Two birthday gifts

October 30 was my birthday. It is nice to have birthdays and also friends. I got even gifts. Thank You! Two of the gifts made me especially happy. As a matter fact, I am so proud that I want to tell about them to all of you!

The first gift

During my friday morning blog walk I found that Peter Woit had told at my birthday about a possible discovery of a new long-lived particle by CDF experiment. There is a detailed paper [1] with title Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV by CDF collaboration added to the ArXiv October 29 - the eve of my birthday;-). Thank you!

Since I am too excited to type for details myself, I just copy the brief summary of Peter Woit about the finding.

The article originates in studies designed to determine the b-bbar cross-section by looking for events, where a b-bbar pair is produced, each component of the pair decaying into a muon. The b-quark lifetime is of order a picosecond, so b-quarks travel a millimeter or so before decaying. The tracks from these decays can be reconstructed using the inner silicon detectors surrounding the beam-pipe, which has a radius of 1.5 cm. They can be characterized by their “impact parameter”, the closest distance between the extrapolated track and the primary interaction vertex, in the plane transverse to the beam.

If one looks at events where the b-quark vertices are directly reconstructed, fitting a secondary vertex, the cross-section for b-bbar production comes out about as expected. On the other hand, if one just tries to identify b-quarks by their semi-leptonic decays, one gets a value for the b-bbar cross-section that is too large by a factor of two. In the second case, presumably there is some background being misidentified as b-bbar production.

The new result is based on a study of this background using a sample of events containing two muons, varying the tightness of the requirements on observed tracks in the layers of the silicon detector. The background being searched for should appear as the requirements are loosened. It turns out that such events seem to contain an anomalous component with unexpected properties that disagree with those of the known possible sources of background. The number of these anomalous events is large (tens of thousands), so this cannot just be a statistical fluctuation.

One of the anomalous properties of these events is that they contain tracks with large impact parameters, of order a centimeter rather than the hundreds of microns characteristic of b-quark decays. Fitting this tail by an exponential, one gets what one would expect to see from the decay of a new, unknown particle with a lifetime of about 20 picoseconds. These events have further unusual properties, including an anomalously high number of additional muons in small angular cones about the primary ones.

The lifetime is estimated to be considerably longer than b quark life time and below the lifetime 89.5 ps of K_0,s mesons. The fit to the tail of "ghost" muons gives the estimate of 20 picoseconds.

Second gift

As if this gift give would not have enough I received also a second one! Thank you, thank you! In October 29 also another remarkable paper [2] had appeared in arXiv. It was titled Observation of an anomalous positron abundance in the cosmic radiation . PAMELA collaboration finds an excess of cosmic ray positrons at energies 10→50 GeV. PAMELA anomaly is discussed in Resonaances. ATIC in turn sees an excess of electrons and positrons going all the way up to energies of order 500-800 GeV [3].

Also Peter Woit refers to these cosmic ray anomalies and also to the article LHC Signals for a SuperUnified Theory of Dark Matter by Nima Arkadi-Hamed and Neal Weiner [4], where a model of dark matter inspired by these anomalies is proposed together with a prediction of lepton jets with invariant masses with mass scale of order GeV. The model assumes a new gauge interaction for dark matter particles with Higgs and gauge boson masses around GeV. The prediction is that LHC should detect "lepton jets" with smaller angular separations and GeV scale invariant masses.

TGD explanation of CDF anomaly

Consider first CDF anomaly. TGD predicts a fractal hierarchy of QCD type physics. In particular, colored excitations of leptons are predicted to exist. Neutral lepto-pions would have mass only slightly above two times the charged lepton mass. Also charged leptopions are predicted and their masses depend on what is the p-adic mass scale of neutrino. It is not clear whether it is much longer than that for charged colored lepton as in the case of ordinary leptons. If so, then the mass of charged leptopion is essentially that of charged lepton.

1. There exists a considerable evidence for colored electrons dating back to the seventies see the chapter Recent status of Leptohadron hypothesis of the book "P-Adic Length Scale Hypothesis And Dark Matter Hierarchy" and references therein. The anomalous production of electron positron pairs discovered in heavy ion collisions can be understood in terms of decays of electro-pions produced in the strong non-orthogonal electric and magnetic fields created in these collisions. The action determining the production rate would be proportional to the product of the leptopion field and highly unique "instanton" action for electromagnetic field determined by anomaly arguments so that the model is highly predictive.

2. Also the .511 MeV emission line [5,6] from the galactic center can be understood in terms of decays of neutral electro-pions to photon pairs. Electro-pions would reside at magnetic flux tubes of strong galactic magnetic fields. It is also possible that these particles are dark in TGD sense.

