The generalized Weinberg–Salam model, which is presented in a recent study of Kimm, Yoon, and Cho [Eur. Phys. J. C 75, 67 (2015)], is arising in electroweak theory. In this paper, we prove the existence and asymptotic behaviors at infinity of static and radially symmetric dyon solutions to the boundary-value problem of this model. Moreover, as a by-product, the qualitative properties of dyon solutions are also obtained. The methods used here are the extremum principle, the Schauder fixed point theory, and the shooting approach depending on one shooting parameter. We provide an effective framework for constructing the dyon solutions in general dimensions and develop the existing results.

1.
K.
Kimm
,
J. H.
Yoon
, and
Y. M.
Cho
, “
Finite energy electroweak dyon
,”
Eur. Phys. J. C
75
,
67
(
2015
).
2.
P. A. M.
Dirac
, “
Quantised singularities in the electromagnetic field
,”
Proc. R. Soc. London, Ser. A
133
,
60
72
(
1931
).
3.
K.
Lee
and
E. J.
Weinberg
, “
Nontopological magnetic monopoles and new magnetically charged black holes
,”
Phys. Rev. Lett.
73
,
1203
1206
(
1994
).
4.
Y.
Yang
, “
Dually charged particle-like solutions in the Weinberg–Salam theory
,”
Proc. R. Soc. London, Ser. A
454
,
155
178
(
1988
).
5.
G.
’t Hooft
, “
Magnetic monopoles in unified gauge theories
,”
Nucl. Phys. B
79
,
276
284
(
1974
).
6.
J.
Schwinger
, “
A magnetic model of matter
,”
Science
165
,
757
761
(
1969
).
7.
Y. M.
Cho
and
D.
Maison
, “
Monopole configuration in Weinberg-Salam model
,”
Phys. Lett. B
391
,
360
365
(
1997
).
8.
J.
Hisano
,
T.
Kuwahara
, and
N.
Nagata
, “
Grand unification in high-scale supersymmetry
,”
Phys. Lett. B
723
,
324
329
(
2013
).
9.
M.
Barriola
,
T.
Vachaspati
, and
M.
Bucher
, “
Embedded defects
,”
Phys. Rev. D
50
,
2819
2825
(
1994
).
10.
A. M.
Polyakov
, “
Particle spectrum in quantum field theory
,”
JETP Lett.
20
,
194
195
(
1974
).
11.
S.
Weinberg
, “
A model of leptons
,”
Phys. Rev. Lett.
19
,
1264
1266
(
1967
).
12.
C. P.
Dokos
and
T. N.
Tomaras
, “
Monopoles and dyons in the SU(5) model
,”
Phys. Rev. D
21
,
2940
2952
(
1980
).
13.
P.
Goddard
and
D. I.
Olive
, “
Magnetic monopoles in gauge field theories
,”
Rep. Prog. Phys.
41
,
1357
1437
(
1978
).
14.
B.
Julia
and
A.
Zee
, “
Poles with both magnetic and electric charges in non-Abelian gauge theory
,”
Phys. Rev. D
11
,
2227
2232
(
1975
).
15.
N.
Manton
and
P.
Sutcliffe
,
Topological Solitons
, Cambridge Monographs on Mathematical Physics (
Cambridge University Press
,
Cambridge
,
2004
).
16.
R.
Rajaraman
,
Solitons and Instantons
(
North-Holland
,
Amsterdam
,
1982
).
17.
A.
Actor
, “
Classical solutions of SU(2) Yang–Mills theories
,”
Rev. Mod. Phys.
51
,
461
526
(
1979
).
18.
E. B.
Bogomolny
, “
The stability of classical solutions
,”
Sov. J. Nucl. Phys.
24
,
449
454
(
1976
).
19.
M. K.
Prasad
and
C. M.
Sommerfield
, “
Exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon
,”
Phys. Rev. Lett.
35
,
760
762
(
1975
).
20.
A. A.
Belavin
,
A. M.
Polyakov
,
A. S.
Schwartz
, and
Y. S.
Tyupkin
, “
Pseudoparticle solutions of the Yang-Mills equations
,”
Phys. Lett. B
59
,
85
87
(
1975
).
21.
A.
Jaffe
and
C. H.
Taubes
,
Vortices and Monopoles
(
Birkhäuser
,
Boston
,
1980
).
22.
D.
Maison
, “
Uniqueness of the Prasad-Sommerfield monopole solution
,”
Nucl. Phys. B
182
,
144
150
(
1981
).
23.
J. H.
Rawnsley
, “
Spherically symmetric monopoles are smooth
,”
J. Phys. A: Math. Gen.
10
,
L139
L141
(
1977
).
24.
Y. S.
Tyupkin
,
V. A.
Fateev
, and
A. S.
Shvarts
, “
Particle-like solutions of the equations of gauge theories
,”
Theor. Math. Phys.
26
,
270
273
(
1976
).
25.
F. A.
Bais
and
J. R.
Primack
, “
Integral equations for extended solutions in field theory: Monopoles and dyons
,”
Phys. Rev. D
13
,
819
829
(
1976
).
26.
Y. M.
Cho
, “
Colored monopoles
,”
Phys. Rev. Lett.
44
,
1115
1118
(
1980
).
27.
T. T.
Wu
and
C. N.
Yang
, “
Concept of nonintegrable phase factors and global formulation of gauge fields
,”
Phys. Rev. D
12
,
3845
3857
(
1975
).
28.
M.
Schechter
and
R.
Weder
, “
A theorem on the existence of dyon solutions
,”
Ann. Phys.
132
,
292
327
(
1981
).
29.
Y.
Yang
,
Solitons in Field Theory and Nonlinear Analysis
(
Springer
,
New York
,
2001
).
30.
P.
Bizoń
and
A.
Wasserman
, “
On existence of mini-boson stars
,”
Commun. Math. Phys.
215
,
357
373
(
2000
).
31.
S. P.
Hastings
,
J. B.
Mcleod
, and
W. C.
Troy
, “
Static spherically symmetric solutions of a Yang–Mills field coupled to a dilaton
,”
Proc. Roy. Soc. A
449
,
479
491
(
1995
).
32.
J. B.
Mcleod
and
W. C.
Troy
, “
The Skyrme model for nucleons under spherical symmetry
,”
Proc. R. Soc. Edinburgh, Sect. A
118
,
271
288
(
1991
).
33.
J. B.
McLeod
and
C. B.
Wang
, “
Existence of solutions for the Cho–Maison monopole/dyon
,”
Proc. R. Soc. London, Ser. A
457
,
773
784
(
2001
).
34.
J. A.
Smoller
,
A. G.
Wasserman
,
S.-T.
Yau
, and
J. B.
Mcleod
, “
Smooth static solutions of the Einstein/Yang-Mills equations
,”
Commun. Math. Phys.
143
,
115
147
(
1991
).
35.
X.
Wang
and
Y.
Yang
, “
Existence of static BPS monopoles and dyons in arbitrary (4p − 1)-dimensional spaces
,”
Lett. Math. Phys.
77
,
249
263
(
2006
).
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