7 The other divergent pieces are Using (5) The last integral is evaluated using the proce- dure described in the main text and yields Upon insertion of (9) all terms cancel and A = 0. Here we collect the divergent pieces of J$_{1}$ ( p ), J$_{2}$ ( p ), J$_{3}$ ( p ) and J$_{4}$ ( p ). Putting together the re- sults (5), (9) and (20) we have: Using these results in J $^{div}$( p ) = J div 1 ( p ) + J div 2 ( p ) − J div 3 ( p ) − J div 4 ( p ) it is easy to see the cancellation of the divergent pieces. The Fourier transform of any power of logarith- mic functions [15] can be obtained through the Fourier transform of power functions. Our results are given in Minkowski space, for which we use [32]: ∫ d $^{4}$x e ipx 1 x $_{2}$( − B $^{2}$x$^{2}$) a = − i 4 π 2 p 2 ( − 4 B 2 p 2 ) a Γ(1 + a ) Γ(1 − a ) , (52) J div 1 ( p ) = 1 p 2 { I$_{log}$ ( λ $^{2}$) [ $_{−}$˜ I (2) $_{log}$( ˜ λ − $^{2}$) + b ln ( − p 2 ¯ ˜ λ 2 ) + b 2 ln 2 ( − p 2 ¯ ˜ λ 2 ) + ln ( ¯ ˜ λ 2 α 2 ) ( ˜ I$_{log}$ ( ˜ λ − $^{2}$) + b ln ( − p 2 ¯ ˜ λ 2 ) + 2 b )] + ( ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( ¯ ˜ λ 2 α 2 ) $_{−}$˜ I (2) $_{log}$( ˜ λ − $^{2}$) ) ( 2 b − b ln ( − p 2 λ 2 ))} (48) J$_{1}$ ( p ) = 1 p 2 [ I$_{log}$ ( λ $^{2}$) − b ln ( − p 2 λ 2 ) + 2 b ] × [ $_{−}$˜ I (2) $_{log}$( ˜ λ − $^{2}$) + b ln ( − p 2 ¯ ˜ λ 2 ) + b 2 ln 2 ( − p 2 ¯ ˜ λ 2 ) + ln ( ¯ ˜ λ 2 α 2 ) ( ˜ I$_{log}$ ( ˜ λ − $^{2}$) + b ln ( − p 2 ¯ ˜ λ 2 ) + 2 b ) ] (47) J div 4 ( p ) = 1 p 2 { I$_{log}$ ( λ $^{2}$) ( $_{−}$˜ I (2) $_{log}$( ˜ λ − $^{2}$) + b 2 ln 2 ( − p 2 ¯ ˜ λ 2 ) + b ln − p 2 ¯ ˜ λ 2 ) + ln ( ¯ ˜ λ 2 α 2 ) ˜ I$_{log}$ ( ˜ λ − $^{2}$) + b ln ( ¯ ˜ λ 2 α 2 ) ln ( − p 2 ¯ ˜ λ 2 ) + 2 b ln ( ¯ ˜ λ 2 α 2 )) + ˜ I (2) $_{log}$( ˜ λ − $^{2}$) ( − 1 + ln ( ¯ ˜ λ 2 α 2 )) ( 2 b − b ln ( − p 2 λ 2 )) } (51) J div 3 ( p ) = 1 p 2 { I$_{log}$ ( λ $^{2}$) [ ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( − p 2 α 2 ) +2 b ln ( − p 2 α 2 ) + b ln ( − p 2 α 2 ) ln ( − p 2 ¯ ˜ λ 2 )] + ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( − p 2 α 2 )( 2 b − b ln α 2 λ 2 )) $_{−}$˜ I$_{log}$ ( ˜ λ − $^{2}$) ln 2 − p 2 α 2 )} (50) J div 2 ( p ) = 1 p 2 { I$_{log}$ ( λ $^{2}$) [ ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( − p 2 α 2 ) +2 b ln ( − p 2 α 2 ) + b ln ( − p 2 α 2 ) ln ( − p 2 ¯ ˜ λ 2 )] + ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( − p 2 α 2 )( 2 b − b ln − p 2 λ 2 ))} (49) A = ( I$_{log}$ ( λ $^{2}$) + 2 b ) ∫ Λ k 1 k $^{4}$( p − k ) 2 − b ln − p 2 λ 2 )∫ Λ k 1 k $^{4}$( p − k ) 2 − ( I$_{log}$ ( λ $^{2}$) + 2 b ) ∫ Λ k 1 k $^{2}$( p − k ) 4 + b ∫ Λ k 1 k $^{2}$( p − k ) 4 ln ( − k 2 λ 2 ) (45) 1 p 2 [ ˜ I$_{log}$ ( ˜ λ − $^{2}$) ln ( − p 2 λ 2 ) + 2 b ln ( − p 2 λ 2 ) + b ln ( − p 2 λ 2 ) ln − p 2 ¯ ˜ λ 2 )] (46) VII. APPENDIX B - CANCELATION OF DIVERGENT PIECES VIII. APPENDIX C - FOURIER TRANSFORMS So