CMS observes large excess of diphotons

LHC has started to produce data indicating that the new physics required by very general arguments indeed is there. Lubos told yesterday about a preprint by CMS collaboration showing a very large excess of di-photons in proto-proton collisions. This excess is so large that only a rough systematic error can threat its status.

What has been observed?

The following two data bits give strong hints about what might be involved.

1. From the figure in the posting of Lubos one learns that the distribution for the difference Δφ for the difference of the azimutal angles with respect to the beam direction covers rather evenly the span Δφ <2.80 and the production rate is considerably higher than predicted by QCD calculations except near π where the production rate is smaller than the prediction. From momentum conservation one would expect Δφ∼ π in a good approximation in the cm frame of photons. Unless the resonance does not move with a very high velocity, the photons Δ φ≈ π should hold true quite generally. This gives hints about the production mechanism.

2. Figure 3 of the CMS preprint gives the differential cross section with respect to diphoton invariant mass m_γγ as a function of m_γγ. The distribution has a sharp knee between 45-55 GeV. One might be able to see double peak at invariant masses about 50 GeV and 75 GeV and even third peak around 175 GeV. The differential cross section is however anomalous already around 20 GeV which serves as transverse momentum cutoff for photons

   The naive question by a non-professional is whether there could be resonance decaying to two photons with mass in this range. Δ φ∼ π would be however required if the resonance does not move very fast in the cm frame of colliding protons. The cut on transversal momenta is 20 GeV making 40 GeV transversal energy and I am not absolutely sure whether this could cause the shoulder. The experimenters however speak about shoulder and certainly they would not do this if it were due to the cufoff. Therefore I will assume that the shoulder is genuine.

3. If the shoulder located roughly between 45 GeV and 75 GeV is real, it would seem that the two-photon state must be accompanied by a state with opposite momentum and roughly the same energy and thus moving in opposite direction. This suggests two states with mass(es) in the range [90,150] GeV.

What could it be?

The speculation of Lubos is that the decay of Higgs like state with mass around 119 GeV might explain the finding but admits that standard model Higgs should not produce any visible effect. Even worse, the so called little Higgs alternative would predict a reduction of diphoton production rate. There are also exotic explanations involving large dimensions and exotic gravitons but to my opininion these alternatives belong to the realm of bad science fiction and can be safely forgotten.

In my naive mind frame the strong knee around 55 GeV is something which I find very difficult to not interpret as a bump suggesting the presence of a meson like state. On the other hand, the distribution for Δ φ; does not fit with this simplistic picture.

What about the TGD inspired interpretation? The first interpretation that comes into mind relies on the TGD based view about SUSY, which differs considerably from the standard view.

1. As explained in the earlier posting, TGD could allow the realization of SUSY in which quarks and squarks have same p-adic mass scale- perhaps even masses- before the mixing of hadrons and shadrons allowed by R-parity conservation. The mechanism explaining the experimental absence of squarks would be shadronization proceeding faster than the decay of squarks to quark and electroweak gaugino.
   1. In this framework the mysterious X and Y mesons accompanying charmonium states would be their super partners in a good approximation since the mixing would be small. The mixing of mesons and smesons would be however very large near confinement mass scale and make the other mixed state (identified as eigen state of mass squared matrix) tachyonic and eliminate it from the spectrum. The companion of pion would be tachyonic and excluded from spectrum: this would hold true for all smesons containing light quarks and perhaps also those containing only single light squark if the mass scale of the mass squared matrix is determined by the heavier quark and α_s by the lighter quark so that mixing is very large.

   2. A crucial assumption is that the squarks are dark in the sense of having a non-standard value of Planck constant: otherwise the decay widths of electro-weak gauge bosons would be too large. The phase transition changing the value of hbar and having a purely geometric (topological) meaning in TGD framework would accompany also the mixing process being analogous to mass insertions in the lines of Feynman graph.

2. In TGD framework the proposed view about squarks as particles having common p-adic mass scale with quark is suggested to hold true in both the ordinary M₁₀₇- and M₈₉ hadron physics. There is however no need to assume that M₈₉ squarks are dark. The pion of M₈₉ hadron physics could identified as the earlier 144 GeV Higgs candidate, forgotten but mentioned again by Lubos , would have 119 GeV bump as a lighter companion. The two states would be mixtures of pion and spion. The mass values for the bumps assigned to ρ₈₉ and ω₈₉ and to their spartner candidates allow to estimate the mass of the partner of π₈₉. The mass would near to 119 GeV for which there are slight indications.

How the shoulder around 45-55 GeV could be created from the decays of the partner of π₈₉- a (probably strong) micture of pion and spion. Could the two mixtures of M₈₉ pion and its spartner with masses (say) 119 GeV and 144 GeV (one should not take these number too literally) be responsible for the effect as the indications about two peaked structure suggest? Could the spionic parts of the states produce the events diphoton events.

