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On a Singular Solution in Higgs Field (III’) - The Photoelectric Conversion of Gamma-ray from an
Axion-like Pseudo Nambu-Goldstone Boson by Multi-Excited Ur-SM Higgs Boson.
Kazuyoshi Kitazawa
To cite this version:
Kazuyoshi Kitazawa. On a Singular Solution in Higgs Field (III’) - The Photoelectric Conversion
of Gamma-ray from an Axion-like Pseudo Nambu-Goldstone Boson by Multi-Excited Ur-SM Higgs
Boson.. The 60th Japan National Congress for Theoretical and Applied Mechanics 2011, National
Committee for IUTAM, Mar 2011, Tokyo, Japan. pp.06, �10.11345/japannctam.60.0.267.0�. �hal-
01397215�
1
On a Singular Solution in Higgs Field (III') - The Photoelectric Conversion of Gamma-ray from an Axion-like Pseudo Nambu-Goldstone Boson by Multi-Excited Ur-SM Higgs Boson.
Kazuyoshi KITAZAWA, Mitsui Chemicals
FAX: 03-6253-4244, E-mail: [email protected]
The possibility that a photon of 492 MeV which would be radiated from the tightly bound fermion (top quark)-antifermion (top quark_bar) coupling during condensing to ur-SM Higgs boson (fullerene type quasicrystal of 240 Glueballs) converts to a pseudo Nambu-Goldstone boson (axion-like particle: ALP) under certain color magnetic field, is suggested by the latest gamma-ray observing data of supernova remnant-Cassiopeia A . We show then the produced ALP, after decayed into two photons, elementarily excites an ur-SM Higgs boson by their multi-exciton actions and becomes itself 2*240 electron pairs; on the other hand, the SM Higgs boson may finally transform to an aggregate of pseudo-scalar mesons (spin 0) in truncated-octahedron. As the existence of this 'heavy' ALP could solve CP invariance problem in strong force (= naturalness of minimum theta), to confirm this by observation is to be surely expected. We will also discuss about the predictable respective state of superconductivity in two processes above.
１．Introduction
In preceding paper 1) the author discussed the mass and the basic structure of SM Higgs boson with reference to bound top quark-pair by obtaining asymptotic solution for their equation of motion of nonlinear Klein-Gordon type-PDE via ‘mass triangle method’. Where we saw that SM Higgs boson (H0) will consist of a number of mesons each of which is composed of two gluons (glueball: GB), after emitting a photon of 492 MeV. The GB mass value calculated of ground state is around at 502.55 MeV/c2 which is expected as f0(600) meson’s mass. 2)
In this paper we at first show that our calculated mass values of f0(1370), f0(1500) and f0(1710) are within each f0 meson’s mass from experiment and they also crystallize into respective fullerene structure as well as f0(600). Then we propose each mass-expression for H0 of f0-meson with several light pseudo- scalar mesons such as
0,K0,K0, K,π±,π0 and GB. All of ur-SM Higgs boson and its relatives of fullerene structure will finally transit to SM Higgs boson (H0) of truncated-octahedron (tr-O), after excited by two gamma-rays originated from an ALP which was produced from the one photon of 492 MeV.２．Analysis and the Result 2.1 Equation for f0 Meson Mass
We have discussed in preceding paper (III) 1) the relation between GB mass (MGB) and the SM Higgs boson mass (MH0).
The general formula of f0 meson mass is to be expressed as
(fo)i H0 i GB i
M M N M
, (1) where Ni : the number of vertex for (f0) i meson in fullerene structure and
i: GB-inclusion ratio. From eq.(1), calculated f0mesons’ masses are well consistent with (or at least within) experimental values as shown in Table 1. Here we adopted
1
90,
280,
370
N
N
N
(2)for f0(1370), f0(1500) and f0(1710) respectively. And MH0 =120.611 GeV/c2 which was obtained in preceding paper (I) 1). Hence the total number of GB which is included in H0 is computed by eq.(4) since we let regarding GB-inclusion ratio to obey eq.(3), adding to (1).
