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Show that all combinations of a quark and an antiquark produce only integral charges. Thus mesons must have integral charge.

asked
User Xenyal
by
8.5k points

1 Answer

1 vote

Answer:

Quarks and antiquarks come in six different flavors: up (

u), down (

d), charm (

c), strange (

s), top (

t), and bottom (

b). Each flavor of quark has a specific electric charge:

Up quark (

u):

+

2

3

+

3

2

e

Down quark (

d):

1

3

3

1

e

Charm quark (

c):

+

2

3

+

3

2

e

Strange quark (

s):

1

3

3

1

e

Top quark (

t):

+

2

3

+

3

2

e

Bottom quark (

b):

1

3

3

1

e

Where

e represents the elementary charge (

1.602

×

1

0

19

e≈1.602×10

−19

Coulombs).

Now, let's consider various combinations of quarks and antiquarks to form mesons:

Quark-Antiquark Pair with Different Flavors:

When you combine a quark with an antiquark of a different flavor, their charges add up algebraically.

For example, a

ˉ

u

d

ˉ

pair would have a charge of

(

2

3

(

1

3

)

)

=

3

3

=

1

(

3

2

−(−

3

1

))e=

3

3

e=1e.

Similarly, any combination of different flavor quark-antiquark pairs will result in charges that are multiples of the elementary charge (

e), which are integral charges.

Quark-Antiquark Pair with the Same Flavor:

When you combine a quark with an antiquark of the same flavor, their charges will cancel out to zero.

For example, a

ˉ

u

u

ˉ

pair would have a charge of

(

2

3

2

3

)

=

0

(

3

2

3

2

)e=0e.

This also applies to other same-flavor quark-antiquark pairs, resulting in zero charge.

Since all combinations of quarks and antiquarks either produce integral charges or zero charges, mesons, which are composed of a quark-antiquark pair, will always have charges that are integral or zero. This is a fundamental property of the strong force and the quark model of particle physics.

answered
User Zep
by
8.9k points