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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