The MOLLER experiment will measure the weak charge of the electron, $Q^e_W =
1 - 4\sin^2\theta_W$, with a precision of 2.3% by measuring the
parity-violating asymmetry in electron-electron (M\oller) scattering. This
measurement will provide an ultra-precise measurement of the weak mixing angle,
$\sin^2\theta_W$, which is on par with the two most precise collider
measurements at the Z$^0$-pole. The precision of the experiment, with a
fractional accuracy in the determination of $\sin^2\theta_W$ $\approx 0.1$%,
makes it a probe of physics beyond the Standard Model with sensitivities to
mass scales of new physics up to 7.5 TeV.Comment: Proceedings from PAVI 11 to be published in Nuovo Cimento 

Mammei, Juliette

English

arXiv

The MOLLER experiment will measure the weak charge of the

electron, QeW = 1 − 4 sin2 θW, with a precision of 2.3% by measuring the parityviolating asymmetry in electron-electron (Møller) scattering. This measurement will

provide an ultra-precise measurement of the weak mixing angle, sin2 θW, which is on par with the two most precise collider measurements at the Z0-pole. The precision of the experiment, with a fractional accuracy in the determination of sin2 θW ≈ 0.1%, makes it a probe of physics beyond the Standard Model with sensitivities to mass scales of new physics up to 7.5TeV

