Spin(10) axion models are constructed which offer the possibility that axions comprise all or a significant part of the dark matter of the Universe

Holman, R.

Lazarides, G.

Shafi, Q.

English

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https://ntrs.nasa.gov/search.jsp?R=19830011314 2020-03-21T03:54:17+00:00Z
(NASA-TM-84939) AYICNS AND THE DPRR MATTER 	 N83-19585
OF THE UNIVERSE (NASA) 	 13 p HC A02/hF A01
CSCL 20H
Unclas
G3/72 08901
4
i
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Technical Memorandum 84939
f
Axions and the Dark
Matter of the Universe
R. Holman, G. Lazarides,
and Q. Shafi
NOVEMBER 1982
National Aeronautics and
Space Administration
r,jddard Specs Flight Center
Greenbelt, Maryland 20771
,a
Abstract
Spin(10) axion models are constructed which offer the intriguing
possibility that axions comprise all or a significant part of the dark matter
of the Universe.
3a
Although axion models 1) can solve the stro Ag CP problem, there are
potential cosmological problems associated with them. One of these is the
domain wall problem 2) . A discrete subgroup of the global, anomalous Peecei-
Quinn (PQ) U(1) symmetry may remain unbroken by the QCD gluon anomaly 3).
This symmetry is then broken spontaneously and domain walls are formed. A.
second problem of axion models has been pointed out recently 4) . This problem
has to do with the fact that since the axion couplings to matter have to be
weak, the axions will essentially decouple as soon as they are produced.They
may then give rise to an unacceptably large energy density in the present
universe.
The analyses of ref. [4] imply that for axion models to be consistent
with standard cosmology, the vacuum expectation value (vev) that breaks the
PQ symmetry fl) must be less than 10 12 GeV f2) . This clearly indicates that
axion models moot have intermediate mass scales, and rules out the simplest
axion models based on SU(S) 6).
In this note, we give examples of models which have PQ symmetries which
are broken at an intermediate scale. These models offer the intriguing
possibility that axions comprise all or a significant portion of the dark
matter of the Universe 4) . They also incorporate the solution of the domain
wall problem devised in ref. [7]. The solution is to construct the PQ
symmetry so that the action of the residual, discrete PQ symmetry coincides
with the action of the cinter of the gauge group f3) . The various domains
then become gauge equivalent. In the process of spontaneous symmetry
breaking, hybrid strings form which become the boundaries of a single domain
wall that terminates on them. The string and wall system rapidly decays 8)
and there is essentially no effect on standard cosmology.
We now proceed to construct our models. The gauge group is Spin (10) as
PRECEDING PAGE 8LAINK NOT FILMED
,	
a
,A
	
ORIGINAL PAGE IS	 4
OF PbOR QUALITY
in ref. [7]. The fermion content is given by
* (1) (1 - 1. 2 . 3 )	 .	 *10(a) (a - 1,2)	 .	 (1)16
where the subscripts denote the dimension of the Spin ;(10) representation to
which the various fields belong. The U(1) PQ transformation properties of the
fermion fields are:
1M + eie *16 i) (i - 1.2.3). * (a)+ e-218 *10 (a) (a - 1 . 2 ).	 (2)
and were chosen so that the residual, discrete PQ symmetry coincides with the
center, Z41 of Spin (10). If we had not included * (a) (a - 1,2), the residual
PQ symmetry would be Z 121 which is, of course, too large to be embedded in
Z4 9).
We first consider the following symmetry breaking chain of Spin(10) f4):
210	 126 45
Spin ( 10) M-+ SUc ( 3) x SUL(2) x SUR( 2) x U(1)B-L
	
-^
1	 M2
10
SUc (3) x SUL (2) x UM M su (3) x U(1)EM ,	 (3)
w
where the Biggs fields necessary to implement this chain are as indicated.
Under U(1) PQ , the Higgs fields transform as follows:
(210) (2 1 0) (126) 20 (126)	 (45) 40 (45)	 (101 -2ie (10)
^^	 r4	 ie	 m	 .® 'e	 .O	 a	 (4)
As in the fermion case, these U(1) PQ
 transformation properties ensure that the
action of the residual PQ symmetry on these fields is identical to that of the
center of Spin(10). Note that all Higgs fields except for 
x(210) 
are
oa!31NOAR PAGE IS
OF PO	
s	 "
complex.
The allowed Yukawa couplings are (in schematic form):
(10)	 (126)+	 (45)
*16 #16 #	 , *16 * 16 4	 ' *10 *10 0	 (5)
The allowed Higgs couplings include
0 (210) 4 (126)+x (126)+x (45) ' #(210)x(126)+0(10)(45)'
x (210) x (126) x(10)	
(6)
These couplings guarantee that U(1)pQ is the only global symmetry present.
They also guarantee that 
(41)+
 