3. There is also evidence for colored excitations of muon and muo-pion [7,8]. TGD based model is discussed here. Muo-pions could be produced by the same mechanism as electro-pions in high energy collisions of charged particles when strong non-orthogonal magnetic and electric fields are generated.

Also t-hadrons are possible and CDF anomaly can be understood in terms of a production of t-hadrons as the following argument demonstrates.

1. t-QCD at high energies would produce "lepton jets" just as ordinary QCD. In particular muon pairs with invariant energy below 2m(t) ~ 3.6 GeV could be produced by the decays of neutral t-pions. The production of monochromatic gamma ray pairs is predicted to dominate the decays. Note that the space-time sheet associated with both ordinary hadrons and t lepton correspond to the p-adic prime M₁₀₇=2¹⁰⁷-1.

2. One can imagine several options for the detailed production mechanism. One can imagine several options for the detailed production mechanism in strong non-orthogonal fields E and B of colliding proton and antiproton creating τ-pions.
   1. The decay of virtual t-pions created in these fields to pairs of leptobaryons generates lepton jets. Since colored leptons correspond to color octets, lepto-baryons could correspond to states of form LLL or L[`L]L.
   2. The option inspired by a blog discussion with Ervin Goldfein is that a coherent state of t-pions is created first and is then heated to QCD plasma like state producing the lepton jets like in QCD.
   3. The option inspired by CDF model is that a p-adically scaled up variant of on mass shell neutral t-pion having k=103 and 4 times larger mass than k=107 t-pion is produced and decays to three k=105 t-pions with k=105 neutral t-pion in turn decaying to three k=107 t-pions.

3. The basic characteristics of the anomalous muon pair prediction seems to fit with what one would expect from a jet generating a cascade of t-pions. Muons with both charges would be produced democratically from neutral t-pions; the number of muons would be anomalously high; and the invariant masses of muon pairs would be below 3.6 GeV for neutral t-pions and below 1.8 GeV for charged t-pions if colored neutrinos are light.

4. The prediction for neutral leptopion mass is 3.6 GeV and same as in the paper of CDF collaboration [13], which had appeared to the arXiv Monday morning as I learned from the blog of Tommaso. The masses for particles h₂, h₂ and h₁ suggested in the article were 3.6 GeV, 7.3 GeV, and 15 GeV. p-Adic length scale hypothesis predicts that allowed mass scales come as powers of sqrt(2) and these masses come in good approximation as powers of 2. Several p-adic scales appear in low energy hadron physics for quarks and this replaces Gell-Mann formula for low-lying hadron masses. Therefore one can ask whether these masses correspond to neutral tau-pion with p= M_k=2^k-1, k=107) and its scaled up variants with p=about 2^k, k= 105, and k=103 (also prime). The prediction for masses would be 3.6 GeV, 7.2 GeV, 14.4 GeV.

   The model however differs from TGD based model in many respects and the powers of two follow from the assumed production mechanism. h₁ is assumed to be pair produced and decay to h₂ pair decaying in turn to h₃ pair. The decay of free τ-pion to two τ-pions is forbidden by parity conservation but can take place in E·B "instanton" bacground inducing parity breaking so that the decay cascade is possible also for τ-pions. The lightest state is assumed to be neutral and to decay to a τ pair. In TGD framework both charged and neutral τ-pions are possible. The correct prediction for the lifetime provides a strong support for the identification of long-lived state as charged τ-pion with mass near τ mass so that the decay to μ and its antineutrino dominates. Neutral τ-pion lifetime is 1.12×: 10^-17 seconds as will be found. For its higher excitations decay rate to two photons would scale as the mass of τ-pion. The decay rate to two leptopions

5. The lifetime of 20 ps can be assigned with charged t-pion decaying weakly only into muon and neutrino. This provides a killer test for the hypothesis. In absence of CKM mixing for colored neutrinos, the decay rate to lepton and its antineutrino is given by

   
   

   G(pt® L+ n   L  ) = G2m(L)2 f2(p)(m(pt)2-m(L)2)2 4pm3(pt) .

   The parameter f(p_t) characterizing the coupling of pion to the axial current can be written as f(p_t) = r(p_t)m(p_t). For ordinary pion one has f(p) = 93 MeV and r(p)=.67. The decay rate for charged t-pion is obtained by simple scaling giving

   
   

   G(pt® L+ n   L  ) = 8x2 u2 y3(1-z2) 1 cos2(qc) G(p® m+ nm   ),

   
   

   x = m(L) m(m) , y= m(t) m(p) , z = m(L) 2m(t) , u = r(pt) r(p) .

