Article

# Effects of terrestrial tides on the LEP beam energy

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## Abstract

The circular e+e− collider LEP located near Geneva is used to investigate the properties of the Z boson. The measurements of the Z boson mass and resonance width are of fundamental importance for the standard model of the electroweak interactions. They require a knowledge of the LEP beam energy with a precision of ∼ 20 ppm, which is provided by a measurement of the electron spin precession frequency. To extrapolate beam energy calibrations over a longer period of time, effects causing energy changes have to be taken into account. Among these are the terrestrial tides due to the sun and moon which move the Earth surface up and down. The lateral components of this motion modify the 26.7 km LEP circumference by about 1 mm. This change in length results in variations of the beam energy up to 120 ppm. We present results of measurements on the influence of terrestrial tides on the LEP beam energy that have been performed in 1992 and 1993.

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... Finally, the knowledge of the beam-energy spread in 1993, 1994 and 1995 is summarized (Section 12). This is an important correction to Z and to the peak cross-section. ...
... where g m 9) is the correction to be applied to the measured local acceleration due to gravity [11] and k G = ( 82 4)=(ms 2 ) is a coecient estimated from the measured deformation of the LEP ring as detected by the Beam Orbit Measurement system [18]. The reliability of the modelling of such deformation has been proven in dedicated experiments, by comparison with energy changes as measured by the RD technique [12]. To e v aluate the eect of a possible phase-shift of the model (due for example to the nite binning in time) the changes in the energy due to a relative c hange of 7:5 minutes, corresponding to half of the recording interval, have been modelled: the largest change on the average centre-of-mass energy is 0.2 MeV. ...
... radius. The correction is E = K radius R (12) where R is the measured variation of the radial beam position at the BOMs. It is proportional to the variation of the radius of LEP. ...
Article
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The determination of the centre-of-mass energies from the LEP1 data for 1993, 1994 and 1995 is presented. Accurate knowledge of these energies is crucial in the measurement of the Z resonance param eters. The improved understanding of the LEP energy behaviour accumulated during the 1995 energy scan is detailed, while the 1993 and 1994 measurements are revised. For 1993 these supersede the pr eviously published values. Additional instrumentation has allowed the detection of an unexpectedly large energy rise during physics fills. This new effect is accommodated in the modelling of the beam-energy in 1995 and propagated to the 1993 and 1994 energies. New results are reported on the magnet temperature behaviour which constitutes one of the major corrections to the average LEP ene rgy. The 1995 energy scan took place in conditions very different from the previous years. In particular the interaction-point specific corrections to the centre-of-mass energy in 1995 are more complicated than previously: these arise from the modified radiofrequency-system configuration and from opposite-sign vertical dispersion induced by the bunch-train mode of LEP operation. Finall y an improved evaluation of the LEP centre-of-mass energy spread is presented. This significantly improves the precision on the Z width.
... ±2 mm for C of 100 km [22,66,67]. For a momentum compaction factor of χ 10 −5 the corresponding energy changes reaches ±2 · 10 −3 or ±90 MeV around the Z resonance. ...
... Invariant mass distribution of 10 5 muon pairs in the CLD detector, at centre-ofmass energies of (left-to-right) 87.9, 91.2 and 94.3 GeV respectively; the width of the distribution is dominated by the muon momentum measurement uncertainty. The data correspond to 521 pb −1 , 69 pb −1 , and 257 pb −1 , which can be acquired in 4 minutes, 35 seconds and 2 minutes respectively 9.3 Additional machine and beam monitoring tools 9.3.1 Orbit monitoring Earth tides induce roughly 1 mm peak-to-peak amplitude circumference changes of the LEP/LHC ring [22,66,67], while longer term geological deformations induced seasonal circumference variations of around 2 mm [9]. Due to the infrequent energy calibrations at LEP, which left many coasts un-calibrated, it was essential to be able to correct for such circumference changes that could affect the LEP energy by up to 20 MeV at the Z pole (and more than twice as much at higher energies). ...