Mammei, J.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2012-11284-7Colloquia: PAVI11IL NUOVO CIMENTO Vol. 35 C, N. 4 Luglio-Agosto 2012The MOLLER experimentJ. Mammei for the MOLLER CollaborationUniversity of Massachusetts, Amherst - Massachusetts, USAricevuto il 14 Ottobre 2011; approvato il 5 Maggio 2012pubblicato online il 3 Luglio 2012Summary. — The MOLLER experiment will measure the weak charge of theelectron, QeW = 1 − 4 sin2 θW , with a precision of 2.3% by measuring the parity-violating asymmetry in electron-electron (Møller) scattering. This measurement willprovide an ultra-precise measurement of the weak mixing angle, sin2 θW , which is onpar with the two most precise collider measurements at the Z0-pole. The precision ofthe experiment, with a fractional accuracy in the determination of sin2 θW ≈ 0.1%,makes it a probe of physics beyond the Standard Model with sensitivities to massscales of new physics up to 7.5TeV.PACS 12.15.-y – Electroweak interactions.PACS 12.15.Mm – Neutral currents.PACS 11.30.Er – Charge conjugation, parity, time reversal, and other discretesymmetries.1. – IntroductionThe Standard Model (SM) summarizes our knowledge of fundamental particles andtheir interactions. Polarized electron scattering off unpolarized targets provides a cleanwindow to study weak neutral current interactions by measuring the parity-violatingasymmetry, APV . The MOLLER experiment will test the SM prediction of the weakmixing angle, sin2 θW , by measuring APV in polarized electron scattering from atomicelectrons (Møller scattering). The APV is defined byAPV =σR − σLσR + σL,(1)where σR (σL) is the scattering cross section of incident right- (left-) handed electrons.At four-momentum transfers much smaller than the mass of the Z0 boson, Q2  M2Z ,APV is dominated by the interference between photon and Z0 boson exchange [1]. Theleading order Feynman diagrams relevant for Møller scattering, which involve both directc© Societa` Italiana di Fisica 203204 J. MAMMEI for the MOLLER COLLABORATIONe−e− e−e− e−e− e−e−Ze−e− e−e−Ze−e−e−e−Fig. 1. – Feynman diagrams for Møller scattering at tree level (reproduced from ref. [3]).and exchange diagrams that interfere with each other, are shown in fig. 1. The resultingasymmetry is given by [2]APV = mEGF√2πα4 sin2 θ(3 + cos2 θ)2QeW = mEGF√2πα2y(1− y)1 + y4 + (1− y)4QeW ,(2)where α is the fine structure constant, GF the Fermi constant, E the incident beamenergy, m the electron mass, θ the scattering angle in the center of mass frame, andy ≡ 1−E′/E, where E′ is the energy of one of the scattered electrons.Within the SM the weak charge of the electron, QeW , is proportional to the prod-uct of the electron’s vector and axial-vector couplings to the Z0 boson, and the weakneutral current amplitudes are functions of the weak mixing angle sin2 θW . The worldaverage of the two most precise independent determinations of sin2 θW is consistent withother electroweak measurements and constraints on the Higgs boson mass MH , but themeasurements actually differ by over 3 standard deviations. Choosing one or the othercentral value ruins this consistency and implies very different new high-energy dynam-ics. We propose to measure sin2 θW to a sensitivity of δ(sin2 θW ) = ±0.00029, the onlymethod available in the next decade to directly address this issue at the same level ofprecision and interpretability.MOLLER will also be the most sensitive probe of new flavor and CP-conservingneutral current interactions in the leptonic sector, sensitive to interaction amplitudes assmall as 1.5× 10−3 times the Fermi constant. New neutral current interactions are bestparameterized model-independently at low energies by effective four-fermion interactions.Focusing on vector and axial-vector interactions between electrons and/or positrons, suchan interaction Lagrangian takes the form [4]Le1e2 =∑i,j=L,Rg2ij2Λ2e¯iγμeie¯jγμej ,(3)where eL/R = 12 (1 ∓ γ5)ψe are the usual chirality projections of the electron spinor, Λthe mass scale of the new contact interaction and gij = g∗ij coupling constants, withgRL = gLR. For the proposed measurement with 2.3% total uncertainty (and no ad-ditional theoretical uncertainty) the resulting sensitivity to new four-electron contactinteraction amplitudes g2RR − g2LL is ∼ 7.5TeV. The proposed measurement will greatlyextend the current sensitivity of four-electron contact interactions, both qualitatively andquantitatively, and is complementary to direct searches.It is straightforward to examine the reach MOLLER will have in specific models (themass scale depends on the size of the coupling) [5]. As a specific example, a comprehensiveanalysis of the MOLLER sensitivity to TeV-scale Z ′ bosons has recently been carriedout [6] for a large class of models contained in the E6 gauge group, where Z ′ bosons withthe same electroweak charges as SM particles are motivated because they arise in manyTHE MOLLER EXPERIMENT 205Fig. 2. – 90% C.L. exclusion regions for a 1.2TeV Z′ from the E6 gauge group for E158, andassuming future experiments measure the SM value.superstring models as well as from a bottom-up approach [7]. These models are spannedby two parameters α and β in the range ±π/2. α = 0 corresponds to the E6 modelsconsidered for example in ref. [8], while α = 0 can be interpreted as non-vanishing kineticmixing, assuming that this kinetic mixing has been undone by field re-definitions. β = 0correspond to SO(10) models, which include models based on left-right symmetry.The MOLLER reach for a 1.2TeV Z ′ from this model class, assuming the valuepredicted by the SM is measured, is shown in fig. 2, while fig. 3 shows the allowableregion assuming MOLLER instead measures a value half-way between the SM value andthe E158 central value. The current region excluded by E158 is shown in both figures inyellow. Thus, the combination of potential MOLLER and LHC anomalies would pointto a small list of Z ′ models, whose effects on other precision electroweak observables canthen be further explored at LHC and elsewhere.However, if MOLLER measures a central value consistent with E158, then a clearviolation of the SM would be established at more than 5σ. We note that no Z ′ from theabove mentioned model class could explain such a MOLLER deviation.Fig. 3. – 90% C.L. exclusion regions for a 1.2TeV Z′ from the E6 gauge group for E158, andassuming the MOLLER value is half-way between E158 and the SM.206 J. MAMMEI for the MOLLER COLLABORATIONFig. 