   If the p-adic mass scale of the colored neutrino is same as for ordinary neutrinos, the mass of charged leptopion is in good approximation equal to the mass of t and the decay rates to t and electron are much slower than to muons so that muons are produced preferentially.

6. For m(t)=1.8 GeV and m(p) = .14 GeV and the same value for f_p as for ordinary pion the lifetime is obtained by scaling from the lifetime of charged pion about 2.6×10^-8 s. The prediction is 3.31×10^-12 s to be compared with the experimental estimate about 20×10^-12 s. r(p_t)=.41r_p gives a correct prediction. Hence the explanation in terms of t-pions seems to be rather convincing unless one is willing to believe in really nasty miracles.

7. Neutral t-pion would decay dominantly to monochromatic pairs of gamma rays. The decay rate is dictated by the product of leptopion field and "instanton" action (inner product of E and B reducing to a total divergence) and is given by

   
   

   G(pt® g+g) = aem2m3(pt) 64p3 f(pt)2 = 2x-2y ×G(p® g+g) ,

   
   

   x = f(pt) m(pt) , y = m(t) m(p) ,

   
   

   G(p® g+g) = 7.37   eV .

   The predicted lifetime is 1.17×10^-17 seconds.

8. Second decay channel is to lepton pairs, with muon pair production dominating for kinematical reasons. The invariant mass of the pairs is 3.6 GeV of no other particles are produced. Whether the mass of colored neutrino is essentially the same as that of charged lepton or corresponds to the same p-adic scale as the mass of the ordinary neutrino remains an open question. If colored neutrino is light, the invariant mass of muon neutrino pair is below 1.78 GeV.

PAMELA and ATIC anomalies in TGD framework

TGD predicts also a hierarchy of hadron physics assignable to Mersenne primes. The mass scale of M₈₉ hadron physics is by a factor 512 higher than that of ordinary hadron physics. Therefore a very rough estimate for the nucleons of this physics is 512 GeV. This suggest that the decays of M₈₉ hadrons are responsible for the anomalous positrons and electrons up to energies 500-800 GeV reported by ATIC collaboration. An equally naive scaling for the mass of pion predicts that M₈₉ pion has mass 72 GeV. This could relate to the anomalous cosmic ray positrons in the energy interval 10-50 GeV reported by PAMELA collaboration. Be as it may, the prediction is that M₈₉ hadron physics exists and could make itself visible in LHC.

The surprising finding is that positron fraction (the ratio of flux of positrons to the sum of electron and positron fluxes) increases above 10 GeV. If positrons emerge from secondary production during the propagation of cosmic ray-nuclei, this ratio should decrease if only standard physics is be involved with the collisions. This is taken as evidence for the production of electron-positron pairs, possibly in the decays of dark matter particles. In fact, I found that I have told Recent Status of Leptohadron Hypothesis about production of anomalous electron-positron pairs in hadronic reactions [9,10,11,12] as evidence for lepto-hadron hypothesis.

Leptohadron hypothesis predicts that in high energy collisions of charged nuclei with charged particles of matter it is possible to produce also charged electro-pions, which decay to electrons or positrons depending on their charge and produce the electronic counterparts of the jets discovered in CDF. This proposal - and more generally leptohadron hypothesis - could be tested by trying to find whether also electronic jets can be found in proton-proton collisions. They should be present at considerably lower energies than muon jets. The simple-minded guess is that for proton-proton collisions the center of mass energy at which the jet formation begins to make itself visible is in constant ratio to the mass of charged lepton. From CDF data this ratio is around s^1/2/m(τ)=x < 10³. For electropions the threshold energy would be around 10^-3x×.5 GeV and for muo-pions around 10^-3x× 100 GeV.

Does a phase transition increasing the value of Planck constant take place in the production of leptopions?

The critical argument of Tommaso Dorigo in his blog inspired an attempt to formulate more precisely the hypothesis Ös/m_t > x < 10³. This led to the realization that a phase transition increasing Planck constant might happen in the production process as also the model for the production of electro-pions in heavy ion collisions requires.

Suppose that the instanton coupling gives rise to virtual neutral leptopions decaying to pairs of leptobaryons producing the jets. E and B could be associated with the colliding proton and antiproton or quarks.

1. The amplitude for leptopion production is essentially Fourier transform of E·B, where E and B are the non-orthogonal electric and magnetic fields of the colliding particles. At the level of scales one has t ~ hbar/E, where t is the time during which E·B is large enough during collision and E is the energy scale of the virtual leptopion giving rise to the jet.