3
1
1
i
i
. (3)3
1
GB i 240.
i
N
N
(4)Table 1 f0 mesons’ mass valuesMeV/c2.
Actually over three decades ago, Rossi and Veneziano3), also Igarashi et al 4) have described gauge invariant junction type baryonium of S0j2iandM2mj2m, where j, i and m denote respective number of junction, junction-pair (equivalent to GB) and quark-pair (meson) , as shown in Fig.1. Recently, Csörgó et al 5) showed gluon junction networks of truncated-polyhedrons.
Fig. 1 Junction type of baryonium.4)
Therefore we shall apply this junction type to be able to describe H0 with f0-mesons of the fullerene structure. For H0 with f0(1500) of pure GB’s we may construct it as an aggregation of 12 units ofS010and 30 units of S012. For H0 with f0(1370) or with f0(1710) we must construct it as mixed one from a GB and several certain light pseudo-scalar mesons, because f0(1370) and f0(1710) have both been interpreted that they are not consisted only of GB’s. We propose their mass- structure formulae as
Our calculation Experiment 2) f0(600) 502.55 400-1200 f0(1370) 1340.1 1200-1500 f0(1500) 1507.6 1505
6f0(1710) 1723.0 1720
62
0 0(1710)
1
GB ,
3 4
i f
m
K K
m
(5)
0 0
0 0(1370)
3 70
GB
90 90
,
2 70 75 40
3 90 90 90 i
f
m K
K
m
(6)
which give mass values of 1723.0 and 1340.1MeV/c2 respective- ly, reproducing the calculated values in Table 1 which have been obtained from eq.(1). Here we should remind that H0 would be constructed by 70* f0(1710)- or 90* f0(1370)-fullerene of eq.(2). So the factor (70/90) for K0 or
K
in eq.(6) is considered. While the factor (1/3) in eq.(5) is expected from that 3*[fullerene number of H0 with f0(1500) of pure GB] = 240. Because, H0 with f0(1500) might have resonant mass of 3*(mass of GB for ground state) at each 80 vertexes.1)2.2 Axion-like Pseudo Nambu-Goldstone Boson
It is widely believed 6) that strong CP invariant problem (or ‘the naturalness of minimum theta’) is to be solved by the existence of axion. We shall hereafter study on certain ‘heavy’ axion-like particle (ALP), although up to now rather light axions have been comprehensively searched both theoretically and experimentally.
In astrophysics, Cassiopeia A (Cas A) has been well recognized as a gamma-ray emitting supernova remnant which has young neutron star at the center.7) Recently, Giannotti et al 8) derived new constraints on the coupling of heavy pseudo-scalar ALP’s to photons, based on the gamma-ray flux expected from the decay of these particles into photons, from the data of Cas A, etc..
Hence we here point out the possibility that a photon of our 492 MeV which would be radiated from the tightly bound top quark_anti-top quark coupling during condensing to ur-SM Higgs boson (fullerene type quasicrystal of 240 Glueballs) converts to a pseudo Nambu-Goldstone boson (ALP) under certain color magnetic field around the shell of GB fullerene.
Then the produced ALP, after it decayed into two photons, elementarily excites an ur-SM Higgs boson by their multi-exciton actions and becomes itself 2*240 electron pairs.
These processes are described as
t t *
H0, where H condenses to GB fullerene. 0 (7)Primakoff
a (
axion) ,
(8-1)Primakoff
2 ,
a
(8-2)
0
+
2 photoelectricH
2 240 * e e .
ur
(9) Eqs.(8-1) and (8-2) express respective conversions both by Primakoff effect 9) at impinging inward and re-impinging outward to color magnetic field around ur-H0 as shown in Fig.2.Fig. 2 Gamma-ray and Color Magnetic Field around Ur-H0.