-+ 
(41) 
is not a symmetry of the LagrangiAin so
that the domain wall problems associated with this symmetry can be avoided 12).
Now <; 
(210)
> cannot break U(1)pQ since it is neutral under U(1)pQ . Hence
U(1)pG
 is broken at the intermediate scale M 2 by <^ (126)
	 (45)
>, 0
	 >.	 Both of
these vev's are needed at this stage, since, if only one of them is used, then
A linear combination of the U(1)p Q generator and B-L will remain unbroken.
We next use the one-loop renormalization group equations for the various
coupling constants to calculate M 1
 and M2 in terms of sin2 ew(MV.) and a8(Mw).
We also include the following Higgs contributions: 13) between M2
 and M1 .?e
include the (1, 1, 3, +1) and (1, 3, 1, -1) components of the 126, the (1, 3,
1, 0), (1, 1, 3, 0) components of the 45 and the (1, 2, 2, 0) components of
the 10, where we have decomposed the Spin(10) representations under the
subgroup SUc (3) x SUL(2) x SUR(2) x U(1) 1/2(B-L) .	 Between Mw and M2 we only
take the contribution of a single SUL(2) doublet (the Weinberg-Salam
doublet). The fermions in the 10 acquire masses - M 2 and so contribute to the
renormalization group equations between M 2
 and Mi.
t	
"	
,
ORIGINAL PAGE,U
OF POOR QA4ITY
We find that for sin28w(M^) < 0.21, M2
 is too high to comply with the
constraints of ref. [4). Table 1 below shows how M l
 and M2
 vary as functions
of 9 ,,n2ew( w)  and a. %Mw). We have taken sin28wV - 0.22, 0.23 and
as l (M
w 
) -7.5, 8.0, 9.0. 14)
sin2 8w(MW)
	