Preprint
The first stage of the FCC (Future Circular Collider) is a high-luminosity electron-positron collider (FCC-ee) with centre-of-mass energy ranging from 88 to 365 GeV, to study with high precision the Z, W, Higgs and top particles, with samples of $5 \times 10^{12}$ Z bosons, $10^8$ W pairs, $10^6$ Higgs bosons and $10^6$ top quark pairs. A cornerstone of the physics program lays in the precise (ppm) measurements of the W and Z masses and widths, as well as forward-backward asymmetries. To this effect the centre-of-mass energy distribution should be determined with the high precision. This document describes the capacity offered by FCC-ee, starting with transverse polarization of the beams around the Z pole and the W pair threshold. A running scheme based on regular measurements of the beam energy by resonant depolarization of pilot bunches, during physics data taking, is proposed. The design for polarization wigglers, polarimeter and depolarizer is outlined. The $e^\pm$ beam energies will be monitored with a relative precision of $10^{-6}$. The centre-of-mass energy is derived subject to further corrections, related to the beam acceleration, synchrotron radiation and beamstrahlung; these effects are identified and evaluated. Dimuon events $e^+e^- \to \mu^+ \mu^-$, recorded in the detectors, provide with great precision the beam crossing angle, the centre-of-mass energy spread, and the $e^+$ and $e^-$ energy difference. Monitoring methods to minimize absolute error and relative uncertainties are discussed. The impact on the physics measurements is given. A programme of further simulations, design, monitoring and R&D is outlined.
... The energies follow the CTE tide predictions, with the exception of a few points that may indicate small uncontrolled energy fluctuations. Using all measurements the following value of κ tide is extracted for the CTE model [36] : ...
... This estimate is in good agreement with our measurements. More details on the tide effects can be found in [34,36]. ...
Article
Full-text available
To improve the accuracy on the measurements of the Z boson resonance mass Mz and width Gamma_z, the Large Electron Positron collider (LEP) was run in "Energy Scan" mode during the 1993 and 1995 operation by choosing the CM energy E_CM=E_e^++E_e^- to correspond to the peak of the Z resonance and to two values about 880 MeV above and below the peak. To reduce the systematic contribution to the overall errors on MZ and GammaZ the value of the Absolute Beam Energy has to be known to the best possible accuracy. Several methods for precise Energy Calibration have been considered before adopting the Resonant Depolarization (RD) technique which, when a 10% transverse polarization is available in a reproducible way, provides a 2×10-5 precision ( ~±1 MeV at the Z energies). Operational Beam Energy Calibration by Resonant Depolarization has been successfully implemented and extensively used. A detailed description of the RD method is presented in the talk together with a general overview of other possible techniques.
... The observed variations agree well with the expectations from geophysical calculations. The measurement of the LEP beam energy clearly demonstrated that eect of the terrestrial tides on the LEP ring circumference and beam energy 27 . ...
Article
The LEP experiment has nished in November 2000 after 12 years of operation. Highlights of the LEP accelerator and 4 LEP experiments, ALEPH, DELPHI, L3 and OPAL are reviewed.
... This estimate is in good agreement with our measurements. More details on the tide effects can be found in [34, 36]. ...
Article
Full-text available
To improve the measurements of the Z boson mass and resonance width, the 1993 Large Electron Positron Collider (LEP) run was devoted to a three point beam energy scan, with one point close to the peak of the Z resonance and two points roughly 880 MeV below and above the peak. Operational energy calibration by resonant depolarization was successfully commissioned for all three beam energies. 24 energy calibrations were performed at the end of physics fills. The accuracy of each calibration is better than 1 MeV. About one third of the total integrated luminosity was recorded in calibrated fills below and above the resonance and a regular tracking of the beam energies throughout the scan was possible. The evolution of the beam energies in the course of the year showed a large variation of up to 20 MeV. Results from the energy calibrations will be presented and possible explanations for the changes of the beam energy during the year will be described.
... It is well known ( [74,75]) that the gravitational forces of the moon and sun affect the operation of large accelerators. Both cause terrestial tides that induce a quadrupolar deformation of the earth crust which eventually changes the physical circumference of the machine. ...
Article
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Many contemporary philosophers of physics (and philosophers of science more generally) follow Bertrand Russell in arguing that there is no room for causal notions in physics. Causation, as James Woodward has put it, has a ‘human face’, which makes causal notions sit ill with fundamental theories of physics. In this paper I examine a range of anti-causal arguments and show that the human face of causation is the face of scientific representations much more generally. Physics, like other sciences, is deeply permeated with causal reasoning.
... It is noteworthy that, despite of an extremely small momentum compaction factor, temperature variation does not appreciably affect the LEP circumference. The largest relative energy excursions at LEP, of the order of 10 −4 , are caused by tidal effects [73]. Aside from the increased sensitivitiy to temperature, the low momentum compaction also increases the likelihood of longitudinal single-bunch instabilities. ...
