Good bye large extra dimensions and MSSM

New results giving strong constraints on large extra dimensions and on the parameters of minimally supersymmetric standard model (MSSM) have come from LHC and one might say that both larger extra dimensions and MSSM are experimentally excluded.

The problems of MSSM

According to the article The fine-tuning price of the early LHC by A. Strumia the results from LHC reduce the parameter space of MSSM dramatically. Recall that the king idea of MSSM is that the presence of super partners tends to cancel the loop corrections from ordinary particles giving to Higgs mass much larger correction that the mass itself. Unfortunately, the experimental lower bounds on masses of superpartners are so high and the upper bound on Higgs mass so low that the superpartners cannot give rise to large enough compensating corrections. The means need for fine-tuning even in MSSM known as little hierarchy problem.

Also the article Search for supersymmetry using final states with onelepton, jets, and missing transverse momentum with the ATLAS detector in s^1/2 = 7 TeV pp collisions by ATLAS collaboration at LHC poses strong limits on the parameters of MSSM implying that the mass of gluino is above 700 GeV in the case that gluino mass is same as that of squark. The essential assumption is that R-parity is an exact symmetry so that the lightest superpartner is stable. The signature of SUSY is indeed missing energy resulting in the decay chain beginning with the decay of gluino to chargino and quark pair followed by the decay of chargino to W boson and neutralino representing missing energy.

A theorists with a modest amount of aesthetic sense would have made the unavoidable conclusions long time ago but the fight of theory against facts has continued. Maybe some corner of the parameter might give what one wants?! This has been the hope. The results from LHC however do not leave much about this dream. One must try something else.

The difficulties of large extra dimensions

One example of this something else are large extra dimensions implying massive graviton, which could provide a new mechanism for massivation based on the idea that massive particle in Minkowski space are massless particles in higher dimensional space (also essential element of TGD). This could perhaps the little hierachy problem if the mass of Kaluza-Klein graviton is in TeV range.

The article LHC bounds on large extra dimensions by A. Strumia and collaborators poses very strong constraints on large extra dimensions and mass and effective coupling constant parameter of massive graviton. Kaluza-Klein graviton would appear in exchange diagrams and loop diagrams for 2-jet production and could become visible in higher energy proton-proton collisions at LHC. KK graviton would be also produced as invisible KK-graviton energy in proton-proton collisions. The general conclusion from data gathered hitherto shrinks dramatically the allowed parameter space for the KK-graviton. I must say that for me the idea of large dimensions is so ugly that the results are not astonishing. Aether hypothesis was a beauty compared with this beast.

Could TGD approach save super-symmetry?

What is left? Should we follow the example of landscapeologists and just accept anthropic principle giving up all attempts to understand electroweak symmetry breaking?

Not at all! In TGD framework -which of course represents bad theoretical physics from the point of view of hegemony- the situation is not at all so desolate. Due to the differences between the induced spinor structure and ordinary spinors, Higgs corresponds to SU(2) triplet and singlet in TGD framework rather than complex doublet. The recent view about particles as bound states of massless wormhole throats forced by twistorial considerations and emergence of physical particles as bound states of wormhole contacts carrying fermion number and vibrational degrees of freedom strongly suggests- I do not quite dare to say "implies"- that also photon and gluons become massive and eat their Higgs partners to get longitudinal polarization they need. No Higgs- no fine tuning of Higgs mass- no hierarchy problems.

Note that super-symmetry is not given up in TGD but differs in many essential respects from that of MSSM. In particular, super-symmetry breaking and breaking of R-parity are automatically present from the beginning and relate very closely to the massivation. Therefore neutralino is unstable against decay to neutrino-antineutrino pair if the mass of the neutralino is larger than twice the mass of neutrino. The decay of the neutralino must also take place with high enough rate. The rate is determined by the rate with which right handed neutrino transforms to a left handed one. The rate is dictated by the mixing of M⁴ and CP₂ gamma matrices.

1. If the gamma matrices were induced gamma matrices, the mixing would be large by the light-likeness of wormhole throats carrying the quantum numbers. Induced gamma matrices are however excluded by internal consistency requiring modified gamma matrices obtained as contractions of canonical momentum densities with imbedding space gamma matrices. Induced gamma matrices would require the replacement of Kähler action with 4-volume and this is unphysical option.

