Proposal to Measure Muon Anomalous Magnetic Moment

1. e Momentum Spin A proposal to measure the muon anomalous magnetic moment to 0.14 ppm precisionThe New g-2 Collaboration • Is the science compelling? • Is Fermilab the right place? • Is the experiment well designed? • Is it cost effective? D. Hertzog and L. Roberts – PAC Fermilab – March 6, 2009

2. Built on the foundation of E821, with important new strength added a @ 20 Institutions List does not include the many PDRAs and Students who will join an approved effort

3. p p g m Z m p p B Weak Had LbL Had VP Had VP QED am= (g – 2)/2 is non-zero because of virtual loops, which can be calculated very precisely Known well Theoretical work ongoing dam = 51 x 10-11 arXiv:0809.3085 Eduardo De Rafael (CPT)

4. Where we are and where we are going • Present Status: • Experimental uncertainty = 63 x 10-11 (0.54 ppm) • 0.46 ppm statistical • 0.28 ppm systematic • Theory uncertainty = 51 x 10-11 (0.44 ppm) Leads to Dam(Expt – Thy) =295 ± 81 x 10-11 3.6 s Limit was counts • Expected situation after experiment: • Experimental uncertainty: 63  16 x 10-11 • 0.1 ppm statistical  21x the E821 events • 0.1 ppm systematic overall • 0.07 ppm field  0.17  0.07 • 0.07 ppm wa0.21  0.07 • Theory uncertainty: 51  30 x 10-11 Future: Dam(Expt – Thy) =xx ± 34 x 10-11 (If xx remains 295, the deviation from zero would be close to 9s)

5. Precise knowledge of amwill aid in discrimination between a wide variety of standard model extensions • UED models (1D) typically predict “tiny” effects • Incompatible with a Dam of ~ 300 x 10-11 • SUSY models – there are many – predict am contributions of about the observed magnitude for Dam • These are rather well studied, so we will consider a few cases • The “Uninvented” – perhaps most importantly, sets a stringent experimental constraint for any new models

6. SUSY: Muon g-2 is very sensitive through loops, which are amplified by tanb Difficult to obtain at the LHC See full Topical Review: D. Stöckinger J.Phys. G34 (2007) R45-R92

7. UED The Snowmass Points and Slopes are 10 representativeSUSY models with typical parameters for MSUSY masses and tanb, etc. They serve as test points to indicate the discrimination power of experiments. Muon g-2 is a powerful discriminatorno matter where the final value lands Illustration of “resolving power” among SUSY models Present Present Future? Universal Extra Dimensions 1D Model Models SPS Definitions

8. Suppose the MSSM reference point SPS1a* is realized and parameters are determined by global fit from full LHC data • sign(m) difficult to obtain from the collider • tanbpoorly determined by collider New g-2 Old g-2 LHC (Sfitter) 2s 1s g-2 is complementary to the LHC * SPS1a is a ``Typical '' mSUGRA point with intermediate tanb = 10

9. Connection between am, EDM and the charged Lepton Flavor Violating transition moment m → e SUSY slepton mixing am(real) EDM (imaginary) m→ e

10. The keys to an improved precision experiment are: more stored muons and reduced systematic errors • Build on a proven formula • E821  studies to improve at BNL, J-PARC, or FNAL  P989 • Many studies completed, much documentation • Shovel-ready experiment • Why Fermilab is uniquely appropriate • Aligned with laboratory direction toward Intensity Frontier • For example, synergistic with Mu2e • Runs parasitically with Main-Injector neutrinos • Efficient use of facility • Proton intensity and beam structure ideal for required statistics • 1.8 x 1011 events in final fits • Reduced hadronic-induced background at injection • Long decay beamline is key to reducing many systematic errors • Increased fill frequency reduces instantaneous rate • x4 at FNAL compared to BNL

11. Double Blind Analysis The measurement involves determining 3 quantities to high precision (1) Precession frequency (2) Muon distribution (3) Magnetic field map B

12. A consistent set of measurements with a steady improvement in precision.

13. n p+ m+ 4 key elements of the g-2 measurement • Polarized muons forward decays, captured in FODO, ~97% polarized source • Precession proportional to (g-2) • Pm magic momentum = 3.094 GeV/c E field doesn’t affect muon spin when g = 29.3 • Parity violation in the decay gives average spin direction µ

14. Uses 6/20 batches* parasitic to n program Proton plan up to AP0 target is almostthe same as for Mu2e Uses the same target and lens as the present p-bar program Modified AP2 line (+ quads) New beam stub into ring Needs simple building near cryo services Polarized muons delivered and stored in the ring at the magic momentum, 3.094 GeV/c *Can use all 20 if MI program is off

15. The 900-m long decay beam reduces the pion “flash” by x20 and leads to 6 – 12 times more stored muons per proton (compared to BNL) Flash compared to BNL Stored Muons / POT

16. incoming muons Quads The Storage Ring exists and will be moved to FNAL Power supplies Quads Vacuum system Fiber harps Kickers

17. Into the ring m AP-3 stub • Beamline “stub” Design for FNAL • Open-end inflector* x2 increase in transmission • Kicker deflects beam onto orbit Improvements planned for pulse shape / magnitude Existing Proposed *This was built at one-third length, tested, but final design had closed ends

18. NA2 2.5 ns samples N A <A>=0.4 An “event” is an isolated electron above a threshold. e+

19. 2.5 ns samples An “event” is an isolated electron above a threshold. e+

20. Segmenting detectors will reduce pileup. New W-SciFi calorimeter built and tested (and published) • 20-fold segmentation for PMTs • 0.7 cm X0 • 10% resolution at 2 GeV • R&D option, 35-fold segmentation using onboard SiPM Low E High E

