Answered>Order 9963

B mesons are made up of two quarks, a very heavy b quark and one of the light quarks (either and up or down or strange quark). A common approximation used for modeling mesons is to take the force between the two quarks to be a constant, independent of distance. We will denote this force as F0 = the constant force between two quarks (in the literature this is usually called the hadronic string tension). Then the potential energy of the light quark is U = F0r, where r is the radial distance of the light quark from the heavy quark. In this problem you shall adapt the Bohr model to describe the B mesons. Assume the heavy b quark is at rest and the light quark moves around it in a circular orbit. Following Bohr, we shall assume that the angular momentum of the light quark is quantized, r x p = n (hbar) where n = 1, 2, 3, …

Then a) Calculate the formula for the quantized radii of the circular orbits as a function of n, , m = mass of the light quark, and F0.

b) Calculate the formula for the quantized energy, E = p2 /2m + F0r as a function of n, , m and F0.

c) Splitting between the ground state and the first excited state of the B mesons is about 0.50 GeV. Studies of light quarks have found the “hadronic string tension” to be F c 0 = 0.19 GeV2 . Using these numbers, calculate the rest mass energy of a light quark.

The number you come up with will not match exactly the standard values in the literature for the light quark constituent masses because we are assuming that the motion is nonrelativistic, while really it is relativistic.