Page.htm

P. B. Burt, “Quantum Mechanics and Nonlinear Waves” (Harwood Academics Press, N.Y. 1981).