Consider first the mass formula for the hadrons at IR Regge trajectories.
- There are two options depending on whether the mass squared or mass for hadron and for the flux tubes are assumed to be additive. p-Adic physics would suggest that if the p-adic primes characterizing the flux tubes associated with hadron and hadron proper are different then mass is additive. If the p-adic prime is same, the mass squared is additive.
- The simplest guess is that the IR stringy spectrum is universal in the sense that m0 does not depend on hadron at all. This is the case if the flux tubes in question correspond to hadronic space-time sheets characterized by p-adic prime M107 in the case of ordinary hadron physics. This would give for the IR contribution to mass the expression
m2=(m02+ nm12)1/2 .
- The net mass of hadron results from the contribution of the "core" hadron and the stringy contribution.
If mass squared is additive, one obtains
m(Hn)= [m2(H0) +m02+ nm12]1/2,
where H0 denotes hadron ground state and Hn its excitation assignable to magnetic flux tube. For heavy hadrons this would give the approximate spectrum
m(Hn)≈ m(H0)+ [m02+nm12]/2m(H0) .
The mass unit for the excitations decreases with the mass of the hadron.
- If mass is additive as one indeed expects since the p-adic primes characterizing heavy quarks are smaller than hadronic p-adic prime, one obtains
m(Hn)= m(H0)+ (m02+ nm12)1/2 .
For m02>> m12 one has
m(Hn)= m(H0)+ m0+ nm12/2m0 .
If the flux tubes correspond to p-adic prime. This would give linear spectrum which is same for all hadrons.
There is evidence for this kind of states.
- Tatischeff and Tomasi-Gustafsson claim the existence of states analogous to ordinary pion with masses 60, 80, 100, 140,.... MeV. Also nucleons have this kind of satellite states.
- Second piece of evidence comes from two articles by Eef van Beveren and George Rupp. The first article is titled First indications of the existence of a 38 MeV light scalar boson. Second article has title Material evidence of a 38 MeV boson . The basic observations are following. The rate for the annihilation e++e-→ uubar assignable to the reaction e++e-→ π+π- has a small periodic oscillation with a period of 78+/- 2 MeV and amplitude of about 5 per cent. The rate for the annihilation e++e-→ bbbar, assignable to the reaction e++e-→ Υπ+π- has similar oscillatory behavior with a period of 73+/- 3 MeV and amplitude about 12.5 per cent. The rate for the annihilation ppbar→ cbbar assignable to the reaction e++e-→ J/Ψπ+π- has similar oscillatory behavior with period of 79+/- 5 MeV and amplitude .75 per cent.
In these examples universal Regge slope is consistent with the experimental findings and supports additive mass formula and the assignment of IR Regge trajectories to hadronic flux tubes with fixed p-adic length scale.
What does one obtain if one scales up the IR Regge trajectories to the M89 which replaces Higgs in TGD framework?
- In the case of M89 pion the mass differences 20 MeV and 40 MeV appearing in the IR Regge trajectories of pion would scale up to 10 GeV and 20 GeV respectively. This would suggest the spectrum of pion like states with masses 115, 125, 145, 165 GeV. What makes this interesting that ATLAS reported during last year evidence for a signal at 115 GeV taken as evidence for Higgs and CDF reported before this signal taken as evidence for Higgs around 145 GeV! 125 GeV is the mass of the the most recent Higgs candidate. Could it be that all these reported signals have been genuine signals - not for Higgs- but for M89 pion and corresponding spion consisting of squark pair and its IR satellites?
- I the case of M89 hadron physics the naive scaling of the parameters m0 and m1 by factor 512 would scale 38 MeV to 19.5 GeV.