]>NUPHB13705S0550-3213(16)30059-110.1016/j.nuclphysb.2016.04.021S0550-3213(15)00225-410.1016/j.nuclphysb.2015.06.022The AuthorsErratumFig. 6GUT-scale particle mass dependence on renormalization factor of proton decay. Left panel shows MHC dependence for MΣ=MX=2×1016 GeV. Right panel shows MΣ dependence for MHC=MX=2×1016 GeV. Dotted line shows the degenerate mass case in each panels.Fig. 7Ratio of short-range renormalization effects with and without threshold effect in the minimal SUSY SU(5) GUT with light vector-like matters. We take n5=1,⋯,4 in solid lines from top to bottom. The case of the minimal SUSY SU(5) with no light vector-like matter is shown in dotted line.Fig. 8Partial proton lifetime (p→π0+e+) in vector-like extension scenario. In solid (dotted) lines, we take n5=0,1,⋯,4 with (without) threshold corrections at GUT scale. Deep gray (gray) region corresponds to experimental excluded region by Super-Kamiokande (the future sensitivity by the Hyper-Kamiokande).ErratumErratum to “Threshold corrections to baryon number violating operators in supersymmetric SU(5) GUTs” [Nucl. Phys. B 898 (2015) 1–29]JunjiHisanoabcTakumiKuwaharab⁎kuwahara@th.phys.nagoya-u.ac.jpYujiOmuraaaKobayashi–Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya 464-8602, JapanKobayashi–Maskawa Institute for the Origin of Particles and the Universe (KMI)Nagoya UniversityNagoya464-8602JapanbDepartment of Physics, Nagoya University, Nagoya 464-8602, JapanDepartment of PhysicsNagoya UniversityNagoya464-8602JapancKavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba 277-8584, JapanKavli IPMU (WPI)UTIASUniversity of TokyoKashiwaChiba277-8584Japan⁎Corresponding author.Editor: Hong-Jian HeWe have found an error in the third line of an equation (3.10). The corrected formula for Eq. (3.10) is given as(3.10)16π22g52Σ‾X(p2)=[12(N5+N5‾)+32(N10+N10‾)]B(p2,0,0)+256B(p2,MΣ2,MX2)+56B(p2,MΣ242,MX2)+B(p2,MMHC2,0)+512MX2[3A(p2,MX2,0)+10A(p2,MX2,MΣ2)+2A(p2,MX2,MΣ24)]−5C2(G)p24A(p2,MX2,0)−12C2(G)B(p2,MX2,0)+(p2-independent terms), since an equation (A.26) is replaced by(A.26)KvΣX=−10g52vΣ{Σ(3,2)[GX−WX+560BX]+Σ(3⁎,2)[GX†−WX†+560BX†]}+ h.c.We used these formulae for numerical evaluations. Besides, we have also found an additional error in numerical calculations, which we underestimated the vacuum polarization from gauge multiplets. The numerical values Eqs. (4.9) and (4.11) should be respectively replaced by(4.9)λ1|vac.=λ2|vac.=Σ(0)MX2+Σ(0)=−3.68×10−2,(4.11)λ1(MGUT)=−2.66×10−2,λ2(MGUT)=−2.53×10−2. The numerical results Eqs. (4.13) and (4.15), which are defined in Eq. (4.12) and describe the short range renormalization factors of Wilson coefficients, should be replaced by(4.13)AS(1)=2.025,AS(2)=2.118, for the case of MΣ=MΣ24, and(4.15)AS(1)=2.014,AS(2)=2.107, for the case of MΣ=5MΣ24. As a result, in the minimal SUSY SU(5) GUT, we found the corrected numerical values for R defined in Eq. (4.14) as R=1.052 for the case of MΣ=MΣ24, and R=1.041 for the case of MΣ=5MΣ24.Figs. 6–8 should be replaced by the following figures.Our conclusion is also changed as follows. In the minimal SUSY SU(5) GUT, the partial proton decay rate (p→π0+e+) is enhanced about 5% due to the threshold corrections to the baryon-number violating dimension-six operators. From vector-like superfields, the additional contribution to the vacuum polarization of X-boson can be positive as long as the vector-like masses can be negligible. This additional contribution cancels with the contribution via the vacuum polarization λi|vec.(i=1,2) in the minimal SUSY SU(5). Therefore, in the vector-like extension of the minimal SUSY SU(5) GUT, the effects of threshold corrections can become smaller when the number of vector-like superfields increases.