Has CMS collaboration observed strange M89 baryon?

In his recent posting Lubos tells about a near 3-sigma excess of 390 GeV 3-jet RPV-gluino-like signal reported by CMS collaboration in article Searh for Three-Jet Resonances in p-p collisions at sqrt(s)=7 TeV. This represents one of the long waited results from LHC and there are good reason to consider it at least half-seriously. This posting contained in its original version some errors which have been corrected.

Gluinos are produced in pairs and in the model based on standard super-symmetry decay to three quarks. The observed 3-jets in question would correspond to a decay to uds quark triplet. The decay would be R-parity breaking. The production rate would however too high for standard SUSY so that something else is involved if the 3 sigma excess is real.

Signatures for standard gluinos correspond to signatures for M₈₉ baryons in TGD framework

In TGD Universe gluinos would decay to ordinary gluons and right-handed neutrino mixing with the left handed one so that gluino in TGD sense is excluded as an explanation of the 3-jets. In TGD framework the gluino candidate would be naturally replaced with k=89 variant of strange baryon λ decaying to uds quark triplet. Also the 3-jets resulting from the decays of proton and neutron and Δ resonances are predicted. The mass of ordinary λ is m(λ,107)=1.115 GeV. The naive scaling by a factor 512 would give mass m(λ,107)= 571 GeV, which is considerably higher than 390 GeV. Naive scaling would predict the scaled up copies of the ordinary light hadrons so that the model is testable.

It is quite possible that the bump is a statistical fluctuation. One can however reconsider the situation to see whether a less naive scaling could allow the interpretation of 3-jets as decay products of M₈₉ λ baryon.

Massivation of hadrons in TGD framework

Let us first look the model for the masses of nucleons in p-adic thermodynamics (see this).

1. The basic model for baryon masses assumes that mass squared -rather than energy as in QCD and mass in naive quark model- is additive at space-time sheet corresponding to given p-adic prime whereas masses are additive if they correspond to different p-adic primes. Mass contains besides quark contributions also "gluonic contribution" which dominates in the case of baryons. The additivity of mass squared follows naturally from string mass formula and distinguishes dramatically between TGD and QCD. The value of the p-adic prime p≈ 2^k characterizing quark depends on hadron: this explains the mass differences between baryons and mesons. In QCD approach the contribution of quark masses to nucleon masses is found to be less than 2 per cent from experimental constraints. In TGD framework this applies only to sea quarks for which masses are much lighter whereas the light valence quarks have masses of order 100 MeV.

   For a mass formula for quark contributions additive with respect to quark mass squared quark masses in proton would be around 100 MeV. The masses of u, d, and s quarks are in good approximation 100 MeV if p-adic prime is k=113, which characterizes the nuclear space-time sheet and also the space-time sheet of muon. The contribution to proton mass is therefore about 3^1/2× 100 MeV.

   Remark: The masses of u and d sea quarks must be of order 10 MeV to achieve consistency with QCD. In this case p-adic primes characterizing the quarks are considerably larger. Quarks with mass scale of order MeV are important in nuclear string model which is TGD based view about nuclear physics (see this).

2. If color magnetic spin-spin splitting is neglected, p-adic mass calculations lead to the following additive formula for mass squared.

   M(baryon)= M(quarks)+ M(gluonic) , M²(gluonic) = nm²(107) .

   The value of the integer n can be predicted from a model for the TGD counterpart of the gluonic contribution (see this). m²(107) corresponds to p-adic mass squared associated with the Mersenne prime M₁₀₇ =2¹⁰⁷-1 characterizing hadronic space-time sheet responsible for the gluonic contribution to the mass squared. One has m(107) =233.55 MeV by scaling from electron mass m_e≈ 5^1/2× m(127)≈ 0.5 MeV and from m(107)=2^(127-107)/2× m(127).

3. For proton one has

   M(quarks)= [∑_quarks m²(quark)]^1/2 ≈ 3^1/2× 100 MeV

   for k(u)=k(d)=113 (see this).

Super-symplectic gluons as TGD counterpart for non-perturbative aspects of QCD

A key difference as compared to QCD is that the TGD counterpart for the gluonic contribution would contain also that due to "super-symplectic gluons" besides the possible contribution assignable to ordinary gluons.

1. Super-symplectic gluons do not correspond to pairs of quark and and antiquark at the opposite throats of wormhole contact as ordinary gluons do but to single wormhole throat carrying purely bosonic excitation corresponding to color Hamiltonian for CP₂. They therefore correspond directly to wave functions in WCW ("world of classical worlds") and could therefore be seen as a genuinely non-perturbative objects allowing no description in terms of a quantum field theory in fixed background space-time.

