Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB) complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

MOONLIGHT: A NEW LUNAR LASER RANGING RETROREFLECTOR AND THE LUNAR GEODETIC PRECESSION

Since the 1970s Lunar Laser Ranging (LLR) to the Apollo Cube Corner Retroreflector (CCR) arrays (developed by the University of Maryland, UMD) supplied almost all significant tests of General Relativity (Alley et al., 1970; Chang et al., 1971; Bender et al.,1973): possible changes in the gravitational constant, gravitational self-energy, weak equivalence principle, geodetic precession, inverse-square force-law. The LNF group, in fact, has just completed a new measurement of the lunar geodetic precession with Apollo array, with accuracy of 9 × 10−3, comparable to the best measurement to date. LLR has also provided significant information on the composition and origin of the moon. This is the only Apollo experiment still in operation. In the 1970s Apollo LLR arrays contributed a negligible fraction of the ranging error budget. Since the ranging capabilities of ground stations improved by more than two orders of magnitude, now, because of the lunar librations, Apollo CCR arrays dominate the error budget. With the project MoonLIGHT (Moon Laser Instrumentation for General relativity High-accuracy Tests), in 2006 INFN-LNF joined UMD in the development and test of a new-generation LLR payload made by a single, large CCR (100mm diameter) unaffected by the effect of librations. With MoonLIGHT CCRs the accuracy of the measurement of the lunar geodetic precession can be improved up to a factor 100 compared to Apollo arrays. From a technological point of view, INFN-LNF built and is operating a new experimental apparatus (Satellite/lunar laser ranging Characterization Facility, SCF) and created a new industry-standard test procedure (SCF-Test) to characterize and model the detailed thermal behavior and the optical performance of CCRs in accurately laboratory-simulated space conditions, for industrial and scientific applications. Our key experimental innovation is the concurrent measurement and modeling of the optical Far Field Diffraction Pattern (FFDP) and the temperature distribution of retroreflector payloads under thermal conditions produced with a close-match solar simulator. The apparatus includes infrared cameras for non-invasive thermometry, thermal control and real-time payload movement to simulate satellite orientation on orbit with respect to solar illumination and laser interrogation beams. These capabilities provide: unique pre-launch performance validation of the space segment of LLR/SLR (Satellite Laser Ranging); retroreflector design optimization to maximize ranging efficiency and signal-to-noise conditions in daylight. Results of the SCF-Test of our CCR payload will be presented. Negotiations are underway to propose our payload and SCF-Test services for precision gravity and lunar science measurements with next robotic lunar landing missions. In particular, a scientific collaboration agreement was signed on Jan. 30, 2012, by D. Currie, S. Dell’Agnello and the Japanese PI team of the LLR instrument of the proposed SELENE-2 mission by JAXA (Registered with INFN Protocol n. 0000242-03/Feb/2012). The agreement foresees that, under no exchange of funds, the Japanese single, large, hollow LLR reflector will be SCF-Tested and that MoonLIGHT will be considered as backup instrument

Inclusive Search for Anomalous Production of High-pT Like-Sign Lepton Pairs in Proton-Antiproton Collisions at sqrt{s}=1.8 TeV

We report on a search for anomalous production of events with at least two charged, isolated, like-sign leptons with pT > 11 GeV/c using a 107 pb^-1 sample of 1.8 TeV ppbar collisions collected by the CDF detector. We define a signal region containing low background from Standard Model processes. To avoid bias, we fix the final cuts before examining the event yield in the signal region using control regions to test the Monte Carlo predictions. We observe no events in the signal region, consistent with an expectation of 0.63^(+0.84)_(-0.07) events. We present 95% confidence level limits on new physics processes in both a signature-based context as well as within a representative minimal supergravity (tanbeta = 3) model.Comment: 15 pages, 4 figures. Minor textual changes, cosmetic improvements to figures and updated and expanded reference