081(Mw)	 M2(GeV)	 Ml(GeV)
0.22 7.5 3.4x1012 3.4x1015
0.22 8.0 4.9x1012 2.1x1015
0.22 9.0 1.0x1013 1.0x1015
0.23 7.5 1.1x1011 6.0x1015
0.23 8.0 1.6x1011 3.7x1015
0.23 9.0 3.3x1011 1.4x1015
Table 1: Ml and M2 as functions of sin2 8w(Mw) and as l (Mw) for the chain of
Eq (3).
We expect two-loop contributions to reduce M l
 and M2
 by a factor of 2-
4. From Table 1 we see that there is a non-trivial range of values
of sin2 8w(Mw) and a s (Mw) which are consistent with low energy experiments and
alloy us to satisfy the constraints of refs. [4, 51. We also see that there
are values of the parameters for which M 2/9 saturates or nearly saturates its
upper bound of 1012 Gev, where g is a typical gauge coupling constant. In
this case, the axioms of this model could comprise all or most of the dark
matter of the Universe-4)
There are other intermediate symmetry groups that could have been used in
place of SU „ (3) x SUL(2) x SUR(2) x U(1) B-L
 in Eq (3). One of these is the
6
7
ORIGINAL PAG IS
OF POOR QUALITY
Pati-Salem subgroup 10) SUc (4) x SUL(2) x SUM R . However, the mass scales
in this case cannot satisfy.the required constraints. Another subgroup is
we ( 4 ) x SUL(2) x U(i)R. In this chain, we use a combination of a real 45"
and a real 54 both with PQ charge zero to implement the first breaking
(neither can do it alone). We also employ the same Higgs with the same PQ
charges as in Eqs. (3, 4) to implement the remaining symmetry breakings. The
feruions are as in Eqs. (1, 2), whereas the Riggs couplings include 54 x 126+
x 126+ x 45 and 54 x 10 x 10 x 45. Note that a 126 + x 126 x 45' coupling
exists which eliminates the domain wall problem associated with the 45' which
performs the first breaking. As in the previous chain, we have used the
renormal!.zation group equations to calculate M 1 and M2 in terms
of sin2 ew(Mw) and a s (Mw). We have included the following Higgs
contributions: between M2
 and M1
 we include the (TU, 1, -1) component of 126,
the (15, 1, 0) component of 45 and (1, 2, 1/2) coming from 10. Between M w and
M2 we include the Weinberg-Salam doublet only. The above decompositions are
with respect to SUc (4) x SUL(2) x U(1) R .	 Note that the fermions in the 10
contribute to the renormalization group equations between M2
 and M1 . The
results for M 1 and M2 for this chain are given in Table 2 below.
sin29w(Mw ) a;l(Mw) ?-12 (GeV) M1(GeV)
0.22 7.5 3.5x1011 2.0x1015
0.22 8.0 6.Z.c1011 1.3x1015
0.22 9.0 1.9x1012 5.7xin14
0.23 7.5 3.7x109 2.6x1015
0.23 8.0 6.6x109 1.7x1015
0.23 9.0 2.0x1010 7.2x:014
Table 2: M1 and M2 as functions of sin 2 6w(Mw), a s (Mw ) with SUc (4) x SUL(2) x
U(1)R
F
as the intermediate symmetry group.
aORIGINAL PAGE W	 8
OF POOR QUALITY
As in the previous case, we see that this pattern of symmetry breaking
can also accomodate very nicely the bounds of refs. 14, 51. We also see that
axions can make up most or all of the dark matter of the Universe in this
scheme too.
We now turn briefly to the phenomenology of the models discussed above.
We expect that gauge boson mediated proton dec,3y will occur in the model with
a lifetime which can vary from 1-104 times the SU(5) lifetime for the
SUc (3) x SUL(2) x SUR(2) x TIM B-L chain and from 1-102 times the SUM
lifetime for the SU c (4) x SUL(2) x U(1)R chain. We also note that if
neutrinos acquire a mass through the mechanism of ref. [15], then as M 2 varies
between 1012 GeV and 109 GeV, the heaviest neutrino in our models can have a
mass ranging from 0.1 ev to 100 ev M . Hence the dominant component of the
dark matter of the Universe can vary from axions to neutrinos as M2 varies
between 1012 GeV and 109 GeV respectively. Finally, we note that the
superheavy fermions * 10(a) , whose masses are of the order of M 2 , will also
contribute to the generation of baryon asymmetry.
To summarize, we have constructed Spin(10) axion models which are
compatible with all known cosmological constraints. Moreover, they offer the
possibility that the axions provide all, or a significant fraction of the dark
matter of the Universe.
Acknowledgements
R. H. was supported by an NRC/NAS Posdoctoral Research Fellowship. The
research of G. L. is partially sponsored by the Department of Energy, Grant
No. DE-A CO2-82 ER 400033. B000. Q. S. would like to thank the NASA/Goddard
Space Flight Center and especially Floyd Stecker for hospitality.
T9
Footnotes
fl) Recall that axion couplings and sasses are inversely propotional to this
vev.
f2) Stellar evolution constraints 5) demand that it be greater than 109 Gay.
f3) The center of the group is the subgroup which commutes with all elements
of the group. The center of SU(N) is isomorphic to Zn
 and that of
Spin(4n+2) to Z4•
A) The group SUc (3) x SUL(2) x SUR(2) x U(1) B-L was first considered in ref.
[10). The chain in Eq (3) has been considered in connection with axion
models in ref. (11). However, the models of ref. (11) had the
topological domain wall problem of ref. (3).
f5) Assuming a top-quark mass of - 20 GeV.
10'
ORIGINAL PAGE IS
OF POOR QUALITY
References.
1. R. D. Peccei and H. Quinn, Phys. Rev. Lett. 38 (1977), 1440; S. Weinberg,
Phys. Rev. Lett. 40 (1978), 223; F. Wilczek, Phys. Rev. Lett. 40 (1978),
279; J. Rim, Phys. Rev. Lett. 43 (1979), 103; M. Dine, W. Fischler and A.
Srednicki, Phys. Lett. 1043 (1981), 199.
2. T. W. B. Ribble, J. Phys. A9 (1996) 1387; .a. B. Zel'dovich, I. Yu.
Kobzarev and L. B. 0kun, Scviet Physics JETP 41 (1975), 1.
3. P. Sikivie, Phys, Rev. Lett. 48 (1982), 1156.
4. J. Preskill, M. B. Wise and F. Wilczek, Rarvard Preprint (1982); L. F.
Abbott and P. Sikivie, Brandeis Preprint (1982).
5. D. A. Dicus, E. W. Kolb, V. L. Teplitz and R. V. Wagoner, Phys. Rev. D18
(1978), 1829.
6. M. B. Wise, H. Gee-Z' •_nd S. L. Glashow, Phys. Rev. Lett. 47 (1981), 402.
7	 G. Lazarides and Q. Shafi, Phys. Lett. 1153 (1982), 21.
8. T. W. B. Kibble, G. Lazarides and Q. Shafi, Phys. Rev. D26 (1982), 435.
A. Everett and A. Vilenkin, Tufts preprint (1982).
9. S. Barr, D. R?iss, and A. Zee, Phys. Lett. 116E (1982), 227; H. Georgi. and
M. B. Wise, Phys. Lett. 116B (1982), 123.
11. R. N. Mohapatra, G. Senjanovic, Brookhaven Preprint (1982); D. Raise,
Phys. Lett. 109B (1982), 365.
12. G. Lazarides, Q. Shafi and T. Walsh, Nucl. Phys. B195 (1982), 157.
13. F. del Aguila and L. E. Ibanez, Nucl. Phys. B177 (1981), 60.
14. J. E. Kim, P. Langacker, M. Levine and R. H. Williams, Rev. Mod. Phys. 53
(1981), 211; P. Langacker, Phys. Rep. 72 (1981), 185; W. Marciano and A.
Sirlin, Phys. Rev. Lett. 40 (1981), 163.
15. M. Gell-Mann, P. Ramond and R. Slansky in Supergravity, P. Van
Nieuaenhuzen and D. Z. Freedman (eds), (North Holland 1979), 315.


Axions and the dark matter of the universe

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