193 Appendix B Power Law R$_{AA}$ B.1 Fragmentation Functions The fragmentation function D h $_{q}$( z ), where z = 2 E$_{h}$/Q , gives the probability of producing hadron h of energy E$_{h}$ from parton q in a process of total energy Q . If we take the problem as the production of a quark and an antiquark and ignore all masses then, in the center of mass frame, each parton carries half the total energy, Therefore Conservation of energy then demands p$_{q}$ = E$_{q}$ = ∑ h E$_{h}$ = Q/ 2 . (B.1) z = 2 E$_{h}$ Q = E$_{h}$ p$_{q}$ = p$_{h}$ p$_{q}$ . (B.2) ∑ h ∫ 1 0 zD h $_{q}$( z ) dz = ∑ h 2 〈 E$_{h}$ 〉 Q = 1 . (B.3)