Journal of Modern Physics, 2013, 4, 991-993
http://dx.doi.org/10.4236/jmp.2013.47133 Published Online July 2013 (http://www.scirp.org/journal/jmp)
Vector Boson Mass Spectrum from Extra Dimension
Dao Vong Duc1, Nguyen Mong Giao2
1Institute of Physics, Hanoi, Vietnam
2Institute of Physics, Ho Chi Minh City, Vietnam
Email: dvduc@iop.vast.ac.vn, nmgiao2011@yahoo.com.vn
Received April 29, 2013; revised May 31, 2013; accepted June 28, 2013
Copyright © 2013 Dao Vong Duc, Nguyen Mong Giao. This is an open access article distributed under the Creative Commons At-
tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop-
erly cited.
ABSTRACT
Based on the mechanism for mass creation in the space-time with extradimensions proposed in our previous work,
(arXiv: 1301.1405 [hep-th] 2013) we consider now the mass spectrum of vector bosons in extradimensions. It is shown
that this spectrum is completely determined by some function of compactification length and closely related to the met-
ric of extradimensions.
Keywords: Boson Mass Spectrum; Extra Dimensions
1. Introduction
The topology of space-time extradimensions has been a
subject of intensive study in various aspects during the
last time [1-8]. On the other side, the problem of particle
masses, especially for gauge vector bosons, remains to be
of actual character.
In our previous work [9] we have proposed a mecha-
nism for the creation of particle masses based on the pe-
riodicity condition dictated from the compactification of
extradimensions. In this approach the original field func-
tions depend on both ordinary space-time coordinates
and those for extradimensions, the ordinary field func-
tions for ordinary 4-dimensional space-time are consid-
ered as effective field functions obtained by integration
of the original ones over extraspace-time.
The mass of vector bosons has been treated in [9] for
the simplest case with one extradimension. Along this
line, in this work we extend the results to the general
case for arbitrary number of extradimensions.
2. Effective 4-Dimensional Vector Fields
As in [9], we denote the 4 + d dimensional coordinate
vector by xM with ,5,6, ,4
d
. The Greek in-
dices will be used for conventional 4-dimensional Lor-
entz indices, 0,1, 2, 3
4aa
. For convenience we will use
the notations ,1,2,,
xa d
,,
, and express the
field function of coordinates as
Ma
with the periodicity condition supposed to be of the form:
xFxyFxy
;,
aa
aF
xyLfF xy
a
(1)
where
is some parameter function depending on the
compactification length L(a).
The Condition (1) corresponds to the equation:
,,
a
F
a
xygF xy
y
(2)
with the relations:
.
e,
1ln 2π,
a
aF
Lg
a
F
aa
FF
a
f
fninZ
L
(3)
In general we can put:
i
e
1ln i2π
a
F
aa
FF
aaa
FFF
a
f
n
L
(4)
a
a
where
and
are some functions of .
a
L
a
F
For neutral field,
,
is real and therefore
0, 0
a
Fn
.
We now consider the neutral vector field
,
My
Vx
satisfying the periodicity condition.
,,
M
aa
a
MVM
Vxy LfVxy (5)
,,
M
a
MVM
aVxyg Vxy
y
(6)
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