Erratum: New methods of testing Lorentz violation in electrodynamics

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by  Michael Hohensee

Erratum: New methods of testing Lorentz violation in electrodynamics
Michael Hohensee,1,2,∗ Alex Glenday,1,2 Chih-Hao Li,2 Michael Edmund Tobar,3 and Peter Wolf4
1Department of Physics, Harvard University, Cambridge, Massachusetts 20138, USA
2Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
3School of Physics, the University of Western Australia,
35 Stirling Hwy, Crawley 6009, Western Australia, Australia
4LNE-SYRTE, CNRS, UPMC, Observatoire de Paris, 75014 Paris, France
(Dated: February 2, 2008)
In an earlier paper [1] (hep-ph/0408006), the bound on the Standard Model Extension photon-
sector parameter κ˜tr [2] (hep-ph/0205211) set by the heavy-ion storage-ring experiment of
Saathoff et al. [3] was incorrectly reported. We show that the correct bound on κ˜tr which resulted
from this experiment is in fact 2.2×10−7.
7
0
Inthe originalderivationofthe leadingorderLorentz- Further expanding the second order term to first order
0
violating effects of κ˜ to the Ives-Stilwell observable in κ˜ , we find that
2 tr tr
n νaνp/ν02, second order and higher terms in βat = vat/c
Ja wtimeree-vnaerygliencgt,edfra[m1].e-deIpnendtheinst lfiamcitto,rsanodf oarpdaerrtufnriotmy, βa2t(cid:18)cc22 + cc22 − cc2c −1(cid:19)=2βa2tκtr (3)
a nonzero κ˜ produces a shift of the Ives-Stilwell ob- a p a p
0 tr
3 servable that is proportional to 4βatβlabκ˜tr. For ter-
restrial experiments, we take βlab ∼ β⊕, noting that withnotime-variationduetotheEarth’schangingveloc-
ity in the Sun-centered frame. Combining (3) with the
1 the laboratory’s velocity relative to the preferred (Sun-
v centered) frame is dominated by the Earth’s orbital ve- result of [1] we obtain, to lowest order in κtr,
2 locity, β⊕ ∼10−4 [6].
125 6×Fo1r0−S2aaisthfoaffr laanrgdercotlhlaabnoβra⊕t.orBseicnau[3se],ohfotwheisv,ewr,eβmatus≃t ννp0ν2a =1+2κtr(cid:2)βa2t+2βatβ⊕(...)(cid:3)+O(cid:0)κ˜2tr(cid:1), (4)
0 consider terms proportional to βa2t. Noting that (equa-
7 tion (10) of [1]) where as specified in equation (12) of [1] (...) repre-
0 sents sinusoidally varying terms of order unity. In the
h/ ν =ν 1−βa2t , and ν =ν 1−βa2t , (1) limit βat ≫β⊕, the βa2t “DC” term dominates the time-
p p 01−pβ (c/c ) a 01+pβ (c/c ) dependent sidereal term. Thus the previously derived
at p at a
- equation (12) in [1] is only valid when βat < β⊕. Upon
p
e then to second order in βat, comparisonto the RMS [4, 5] parameter αˆ (see equation
h (2)of[3])boundedbySaathoff et al.,we findthatinthe
iv: ννp0ν2a =1+βat(cid:18)ccp − cca(cid:19)+βa2t(cid:18)cc2a2 + cc2p2 − cac2cp −1(cid:19). lbimouintdthoantκ˜βtart. ≫Weβt⊕h,eraefboroeuncdonocnludαˆeitshaeqtutihvealleinmtittoseat
X (2) on κ˜ by [3] is κ˜ <2.2×10−7.
tr tr
∗ThanksDavidPhillipsandItayYavinforhelpfuldiscussions.
r
a
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Rev.D 71, 025004 (2005). [4] H. P.Robertson, Rev. Mod. Physics 21, 378 (1949).
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(2002). [6] There are also contributions to βlab from βr, the compo-
[3] G. Saathoff, S. Karpuk, U. Eisenbarth, G. Huber, nent of the lab’s motion dueto theEarth’s spin, but this
S. Krohn, R. M. Horta, S. Reinhardt, D. Schwalm, is far smaller than β⊕.
A. Wolf, and G. Gwinner, Phys. Rev. Lett. 91, 190403