2. In the interior Kähler action defines the canonical momentum densities and near wormhole throats the mixing is large: one should note that the condition that the modified gamma matrices multiplied by square root of metric determinant must be finite. One should show that the weak form of electric-magnetic duality guarantees this: it could even imply the vanishing of the limiting values of these quantities with the interpretation that the space-time surfaces becomes the analog of Abelian instanton with Minkowski signature having vanishing energy momentum tensor near the wormhole throats. If this is the case, Euclidian and Minkowskian regions of space-time surface could provide dual descriptions of physics in terms of generalized Feynman diagrams and fields.

3. At wormhole throats Abelian Chern-Simons-Kähler action with the constraint term guaranteeing the weak form of electric-magnetic duality defines the modified gamma matrices. Without the constraint term Chern-Simons gammas would involve only CP₂ gamma matrices and no mixing of M⁴ chiralities would occur. The constraint term transforming TGD from topological QFT to almost topological QFT by bringing in M⁴ part to the modified gamma matrices however induces a mixing proportional to Lagrange multiplier. It is difficult to say anything precise about the strength of the constraint force density but one expect that the mixing is large since it is also large in the nearby interior.

If the mixing of the modified gamma matrices is indeed large, the transformation of the right-handed neutrino to its left handed companion should take place rapidly. If this is the case, the decay signatures of spartners are dramatically changed as will be found and the bounds on the masses of squarks and gluinos derived for MSSM do not apply in TGD framework.

In TGD framework p-adic length scale hypothesis (see this and this) allows to predict the masses of sleptons and squarks modulo scaling by a powers 2^1/2 determined by the p-adic length scale by using information coming from CKM mixing induced by topological mixing of particle families in TGD framework.

1. If one assumes that the mass scale of SUSY corresponds to Mersenne prime M₈₉ assigned with intermediate gauge bosons one obtains unique predictions for the various masses apart from uncertainties due to the mixing of quarks and neutrinos.

2. In first order the p-adic mass formulas reads as

   m_F=(n_F/5)^1/2 2^(127-k_F)/2m_e ,

   n_L= (5,14,65), n_ν= (4,24,64) , n_U=(5,6,58), n_D=(4,6,59).

   Here k_F is the integer characterizing p-adic mass scale of fermion via p≈ 2^k_F. The values of k_F are not listed here since they are not needed now. Note that electroweak symmetry breaking distinguish U and D type fermions is very small when one uses p-adic length scale as unit.

   By assuming k_F=89 for super-partners one obtains in good approximation (the first calculation contained erranous scaling factor)

   m_sL/GeV = (262, 439, 945) ,

   m_sν/GeV = (235, 423, 938) ,

   m_sU/GeV = (262, 287, 893) ,

   m_sD/GeV = (235, 287, 900) .

3. The simplest possibility is that also electroweak gauginos are characterized by k=89 and have same masses as W and Z in good approximation. Therefore sW could be the lightest super-symmetric particle and could be observed directly if the neutrino mixing is not too fast and allowing the decay sW+ν. Also gluinos could be characterized by M₈₉ and have mass of order intermediate gauge boson mass. For this option to be discussed below the decay scenario of MSSM changes considerably. Also Higgsino (note that entire Higgs would be eaten by the massivation of all electroweak gauge bosons in the simpleset scenario) could be produced in the decay and would naturally have electroweak mass scale.

4. It should be noticed that the single strange event reported 1995 (see the previous posting) gave for the mass of selectron the estimate 131 GeV which corresponds to M₉₁ instead of M₈₉. This event allowed also to estimate the masses of Zino and corresponding Higgsino. The results are summarized by the following table:

   m(se)=131 GeV , m(sZ⁰)=91.2 GeV , m(sh)=45.6 GeV .

   If one takes these results at face value one must conclude either that M₈₉ hypothesis is too strong or M_SUSY corresponds to M₉₁ or that M₈₉ is correct identification but also sfermions can appear in several p-adic mass scales.

The decay cascades searched for in LHC are initiated by the decay q→ sq+sg and g→ sq+ sq_c. Consider first R-parity conserving decays. Gluino could decay in R-parity conserving manner via sg→ sq+ q. Squark in turn could decay via sq→ q₁+sW or via sq→ q+sZ⁰. Also Higgsino could occur in the final states. For the proposed first guess about masses the decay sW→ ν_e+se or sZ⁰→ ν_e+sν_e would not be possible on mass shell.

If the mixing of right-handed and left-handed neutrinos is fast enough, R-parity is not conserved and the decays sg→ g+ν and sq→ q+ν could take place by the mixing ν_R→ ν_L following by electroweak interaction between ν_L quark or antiquark appearing as composite of gluon. The decay signature in this case would be pair of jets (quark and antiquark or gluon gluon jet both containing a lonely neutrino not accompanied by a charged lepton required by electroweak decays. Also the decays of electroweak gauginos and sleptons could produce similar lonely neutrinos.

