### Low mass exotic mesonic structures as evidence for dark scaled down variants of weak bosons?

During last years reports about low mass exotic mesonic structures have appeared. It is interesting to combine these bits of data with the recent view about TGD analog of Higgs mechanism and find whether new predictions become possible. The basic idea is to derive understanding of the low mass exotic structures from LHC data by scaling and understanding of LHC data from data about mesonic structures by scaling back.

- The article
*Search for low-mass exotic mesonic structures: II. attempts to understand the experimental results*by Taticheff and Tomasi-Gustafsson mentions evidence for exotic mesonic structures. The motivation came

from the observation of a narrow range of dimuon masses in Σ^{+}→ pP^{0}, P^{0}→ μ^{-}μ^{+}in the decays of P^{0}with mass of 214.3 +/- .5 MeV: muon mass is 105.7 MeV giving 2m_{μ}=211.4 MeV. Mesonlike exotic states with masses M = 62, 80, 100, 181, 198, 215, 227.5, and 235 MeV are reported. This fine structure of states with mass difference 20-40 MeV between nearby states is reported for also for some baryons.

- The preprint
*Observation of the E(38) boson*by Kh.U. Abraamyan et al reports the observation of what they call E(38) boson decaying to gamma pair observed in d(2.0 GeV/n)+C,d(3.0 GeV/n)+Cu and p(4.6 GeV)+C reactions in experiments carried in JINR Nuclotron.

In TGD framework situation is different. The basic characteristic of TGD Universe is fractality. This predicts new physics in all scales although standard model symmetries are fundamental unlike in GUTs and are reduced to number theory. p-Adic length scale hypothesis characterizes the fractality.

- In TGD Universe p-adic length scale hypothesis predicts the possibility of scaled versions of both strong and weak interactions. The basic objection against new light bosons is that the decay widths of weak bosons do not allow them. A possible manner to circumvent the objection is that the new light states correspond to dark matter in the sense that the value of Planck constant is not the standard one but its integer multiple.

The assumption that only particles with the same value of Planck constant can appear in the vertex, would explain why weak bosons do not decay directly to light dark particles. One must however allow the transformation of gauge bosons to their dark counterparts. The 2-particle vertex is characterized by a coupling having dimensions of mass squared in the case of bosons, and p-adic length scale hypothesis suggests that the primary p-adic mass scale characterizes the parameter (the secondary p-adic mass scale is lower by factor p

^{-1/2}and would give extremely small transformation rate).

- Ordinary strong interactions correspond to Mersenne prime M
_{n}, n=2^{107}-1, in the sense that hadronic space-time sheets correspond to this p-adic prime. Light quarks correspond to space-time sheets identifiable as color magnetic flux tubes, which are much larger than hadron itself. M_{89}hadron physics has hadronic mass scale 512 times higher than ordinary hadron physics and should be observed at LHC. There exist some pieces of evidence for the mesons of this hadron physics but masked by the Higgsteria.

The original proposal that 125 GeV state could correspond to pion of M

_{89}physics was wrong. The modified proposal replaces the Minkowskian pion (that is ordinary pion) with its Euclidian variant assignable to a flux tube connecting opposite throats of wormhole contact. Euclidian pion would provide masses for intermediate gauge bosons via the analog of Higgs mechanism involving instanton density non-vanishing only in Euclidian regions but giving a negligible contribution to fermion masses: this would solve the hierarchy problem motivating space-time*N*=1 SUSY not possible in TGD Universe. The expectation is that Minkowskian M_{89}pion (the real one!) has mass around 140 GeV assigned to CDF bump.

- In the leptonic sector there is evidence for leptohadron physics for all charged leptons labelled by Mersenne primes M
_{127}, M_{G,113}(Gaussian Mersenne), and M_{107}. One can ask whether the above mentioned resonance P^{0}decaying to μ^{-}μ^{+}pair could correspond to pion of muon-hadron physics consisting of a pair of color octet excitations of muon. Its production would presumably take place via production of virtual gluon pair decaying to a pair of color octet muons.

