Erratum: Recursive construction of Higgs�multiparton loop amplitudes:The last of the ‘‘�-nite’’ loop amplitudes

[Phys. Rev. D 74, 094021 (2006)]

Carola F. Berger, Vittorio Del Duca, and Lance J. Dixon(Received 4 September 2007; published 1 November 2007)

DOI: 10.1103/PhysRevD.76.099901 PACS numbers: 12.38.Bx, 14.80.Bn, 11.15.Bt, 11.55.Bq, 99.10.Cd

An error was made in the initial conditions for the recursion relations for the amplitudes AL�sn ��; j�f � presented in

Sec. VII. The result is that the lower limit in the sum for the quantityQ�0 in Eq. (7.11) should be l � 2, not l � 3. The same

replacement should be made in Eq. (7.14). The verification of the recursion relation for AL�sn ��; j�f � is unaltered, except

that in the text four lines below Eq. (7.18), the single sum over l for Q̂�0 now contains �n� 3� terms, not �n� 4�.

Because of this error, in Sec. VIII four equations for the � �qqg amplitudes need to be corrected:

AL�s3 ��; 1�f ; 2�f ; 3

�� � 2i�2 3�2

�1 2��i2

h1 2i�2 3�

h2 3i� Atree

3 ��y; 1�f ; 2

�f ; 3

��

��2�

s12

2s23

�; (8.20)

A3;1��; 1�f ; 2�f ; 3

�� � �2Atree3 ��

y; 1�f ; 2�f ; 3

�� �i2

�1�

1

N2c

�h1 2i�2 3�

h2 3i� Atree

3 ��y; 1�f ; 2

�f ; 3

��

��2�

�1�

1

N2c

�s12

2s23

�;

(8.21)

A3;1��y; 1�f ; 2

�f ; 3

�� � Atree3 ��

y; 1�f ; 2�f ; 3

��

�V1 �

s12

2s23� 2�

1

N2c

�V2 �

s12

2s23

��nfNcV3 �

nsNcV4

�; (8.27)

A3;1�A; 1�f ; 2�f ; 3

�� � iAtree3 ��

y; 1�f ; 2�f ; 3

��

�V1 �

s12

s23� 4�

1

N2c

�V2 �

s12

s23

��nfNcV3 �

nsNcV4

�: (8.28)

The s12=�2s23� terms in Eq. (8.27) now cancel similar terms in V1 and V2 in Eqs. (8.23) and (8.24). Finally, in the text belowEq. (8.20), the R type amplitude does not vanish, but is given by

AR3 ��; 1�f ; 2

�f ; 3

�� � �AL3 ��; 1�f ; 3

�; 2�f � � �i2

h1 2i�2 3�

h2 3i:

We thank Yorgos Sofianatos for helping us uncover this error.

PHYSICAL REVIEW D 76, 099901(E) (2007)

1550-7998=2007=76(9)=099901(1) 099901-1 © 2007 The American Physical Society