2. The description of the massivation of super-symplectic gluons using p-adic thermodynamics allows to estimate the integer n characterizing the gluonic contribution. Also super-symplectic gluons are characterized by genus g of the partonic 2-surface and in the absence of topological mixing g=0 super-symplectic gluons are massless and do not contribute to the ground state mass squared in p-adic thermodynamics. It turns out that a more elegant model is obtained if the super-symplectic gluons suffer a topological mixing assumed to be same as for U type quarks. Their contributions to the mass squared would be (5,6,58)× m²(107) with these assumptions.

3. The quark contribution (M(nucleon)-M(gluonic))/M(nucleon) is roughly 82 per cent of proton mass. In QCD approach experimental constraints imply that the sum of quark masses is less that 2 per cent about proton mass. Therefore one has consistency with QCD approach if one uses linearization of the mass formula as effective linear mass formula.

What happens in the transition M_{107→ M89?}

What happens in the transition M₁₀₇→ M₈₉ depends on how the quark and gluon contributions depend on the Mersenne prime.

1. One can also scale the "gluonic" contribution to baryon mass which should be same for proton and λ. Assuming that the color magnetic spin-spin splitting and color Coulombic conformal weight expressed in terms of conformal weight are same as for the ordinary baryons, the gluonic contribution to the mass of p(89) corresponds to conformal weight n=11 reduced from its maximal value n=3× 5=15 corresponding to three (see this). The reduction is due to the negative colour Coulombic conformal weight. This is equal to M_g= 11^1/2 × 512× m(107), m(107) =233.6 MeV, giving M_g= 396.7 GeV which happens to be very near to the mass about 390 GeV of CMS bump. The facts that quarks appear already in light hadrons in several p-adic length scales and quark and gluonic contributions to mass are additive, raises the question whether the state in question corresponds to p-adically hot (1/T_p∝ log(p)≈ klog(2) ) gluonic/hadronic space-time sheet with k=89 containing ordinary quarks giving a small contribution to the mass squared. Kind of overheating of hadronic space-time sheet would be in question.

2. The option for which quarks have masses of thermally stable M₈₉ hadrons with quark masses deduced from the questionable 150 GeV CDF bump identified as the pion of M₈₉ physics does not work.
   1. If both gluonic and quark contributions scale up by factor 512, one obtains m(p,89)=482 GeV and m(λ,89)=571 GeV. The values are too large.

   2. A more detailed estimate gives the same result. One can deduce the scaling of the quark contribution to the baryon mass by generalizing the condition that the mass of pion is in a good approximation just m(π)=2^1/2m(u,107) (Goldstone property). One obtains that u and d quarks of M₈₉ hadron physics correspond to k=93 whereas top quark corresponds to k=94: the transition between hadron physics would be therefore natural. One obtains m(u,89)=m(d,89)=102 GeV in good approximation: note that this predicts quark jets with mass around 100 GeV as a signature of M₈₉ hadron physics.

      The contribution of quarks to proton mass would be M_q= 3^1/2× 2^(113-93)/2m(u,107)≈ 173 GeV. By adding the quark contribution to gluonic contribution M_g=396.7 GeV, one obtains m(p,89)= 469.7 GeV which is rather near to the naively scaled mass 482 GeV and too large. For λ(89) the mass is even larger: if λ(89)-p(89) mass difference obeys the naive scaling one has m(λ,89)-m(p,89)=512× m(λ,107)-m(p,107). One obtains m(λ,89)= m(p,89)+m(s,89)-m(u,89)= 469.7+89.6 GeV = 559.3 GeV rather near to the naive scaling estimate 571 GeV. This option fails.

Maybe I would be happier if the 390 GeV bump would turn out to be a fluctuation (as it probably does) and were replaced with a bump around 570 GeV plus other bumps corresponding to nucleons and Δ resonances and heavier strange baryons. The essential point is however that the mass scale of the gluino candidate is consistent with the interpretation as λ baryon of M₈₉ hadron physics. Quite generally, the signatures of R-parity breaking standard SUSY have interpretation as signatures for M₈₉ hadron physics in TGD framework.

For a summary about indications for M₈₉ see appropriate section in the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic length scale hypothesis and dark matter hierarchy". See also the short pdf article Is the new boson reported by CDF pion of M89 hadron physics? at my homepage.