CPTand Lorentz Tests in Hydrogen and Antihydrogen

Abstract

Signals for CPT and Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy. We show that certain 1S-2S and hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of the fine-structure constant. [S0031-9007(99) PACS numbers: 11.30. Er, 12.20.Fv, 32.10.Fn, 32.80.Pj Experimental and theoretical studies of the spectrum of hydrogen (H) have historically been connected to several major advances in physics [1]. The recent production and observation of antihydrogen (H) [2,3] makes it plausible to consider a new class of spectroscopic measurements involving high-precision comparisons of the spectra of H and H [4]. The two-photon 1S-2S transition has received much attention because an eventual measurement of the line center to about 1 mHz, corresponding to a resolution of one part in 10 18 , appears feasible [5]. It has already been measured to 3.4 parts in 10 14 in a cold atomic beam of H [6] and to about 1 part in 10 12 in trapped H [7]. Proposed H spectroscopic investigations involve both beam and trapped-atom techniques [8,9].We consider here the use of spectroscopy of free or magnetically trapped H and H to search for CPT and Lorentz violation. The discrete symmetry CPT is an invariance of all local Lorentz-invariant quantum field theories of point particles [10], including the standard model and quantum electrodynamics (QED). However, the situation is less clear for a more fundamental theory combining the standard model with gravity, such as string theory, where spontaneous breaking of these symmetries may occur [11]. Low-energy manifestations would be suppressed by a power of the ratio of the low-energy scale to the Planck scale, so only a few exceptionally sensitive experiments are likely to detect them.In this paper, we show that effects of this type from the Planck scale can appear in H and H spectra at zeroth order in the fine-structure constant. Moreover, these effects are theoretically detectable not only in 1S-2S lines but also in hyperfine transitions.Our analysis is performed in the context of a standardmodel and QED extension [12] incorporating the idea of spontaneous CPT and Lorentz breaking at a more fundamental level. This quantum field theory appears at present to be the only existing candidate for a consistent extension of the standard model based on a microscopic theory of CPT and Lorentz violation. Desirable features such as energy-momentum conservation, gauge invariance, renormalizability, and microcausality are expected [12]. The theory has been applied to photon properties [12] [18]. To examine the spectra of free H and H, it suffices to perform a perturbative calculation in the context of relativistic quantum mechanics. In this approach, the unperturbed Hamiltonians and their eigenfunctions are the same for H and H. Moreover, all perturbative effects from conventional quantum electrodynamics are also identical for both systems. However, the CPT -and Lorentz-breaking couplings for the electron and positron can provide d...

Rydberg-state mixing in the presence of an external electric field: Comparison of the hydrogen and antihydrogen spectra

“…Nonetheless, it was shown that signals for CPT symmetry and the Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy [7]. Effects of this type can appear in H andH spectra at zeroth order in the fine-structure constant and are detectable not only in spin-mixed 1s-2s lines but also in spin-flip hyperfine signals.…”

Detection of Trapped Antihydrogen

“…Although the 1S −2S transition line is the ultimate experimental goal, CPT -violating effects may also appear in other hydrogen energy splittings [15]. Other attractive comparative measurements include, the 2S 1/2 − 2P 1/2 Lamb shift [1] and the ground-state hyperfine structure [16][17][18].…”

The Lorentz-Violating Extension of the Standard Model

“…The SME is a dynamical model constructed to contain all Lorentz-and CPT-violating lagrangian terms consistent with coordinate independence, which is a fundamental requirement to be discussed below. To date, numerous Lorentz-and CPT-violation tests involving hadrons [8][9][10][11][12][13][14][15][16][17][18][19][20][21], protons and neutrons [22][23][24][25][26][27][28][29][30][31], electrons [31][32][33][34][35][36][37][38][39][40][41], photons [42][43][44][45][46][47], muons [48][49][50], and neutrinos [2,[51][52][53][54] have been analysed or identified within th...…”