6. The spectroscopy of mesons which contain at least one \"bottom\" quark (b qua

Question

6. The spectroscopy of mesons which contain at least one "bottom" quark (b quark of 45 GeV/e') is obeerved to inchude a ground-state T meson and a first excited state T meson. The decay of the T' meson to the T meson releases 560 MeV of energy. If the b quark in an T meson can be assumed to be governed by a potential which gives rise to harmonic motion in a single coordinate z which describes the displacement of the b quark (0) What is the magnitude of the force constant K confining a b quark in an T meson How does it compare to the force constant discussed in the lectures for simple harmonic motion in molecules (10 N m-1) ? (i) How "big" is the T meson? Is it bigger or smaller than the size of the proton (1 fm = 10-15 m)? (ii) Is it possible to extract a b quark from an T meson?

Explanation / Answer

1)The force constant for SHM is F=-kx.color force binds the quarks together..The strong nuclear force is actually the residual effect of color force..but since it is given here that b quark in a epsilon meson is governed by a potential which gives rise to SHM the constant in this case is same as that of SHM..

2)epsilon meson has a mass of 9.46Gev/c^2 whereas proton has a mass of 938.272MeV/c^2.It is around 1.2 times the size of proton.

3)b quark has a mass of 4.18Gev/c^2. it is possible to remove b quark if supplied it with more then 5.28Gev/c^2 energy.

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