Quarks and Antiquarks
An overview of quarks and antiquarks including solutions to the questions on hadrons from the Egglescliffe Physics Website
Particles Main  HadronPhysics

Introduction to Quarks

Quarks are  the elementary constituents from which Hadrons (baryons and mesons) are made. There are three main types (or flavors) of quark known as Up, Down and Strange. Each type of quark has different properties of mass, charge, baryon number and strangeness as shown in the table below.
 
 

Name
Symbol
Mass (MeV)
Charge
Baryon Number
Strangeness
Up
u
310
+2/3
1/3
0
Down
d
310
-1/3
1/3
0
Strange
s
505
-1/3
1/3
-1

There are also three other much more massive quarks: Charm, Top and Bottom (sometimes called Truth and Beauty) but these are much rarer and the Top/Truth quark was only discovered in 1997.
Quarks also have a corresponding antiquark which has similar properties but opposite and equal charge. Antiquarks have the same symbol as the quark but with an underline i.e. an antidown has the symbol d.
Any particle containing quarks is termed a Hadron, however quarks do not ever exist on their own but bound into quark-antiquark pairs or triplets by the strong force. This is known as quark confinement.
In a triplet there will be three quarks (q q q) or three antiquarks (qqq ) but never a mixture, for example a proton consists of two up quarks and a down quark, these are called Baryons. In a pair there will always be one quark and one antiquark (q q )but never two quarks or two antiquarks, an example of this is the Pion, these are caled Mesons.
.
The following table shows the quark configuration and properties of some common Hadrons (These are the ones relevant to the AQA A-Level syllabus 2001)
 
 

Family
Name
Symbol
Quark composition
Charge
Strangeness
Rest Mass
Mesons
Pion
p+
ud
+1
0
140
p0
uu OR dd
0
0
135
p-
dd
-1
0
140
Kaon
K+
us
+1
+1
494
K0
ds OR sd
0
+1/-1
498
Baryons
Proton
p
uud
+1
0
938
Neutron
n
udd
0
0
939


Conservation Laws

During a nuclear reaction properties such as charge (Q), baryon number (B) and Strangeness (S) are conserved.

In a reaction involving the strong force all three (Q,B,S) are conserved. But in reactions involving the weak force only charge and baryon number are conserved.



Solutions to selected Questions

From Hadrons 1

 2) K+ --> p0 + m- + nm cannot occur because conservation of charge means that there cannot be a +1 charge on one side and a 0 + (-1)  +0 = -1 charge on the other.

 3) n --> p + e- + ne

 Charges:
LHS has Q = 0 charge
RHS has Q = (+1) + (-1) + 0 = 0 charge
Therefore charge is conserved

 Baryon number:
LHS has B = 1
RHS has B = 1 + 0 + 0 = 1
Therefore baryon number is conserved

 Lepton number:
LHS has L = 0
RHS has L = 0 + (+1) + (-1) = 0
Therefore lepton number is conserved

 5) The particle tracks are due to a magnetic field perpendicular to the plane of the particle motion. In accordance with the left hand rule this causes the +ve particles (e+) to curve anticlockwise and so generally be on the right of the bubble chamber. However -ve particles (e-, W- and p- ) rotate clockwise and so tend to be on the right of the bubble chamber. A particle with no charge ( p, K0, X0 and L0 ) will have a straight path and will leave no visible track. The more massive the particle ( p = BqR) the larger the initial radius of the curve, so low mass charged particles will form a tightly wound spiral.

 Charge, lepton number and baryon number are conserved for all the events, here are two examples:
 
 

K- + p --> W- + K+ + K0

Charge:
Before: -1 + 1 = 0
After: -1 + 1 + 0 = 0
Baryon number:
Before: 1 + 0 = 1
After: 1 + 0 + 0 = 1
Lepton number:
Before: 0 + 0 = 0
After: 0 + 0 + 0 = 0
Therefore Q, B and L are conserved.
W- --> X0 + p-

Charge:
Before: -1
After: -1 + 0 = -1
Baryon number:
Before: 1
After: 1 + 0 = 1
Lepton number:
Before: 0
After: 0 + 0 = 0
Therefore Q, B and L are conserved.

7) This is likely to be a strong interaction because Q,B,L and S are all conserved.

 8) This is a weak interaction as strangeness changes by +1 in each decay. Remember strangeness only changes in weak interactions and is conserved in strong and electromagnetic interactions.



From Hadrons 2

10) Time for light to cross an atom:

 Diameter of atom: approx 10-9 m
Speed of light: approx 3x108 ms-1

 Therfore time taken to cross atom = 10-17 s

 The lifespan of a L0 hyperon is about 10-10. From above it can be seen that light can cross an atom 10 million times in the lifetime of a L0 hyperon. So in some respects it lives quite a long time. Elementary particle resonances may be as short lived as 10-23 seconds !

 Distance = 0.5 x 3x108 x 1.2x10-10
                 = 0.018 m

 12) These energies have been calculated using relativistic mechanics.
See Eg: Relativity Problems 2 . Click here to see the relativistic formula for kinetic energy.

Speed /c 0.1 0.5 0.9 0.95 0.99 0.995
KE (J) Proton 8x10-13 2x10-11 2x10-10 3x10-10 9x10-10 1x10-9
Truth quark 1x10-11 5x10-10 5x10-9 8x10-9 2x10-8 3x10-8

The truth quark on its own has a K.E. 23 times that of a proton at comparable speeds.

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Page Contributed by Michael Keith, Yr.13 student 2001