Article
Full-text available
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... An issue that needs to be resolved for a sensitive LLI study at the GF is the significant daily variation of the beam energy known for the LHC tunnel since the Z-boson LEP era [27]. The amplitude of this variation (∆γ beam /γ average beam ) is on the scale of 10 −4 and not exactly predictable due to contributions from several tidal effects and weather conditions. ...
Preprint
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... This eect produces a beam orbit -beam energy relationship, where bybeambybeam orbit' we denote the relative position of the beam with respect to the LEP ring. As we h a v e seen, in absolute scale the beam orbit is constant and dened by the RF frequency, whereas the size of the LEP ring itself is in uenced by geological factors, like terrestrial tides [7] and other long term variations [8] that have sizeable eects on its total length. The centre of mass energy at each i n teraction point is further in uenced by the RF system which is not symmetric with respect to the four LEP experiments resulting in small, calculable, dierences [9]. ...
Article
Full-text available
An overview of electroweak physics with emphasis on recent results from LEP is presented. The combination of high statistics and accurate energy determination during the 1993 LEP scan improve the accuracy on nearly all electroweak observables by signicant amounts. Despite this increased accuracy, the agreement of the data and the Standard Model predictions is remarkable. The pure electroweak part of the theory is seen for the rst time, since data are now accurate enough to show a deviation from the pure QED radiative corrections. Standard model ts constrain the mass of the top to a narrow range around 170 GeV. Conrmation of the recent evidence for top quark production will start to constrain the mass of the Higgs, albeit weakly.
... The circumference of the LHC is oscillating periodically due to Earth tides [20]. The peak-to-peak relative energy swing due to tides reaches 0.014% which corresponds to a rf frequency swing (to maintain the beam in the center) of 17 Hz. ...
Article
Full-text available
As a result of the excellent quality of the Large Hadron Collider (LHC) experimental detectors and the accurate calibration of the luminosity at the LHC, uncertainties on the LHC beam energy may contribute significantly to the measurement errors on certain observables unless the relative uncertainty is well below 1%. Direct measurements of the beam energy using the revolution frequency difference of proton and lead beams combined with the magnetic model errors are used to provide the energy uncertainty of the LHC beams. Above injection energy the relative uncertainty on the beam energy is determined to be ±0.1%. The energy values as reconstructed and distributed online to the LHC experiments do not require any correction above injection energy. At injection a correction of +0.31 GeV/c must be applied to the online energy values.
... It is well known ( [74,75]) that the gravitational forces of the moon and sun affect the operation of large accelerators. Both cause terrestial tides that induce a quadrupolar deformation of the earth crust which eventually changes the physical circumference of the machine. ...
Article
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... – ÖÖ××´ØÖÖ××´Ø Ý Ø ¬ÐÐ µ is the term accounting for the rise of the bending field due to the parasitic currents flowing along the beam-pipe. It is parametrized as a function of the time-of-day, Ø Ý , and time since the magnet reached the final field, Ø ¬ÐÐ – ØØØØ is the correction due to the effect of the Earth tides [8]. ...
Article
The Large Electron Positron accelerator (LEP) is a storage ring which has been operated since 1989 at the European Laboratory for Particle Physics (CERN), located in the Geneva area. It is intended to experimentally verify the Standard Model theory and in particular to detect with high accuracy the mass of the electro-weak force bosons. Electrons and positrons are accelerated inside the LEP ring in opposite directions and forced to collide at four locations, once they reach an energy high enough for the experimental purposes. During head-to-head collisions the leptons loose all their energy and a huge amount of energy is concentrated in a small region. In this condition the energy is quickly converted in other particles which tend to go away from the interaction point. The higher the energy of the leptons before the collisions, the higher the mass of the particles that can escape. At LEP four large experimental detectors are accommodated. All detectors are multi purpose detectors covering a solid angle of almost 4. . The first period of operation of LEP (1989-1995) has been to the scan of the Z boson energy range, and the electrons and positrons beams were accelerated up to about 45 GeVper beam (see section 1.3.1). Since the end of 1995 LEP is devoted to operate at higher energies, up to more than 100 GeVper beam in the 1999-2000 runs. It was thus possible to investigate the W boson properties and the HiggÂs particle existence, in case its mass reveals to be at this energy level. The types of event (i.e. the fundamental particles) which can be detected depends on the lepton energy before colliding (see Fig. 1.2). The particle beams energy calibration is thus a focal point for a successful operation of the collider. During normal operation electrons and positrons are bent inside the ideal circular trajectory by mean of a number of dipole magnets. The energy of the leptons depends on the total dipole field along their trajectory. The