J. Modern Physics, 2010, 1, 108-109
doi:10.4236/jmp.2010.12016 Published Online June 2010 (http://www.SciRP.org/journal/jmp)
The Empirical Rule for Calculating the Electric
Charge of Elementary Particles
Aydin G. Kyazym-zade
Semiconductor Physics Department, Baku State University, Baku, Azerbaijan
Received March 28th, 2010; revised May 7th, 2010; accepted May 21st, 2010.
Abstract
The empirical rule for calculation of electric charges of the elementary particles is offered. The given rule contains two
parameters: full number of colors Nc of which color of the given particle is formed and a color index L - number of col-
ors which the given particle possesses. The offered rule allows calculating electric charges of all elementary particles -
leptons, quarks and intermediate vector bosons.
Keywords: Elementary Particles, Leptons, Quarks, Intermediate Vector Bosons
1. Introduction
As is well known [1] without antiparticles experimen-
tally opened 12 fermions (6 leptons and 6 quarks) and
4 intermediate vector boson: carrier of strong interac-
tions (gluon-g), carrier of electromagnetic interactions
(photon -), and carriers of weak interactions (the neu-
tral weak boson Z0 and charged weak bosons W,
which are the antiparticles to each other). All these
particles are elementary, i.e., at the present level of
knowledge they do not consist of more elementary par-
ticles. Symbols designations and electric charges Q (in
units of elementary charge) of these particles are
shown in Table 1.
In this paper we propose a generalized empirical rule
for calculating the electric charges of all elementary par-
ticles - leptons, quarks and intermediate vector bosons.
2. Some Preliminary Remarks
As far as we know, currently there is no generalized rule
for calculating the charge of all elementary particles, i.e.
quarks, leptons and intermediate bosons. There is only
a generalized formula of Gell-Mann-Nishidzhimy [2],
whereby the electric charge of quark (in units of elemen-
tary charge) is expressed through the internal quantum
numbers
Q = Iz+(B+S+C-b+t) (1)
which define the so-called flavor quark. Here, Iz - the
projection of the isotopic spin I, B - baryon number, S -
strangeness, C - charm, b - beauty, t - the truth quark.
Doubled value of the second term Y = B + S + C – b + t
is called hypercharge. The values of quantum numbers
and the resulting electric charge of quarks are given in
Table 2.
In the electroweak theory introduces the concept of
“weak hypercharge” Yw distinguishing leptons left and
right helicity. At the same time 1
w
L
Y for the “left”
leptons and 2
w
R
Y

 for the “right” leptons. Such in-
troduction of the weak hypercharge and the assumption
Table 1. Elementary particles
Particles Symbols designations Q
upper rowe   0
Leptons bottom rowe
  –1
upper rowu c t +2/3
Quarks bottom rowd
s b –1/3
upper rowZ0 0
g 0
Bosons bottom rowW
1
Table 2. Characteristics of quarks
Aroma
of quarkB
I Iz S Cb t Q
u 1/31/2 +1/2 0 00 0 2/3
d 1/31/2 –1/2 0 00 0 1/3
c 1/3 0 0 0 10 0 2/3
s 1/3 0 0 -1 0 0 0 –1/3
t 1/3 0 0 0 00 1 2/3
b 1/3 0 0 0 01 0 –1/3

The Empirical Rule for Calculating the Electric Charge of Elementary Particles 109
that the isotopic spin I = 1/2 for the “left” lepton and I =
0 for the “right” lepton can be used to calculate the
charge leptons the same formula as for hadrons:
2
w
w
z
Y
QI , (2)
where w
z
I
— the third component “of the weak isotopic
spin” of the “left” leptons (Iz = –1/2 for
L
e
and Iz =
1/2 for eL

).
In [3] proposed a formula whereby the electric charge
of quark (in units of elementary charge) is expressed
through the number of colors Nc:
11 1,
2c
QN




(3)
where the plus sign corresponds to the upper line of
quarks (u, c, t) and the minus sign corresponds to the
bottom line of quarks (d, s, b). Given Nc = 3 we obtain Q
= +2/3 for quarks of upper line and Q = –1/3 for quarks
of bottom line.
3. Proposal Rule
The Formula (3) allows calculating of electric charges
only for quarks. We propose a generalized rule that the
electric charge of quarks, leptons and intermediate bos-
ons is expressed in terms of the number of colors Nc
(which make up the color of a given particle), the color
index L (number of colors which the given particle pos-
sesses) and is given (in units of elementary charge) by
the formula:
311.
621
c
c
NL
QLN


 



(4)
Here, L- is a certain color index, which is set L = 1 in
the presence of one color, L = 2 in the presence of two
color and L=0 in the absence of color of the particles.
Plus sign corresponds to quarks and leptons of the upper
line (u, c, t  
e,

 ,


), and the minus sign corresponds to
quarks and leptons of the bottom line (d, s, b, e,  ,  ). If
we assume that the leptons are colorless, i.e. for them L=
0 and Nc = 0, then from Formula (4) we obtain Q = 0 for
leptons the upper line (plus sign) and Q = –1 for leptons
bottom line (minus sign). For quarks L = 1 and Nc = 3.
In this Formula (4) coincides with Formula (3) and for
the charge of quarks we obtain the above values.
Equation (4) also allows us to calculate the electric
charges of the intermediate vector bosons , Z0, W– and
g. When L = 0 and Nc = 0 Formula (4) gives the value
of Q = 0 and Q = –1, respectively for the intermediate
bosons , Z0 (plus sign) and W– (minus sign). A gluon
electric charge Q = 0 is obtained from (4) with the sign
“minus” in parenthesis, if we assume that L = 2 and Nc
= 3, since the gluon is not one, but two color index.
In conclusion, we note that the electrical charges an-
tileptons, quarks and W+ boson can also be calculated by
Formula (4), taken with opposite sign.
REFERENCES
[1] L. B. Okun, “Current Status of Elementary Particle Phys-
ics,” Physics-Uspekhi, Vol. 41, No. 6, June 1998, pp.
553-558.
[2] L. B. Okun, “Leptons and Quarks,” Nauka, Moscow, 1990.
[3] R. N. Rogalev, “The Remark on Use Kiral Anomalies for
Definition of Number of Colours,” Nuclear Fizika, Vol.
66, No. 1, January 2003, pp. 195-198.