The lower bound to quark masses from LHC is about 600 GeV and 800 GeV for gluon masses assuming light neutralino is slightly above the proposed masses of lightest squarks (see this). These masses are allowed for R-parity conserving option if the decay rate producing the chargino is reduced by the large mass of chargino the bounds become weaker. If the decay via R-parity breaking is fast enough no bounds on masses of squarks and gluinos are obtained in TGD framework but jets with neutrino unbalanced by a charged lepton should be observed.

The anomalous magnetic moment of muon as a constraint on SUSY

The anomalous magnetic moment a_μ== (g-2)/2 of muon has been used as a further constraint on SUSY. The measured value of a_μ is a_μ^exp=11659208.0(6.3)× 10⁻¹⁰. The theoretical prediction decomposes to a sum of reliably calculable contributions and hadronic contribution for which the low energy photon appearing as vertex correction decays to virtual hadrons. This contribution is not easy to calculate since non-perturbative regime of QCD is involved. The deviation between prediction and experimental value is Δ a_μ(exp-SM)= 23.9(9.9)× 10^-10 giving Δ a_μ(exp-SM/)/a_μ= 2× 10^-6. The hadronic contribution is estimated to be 692.3× 10^-10 so that the anomaly is 3 per cent from the hadronic contribution. This suggests that the uncertainties due to the non-perturbative effects could explain the anomaly.

It has been proposed that the loops involving superpartners could explain the anomaly. In order to get some idea of the situation one can just assume that QFT calculation makes sense as an approximation also in TGD framework and try to identify the TGD counterparts and also the values of the parameters appearing in MSSM calculation.

In one-loop order one would have the processes μ→ sμ+ sZ⁰ and μ → sμ_μ+ sZ⁰. The situation is complicated by the possible mixing of the gauginos and Higgsinos and in MSSM this mixing is described by the mixing matrices called X and Y.

1. The basic outcome is that the mixing is proportional to the factor m_μ²/m_SUSY². One expects that in the recent situation m_SUSY=m_W is a reasonable guess so that the mixing is large and could explain the anomaly. Second guess is as M₈₉ p-adic mass scale.

2. In MSSM the mixing is also proportional to tan(β) factor where the angle β characterizes the ratio of mass scales of U and D type fermions fixed by the ratio of Higgs expectations for the two complex Higgs doublets (see the reference). The value of the parameter tan(β) also characterizes in MSSM the ratio of vacuum expectation values of two Higgses and cannot be fixed from this criterion since in TGD framework one has one scalar Higgs and pseudoscalar Higgs decomposing to triplet and singlet under SU(2). One can however use the fact that β also characterizes the mixing of sW and charged Higgsino parametrized as by a matrix whose rows are given by

   X₁ = (M₂, M_W2^1/2cos(β)) ,

   X₂ =(M_W2^1/2cos(β) , μ) .

   This parameterization makes sense in TGD framework with M₂ and μ identified as masses of wino and charged Higgsino before mixing giving rise to their physical masses (note that the sign of μ can be negative). The first guess is that apart from p-adic mass scale same has M₂=-μ= m: this guarantees identical masses for the mixed states in accordance with the ideas that different masses for particles and sparticles result from the different p-adic length scale. For cos(β)=1/2^1/2 this would give mass matrix with eigen values

   (M,-M), M= (m²+m_W²)^1/2,

   so that the masses of the mixed states would be identical and above m_W mass for p=M₈₉. Symmetry breaking by the increase of the p-adic length scale could however reduce the mass of the other state by a power of 2^1/2.

3. In MSSM 4× 4 matrix is needed to describe the mixing of neutral gauginos and two kinds of neutral Higgsinos. In TGD framework second Higgs (if it exists at all) is pseudo-scalar and does not contribute and the 2× 2 matrices describe the mixing also now.
   1. Since Higss and Higgsino have representation content 3+1 with respect to electroweak SU(2) in TGD framework, one can speak about sh_B, B= W,Z,γ. An attractive assumption is that Weinberg angle characterizes also the mixing giving rise to sZ and sγ on one hand and sh_γ and sh_Z on the other hand. This would reduce the mixing matrix to two 2× 2 matrices: the first one for sγ and sh_γ and the second one for sZ and sh_Z.