4. – CAD model of the conceptual layout of the experiment, looking upstream. The targetchamber is located in the upper left, then the upstream and hybrid toroids, Roman pots forthe tracking detectors, and the main detector stand, with background detectors at the fardownstream end in the lower right.2. – Experimental overviewThe MOLLER experiment will run in Hall A at Jefferson Laboratory, making use ofthe 11GeV longitudinally polarized (∼ 85%) electron beam, generated via photoemissionon a GaAs photocathode by circularly polarized laser light. The target is a 1.5m liquidhydrogen target capable of dissipating 5 kW of beam power. Møller electrons in the fullrange of the azimuth (achieved by using an odd number of coils and identical particlescattering) and polar angles 5mrad < θlab < 17mrad, will be separated from backgroundand focused ∼ 30m downstream of the target by a spectrometer system consisting of apair of toroidal magnet assemblies and precision collimators (fig. 4). The upstreammagnet is a traditional resistive toroidal magnet, while the downstream magnet has anovel shape designed to focus the large range of scattered electron angles and energies.The Møller electrons will be incident on a system of quartz detectors in which theresulting Cherenkov light will provide a relative measure of the scattered flux. Rapid po-larization (helicity) reversal of the electrons will be used to suppress spurious systematiceffects. APV will be extracted from the fractional difference in the integrated Cherenkovlight response between helicity reversals. Additional systematic suppression below thepart-per-billion (ppb) level will be accomplished by periodically reversing the sign ofthe physics asymmetry. We plan to introduce this “slow helicity reversal” with threeindependent methods: the introduction of an additional half-cycle g − 2 rotation to theelectrons in the recirculating arcs of the accelerator, the use of an insertable half-waveplate in the injector, and a full flip of the beam polarization direction with the aid of twoWien rotators and a solenoid lens (the “Double Wien”).Simultaneously with data collection, fluctuations in the electron beam energy andtrajectory and their potential systematic effects on APV will be precisely monitored,active feedback loops will minimize beam helicity correlations, and detector responseto beam fluctuations will be continuously calibrated. Background fractions and theirhelicity-correlated asymmetries will be measured by dedicated auxiliary detectors. Theabsolute value of Q2 will be calibrated using tracking detectors. The electron beamTHE MOLLER EXPERIMENT 207Table I. – Summary of projected fractional systematic errors on the measurement of QeW . Thefractional statistical error is 2.1%.Error Source Fractional Error (%)absolute value of Q2 0.5beam (second order) 0.4beam polarization 0.4e + p(+γ)→ e + X(+γ) 0.4beam (position, angle, energy) 0.4beam (intensity) 0.3e + p(+γ)→ e + p(+γ) 0.3γ(∗) + p→ π + X 0.3transverse polarization 0.2neutrals (soft photons, neutrons) 0.1Total systematic 1.1polarization will be measured continuously by two independent polarimeter systems.The predicted value of APV for the proposed experimental design is ∼ 35 ppb and ourgoal is to measure this quantity with a precision of 0.73 ppb. We tabulate our estimatesof the most important systematic errors in table I.3. – Experiment status and plansWe are proposing to take data in three separate run periods to ensure that importanttechnical milestones are met and that each run will provide publishable results that willsignificantly add to our knowledge of electroweak physics to date. While the MOLLERapparatus is being designed for a beam current of 85μA at 11GeV, we have assumed abeam current of 75μA and a beam polarization of 80% in formulating the run plan. Ifhigher beam current and/or higher beam polarization are considered routine, the amountof time needed to run could correspondingly be reduced using the appropriate P 2I factor.In order to estimate the time needed to reach the desired statistical accuracy it isnecessary to take into account both the overall efficiency and how close one can ap-proach counting statistics in an instantaneous raw asymmetry measurement. The overallefficiency depends on the efficiency of the apparatus itself and the accelerator efficiency,which we estimate as 90% and 70% respectively, for an overall efficiency of 60%. At960Hz, the width of the measured asymmetry per pulse pair, σ(Ai), is 83 ppm, butthis width depends on the sources of additional fluctuations. However, we are unlikely toachieve the best efficiency or asymmetry width at first, so we assumed total efficiencies of40, 50 and 60%, respectively, and asymmetry widths of 100, 95 and 90 ppm, respectively,for the three running periods. This leads to run periods of 11, 30 and 60 weeks (includingcommissioning) with expected statistical errors of 11%, 4.0% and 2.4%, respectively.MOLLER is a fourth generation parity-violation experiment at Jefferson Laboratory.Apart from the obvious challenge of measuring a raw asymmetry with a statistical errorless than 1 ppb, an equally challenging task is to calibrate and monitor the absolutenormalization of APV at the sub-1% level. The collaboration continues to gain extensive208 J. MAMMEI for the MOLLER COLLABORATIONexperience on all aspects of such measurements as work continues on executing the thirdgeneration experiments PREX [9] and Qweak [10]. Simulation and design of the variousaspects of MOLLER are ongoing, and is expected to take two to three years. Work is alsobeing done to improve beam transport and instrumentation. In addition, upgrades to theCompton and Møller polarimeters are being planned. It is envisioned that constructionand assembly will take three years, to be followed by three data collection periods withprogressively improved statistical errors and systematic control over a subsequent threeto four year period.∗ ∗ ∗Thanks to the organizers for a wonderful meeting. This work is funded in part by USDepartment of Energy Grant No. DE-FG02-88R40415-A018.REFERENCES[1] Zel’dovich Ya. B., Sov. Phys. JETP, 94 (1959) 262.[2] Derman E. and Marciano W. J., Ann. Phys. (N.Y.), 121 (1979) 147.[3] Czarnecki A. and Marciano W. J., Int. J. Mod. Phys. A, 15 (2000) 2365.[4] Eichten E., Lane K. D. and Peskin M. E., Phys. Rev. Lett., 50 (1983) 811.[5] Ramsey-Musolf M. J., Phys. Rev. C, 60 (1999) 015501.[6] Erler J. and Rojas E., private communication.[7] Erler J., Nucl. Phys. B, 586 (2000) 73.[8] Chang W. F., Ng J. N. and Wu J. M. S., Phys. Rev. D, 79 (2009) 055016.[9] Kumar K., Michaels R., Souder P. and Urciuoli G., The Lead Radius ExperimentPREX, E06-002, http://hallaweb.jlab.org/parity/prex/.[10] Carlini R., The Qweak Experiment, http://www.jlab.org/Hall-C/Qweak/index.html.

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