- The meson-like exotic states seem to be arranged along Regge trajectories but with string tension lower than that for the ordinary Regge trajectories with string tension T=.9 GeV
^{2}. String tension increases slowly with mass of meson like state and has three values T/GeV^{2}∈ {1/390 , 1/149.7, 1/32.5} in the piecewise linear fit discussed in the article. The TGD inspired proposal has been that IR Regge trajectories assignable to the color magnetic flux tubes accompanying quarks are in question. For instance, in hadrons u and d quarks - understood as constituent quarks - would have k=113 quarks and string tension would be by naive scaling by a factor 2^{107-113}=1/64 lower: as a matter of fact, the largest value of the string tension is twice this value. For current quark with mass scale around 5 MeV the string tension would be by a factor of order 2^{107-121}=2^{-16}lower.

^{36}coming from the scaling of the factor 1/m

_{W}

^{4}in the simplest scattering involving weak boson exchange.

- The naive estimate for the mass of M
_{107}Euclidian pion is r× 125 GeV , r=2^{(89-107)/2}=2^{-9}: this would give m (π_{E,107})=244 MeV. The highest state in the IR Regge trajectory mentioned in the article has mass 235 MeV. The weak bosons of M_{107}weak physics would have masses obtained by using the same scaling factor. This would give 156 MeV for W_{107}and 176 MeV for Z_{107}. It seems that these states with these masses do not belong to the reported list M = 62, 80, 100, 181, 198, 215, 227.5, and 235 MeV of masses. For k=109, which is also prime, one obtains states with m (π_{E,109})=122 MeV, m (W_{109})=m (Z_{109}) =88 MeV for vanishing value of Weinberg angle. Also these states seem to be absent from the spectrum listed above.

- In the original version of dark matter hierarchy the scalings hbar→ rhbar of Planck constant were restricted to r=2
^{11}, which is in a reasonable approximation equal to proton/electron mass ratio. If one replaces k=107 with k=111, which corresponds to a scaling of M_{89}masses by a factor 2^{-11}, one obtains scaling of M_{107}masses downwards by a factor 1/4.

Euclidian pion π

_{E,111}would have mass 61 MeV: this is near to the mass 62 MeV reported as the mass of the lowest lying mesonlike state at IR Regge trajectory. W_{111}and Z_{111}would have masses 39 MeV and 44 MeV for the standard value of Weinberg angle. Z decays to gamma pairs radiatively via intermediate W pair: could Z_{111}correspond to E(38) with mass 39 MeV? If the Weinberg angle is near to zero, the masses of W_{111}and Z_{111}are degenerate, and one would have 39 MeV mass for both. The accuracy of the mass determination for E(38) is 3 MeV so that the mass would be consistent with the identification as Z_{111}. Note that small Weinberg angle means that the ratio g^{'}/g for U(1) and SU(2) couplings is small (U(1) part of ew gauge potential corresponds to Kähler potential for CP_{2}in TGD framework).

- These observations inspire the question whether k=111=3× 37 scaled variant of weak physics could be involved. One can of course ask why the Gaussian Mersenne M
_{G,k}, k=113, assigned to nuclear space-time sheet, would not be realized in dark nuclear physics too. For this option masses would be scaled down a further factor of 1/2 to 19.5 MeV for weak bosons and to 30.5 MeV for Euclidian pion. Could it be that dark nuclear physics must correspond to different p-adic length scale differing by a factor 2 from that associated with ordinary nuclear physics? What is interesting is that one of the most long standing interpretational problems of quantum TGD was the fact that the classical theory predicts long ranged classical weak fields: the proposed solution of the problem was that the space-time sheets carrying these fields correspond to a non-standard value of Planck constant.

