As with the issue presented by Luis Sancho, dibaryon is a neutral, smaller version of a strangelet, so it is also more closely bound than nuclei or the partly strange hypernuclei. It is completely neglected for risk consideration - like with neutral strangelets - in all safety reviews; despite what appears to be the potential from surrounding thermal motion, for potential catalysis with these particles. (An extended dibaryon catalysis mechanism is discussed as occurring within neutron stars by Schaffner Bielich http://arxiv.org/abs/nucl-th/0011078v1 (and published)).
This neutral particle (udsuds), has the equivalent of only two baryons in it. As I understand, the thermal model formula (A.1) p.14 of LSAG report http://arxiv.org/abs/0806.3414 gives a (0..1) ‘penalty factor’ Pf for producing a double A=2 nuclei (approximated for strangelets or here dibaryon); that is, for each single nucleon produced in a collision. (In the spreadsheet I more appropriately apply per strange baryon produced and only within the dangerous slowest velocity range).:
Pf=(Y(A)/Y(A-1)) = exp(-(mN-(baryon chem potential))/T)
{Formula (A.1)}
where Y is the relevant yield, A is the relevant atomic mass number, mN is mass of nucleon, T is relevant post collision temperature.
To obtain lsag’s yield estimates per produced nucleon in a collision, of 3x10^-25 and 1x10^-49 in their A=10 or A=20 respective estimates for strangelet production (see spreadsheet), LSAG would have to take the result from this formula to the power {exp column of spreadsheet} of A. For the dibaryon case, it would be 2. (As lsag say - they approximate by considering standard nuclei here, so I assume the nucleon mass is averaged at 983.7, before finally, the slight binding energy per nucleon is subtracted for the applied m(N) value).
But, as I was saying, already for this dibaryon case, Y(A)/Y(A-1) is the 0..1 ’suppression’ or penalty factor for producing a double nuclei, per single nucleon produced. ‘Penalty’- perhaps that is because punishment is brought out for awkward results of exploration of nonzero risks - especially when it comes out of their own supposed ’safe’ formulae. Well, punishment metaphors won’t help.
So, for A= 10 they seem to be taking ten multiples of the {chance (0..1) after collision of one extra nucleon assembling from existing nucleon or nuclei}
or
(Y(A)/Y(A-1))^A.
For A=10, this would mean
Y(1)/Y(0) x Y(2)/Y(1) x .. x Y(9)/Y(8) x Y(10)/Y(9)
where Y(2)/Y(1) = Y(3)/Y(2) = .. = Y(10)/Y(9)
But what’s in the first term above? Y(0) ie the yield of nucleons without any nucleons. Difficult to see what that would be .. 0, infinity?; but certainly the requisite Y(0) = Y(1), so as to yield one, isn’t credible. For dibaryons, the result from this LSAG approach would be the square of revised suppression factor value - hence a much decreased likelihood.
Furthermore the LSSG 2003* report has this formula at the end of their discussion of the similar coalescence model and for the same stage of the calculation.
‘N(A) ≈ 100 × Pf(A−1)’
where N(A) is strangelet yield per collision and 100 is number of nucleons per collision. Here, Pf is equivalent in meaning to thermal Pf.
Agreed, ^(A-1) (along with number of nucleons per collision) is what I use at this stage for thermal model.
What are the implications?
For A=10 the likelihood increases by 285 times. Now the chance goes up to 1 in 2 billion - high enough to justify stopping LHC according to Nuclear physicist Francesco Calogero (reasonably), but then it already was with earlier calculation at above 1 in a trillion.
Could the risks be greater than that?
Well, A=10 is given as if it is the well established theoretical position, but the basis given in CERN’s LSSG 2003 report* is based on the need, from surface tension considerations for above a mass of 85MeV/c^2 to be included within the strangelet for A<10. No references, or clear argument are provided. Elsewhere, A=7 is given as a minimum with more assurance (as discussed by Schaffner-Bielich et al. Phys Rev C55, p.3038, 1997 with further refs).
In the last case, the chance of producing one A=7 strangelet is now recalculated at a very significant, one in 100 for LHC pb-pb lifetime (one in 210 at RHIC).
That is to forget the huge production of the (neutral) dibaryons - that is an estimated 22 billion undisruptible, central rapidity range dibaryons over RHIC and LHC lifetimes. Thermal catalysis from each would be slower than through the initial strangelet to nuclei Coulomb attraction of negative strangelets, but that is only per dibaryon. Each dibaryon then fuses first to become a A=28-56 neutral strangelet from which it grows.
I had expected that similar, or much greater numbers of undisruptible dibaryon would have emerged from cosmic rays. But I can see that, like with strangelets, the production of these particularly closely bound quark systems could well only be possible in the central qgp where the quark density is already far higher than with ordinary nuclei or from the non qgp parts of the ion ion collisions. This higher density at core of immediate post collision has has been shown by Weiner et al. http//arxiv.org/abs/ 0810.4465v3. LSAG themselves say the qgp is restricted to half light speed - hence around the centre of mass of the initial collision system near ‘central rapidity’.
So in this case all dibaryons and strangelets from cosmic rays would be disrupted at inevitable high speed (accepted by all safety reviews).
So, the over application of ‘penalty’ factors to keep us safe and contented? - or close down RHIC and LHC .
Eric
* Blaizot J.-P., Iliopoulos J., Madsen J., Ross G.G., Sonderegger P., and Specht H.-J., (2003) ‘Study Of Potentially Dangerous Events During Heavy-Ion Collisions At The LHC: Report Of The LHC Safety Study Group,’ CERN
23/04/10 | Eric Penrose | 08:49:41 am |
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