finalAsol - UNIVERSITY OF CALIFORNIA SANTA BARBARA...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Physics Physics 221A Quantum Field Theory Fall 2007 http://www.kitp.ucsb.edu/~joep/Web221A/221A.html FINAL EXAM SOLUTIONS 1. a) The propagator for field i = A,B,C is- i/ ( k 2 + m 2 i- i ). There is an ABB vertex- ig and a CBB vertex- ih . b) This is identical to Srednicki Ex. 11.1, from HW#5, except that g is replaced by g/ 2. Hence (see HW solutions) Γ = g 2 q m 2 A- 4 m 2 B 32 πm 2 A . c) The graph is a loop of B fields with one A and two C propagators attached. An example of this type from the Standard Model is the decay of the Higgs to two gluons through a top quark loop. d) This is identical to the calculation in Chapter 16, except that (1) we are in d = 4, and (2) there are two kinds of vertex, couplings g and h . Therefore, start with Eq. 16.1, with d = 4 and with g 3 replaced by gh 2 . Carrying through to 16.8 at ε = 2 we have T = gh 2 32 π 2 Z dF 3 D- 1 . Note that there are no factors of ˜ μ because the couplings are defined in d = 4 from the start. Also, from 16.5 we have D = x 1 x 3 k 2 1 + x 2 x 3 k 2 2 + x 1 x 2 k 2 3 + m 2 B = m 2 B- x 1 x 3 m 2 A- x 2 ( x 1 + x 3 ) m 2 C . e) In this limit D → m 2 B and we can use R dF 3 = 1 to find T = gh 2 32 π 2 m 2 B . A coupling 1 2 ˜ gAC 2 would give T = ˜ g , so ˜ g = gh 2 32 π 2 m 2 B . The rate, from part (b), is then Γ = ˜ g 2 q m 2 A- 4 m 2 C 32 πm 2 A = g 2 h 4 q m 2 A- 4 m 2 C 2 15 π 5 m 2 A m 4 B . 1 It is good to check units. The three-scalar couplings g and h have units of m 1 in d = 4, so Γ has units of m 1 as it should....
View Full Document

This note was uploaded on 02/04/2012 for the course PHYS 253A at Harvard.

Page1 / 4

finalAsol - UNIVERSITY OF CALIFORNIA SANTA BARBARA...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online