   2. A further attractive assumption is that the mass matrices describing mixing of gauginos and corresponding Higgsinos are in some sense universal with respect to electroweak interactions. The form of the mixing matrix would be essentially same for all cases. This would suggest that M_W is replaced in the above formula with the mass of Z⁰ and photon in these matrices (recall that it is assumed that photon gets small mass by eating the neutral Higgs). Note that for photino and corresponding Higgsino the mixing would be small. The guess is M₂=-μ= m_Z. For photino one can guess that M₂ corresponds to M₈₉ mass scale.

   These assumptions of course define only the first maximally symmetric guess and the simplest modification that one can imagine is due to the different p-adic mass scales. If the above discussed values for zino and neutralino masses deduced from the 1995 event are taken at face value, the eigenvalues would be +/- (M_Z^2+m^2)^1/2 with m=M_2=-μ for sZ-sh_Z-mixing and the other state would have p-adic length scale k=91 rather than k=89. M and μ would have opposite signs as required by the correct sign for the g-2 anomaly for muon assuming that smuons correspond to k=M₈₉ as will be found.

4. If one accepts the MSSM formula (see the reference)

   m_μ²= m_sL²+M_Z²cos(2β)/2 ,

   and uses the fact the masses of sneutrinos and sleptons are very near to each other, the natural guess is β=+/- π/4 so that one would have tan(β)=1. This corresponds to the lower bound of allowed values of tan(β) and small mass scale for weak gauginos. In MSSM tan(β)>2 is required and this is due to the large value of the m_SUSY.

By using the formulas 56-58 of the reference one obtains for the charged loop the expression

Δ a_μ^+/-=-(21g₂²/32π²)× (m_μ/m_W)²× sign(μ M₂) .

For neutral contribution the expression is more difficult to deduce. As physical intuition suggests, the expression inversely proportional to 1/m_W² since m_W corresponds now m_SUSY although this is not obvious on the basis of the general formulas suggesting the proportionality toi 1/m_sνμ². The p-adic mass scale corresponding to M₈₉ is the natural guess for M_SUSY and would give M_SUSY= 104.9 GeV. The correction has positive sign, which requires that μ and M₂ have opposite signs unlike in MSSM. The sign factor is opposite to that in MSSM because sfermion mass scales are assumed to be much higher than weak gaugino mass scale.

The ratio of the correction to the lowest QED estimate a_μ,0=α/2π can be written as

Δ a_μ⁺/a_μ,0= (21/4)× (1/sin²(θ_W))× (m_μ/m_SUSY)²≈2.73× 10^-5 .

which is roughly 10 times larger than the observed correction (the first calculation contained an error). The contribution Δ a_μ⁰ should reduce this contribution and certainly does. At this moment I am however not yet able to transform the formula for it to TGD context. Also the scaling up of the m_SUSY=m_W by a factor of order 2^3/2 could reduce the correction.

(tan(β)=1,M_SUSY=100 GeV) corresponds to the boundary of the region allowed by the LHC data and g-2 anomaly is marginally consistent with these parameter values (see figure 16 of this). The reason is that in the recent case the mass of lightest Higgs particle does not pose any restrictions (the brown region in the figure). Due to the different mixing pattern of gauginos and higgsinos in neutral sector TGD prediction need not be identidal with MSSM prediction.

The proposed estimate is certainly poor man's estimate since it is not clear how near the proposed twistorial approach relying on zero energy ontology is to QFT approach. It is however encouraging that the simplest possible scenario might work and that this is essentially due to the p-adic length scale hypothesis

Also M-theorists admit that there are reasons for the skepticism

Lubos gives a link to the talk Supersymmetry From the Top Down by Michael Dine, who admits that there are strong reasons for skepticism. Dine emphasizes that the hierarchy problem related to the in-stablity of Higgs mass due to the radiative corrections is the main experimental motivation for SUSY but that little hierarchy problem remains the greatest challenge of the approach. As noticed, in TGD this problem is absent. The same basic vision based on zero energy ontology and twistors predicts among other things

• the cancellation of UV and IR infinities in generalized Feynman (or more like twistor-) diagrammatics,
• predicts that in the electroweak scale the stringy character of particles identifiable as magnetically charged wormhole flux tubes should begin to make itself manifest,
• particles regarded usually as massless eat all Higgs like particles accompanying them (here "predict" is perhaps too strong a statement),
• also pseudo-scalar counterparts of Higgs-like particles which avoid the fate of their scalar variants (there already exist indications for pseudo-scalar gluons).

Combined with the powerful predictions of p-adic thermodynamics for particle masses these qualitative successes make TGD a respectable candidate for the follower of string theory.

For a more details see the chapter p-Adic Particle Massivation: New Physics of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".