2. In order to have jets one must have m(p_t) << E. If the scaling law E µ Ös hold true, one indeed has Ös/m(p_t) > x < 10³.

3. If proton and antiproton would move freely, t would be of the order of the time for proton to move through a distance, which is 2 times the Lorentz contracted radius of proton: τ_free= 2×(1-v²)^1/2 R_p/v = 2hbar/E_p. This would give for the energy scale of virtual t-pion the estimate E = hbar/t_free = Ös/4. x=4 is certainly quite too small value. Actually t > t_free holds true but one can argue that without new physics the time for the preservation of E·B cannot be by a factor of order 2⁸ longer than for free collision.

4. For a colliding quark pair one would have t_free = 4hbar/(s_pair(s))^1/2, where (s_pair(s))^1/2 would be the typical invariant energy of the pair which is exponentially smaller than Ös. Somewhat paradoxically from classical physics point of view, the time scale would be much longer for the collision of quarks than that for proton and antiproton.

The possible new physics relates to the possibility that leptopions are dark matter in the sense that they have Planck constant larger than the standard value.

1. Suppose that the produced leptopions have Planck constant larger than its standard value hbar/hbar₀. This is actually required by the model for electro-pion production since otherwise production cross section is not quite large enough.

2. Assume that a phase transition increasing Planck constant occurs during the collision. Hence t is scaled up by a factor y = hbar/hbar₀. The inverse of the leptopion mass scale is a natural candidate for the scaled up dark time scale. t(hbar₀) ~ t_free, one obtains y ~ (s_min(s))^1/2/4m(p_t) £ 2⁸ giving for proton-antiproton option the first guess Ös/m(p_t) > x < 2¹⁰. If the value of y does not depend on the type of leptopion, the proposed estimates for muo- and electro-pion follow.

3. If the fields E and B are associated with colliding quarks, only colliding quark pairs with (s_pair(s))^1/2 > ( > )m(p_t) contribute giving y_q(s) = (s_pair(s))/s)^1/2×y.

If the τ-pions produced in the magnetic field are on-mass shell τ-pions with k=103, the value of hbar would satisfy hbar/hbar₀<2⁵ and sqrt(s)/m(π_τ)>x<2⁷.

Summary

To sum up, the probability that a correct prediction for the lifetime of the new particle using only known lepton masses and standard formulas for weak decay rates follows by accident is extremely low. Throwing billion times coin and getting the same result every time might be something comparable to this. Therefore my sincere hope is that colleagues would be finally mature to take TGD seriously. If TGD based explanation of the anomalous production of electron positron pairs in heavy ion collisions would have been taken seriously for fifteen years ago, particle physics might look quite different now.

References

[1]CDF Collaboration (2008), Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV.

[2] PAMELA Collaboration (2008), Observation of an anomalous positron abundance in the cosmic radiation.

[3] J. Chang et al. (ATIC) (2005), prepared for 29th International Cosmic Ray Conferences (ICRC 2005), Pune, India, 31 Aug 03 - 10 2005.

[4] N. Arkani-Hamed and N. Weiner (2008), LHC Signals for a SuperUnified Theory of Dark Matter.

[5] E. Churazov, R. Sunyaev, S. Sazonov, M. Revnivtsev, and D. Varshalovich, Mon. Not. Roy. 17. Astron. Soc. 357, 1377 (2005), astro-ph/0411351.

[6] G. Weidenspointner et al., Astron. Astrophys. 450, 1013 (2006), astro-ph/0601673.

[7] X.-G. He, J. Tandean, G. Valencia (2007), Has HyperCP Observed a Light Higgs Boson?,Phys. Rev. D74. http://arxiv.org/abs/hep-ph/0610274.

[8] X.-G. He, J. Tandean, G. Valencia (2007), Light Higgs Production in Hyperon Decay , Phys. Rev. Lett. 98. http://arxiv.org/abs/hep-ph/0610362.

[9] T. Akesson et al (1987), Phys. Lett. B192, 463,
T. Akesson et al (1987), Phys. Rev. D36, 2615.

[10] A.T. Goshaw et al (1979), Phys. Rev. Lett. 43, 1065.

[11] P.V. Chliapnikov et al (1984), Phys. Lett. B 141, 276.

[12]S. Barshay (1992) , Mod. Phys. Lett. A, Vol 7, No 20, p. 1843.

[13] P. Giromini, F. Happacher, M. J. Kim, M. Kruse, K. Pitts, F. Ptohos, S. Torre (2008), Phenomenological interpretation of the multi-muon events reported by the CDF collaboration. .

For details and background see the chapter Recent Status of Leptohadron Hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".