Search for light-speed anisotropies using Compton scattering of high-energy electrons
aa r X i v : . [ h e p - e x ] S e p August 17, 2018 6:22 WSPC - Proceedings Trim Size: 9in x 6in ws-rebreyend-cpt10 Search for light-speed anisotropies using Compton scattering ofhigh-energy electrons
D. Rebreyend on behalf of the experimental team ∗ Laboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1,CNRS/IN2P3, INPG, Grenoble, FranceE-mail: [email protected]
Based on the high sensitivity of Compton scattering off ultra relativistic elec-trons, the possibility of anisotropies in the speed of light is investigated. Theresult discussed in this contribution is based on the γ -ray beam of the ESRF’sGRAAL facility (Grenoble, France) and the search for sidereal variations inthe energy of the Compton-edge photons. The absence of oscillations yieldsthe two-sided limit of 1 . × − at 95 % confidence level on a combinationof photon and electron coefficients of the minimal Standard Model Extension(mSME). This new constraint provides an improvement over previous boundsby one order of magnitude. Experimental searches for anisotropies in c and, more generally, forLorentz violating (LV) processes are currently motivated by theoreticalstudies in the context of quantum gravity. Recent approaches to Planck-scale physics can indeed accommodate minuscule violations of Lorentz sym-metry. The present result is based on a laboratory experiment using only pho-tons and electrons in an environment where gravity is negligible. Lorentzviolation can then be described by the single-flavor QED limit of the flat-spacetime mSME.
In this framework, photons have a modified dispersionrelation: ω = (1 − ~κ · ˆ λ ) λ + O ( κ ) . (1) ∗ J.-P. Bocquet, D. Moricciani, V. Bellini, M. Beretta, L. Casano, A. DAngelo, R. DiSalvo, A. Fantini, D. Franco, G. Gervino, F. Ghio, G. Giardina, B. Girolami, A. Giusa,V.G. Gurzadyan, A. Kashin, S. Knyazyan, A. Lapik, R. Lehnert, P. Levi Sandri,A. Lleres, F. Mammoliti, G. Mandaglio, M. Manganaro, A. Margarian, S. Mehrabyan,R. Messi, V. Nedorezov, C. Perrin, C. Randieri, N. Rudnev, G. Russo, C. Schaerf, M.-L. Sperduto, M.-C. Sutera, A. Turinge, and V. Vegna ugust 17, 2018 6:22 WSPC - Proceedings Trim Size: 9in x 6in ws-rebreyend-cpt10 Here, λ µ = ( ω, λ ˆ λ ) denotes the photon 4-momentum and ˆ λ is a unit 3-vector. The space-time constant mSME ~κ vector specifies a preferred di-rection in the Universe which violates Lorentz symmetry, and can be inter-preted as generating a direction-dependent refractive index of the vacuum n (ˆ λ ) ≃ ~κ · ˆ λ .The basic experimental idea is that in a terrestrial laboratory the photon3-momentum in a Compton-scattering process changes direction due tothe Earth’s rotation. The photons are thus affected by the anisotropies inEq. (1) leading to sidereal effects in the kinematics of the process.The experimental set-up at GRAAL involves counter-propagating in-coming electrons and photons with 3-momenta ~p = p ˆ p and ~λ = − λ ˆ p , re-spectively. The conventional Compton edge (CE) then occurs for outgoingphotons that are backscattered at 180 ◦ , so that the kinematics is essentiallyone dimensional along the beam direction ˆ p . Energy conservation for thisprocess reads E ( p ) + (1 + ~κ · ˆ p ) λ = E ( p − λ − λ ′ ) + (1 − ~κ · ˆ p ) λ ′ , (2)where ~λ ′ = λ ′ ˆ p is the 3-momentum of the CE photon, and 3-momentumconservation has been implemented. At leading order, the physical solutionof Eq. (2) is λ ′ ≃ λ CE (cid:20) γ (1 + 4 γ λ / m ) ~κ · ˆ p (cid:21) . (3)Here, λ CE = γ λ γ λ / m denotes the conventional value of the CE energy.Given the actual experimental data of m = 511 keV, p = 6030 MeV, and λ = 3 . γ ≃ p/m = 11800 and λ CE = 1473 MeV. The numericalvalue of the factor in front of ~κ · ˆ p is about 1 . × . It is this largeamplification factor (essentially given by γ ) that yields the exceptionalsensitivity of the CE to ˜ κ o + .Expressed in the Sun-centered inertial frame ( X, Y, Z ) and taking intoaccount GRAAL’s latitude and beam direction, eq. (3) becomes λ ′ ≃ ˜ λ CE + 0 .