bending field around LEP is monitored by Nuclear Magnetic Resonance (NMR) probes which sample the field in twenty locations. Such measurements provide part of the data for the energy calibration model (see chapter 2). In 1999 a spectrometer has been installed in a section of the LEP ring as a new tool for the beam energy determination. The spectrometer layout mainly consist in an iron-core bending magnet and six Beam Position Monitor (BPM) stations. The main subject of this thesis work relates to the design, development and application of a special system which is able to measure with high accuracy the total integral field of the spectrometer bending dipole. The dissertation begins with a short introduction to CERN and its accelerator complex. Further on the LEP collider is described in detail and the basics of the beam energy calibration are included. Chapter 3 describes the LEP spectrometer, starting from the concept and layout, outlining the dipole magnet characteristics. The chapter ends with the presentation of some measurements performed on the LEP injection magnets in order to investigate the possible thermal effects to be foreseen on the spectrometer magnet. Chapter 4 introduces basics concepts about magnetic measurements techniques, mainly concentrating on the NMR theory and application. Chapter 5 provides the detailed description of our measurement setup based on a travelling mole equipped with magnetic field detectors and monitored with a laser interferometer. The design, realization and test of the whole system is considered. The following chapter gives the results of the first field mapping with the mole system, performed on an standard LEP iron-concrete core dipole, located in a laboratory at ground level. Chapter 7 finally describes the mapping campaign on the LEP spectrometer dipole magnet with a full analysis of the achieved results.
... Large ring interferometers are susceptible to solid Earth tides. This was first found accidentally in the electron-positron storage ring low-energy protons (LEP) [Arnaudon et al., 1995]. Rautenberg et al. [1997] predicted that a lunar signal should be visible in a ring laser gyroscope such as the C-II instrument, a well-engineered square ring with side 1 meter, in the bunker 30 m underground at Cashmere, Christchurch, New Zealand. ...
Article
Full-text available
1] An Earth tide signal at the lunar tidal period of 12 hours 25 min has been detected in the Sagnac frequency record of the C-II ring laser 30 m underground at Christchurch, New Zealand. Its amplitude, one part per million of the Earth rotation signal, is much greater than the value of 40 parts per billion expected. Tiltmeter records show that a substantial part of this amplification is geophysical, the lunar component of tilt having an amplitude of the order of 0.1–0.2 mrad, principally because of ocean loading of Banks Peninsula. The joint records also show effects on the Sagnac frequency associated with cavern deformation under ambient pressure and temperature change and with long-period waves in cavern tilt.
... At LEP polarization was used solely for precise energy calibrations, but it gave the opportunity for some very interesting observations like the effect of the terrestrial tides on the machine length and hence on the beam energy [29]. ...
... It is well known ( [74,75]) that the gravitational forces of the moon and sun affect the operation of large accelerators. Both cause terrestial tides that induce a quadrupolar deformation of the earth crust which eventually changes the physical circumference of the machine. ...
Article
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... Actually, this value would be even smaller due to a changing orientation caused by Earth's rotation and misalignment between the Sun and the Moon. However, the tides also cause a slight deformation of the LHC tunnel (by ≈ 1 mm), over the period of a day [13]. A radial feedback loop allows the RF system to continuously correct the proton beam orbit, keeping it centered [14,15]. ...
Preprint
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... But over a period of weeks central frequency measurements have been made at LEP in 1993 [6]. The observed variation in the LEP central frequency is nicely correlated with the change of the LEP beam energy due to tidal effects [7]. The above measurements have confirmed the assumption that tidal forces vary the energy of the LEP beams at the 10 5 level by changing the circumference (and hence the central frequency) of the machine. ...
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... The beat frequency varies with the ratio A/P of ring area to perimeter. Strain effects from lunar tides have been seen to dominate in the LEP particle storage ring at CERN (Amaudon, 1995). Even with stabilized lasers as detectors, strain effects in the solid Earth are small (Levine and Hall, 1972;Agnew, 1986). ...
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The LHC Collider Ring is proposed to be turned into an ultimate automatic search engine for new physics in four consecutive phases: (1) Searches for heavy particles produced in Central Exclusive Process (CEP): pp -> p + X + p based on the existing Beam Loss Monitoring (BLM) system of the LHC; (2) Feasibility study of using the LHC Ring as a gravitation wave antenna; (3) Extensions to the current BLM system to facilitate precise registration of the selected CEP proton exit points from the LHC beam vacuum chamber; (4) Integration of the BLM based event tagging system together with the trigger/data acquisition systems of the LHC experiments to facilitate an on-line automatic search machine for the physics of tomorrow.
