Question

could you please answer all parts of this question. like and comment are rewarded.

A3. (a) In a proton-antiproton collider experiment, the p and p beams have equal and opposite momenta. In the experiment, the following process occurs p+p+ Dº + Dº The Dº meson is unstable and decays via Dº + K+ + The K+ meson has a lifetime of tK = 1.23 x 10-8s and a decay length of 6.50 m in the rest frame of the Dº meson. The Dº and Dº mesons are produced at rest. Calculate the momentum of the p beam needed to produce the Dº and Dº mesons. You may assume that mpo = mpo and the massess of the other par- ticles are: mk+ = 493 MeV/cº, mx- = 139 MeV/c>, and mp = 938 MeV/c2. (b) The D+ meson has quark composition cd and can decay via the following modes [10] D+ + K + H+ + V D+ +70+ ut + V 9 (i) Using Feynman diagrams to illustrate your answer, explain which decay mode is favoured. (ii) Using the Cabibbo theory, calculate the ratio of the decay rates for these processes. You may assume that 0e = 12.9°, mp+ = 1870MeV/c?, mro = 498 MeV/cº, M70 = 135 MeV/c?, m= 105 MeV/e², and m, = 0 MeV/c. (c) Given the following quark compositions, Dº = cū and D+ = cd, use Feynman diagrams to explain why the process Dº + K+ + T can occur as a lowest order interaction, but the process D+ + K-+*+ + cannot. (d) A Cherenkov counter can be used to detect a mesons. The detector is con- structed from material with refractive index n = 1.95. Calculate the Cherenkov angle of the radiation produced by a 7 meson with kinetic energy T* = 450 MeV. You may assume that m,- = 139 MeV/c2. (7)

Answer 1

(a) Since the energy must be conserved besides the momentum in the process

p+ + Dº + DO

and the D mesons are produced at rest,

hence energy conservation gives

[E: Energy Epteľ =Ego tego 4. om v p²e²+ mph p²e²+ mph + V6 222 +mpet e2 e + m = m пр p and mp [p: momentum of = mão m and үүр DO 2 spher+mpe = 2moe? Po moet - on, p2e²+ mpe an, p² = (m 3 - mee? 2 pi C. -m mo

Hence to know the value of , we require to know the value of
n
.

Now consider the decay

$D^0 \rightarrow K^{+}+ \pi^{-}$.

For momentum conservation, the moments of
-
and $\pi^{-}$ should be equal and opposite in direction since $D^0$ is at rest. Let the momentum of
-
is $p_k$ . Hence the energy conservation gives

2 22 2 4 mpe= 2 m elt ।। c et M 2 k ct ok k where me m = Em kt & mm mt

Now, the lifetime $\tau_k$ and the decay length $d_k$ of   are related as

-

Hence

.

i mpe mpe? 493² +(2-6X10")2 33+ (2.6x10133 Mev 1932+ + on , m SI 5.22x10" Merle2

Therefore

since mp "p=√(5.22x10) 2_9382 Merle - ñ 5.22 X 10" Merle.