1. Solar Axion Flux+* J.D. Vergados, University of Ioannina
+work initiated at:
KAIST University& Center for Axion and Precision Physics Research, IBS, Daejeon, Republic of Korea
*In collaboration with the S. Carolina Experimental group

2. Motivation: A convert to axion physics.
While serving in the dark matter troops, I became an exion enthusiast after my visit to:
KAIST University& Center for Axion and Precision Physics Research, IBS, Daejeon, Republic of Korea, Director Y. Semertzidis
So you have to bear with me. This is the third in a series of seminars presented in the conferences organized by the HSSHEP:
HEP 2015: Axions as dark matter candidates searched for in the standard cavity experiments: via the axion to photon conversion in the presence of a magnetic field. We studied the variation of the width due to the motion of the Earth around the sun (an interesting signature against background.
HEP 2017: Axions as dark matter candidates searched in atomic physics experiments (spin induced atomic transitions). These allow the possibility of detecting axions in a variety of mass scales. Proposed but not undertaken yet. Good signatures, involving cryogenic detectors
HEP 2018 (now): Estimating the production of actions in the sun. Τhe associated flux here in the earth and the axion to photon branching ratio. This is of interest of CAST and Grand Sasso.

3. 1a: Why axions? They are expected to exist!
In the standard model there is a source of CP violation from the phase in the Kobayashi-Maskawa mixing matrix.
Another source is the phase in the interaction between gluons (θ-parameter), expected to be θ of order 1.
The non observation of elementary electron dipole moment is a problem. The introduction of the axion a solves this problem (spontaneous symmetry breaking)

4. P-Q symmetry broken spontaneously<-> axion
The solution is the P-Q (Peccei-Quinn) mechanism.
The Peccei-Quinn-Weinberg-Wiltzek axion (the SM doublet plus a singlet).
Furthermore

5. (1b) More realistic axion models
The problem is that fa is small ( at the EW scale) ma =(Λ2QCD)/fa should be large at the keV scale, but such a particle not seen.
Two models were proposed for the solution
(i) THE KIM-SHIFMAN-VAINSHTEIN-ZAKHAROV (KSVZ) AXION. The SM is expanded to include a singlet scalar and heavy quark doublet. As above one gets couplings to the gluons and the EM field.
(ii) THE DINE-FISCHLER-SREDNICKI-ZHITNISKY (DFSZ) AXION. It extends the S-M with two Higgs doublets, with P-Q symmetry. Lagrangian has a global P-Q chiral symmetry UPQ(1), This is spontaneously broken by an extra singlet, generating a Goldstone boson, the axion (a).

6. Ingredients of axion production in the sun
Axions can be produced in the sun via:
The primakoff effect: Photon to axion conversion in the sun’s magnetic field (continuous spectrum with average energy 3.2 keV )
The de-excitation of the 14.4 keV state of 57Fe
This de-excites primarily via M1 transition to the g.s., but
it can also de-excite via axion production, which is momochromatic 14.4 keV. To estimate the rate in this case one needs:
the axion matter interaction resulting from the quark axion coupling (elementary particle model)
The structure of the g.s. and exited state of of 57Fe (nuclear physics input)
The production rate depends on the matter density and the temperature at the production point, which involve the whole sun.The axion interacts very weakly with matter, even if produced in the Sun’s interior, it will escape. So one needs the density and temperature profile (Standard Solar Model)

7. Obtain the axion-quark coupling:
II: In the context of the two axion models: (a) KIM-SHIFMAN-VAINSHTEIN-ZAKHAROV (KSVZ), (b)THE DINE-FISCHLER-ZITNITSKY (DFZ)
Obtain the axion-quark coupling:
Then we need to evaluate the ME in terms of isospin:

8. (IIa): The second crucial step
Transform the amplitude from the quark to the nucleon level:
There many approaches to determine Δu, Δd, Δs (chiral Lagragians, spin structure of the nucleon etc and, recently, lattice gauge calculations).
The isovector component is determined accurately, from β-decay.
-The isoscalar contributions tend to be small and have sizable uncertainties in them. They have a strong bearing, especially on the neutron couplinq:

9. Nuclear Physics Input Transition: Ji --> Jf
Ground State : Jf=(1/2 )- Excited State : Ji =( 3/2)-
Obtained in a large basis shell model involving both protons and neutrons
The Nuclear Model gives: Ωp=0.1054, Ωn=7932

10. The effective matrix elements
The matrix element for axion production and the matrix element |rME|2 entering the branching ratio for photon to axion production.

11. The axion prodction width Γ (Δ is the energy of the excited state 14
The axion prodction width Γ (Δ is the energy of the excited state 14.4 keV >> axion mass)

12. Results

13. Results (adopted value fa=106 GeV)
Axion production rate (width) in various particle models
Axion to photon branching ratio:
Our favorite model is F (DFSZ, large tanβ for the vacuum expectation values of the doublet)

14. Flux of solar axions
Boltzmann factor-> fraction of excited states found in the sun :
Using Standard Solar model density ρ(x) and temperature T(x) profiles we find:
fr=6.75x 10-7

15. The density and Temperature profiles of the sun

16. Axion flux on earth N* yields the total number of axions produced
The axion flux on earth
Adopting the value of fa=6.3x106 GeV

17. Our best estimate
Our results depend of course on the scale parameter fa. We decided to use the limit on the axion to photon coupling gαγγ : :
gγ is a model dependent factor, 1.95 in the KSVZ model.
Taking gαγγ <1.16 x GeV-1 (CAST), we get fa=6.3x106 GeV
This for model F leads to.
(i) For the axion flux :
(ii) For the axion to photon branching ratio

18. Conclusions: Axion flux estimates are uncertain
(i) The de-excitation of 57Fe* produces a monochromatic 14.4 keV axions with a flux of
(ii) The Primakoff effect: Photon to axion conversion in the sun’s magnetic field continuous spectrum with an average energy 3.2 keV. The total flux about five times larger.
The first mechanism, however, seems favored by its larger energy.
It has also the advantage of the interesting signature: It can be detected by the inverse process
axion+ 57Fe-> 57Fe*
57Fe* can be detected by M1 de-excitation (e.g. the Grand Sasso detector)

19. THE END