91 2 γ λ CE (1 + 4 γ λ / m ) q κ X + κ Y sin Ω t . (4)Incoming photons overlap with the ESRF beam over a 6 . µ -strip detector (128 strips of 300 µ m pitch, 500 µ m ugust 17, 2018 6:22 WSPC - Proceedings Trim Size: 9in x 6in ws-rebreyend-cpt10 thick) associated to a set of fast plastic scintillators. A typical Si µ -stripcount spectrum near the CE is shown in Fig. 1 for the multiline UV mode(364, 351, 333 nm) of the laser used in this measurement. The fitting func-tion, also plotted, is based on the sum of 3 error functions plus backgroundand includes 6 free parameters. The CE position (location of the centralline), x CE , can be measured with an excellent resolution of ∼ µ m. c oun t s ( i n ) x (mm)1.40 1.45 1.50 ! (GeV)CE Fig. 1. Si µ -strip count spectrum near the CE and the fitting function (see text) vs.position x and photon energy ω . The three edges corresponding to the lines 364, 351,and 333 nm are clearly visible. The CE position x CE is the location of the central lineand is measured with a typical accuracy of 3 µ m. A sample of the time series of the CE positions relative to the ESRFbeam covering 24 h is displayed in Fig. 2c, along with the tagging-box tem-perature (Fig. 2b) and the ESRF beam intensity (Fig. 2a). The sharp stepspresent in Fig. 2a correspond to the twice-a-day refills of the ESRF ring.The similarity of the temperature and CE spectra combined with their cor-relation with the ESRF beam intensity led us to interpret the continuousand slow drift of the CE positions as a result of the tagging-box dilationinduced by the x-ray heat load.To get rid of this trivial time dependence, raw data have been fittedwith the sum of two exponential whose time constants have been extractedfrom the time evolution of the temperature data. The corrected and finalspectrum is obtained by subtraction of the fitted function from the rawdata, (Fig. 2d).The usual equation for the deflection of charges in a magnetic fieldtogether with momentum conservation in Compton scattering determinesthe relation between the CE variations ∆ x CE x CE and a hypothetical CE photon ugust 17, 2018 6:22 WSPC - Proceedings Trim Size: 9in x 6in ws-rebreyend-cpt10 a)b)c)d) t (hr)200180160434252.9352.900.015-0.015 I ( m A ) T ( ° C ) x C E ( mm ) ± ( mm ) Fig. 2. Time evolution over a day of a) ESRF beam intensity; b) tagging-box temper-ature; c) CE position and fitted curve; d) δ = x CE − x fit . The error bars on positionmeasurements are directly given by the CE fit. ∆ λ ′ λ ′ :∆ x CE x CE = pp − λ CE ∆ λ ′ λ ′ . (5)To search for a modulation, 14765 data points collected in about 1 weekof data taking have been folded modulo a sidereal day (Fig. 3). The errorbars are purely statistical and the histogram is in agreement with a nullsignal ( χ = 1 . A sin(Ω t + φ )), wehave performed a statistical analysis based on the Bayesian approach. Theresulting upper bound is A < . × − at 95% CL.We next consider effects that could conceal an actual sidereal signal. Be-sides a direct oscillation of the orbit, the two quantities that may affect theresult are the dipole magnetic field and the momentum of the ESRF beam p . All these parameters are linked to the machine operation, and their sta-bility follows directly from the accelerator performance. A detailed analysisof the ESRF database allows us to conclude that a sidereal oscillation of ugust 17, 2018 6:22 WSPC - Proceedings Trim Size: 9in x 6in ws-rebreyend-cpt10 t (hr) +10 -5 -10 -5 ¢¸ ’ ¸ ’ Fig. 3. Full set of data folded modulo a sidereal day (24 bins). The error bars arepurely statistical and agree with the dispersion of the data points ( χ = 1 .
04 for theunbinned histogram). The shaded area corresponds to the region of non-excluded signalamplitudes. any of these parameters cannot exceed a few parts in 10 and is negligible.We can now conclude that our upper bound on a hypothetical siderealoscillation of the CE energy is:∆ λ ′ /λ ′ < . × − (95 % CL) , (6)yielding the competitive limit p κ X + κ Y < . × − (95 % CL) withEq. (4). This limit improves previous bounds by a factor of ten and rep-resents the first test of Special Relativity via a non-threshold kinematicseffect in a particle collision. References
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