I am unable to help you because I do not know 1) the environment you are working in (e+e- production ? hadronic production ?…) 2) “fitting in D mesons with a mass formula given by T Mehen” does not ring a bell to me. Do you mean to say you are fitting the D lineshape with some complex formula (not a simple gaussian or a lorentz*gaussian) ? Also, I do not exactly understand what exactly you are looking for. I think the new PDG will contain data on the new B baryons discovered at the Tevatron, like Sigma_b and Xi_b, but as far as mesons, I am unaware of new discoveries there.

Sorry to be unable to help. Maybe you have a link to more information ? What exactly are you trying to measure ?

Cheers,
T.

thank you for the explanation, which matches my slightly confused knowledge of the issue – it is always good to straighten out one’s doubts by talking to the expert.

As for toponium, I once wrote (FNAL-CONF-02-344-E):

“The large value of Mt implies that the decay time is very short: Gt ~ Mt^3 ~ 1.5 GeV. That value is one order of magnitude larger than the hadronization scale L_QCD: that implies that top quarks cannot bind to form hadrons, and they decay as free particles. The absence of top hadrons can also be inferred from the non-relativistic quark model: on one side, the mass splitting MB**-MB=450 MeV is independent on the heavy quark mass, and must hold for T** and T as well; on the other, the splitting between B* and B depends on 1/M_Q and is thus expected to be smaller for top hadrons. Moreover, toponium states cannot exist, since their width (Gtt ~ 2Gt ~ 3 GeV) is larger than the splitting between 1S and 2S states expected from the perturbative QCD potential. All top resonances therefore merge and act coherently, and what is left in the cross section is only a broad excitation curve.”

I had to quote my own paper because I had forgotten some details of that didactical argument. I included it in my 2002 paper because I was discussing the history of top quark searches, and I thought it was an interesting deductive reasoning.

Cheers,
T.

Sure. For a mass of any hadron containing heavy quark,

m_H = m_Q + {some hadronic stuff} + {stuff suppressed by powers of 1/m_Q}

Here {some hadronic stuff} could be HQET parameter Lambda-bar (roughly, energy of light degrees of freedom, which is independent of HQ mass) or also some energy stored in angular momenum, etc. — but it’s all O(Lambda_QCD). Also, {stuff supressed by powers of 1/m_Q} includes spin effects, kinetic energy of a heavy quark (a.k.a as HQET parameters lambda_2 and lambda_1) and other stuff…

Thus, if you take a difference of m_H** and m_H the m_Q dependent part cancels out. The only m_Q-dependence you can get is via terms that are from {stuff suppressed by powers of 1/m_Q}-part, which disappears in the heavy quark limit.

Hope it helps,

–Alexey.

P.S. I used to give an argument that toponium cannot be formed simply because top quark decays faster than toponium forms. How does your argument for T-hadrons (that you mention above) work? Just curious…

ha! So I am talking to _the_ expert. Very good to know… I have always been fascinated by HQET, since it gives me some ground to visualize what is going on inside heavy hadrons and actually understand a bit about their dynamics. It is the first step towards understanding more, although I think I am bound to stop there…

As for the CDF measurement, if you take the CDF Lambda_b lifetime and divide by the B0 lifetime also measured with the same method by CDF, you get a number with a slightly larger error (due to the fact that the B0 lifetime in CDF is not as precise as the WA) but where you are much safer with respect to unknown systematic effects. In that case, CDF obtains R =1.018+-0.062, which is only 1.7sigma away from the upper bound of the interval you quote… So we are good, I think.

By the way, since you work with HQET and you are willing to explain things, I have a question. I have known for some time that the mass splitting between B** and B hadrons is independent on the heavy quark mass – and so, the same value should divide a hypothetical T** from a T hadron. The argument can be used to explain why top hadrons do not form, in fact. Do you have a simple explanation of the absence of mQ-dependent terms in the B**-B mass ?

Cheers,
T.

Theoretical value for the ratio of the Lamda_b and B lifetimes adopted by the Heavy Flavor Averaging Group (HFAG) is from my paper with two postdocs, Phys. Rev. D70, 094031, 2004 [hep-ph/0407004], which is a “1-sigma” range 0.82 to 0.92 (theoretical uncertainties are not gaussian, that’s why 1-sigma is in quotes). So lower values of that rario are theoretically more feasible — but of course not 0.7-sh that was experimentally favored some years ago. And it is still not clear why D0 gets lower value (granted, with larger uncertainites) than CDF from the same measurement…

To your other comment: While indeed at the leading order in 1/m expansion all heavy hadrons have the same lifetime (b-quark is a static source of color field), the main effects which drive ratios of lifetimes of different heavy mesons and baryons come from (Lambda/m)^3 corrections. These are matrix elements of four-fermion operators that are specifically sensitive to “spectator” effects (i.e. effects of the light quarks). They are numerically larger than (Lambda/m)^2 effects due to phase space factors. All of that is quite well-understood and accepted theoretically. I’ll be happy to talk more about that both here and off-line.

Regards,

–Alexey.

yes, a value above 1 is not easy to accommodate, but 0.8 was also sounding fishy according to theoretical estimates.

I am not sure I understand the rest of your comment. As far as I know, at lowest order in Lambda_QCD/m the b is a static source of color, and it does not affect the hadron lifetime. The lowest order at which lifetime changes are predicted is (Lambda/m)^2, because of spin interactions.

Cheers,
T.

1.041+-0.057 for the ratio of Lambda_b to B lifetimes seems way to large… why is it also larger than the recent D0 measurement in the same channel (of course, they are consistent with each other)? I don’t think there is a single theory prediction out there that claims that the ratio is greater than one…

Regards,

–Alexey.

P.S. Also, the main effect that drives the diference of lifetimes comes from non-perturbative 1/m corrections, not from perturbative QCD corrections…

sure – go ahead. There are several pictures of the island of San Miguel in the posts I wrote last September, and as far as I am concerned you can grab them all.

Cheers,
T.

My comment has nothing to do with physics…I saw a photo you took of the Azores and wonder if we can use it in a TV broadcast in the States. You can contact me at the email I provided. Of course, we will give you screen credit.

Thanks,
Stacey