Complete set of Feynman rules for the MSSM – erratum

This erratum contains clarifications of some statements and the list of corrections of errors found in the paper Complete set of Feynman rules for the Minimal Supersymmetric Standard Model [1]. ∗on leave of absence from Institute of Theoretical Physics, Warsaw University, e-mail address [email protected] 0 Most of the expressions for mass matrices, mixing angles and vertices listed in [1] have been checked during the calculations of the 1-loop radiative corrections in the gauge and Higgs sectors of the MSSM [2, 3]. The 1-loop corrections were calculated in on-shell renormalization scheme, which provide a very strict test of correctness of all formulae entering the expressions for the renormalised quantities: most of the errors in Feynman rules lead immediately to non-cancellation of the divergencies. Only the most exotic vertices like 4-sfermion couplings, several rarely used 2 Higgs boson-2 sfermion couplings and some vertices proportional to the strong coupling were not used and did not pass this test yet. Other vertices can be with good probability considered as checked. Below I list the errors encountered in [1] until now. I point out also some unclear statements and conventions. The page numbers refers to the version published in Phys. Rev. D. 1. Section II, p. 3465, first line. The expression for Yukawa interactions should read as − 1 2 ( ∂W ∂Ai∂Aj ΨiΨj +H.c. ) 2. Section III, p. 3465, point (2). In general the soft SUSY breaking gaugino mass parameters may be complex. Redefinition of the phases of all fermions in the model allows to remove the complex phase only from one gaugino mass parameter. Therefore the most general form of the expression for the gaugino mass terms is Lmass = (m1λ a Gλ a G+ H.c.)+(m2λ i Aλ i A+H.c.)+m3(λBλB +H.c.), where m1, m2 are complex and I have chosen m3 (gluino mass parameter) to be real. One should note that with this definition of Lmass the diagonal entries in the chargino and neutralino mass matrices and the physical gluino mass are equal 2m1, 2m2 and 2m3 respectively. 3. Section III, p. 3465, point (4). Contrary to the statement in [1] trilinear scalar couplings of the form Lsoft = k IJ S H 2∗ i L I iR J + e S H 2∗ i Q I iD J + w S H 1∗ i Q I iU J cannot be generated perturbatively if set once to 0. Still those terms are perfectly allowed from the point of view of construction of the consistent soft broken SUSY model and rarely (or never) taken into account. 4. Section III, p. 3466. Kobayashi-Maskawa matrix C = V + Q2VQ1 introduced in the end of Sec. III is unfortunately defined as the Hermitian conjugation of the standard definition [4]. This convention is consistently used through the paper, so one should only remember about this problem assigning numerical values to the elements of the C matrix. 5. Section IV, p. 3467, 3468. In all expressions for the sfermion mass matrices the D-terms have the wrong sign. Correct expressions can be obtained by the replacement (v 1 − v 2 2) → −(v 2 1 − v 2 2) 6. Section VI, p. 3470 and Appendix B, p. 3486. Correct expression for the charginochargino-Z vertex reads as (PL,R = 1∓γ5 2 ):