In the last stage, two gamma-rays are to be converted to twice of 240*(e+ e－)-pairs by multi-exciton, after elementarily exciting each 240 GB-vertexes of ur-H0 in color magnetic field. Then next time, fragmentation to {GB and light pseudo-scalar mesons}-fullerenes of ’lower’ number may happen. We consider fragmentation of ur-H0 to {f0(1370), f0(1500), f0(1710)}- fullerenes in sec.2.1 is one of major pattern of it. The excess of energy:
2
MeV 2 240 * 2 * c
492 2 240 2 0.511 1.4
photon me
(10) is understood as necessary ‘margin’ to initiate the elementary excitation, which is to be energy of the produced axion (ALP).
Gianotti et al 8) described exclusion plot for ALP models with mass up to 1 GeV/c2, and Peccei-Quinn (PQ) constant fa > 1012 GeV, considering PQ mechanism. We expect similar mechanism in the color magnetic field around ur-H0 of fullerene also, since
‘our ALP’ of 490.56 MeV/c2 falls within the not excluded mass region. To produce such a heavy ALP mass within short distance of femto-meter scale fromγ-ray that high magnetic flux density will be needed. We estimate that it is up to order of 1010 Gauss.
2.3 Possible Superconductivities in ur-H0 and in H0 of tr-O Fukushima et al 10) investigated color superconducting quark matter in a magnetic field, and pointed out the possibility of the 2SCds phase in the interior of the neutron star with extremely strong magnetic field (magnetar). It is now under investigation to reconstruct ur-H0 from a standpoint of that ur-H0 is to be consisted of gluons in the crystalline color superconducting phase of QCD. Also, that H0 of tr-O to whom ur-H0 would be finally decayed, has superconductivity is anticipated.
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３．References
1) K.-Y. Kitazawa: On a Singular Solution in Higgs Field, Theoretical and Applied Mechanics Japan, 57, pp.217-225, 2009; ditto (II), ibid, 58, pp.61-70, 2010; ditto (III), Proceedings of NCTAM, 59, pp.215-216, 2010.
2) K. Nakamura et al: (Particle Data Group), J. Phys. G, 37, 075021 (pp.1-1422), 2010.
3) G.C. Rossi and G. Veneziano: A Possible Description of Baryon Dynamics in Dual and Gauge Theories, Nucl. Phys.
B,123, pp.507-545,1977;Theoretical Aspects of Baryonium Physics, Phys. Rep., 63, pp.153-200, 1980.
4) Y. Igarashi et al: Constituent Rearrangement Model and Hadron Reactions, Prog. Theor. Phys. Suppl., 63, pp.49-279, 1978.
5) T. Csörgó et al: Buckyballs and gluon junction networks on the femtometre scale, J of Phys. G, 30, pp.L17-L25, 2004.
6) R.D. Pecci: The Strong CP Problem and Axions, Lect.
Notes Phys., 741, pp.3-17, 2008.
J.E. Kim et al: Axions and the strong CP problem, Rev.
Mod. Phys., 82, pp.557-601, 2010.
7) W.C.G. Ho and C.O. Heinke : A neutron star with a carbon atmosphere in the Cassiopeia A supernova remnant, Nature, 462, pp.71-73, 2009;
A.A. Abdo et al: Fermi-LAT discovery of GeV gamma-ray emission from the young supernova remnant Cassiopeia A, The Astrophys. J. Lett., 710, pp. L92-L97, 2010.
8) M. Giannotti et al: New constraints for heavy axion-like particles from supernovae, LA-UR 10-05895, 2010; J.
Cosmology and Astroparticle Phys., 01(2011)015.
9) H. Primakoff: Photo-production of neutral mesons in nuclear electric fields and the mean life of the neutral meson, Phys. Rev., 81, p.899, 1951.
10) K. Fukushima et al: Color superconducting matter in a magnetic field, Phys. Rev. Lett., 100, 032008, 2008.
