Bubble Chamber Relativity    

    Teachers Calculations

If we assume that that we have 1 (one) missing particle X, we now know that the energy of the particle is

E_X= 3.53939 GeV

In order to identify the particle X, we have to calculate its mass.

To do that we will use the energy-relation

E² = p² c² + m² c⁴

We have already calculated E_x, and we can find the momentum p_x.

of the particle_, because momentum must be conserved in all processes.

We can then calculate the mass from the expression

Now, we have to calculate p_x, and then p_x², using momentum conservation.

Because the momentum conservation law is a vector law, we can apply the law in x-, y- and z-directions separately. 

From the tables we get (in momentum units GeV/c):

p_x (X) = p_x (K^-) - p_x (p) - p_x (p^-)

p_x (X) = 8.26131 - 0.32426 - 4.49326 = 3.44309

 

and,

 

p_y (X) = - 0.15642 - (-0.45360) - 0.73621 = -0.43903

p_z (X) = 0.01320 - 0.04282 - (-0.51122) = 0.48160

 

This gives us for the X-particle p = 3.50421 GeV/c

From the calculated values of energy and momentum, expression (2) gives us m_X = 497.8 MeV/c².

 Using the particle table you now can identify the neutral particle.