Search for the Supersymmetric Partner of the Top-Quark in ppˉp \bar{p} Collisions at s=1.8TeV\sqrt{s} = 1.8 {\rm TeV}

We report on a search for the supersymmetric partner of the top quark (stop) produced in $t \bar{t}$ events using $110 {\rm pb}^{-1}$ of $p \bar{p}$ collisions at $\sqrt{s} = 1.8 {\rm TeV}$ recorded with the Collider Detector at Fermilab. In the case of a light stop squark, the decay of the top quark into stop plus the lightest supersymmetric particle (LSP) could have a significant branching ratio. The observed events are consistent with Standard Model $t \bar{t}$ production and decay. Hence, we set limits on the branching ratio of the top quark decaying into stop plus LSP, excluding branching ratios above 45% for a LSP mass up to 40 {\rm GeV/c}$^{2}$.Comment: 11 pages, 4 figure

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s}=1.96 TeV using Lepton + Jets Events with Secondary Vertex b-tagging

We present a measurement of the ttbar production cross section using events with one charged lepton and jets from ppbar collisions at a center-of-mass energy of 1.96 TeV. In these events, heavy flavor quarks from top quark decay are identified with a secondary vertex tagging algorithm. From 162 pb-1 of data collected by the Collider Detector at Fermilab, a total of 48 candidate events are selected, where 13.5 +- 1.8 events are expected from background contributions. We measure a ttbar production cross section of 5.6^{+1.2}_{-1.1} (stat.) ^{+0.9}_{0.6} (syst.) pb.Comment: 28 pages, 20 figures. Published in Physical Review

Search for Narrow Diphoton Resonances and for gamma-gamma+W/Z Signatures in p\bar p Collisions at sqrt(s)=1.8 TeV

We present results of searches for diphoton resonances produced both inclusively and also in association with a vector boson (W or Z) using 100 pb^{-1} of p\bar p collisions using the CDF detector. We set upper limits on the product of cross section times branching ratio for both p\bar p\to\gamma\gamma + X and p\bar p\to\gamma\gamma + W/Z. Comparing the inclusive production to the expectations from heavy sgoldstinos we derive limits on the supersymmetry-breaking scale sqrt{F} in the TeV range, depending on the sgoldstino mass and the choice of other parameters. Also, using a NLO prediction for the associated production of a Higgs boson with a W or Z boson, we set an upper limit on the branching ratio for H\to\gamma\gamma. Finally, we set a lower limit on the mass of a `bosophilic' Higgs boson (e.g. one which couples only to \gamma, W, and Z$ bosons with standard model couplings) of 82 GeV/c^2 at 95% confidence level.Comment: 30 pages, 11 figure

Measurement of the ttˉproductioncrosssectionint\bar{t} production cross section in p\bar{p}collisionsat collisions at \sqrt{s}$ = 1.8 TeV

We update the measurement of the top production cross section using the CDF detector at the Fermilab Tevatron. This measurement uses $t\bar{t}$ decays to the final states $e+\nu$+jets and $\mu+\nu$+jets. We search for $b$ quarks from $t$ decays via secondary-vertex identification or the identification of semileptonic decays of the $b$ and cascade $c$ quarks. The background to the $t\bar{t}$ production is determined primarily through a Monte Carlo simulation. However, we calibrate the simulation and evaluate its uncertainty using several independent data samples. For a top mass of 175 $GeV/c^2$, we measure $\sigma_{t\bar{t}}=5.1 \pm 1.5$ pb and $\sigma_{t\bar{t}}=9.2 \pm 4.3$ pb using the secondary vertex and the lepton tagging algorithms, respectively. Finally, we combine these results with those from other $t\bar{t}$ decay channels and obtain $\sigma_{t\bar{t}} = 6.5^{+1.7}_{-1.4}$ pb.Comment: The manuscript consists of 130 pages, 35 figures and 42 tables in RevTex. The manuscript is submitted to Physical Review D. Fixed typo in author lis