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The LEP beam orbit measurement system has been used to study the evolution of the LEP circumference. Radial deformations can be detected with an accuracy of about 20 m. In addition to the periodic and well known tidal distortions, slow variations of the storage ring circumference of about 2 mm are observed. These deformations lead to signiicant v ariations of the beam energy and play a n i m p o r -tant role for energy calibration. We w i l l s h o w the results of orbit measurements performed in 1993 and 1994 and discuss a possible correlation with the water level of the nearby Lake Leman.
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The LEP I program, concluded in 1995, has been a great success. The mass of the Z boson has been measured with a relative precision of ≃2 ⋅ 10−5, allowing stringent tests of the Standard Model. The full data sample has been analyzed, and results are almost final. The first data collected at LEP II during 1996 have already provided a preliminary measurement of the W boson mass. The performance of the LEP machine and experiments is consistent with the goal of ≃30 Mev total error on mW at the end of LEP II.
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Born Approximation Improved Born Approximation Experimental Arrangements Observations Weinberg Angle and ρ Parameter
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Beam orbit distortion in all dispersive sections was observed in the SPring-8 storage ring during beam commissioning. In order to confirm the stability of the radio frequency (RF) synthesizer, a monitoring system was developed. The system consists of a frequency counter referenced to a global positioning system (GPS) receiver. With this system, the output of the synthesizer, which uses an external 10 MHz-Rubidium atomic clock with the time accuracy of Δt/t=10−12Δt/t=10−12, is correctly monitored with 11 digits absolute accuracy, verifying that the synthesizer works well. Measurement of the circumference of the SPring-8 storage ring reveals the effect of tidal forces and seasonal temperature variations on beam orbit. To maintain the center axis of photon radiation in experimental beam lines, a beam energy correction is carried out. The frequency of the RF synthesizer is changed every 5 min with 10-digit accuracy. This corresponds to an energy accuracy of ΔE/E=1.16×10−6ΔE/E=1.16×10−6. The monitoring system for the synthesizer and obtained results are described.
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We present numerous observations of the diffusive motion of the ground and tunnels for scientific instruments and show that if systematic movements are excluded the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement variance dY2 scaling with time and spatial intervals T and L as dY2∝TalphaLgamma with both exponents close to 1 (alpha&ap;gamma&ap;1). We briefly describe experimental methods of the mesoscopic and microscopic ground motion detection used in measurements at physics research facilities sensitive to ground motion, particularly large high energy elementary particle accelerators. A simple mathematical model of the fractal motion demonstrating the observed scaling law is also presented and discussed. This paper is a subsequent full detail publication to [V. Shiltsev, Phys. Rev. Lett. 104, 238501 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.238501].
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The SPring-8 storage ring is under the operation dedicated to synchrotron light users. The stability of the electron beam orbit during long term operation is one of the main goals to be achieved. Data on the beam orbit taken for this purpose show variations in time including a very clear signature of an effect of the earth tide.
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HeNe ring-laser gyros are standard sensors in inertial guidance; mirror reflectances now reach 99.9999%. Present research instruments have an area of ∼ 1 m 2 , a passive quality factor of 10 11 , and a resolution of the frequency difference of counter-rotating optical beams approaching microhertz. In the Sagnac effect, this difference is proportional to the angular velocity. Present resolution is limited by thermal drifts in frequency pulling, itself reflecting mirror backscatter. The capability of ring lasers for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of non-reciprocal refractive indices, including axions and CP violation, are discussed. In standard polarization geometries the observable is necessarily time-reversal odd. Scaling rules for dimensions, finesse etc summarizing past progress and suggesting future potential are given.
