Comparison of M89 hadron physics and Higgs as explanation of 125 GeV bump

The comments of Lubos and Andrew Oh-Willeke to blog posting about LHC data release inspired some comments on my side. These hastily typed comments were imprecise and I decided to write an improved version collecting the main points to a more organized structure. I want also to write about these topics to clarify to myself some important open issues in my own approach and I will do my best to debunk myself in the following. I will very probably make imprecise and even wrong statements. This is work in progress. Apologies.

1. The basic issues

1. The basic issue is whether the signal at LHC is a compelling evidence for Higgs or not. My claim is that it tells only that there is scalar or pseudo-scalar producing the signal and that under rather general assumptions this signal can be even quantitatively equivalent with the Higgs signal for the recently studied signatures.

2. Enthusiasts also forget that the signal cross section has features which do not favor its interpretation in terms of Higgs. Exclusion of Higgs does not mean the exclusion of signal! The clear structures around 135 and 145 GeV have not disappeared, there is a wide bump like structure in the entire region 110-150 GeV, and there is structure at both sides of 300 GeV. All these structures should disappear with increased statistics if Higgs interpretation is correct. We do not know whether this will happen and the natural question is whether one could interpret these structures by replacing Higgs paradigm with something else.

3. Higgs is also disfavored by profound theoretical reasons. It is just around the border of instability against the decay of vacuum. Could this criticality be a signal about the need to replace Higgs with something else? Presumably a microscopic description of particle massivation (provided by TGD already 15 years ago in terms of p-adic thermodynamics). Or are we happy with Higgs phenomenology which only reproduces instead of predicting?

2. Brief summary

The main results hitherto - preliminary of course - are following.

1. Various decay rates of pion like states of M₈₉ hadron physics can be estimated using the generalization of partially conserved axial vector hypothesis (PCAC) stating that the divergence of the axial vector current is proportional to pion field. The proportionality constant is f_πm_π². The divergence of axial current equals to the sum of instanton densities for electro-weak gauge fields and color gauge field plus the divergence of axial vector currents for u and d type quarks assuming that they are massive: this divergence is by Dirac equation proportional to the mass of the quark.

   The contribution of more massive quarks is absent, which is quite a remarkable difference as compared to the standard model Higgs for which the decay amplitudes to massive quark pairs are the most important ones by the proportionality of Higgs-fermion coupling to quark mass. This holds true in M⁴ effective QFT picture: one can hope that it is a good approximation. It is is indeed known to work in orfdinary low energy hadron physics and p-adic fractality suggests that the same holds true for M₈₉ hadron physics .

2. If the generalization of hadronic sigma model involving u and d type is accepted then f_π can be identified as the negative of the vacuum expectation value of sigma field: f_π=-v. The inspection of the decay rates of Higgs in standard model and those predicted by PCAC /Iztykson-Zuber is my source) shows that their structure is identical. This strongly suggests that by replacing Higgs vacuum expectation value by a suitable multiple of sigma field vacuum expectation it might be possible to reproduce all decay rates of standard model Higgs. This would apply also at the level of amplitudes.

   This kind of duality like relation would not be terribly surprising since the structure of these two models is very similar. This would allow to estimate the decay rates of pionlike state to various channels and have very similar results for the decay rates to weak gauge bosons and also to the states produced via the decay to virtual gauge boson pair decaying to quarks or leptons. The direct decays to other than u and d quark pairs do not appear in the lowest order.

3. Assuming X=f_π/m_π=91/140= .65 as for ordinary pion, the decay of pion-like state to gamma pair implied by PCAC is under very natural assumptions by a factor 1.54 times larger that the decay reate of Higgs. The observed signal cross section for gamma pair production by 125 GeV state is by the same factor about 1.5 higher than that predicted by the standard model! The magnitude of f_π=-v= -81.3 GeV is very near to W boson mass 80.4 GeV. f_π=-m_W would give m(π₈₉)= 123.6 GeV which is second favored value for the mass of the resonance.

   This does not yet allow to shout Heureka! and claim that M₈₉ pion hypothesis beats Higgs hypothesis. The production rates for Higgs and pion like state need not be the same. If however the production by fusion of electroweak bosons and gluons dominates and is described by PCAC (action would be just then one has excellent hopes that the production rates are indeed identical. There is also associated production in which W or Z boson emitted by a scattered quark in either proton emits Higgs boson. Also this vertex would be governed by PCAC when Higgs is replaced by M₈₉.

4. The experimental data suggests that Higgs signal is much smaller than the predicted signal above 127 GeV but has bump like structure and at bumps larger than the effective signal from the standard model background. Also the p value telling the probability that standard model background is able to explain the signal cross section has sharp downwards peaks at two other masses about 127 GeV. TGD interpretation would be in terms of pion like states. This interpretation makes sense only if the proportionality coefficient X in f_π=-X m_π is considerably large than its value for ordinary pion and lowest pion like state given by Z= 91/140∼1.54. This reduces the various couplings of pion like state by a factor 1/X². This is of course possible but one should have a good explanation for why X increases with the mass of pseudo-scalar state.

One can clearly say that sigma model for low-lying M₈₉ replaces Higgs mechanism as an approximate QFT description in TGD framework and a duality like relation between sigma model description of the meson decay amplitudes and those of standard model Higgs is highly suggestive.

One can criticize various aspects of the TGD vision about both ordinary and M₈₉ hadron physics. This is good for the simple reason that counter arguments are the best manner to make progress if one is on the right track.

1. TGD SUSY is also in central role if one believes that higher pion like states are there and have an explanation in terms of SUSY. 25 GeV pion like state would be apart from mixing effects spion consisting of squark pair. The assumption is that SUSY is essentially unbroken and that mixing of the quarks implies that mass squared matrix is non-diagonal having element between meson and smeson states.
   1. The first possibility is that second eigenstate is tachyonic due to very strong mixing proportional to α_s and must be excluded from the spectrum.
   2. Second - aesthetically more attractive- option is that second eigenstate indeed is there and quite recently I indeed found evidence for narrow resonances with quantum numbers of pion with mass differences between states typically in the range 10-40 MeV. Some of these might be SUSY states.

2. The experimental evidence suggests that pion has satellites but that their number is much larger than SUSY alone predicts. but that their number is much larger than SUSY alone predicts. The bumpy structure of Higgs-like signal cross section suggests the same for M₈₉ hadron physics. There are two alternative but not mutually exclusive explanations. The color magnetic flux tubes for light quarks have length of the order of Compton length and one could assign to them a string tension and IR Regge trajectories. Another explanation would be in terms of Shnoll effect implying that probability distributions with single peak decompose to distribution with several peaks. The TGD based explanation of Shnoll effect suggests that it is universal and could take place even at the level of particle physics.

3. A strong objection against TGD SUSY is that there is no missing energy signal which should result from the decays of squarks to quark and spartner of W boson decaying in turn to lepton and sneutrino. This objection forces to consider a possible modification of the recent belief system. The covariantly constant right handed neutrino could act as super gauge symmetry annilating physical states. This reduction of SUSY is standard mechanism of SUSY breaking. The color octet CP₂ partial wave of right handed neutrino would generate superpartners. Color confinement would eliminate the decays producing right handed sneutrinos as missing energy. What would be nice is that leptohadrons could be interpreted in terms of color octet sleptons (dark in TGD sense)TGD SUSY would be realized in a similar manner both for leptons and quarks and would have been discovered for decades ago. This is of course a speculation and p-adic mass calculations should be carried out to check whether this proposal really works.

I do not bother to type more and encourage the reader to find the details in the article Higgs or M₈₉ hadron physics? or the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".