- The assumption that Euclidian pion has Regge trajectory conforms with the picture about elementary particle as a flux tube pair at parallel space-time sheets with wormhole contacts at its ends so that a closed monopole flux results. The length of the flux tube connecting different wormhole contacts would be defined by the p-adic length scale defining the weak physics in question. The interpretation of states in terms of IR Regge trajectory gives T
_{111}=1/390 GeV^{2}at the lower end of the spectrum if excited states.

One can estimate the weak string tension from the mass squared difference for the states with masses 60 MeV and 80 MeV as Δ M

^{2}= T_{111}giving 2.8× 10^{-3}GeV^{2}. The lowest value for the experimental estimate is 2.6× 10^{-}3 GeV^{2}: the two values are consistent with each other.

- Scaling back to M
_{89}would gives string tension T_{89}=2^{22}T_{111}= 10.8 × 10^{-3}TeV^{2}. This predicts that first excited state of Euclidion pion has mass about 162 GeV: a bump around this mass value corresponds to one of the many wrong alarms in Higgs hunting. There are indications for an oscillatory bump like structure in LHC data giving the ratio of the observed to predicted production cross section as a function of Higgs mass. This bump structure could reflect the actual presence of IR Regge trajectory for Euclidian pion inducing oscillatory behavior to the production cross section.

- The obvious question is whether also the intermediate gauge bosons should have Regge trajectories so that the TGD counterpart Higgs mechanism would take place for each state in Regge trajectory separately. The flux tube structure made unavoidable by Kähler magnetic charges of wormhole throats indeed suggests Regge trajectories. For M
_{89}weak physics the first excited state of W boson would be 144.5 GeV if one assumes the value of T_{89}estimated above.

**Addition:** 38 MeV particle candidate has raises a lot of attention. Also Lubos Motl and Tommaso Dorigo have commented. I expected Lubos to colorfully debunk the preprint but at this time he did not. Dorigo represents criticism as an experimentalist: I am unable to say anything about this and I am ready to accept that the 38 MeV particle is statistical fake. Tommaso also ridicules the paper on basis of some formal problems such as ridiculously high precision - probably due to taking the numbers directly from MATLAB analysis. Tommaso even wanted to make a $1000 bet that the claim will never be confirmed and accepted by the particle physics community.

It is only human that the attitude of a researcher at LHC to researcher in some little nuclear physics laboratory is like that of a professor to a first year student. I have myself learned during these decades that this attitude torpedoes all attempts to intelligent communication. I share Tommaso's belief that particle physics community under no circumstances will take the claim about 38 MeV particle seriously. Already because it is inconsistent with the basic dogmas such as the decay widths of gauge bosons. If the particle is real, one is forced to dramatically modify the basic dogmas of theoretical particle physics and the community is certainly not mature for this and prefers to continue to test whether proton decays, whether standard SUSY might be there after all, whether black holes might be produced at LHC, and so on.

For some reason the claims of Tatitcheff and Tomaso-Gustafsson about exotic particles in the same mass scale are not commented at all in blogs. Single claim for anomaly cannot of course be taken seriously but if there are two independent claims of this kind, and if some general theoretical framework can relate them, one can ask whether something interesting might be involved. There are of course numerous older anomalies, which have been simply put under the rug - say the anomalies to which I assign the common umbrella term "leptohadron physics" Despite all this refined statistical methods we can see only what we want to see: LHC can see a signature only if it searches for it!

For background see the new chapter Higgs or something else? of "p-Adic length scale hypothesis and dark matter hierarchy", and the article Is it really Higgs?.

## 2 Comments:

The preprint Observation of the E(38) boson by Kh.U. Abraamyan et al reports the observation of what they call E(38) boson decaying to gamma pair.

This was called the E(38) boson by us in http://arxiv.org/abs/arXiv:1102.1863

and

http://arxiv.org/abs/arXiv:1202.1739

Eef van Beveren

Thank you for the information.

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