Erratum to: Dimension-six matrix elements for meson mixing and lifetimes from sum rules
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Received: June 9, 2020 Accepted: June 10, 2020 Published: June 26, 2020
Erratum: Dimension-six matrix elements for meson mixing and lifetimes from sum rules
IPPP, Department of Physics, University of Durham, DH1 3LE, United Kingdom
E-mail: [email protected], [email protected], [email protected] Erratum to: JHEP12(2017)068 ArXiv ePrint: 1711.02100 Eq. (5.15) in the original paper used a wrong numerical expression for the lifetime ratio τ (Bs0 )/τ (Bd0 ) from [16] and should read τ (Bs0 ) = 0.994 ± 0.004, τ (B 0 ) exp τ (Bs0 ) (5.15) = 1.0007 ± 0.0025 0 τ (B ) MS
= 1.0007 ± 0.0014 (had.) ± 0.0006 (scale) ± 0.0020 (1/m4b ), implying an agreement with experiment at the level of 1.4 instead of 1.1 σ as stated originally. Figure 9 is also affected and is updated below. In the original paper we have set color factors in some places to their QCD values with Nc = 3 while keeping them general in others.1 To restore generality one has to change the following eqs. to Nc CF ω12 ω22 αs r ˜ (x, Lω ), 4 π 4 4π Qi ∆ρpert ˜ (ω1 , ω2 ) CF αs Q = r ˜ (x, Lω ), wQ˜ i (ω1 , ω2 ) = pert i pert Nc 4π Qi ρΠ (ω1 )ρΠ (ω2 ) ! µ2ρ CF αs (µρ ) pert ∆BQ˜ (µρ ) = rQ˜ i 1, log 2 , i Nc AQ˜ i 4π 4Λ ∆ρQ˜ i ≡
(3.17) (3.24) (3.25)
which coincide with their counterparts in the original paper in QCD with three colors. 1
We are grateful to A. Grozin and A. Pivovarov for pointing this out to us.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)162
JHEP06(2020)162
M. Kirk, A. Lenz and T. Rauh
lattice )” and “This work (f exp )” in figure 7 We noticed that the labels “This work (fD D were interchanged. The figure with the corrected labels in shown below. Our numerical code for ∆Mq and aqsl used a wrong input value for the top-quark mass.2 The corresponding SM predictions in eqs. (4.4), (4.5), (4.7) and (4.8) change by a small amount to +1.3 −1 ∆MsSM = (16.6±1.7) ps−1 = (16.6+1.2 −1.1 (had.)±0.1 (scale)−1.2 (param.)) ps ,
(4.4)
∆MdSM = (0.56±0.08) ps−1 = (0.56±0.04 (had.)±0.00 (scale)±0.07 (param.)) ps−1 ,
(4.5)
PS +0.2 −5 as, = (2.2±0.3)·10−5 = (2.2±0.1 (had.)+0.0 −0.1 (scale)−0.3 (param.))·10 , sl 1S +0.2 −5 −5 as, = (2.1+0.2 = (2.1±0.1 (had.)+0.0 −0.3 )·10 −0.1 (scale)−0.3 (param.))·10 , sl kin +0.2 −5 as, = (2.2±0.3)·10−5 = (2.2±0.1 (had.)+0.0 −0.1 (scale)−0.3 (param.))·10 , sl
(4.7)
PS −4 ad, = (−4.4+0.6 = (−4.4±0.1 (had.)+0.2 −0.5 )·10 −0.1 sl
(4.8)
(scale)±0.5 (param.))·10−4 ,
which improves the agreement of ∆MdSM with the experimental value to better than one standard deviation. This also affects figure 8 as well as tables 6 and 7 which are corrected below. All our conclusions remain unchanged.
1.4
ETM'14 ETM'15 FNAL/MILC'17 This work (fDexp ) This work (fDlattice )
GeV4
1.2 1.0 0.8 0.6
3 Q1
®
−3/2
Q2
®
6 Q3
®
Q4
®
5/2 Q5
®
Figure 7. Comparison of our results for the ∆C = 2 matrix elements at the scale 3 GeV to the lattice values of ETM’14 [30], ETM’15 [31] and FNAL/MILC’17 [32] The values for the matrix elements of the ETM c
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