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We present a comprehensive survey of the dynamics of spin-polarized beams in high-energy particle accelerators. A major theme of this review is to clarify the distinction between the properties of an individual particle—a spin—and that of a beam—the polarization. We include work from a number of institutions, including high- and medium-energy facilities, synchrotron light sources and muon storage rings (including a proposal to measure the muon electric dipole moment) and, briefly, linear accelerators and recirculating linacs. High-precision tests of the Standard Model using spin-polarized beams are reviewed; also innovative studies using spin dynamics as a tool for accelerator physics per se. We include important historical works as well as modern developments in the field. The fundamental theory is derived in detail, starting from the basic principles of quantum mechanics, electrodynamics and statistical mechanics, as well as 'accelerator physics'. The principal theoretical formulae in the field (Froissart–Stora, Sokolov–Ternov and Derbenev–Kondratenko) are presented, with in-depth attention to the quantum-statistical mechanics, as opposed to purely 'accelerator physics'. Publisher's note. A related review article by the same authors, Siberian Snakes in high-energy accelerators, has been published in Journal of Physics G: Nuclear and Particle Physics, volume 31, page R151
Conference Paper
With a circumference of 26.7 km the LEP ring is subject to long range geological deformations which must be monitored accurately to guarantee a sufficient precision on the beam energy for the LEP experiments. Changes of the LEP circumference can be extracted from the radial position of the closed orbits with an accuracy better than 0.1 mm. The observed tidal deformations with amplitudes of up to 1 mm were found to be in good agreement with geological models. Besides such periodic effects seasonal circumference variations of 2 mm are also observed. A summary of measurements collected between 1993 and 1998 is presented
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The e<sup>+</sup>e<sup>-</sup> collider LEP is used to investigate the Z particle and to measure its energy and width. This requires energy calibrations with ~20 ppm precision achieved by measuring the frequency of a resonance which destroys the transverse beam polarization established by synchrotron radiation. To make this calibration valid over a longer period all effects causing an energy change have to be corrected for. Among those are the terrestrial tides due to the Moon and Sun. They move the Earth surface up and down by as much as ~0.25 m which represents a relative local change of the Earth radius of 0.04 ppm. This motion has also lateral components resulting in a change of the LEP circumference (C<sub>c</sub>=26.7 km) by a similar relative amount. Since the length of the beam orbit is fixed by the constant RF-frequency the change of the machine circumference will force the beam to go off-center through the quadrupoles and receive an extra, deflection leading to an energy change given by ΔC<sub>c</sub>/C<sub>c</sub>~-(α<sub>c</sub>Δ<sub>c </sub>E/E. With the momentum compaction α<sub>c</sub>=1.85 10<sup>-4</sup> for the present LEP optics this gives tide-driven p.t.p. Energy excursion up to about 220 ppm, corresponding to ~18.5 MeV for the Z energy. A beam energy measurement carried out over a 24 hour period perfectly confirmed the effects expected from a more detailed calculation of the tides. A corresponding correction can be applied to energy calibrations
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The results of beam polarization measurements performed in 1990 at the CERN Large Electron Positron storage ring (LEP) are reported. A significant asymmetry was observed in the Compton back-scattered photon distribution when illuminating the LEP electron beam with circularly polarized laser light. The corresponding polarization level is estimated to be 9.1% ± 0.3% (statistical) ± 1.8% (systematic). The validity of the polarization signal was assessed by varying the laser light polarization and by applying to the electron beam known depolarizing resonances. The measurement is consistent with the predicted polarization degree.
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DOI:https://doi.org/10.1103/PhysRevLett.19.1264
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Weak and electromagnetic interactions of the leptons are examined under the hypothesis that the weak interactions are mediated by vector bosons. With only an isotopic triplet of leptons coupled to a triplet of vector bosons (two charged decay-intermediaries and the photon) the theory possesses no partial-symmetries. Such symmetries may be established if additional vector bosons or additional leptons are introduced. Since the latter possibility yields a theory disagreeing with experiment, the simplest partially-symmetric model reproducing the observed electromagnetic and weak interactions of leptons requires the existence of at least four vector-boson fields (including the photon). Corresponding partially-conserved quantities suggest leptonic analogues to the conserved quantities associated with strong interactions: strangeness and isobaric spin.
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Within the Weinberg model mass differences between members of a multiplet generate further mass differences between the neutral and charged vector bosons. The experimental situation on the Weinberg model leads to an upper limit of about 800 GeV on mass differences within a multiplet. No limit on the average mass can be deduced.
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A transverse beam polarization of around 10% reproducibly observed in LEP in 1991. Resonant spin depolarization was performed at four occasions, from September 16 to November 11, providing measurements of the beam energy with a precision of ± 1.5 × 10−5. Several cross-checks were performed to ascertain that the observed resonance corresponds to the fundamental spin precession frequency. The variability of the results, ± 6 × 10−5, is consistent with the expected stability and reproducibility of the machine.
Measurement of the Central Frequency of LEP
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Measurement of the Central Frequency of LEP
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