1. The simplest Feynman diagram for the decay of the pion-like state would describe the turn around of squark backwards in time via the emission of two photons. This would produce onlty Δ φ∼ π events and photons with energies around 60 GeV and 72 GeV for the proposed masses 119 GeV and 144 GeV.

   Comment: 144 GeV is the estimate for the mass of π^+/- ₈₉, one obtains 138 GeV for π⁰ ₈₉: I have earlier neglected electromagnetic mass splitting of pions and approximated pion masses with charged pion mass 140 MeV. This scales the second mass to 69 GeV.

2. For a more complex Feynman diagram exchanged squark turning around in time would emit quark and antiquark transforming in this manner to gluino and back to squark. Another possibility is emission of two gluons. This would give photon pair and something which could be just two hadron jets if the emitted quarks and gluons transform to ordinary quarks.

3. The objection is that this model need not explain the strong concentration of diphoton invariant mass to the range 45-75 GeV since in principle 4-particle final states are in question and phase space distribution does not predict anything like this. p-Adic length scale hypothesis however suggests that the resulting quark pairs actually form a p-adically scaled down variant of the pion like state and have therefore mass, which is half of its mass. This would give rise to a resonance like behavior and impy a strong concentration of the events to the invariant masses which are one half of the mass of the mother particle.

   The p-adically scaled up quarks appear even in the TGD based model of light hadrons and produce mass formula replacing Gell-Mann-Nishijina mass formula (see this). As a matter fact, the naive prediction for the mass of M₈₉ pion is just 512 times the mass of the ordinary neutral pion and gives 69.1 GeV!

4. One must also worry about overall parity conservation required if only strong and electromagnetic interactions are involved with the decay process. Pion is pseudoscalar and the decay of pion to two pions with scaled down mass requires parity breaking in the effective action involving the pion fields only unless the vertex contains derivatives but one cannot build a Lorentz invariant involving 4-D permutation symbol from three pion fields. Should one assume that the process breaks parity conservation and involves therefore weak interactions? Or should one assume that second scaled down pion is replaced with two pions with mass equal 1/4 the mass of the decaying pion to give parity invariant effective interaction Lagrangian as assumed in the model of CDF anomaly. This would predict also diphoton pairs with invariant masses scaled down to 22.5-40 GeV. The differential cross section is anomalous down to the 20 GeV cutoff. One should be able to resolve this issue before one can take the model seriously.

A connection with Aleph anomaly

There is an old anomaly known as Aleph anomaly producing 4-jets states with jet-jet invariant mass of 55 GeV. According to the reference, the anomaly did not survive improved statistics. Delphi and L3 also observed 4-jet anomaly with dijet invariant mass about 68 GeV: this not too far from the mass for p-adically scaled down mass of π₈₉ equal to 69.1 GeV! Remarkably, according to the above reference L3 observation survived the improvement of the statistics!

1. For more than decade ago I proposed an explanation of Aleph anomaly in terms of a meson-like state formed by p-adically scaled up variants of b quark and its antiquark (see this ). The mass of the resonance was predicted correctly using p-adic length scale hypothesis predicting that the mass of scaled up b quark is half octave of the mass of b quark.

2. The model could be generalized by replacing b quark with its super-partner if one assumes that SUSY breaking means only different p-adic mass scale. There is however an aesthetic problem (I take aesthetic arguments very seriously). The model for X and Y mesons assumed that the p-adic mass scale is same: now one should give up this assumption for b quark. The reader has probably already asked whether Aleph anomaly and the recent CMS anomaly could correspond to the same meson like state. 4-jets could be produced when sb and sbbar decay to bbbar pair by emission of gluinos which then exchange quark to produce quark pair or gluon pair. In the decays of X and Y mesons the resulting quark pair would form pion or some other meson. Now two quark or gluon jets by exchanged gluinos would be produced giving altogether four jets.

3. CMS anomaly suggests a different interpretation. Perhaps the 4-jets with di-jet energies around 55 GeV and 68 GeV are produced by the decays of the mixtures of M₈₉ pion and spion with masses around 110 GeV and 144 GeV producing as intermediate state the 2-adically scaled down pions with half of their original masses.

   The same mechanism is assumed also in the model of CDF anomaly discovered for three years ago but already forgotten. Political memory is short! The mechanism would be a modification of that producing the diphoton excess. Squark and anti-squark would transform to quark-antiquark pair giving rise to intermediate scaled down pionlike state decaying to two jets with invariant mass concentrated around the mass of pion-like state. The exchanged gluino emits quark and antiquark or two gluons. Quark antiquark state could also form a scaled down M₈₉ pion before the decay to two jets. The outcome would be four jets with concentration to preferred invariant masses.

For details and background see the chapter New particle physics predicted by TGD: part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".