21. Geant simulation using new detector schemes Event Method NA2 N A <A>=0.4 Traditional method of determining wa is to plot Number vs. Time Here, Asym is the average asymmetry of events above energy threshold cut

22. Geant simulation using new detector schemes Event Method Same GEANT simulation Energy Method A complementary (integrating) method of determining wa is to plot Energy vs. Time Potential method for Project X rates

23. 1 ppm contours The magnet will be carefully shimmed and precisely mapped Measured in situ using an NMR trolley Continuously monitored using 366 fixed probes mounted above and below the storage region (Final BNL) ppm 0.05 0.09 0.05 0.07 0.10 0.17

24. g-2 budget estimate, contingencies included(assumed protons are delivered to AP0 at 15 Hz operation of booster) Relatively standard beamline elements Ring relocation NSF Nucl.+ International PROTONs g-2 & Mu2e need RF Mu2e & g-2 common

25. Technically driven schedule • 2009 • PAC presentation / Stage-1 approval • Some R&D funds made available • Year 0 • Planning / designs / technical reviews • Year 1 • Building started key driver for timeline • Modifications of proton complex • Pack and move ring and other items from BNL • Detector, electronics tests and pre-construction • Re-machine fixed probe locations on vacuum chambers • Year 2 • Install and assemble ring at FNAL • Complete modifications of beamlines related to g-2 • Special rate tests of pion / muon flux at key test points • Detector, electronics production • Year 3 • Complete ring construction and commission • Shim magnet (9 mo) • Calibrations of detectors, integrate counting room, DAQ • Year 4 • Physics commissioning • Start real data taking A fairly uniform flow of funds is required … no big “spike” for any single purchase

26. Immediate R&D tasks • Lithium lens at 18 Hz • Test lithium lens for 18 Hz operation at the reduced power for 3.1 GeV/c beam • Decay channel and stored muon simulations • Complete end-to-end beam simulation to make the most complete and cost-effective choices for • Optimization of the beam focus on the target and Li lens optics • Addition of quads for AP2 beam line and transport efficiency thru AP-3 • Design of beamline stub into ring • Storage ring acceptance versus kicker performance • Half-length kicker plate test • Reduced inductance is key to shorter pulse of greater magnitude; carry out test with a half-length kicker in lab on existing setup • Fixed probe re-positioning • Re-optimize fixed probe locations to increase the number of working fixed probes • Large-scale W/SciFi prototype with SiPM readout • Full-scale prototype; PMT and SiPM readout. • In-vacuum straw chambers for EDM and traceback • A test setup is underway now at FNAL to investigate this concept.

27. Summary • Unique physics opportunity with decades-long track record of being important and influential to our field, including > 1400 citations (170 in 2008) • Will provide important constraints on the interpretation of any new physics found at the LHC or elsewhere • Window of opportunity after Tevatron completion and before the major Mu2e and DUSEL projects take center stage – Our request is 4 x 1020 POT • Great return on investment, given the impact and the natural alignment with FNAL’s future

28. Possible topics for further discussion • Theory • Current / future status of Hadronic Vacuum Polarization • Current / future status Hadronic Light-by-Light • What are the SPS points? • CMSSM Constraints? • Show us more about the Sfitter results w/wo g-2 • How general is the UED “tiny effects” prediction? • Technique • More on a parasitic EDM measurement • wa systematic errors • Why a longer beamline? • What drives the detector choice? • Magnetic field shimming and monitoring • What was used to calculate the beamline rate? • How was the event rate obtained? • What is involved in moving the ring? • Other • More on yellow “proton complex” budget box • What about JPARC? D. Hertzog and L. Roberts – PAC Fermilab – March 6, 2009

29. Back error2 (from F. Jegerlehner) contribution Analyticity and the optical theorem: • Future efforts will reduce errors • Additional KLOE data (in hand, near term) • CMD3 at VEPP2000, up to 2.0 GeV (next 5 years) • perhaps Belle

30. Back |Fp |2 from KLOE, CMD2 and SND agree well weighted contribution recall that:

31. Back Suppose the hadronic contribution increased to remove the difference? • A similar dispersion integral enters elsewhere • Increasing s (s) to remove the (g-2) difference lowers the Higgs mass limit PRD 78, 013009 (2008) • This cross section is important for am and for any precision EW physics. • Future work continues in Frascati and Novosibirsk. Belle is also beginning to explore this possibility.

32. Back arXiv:0901.0306v1 Note, with Dam = 295 x 10-11 … If HLBL is the source of the difference with SM, it would need to increase by 11 s .... Dynamical models with QCD behavior

33. Back The p0 (Goldstone) contribution fixes sign of the contribution From cpt and large Nc QCD • The magnitude of the HLBL is about the same as the magnitude of the 3-loop HVP which can be calculated from the dispersion relation. • It’s hard to believe that the HLBL would be huge compared to the other 3-loop contributions. Examples of other 3-loop hadronic contributions:

34. Back How general is the UED “tiny effects” prediction? • UED models (1D) typically predict “tiny” effects • Incompatible with a Dam of ~ 300 x 10-11 The statement refers to the UED models originally proposed and studied by Appelquist, Cheng, and Dobrescu, and also by Rizzo in 2000/2001. The results for g-2 in the UED models with one extra dimension is (according to these references) below 50 x 10-11 as written in our proposal. While there might be modified UED models with larger contributions to g-2, this again demonstrates that g-2 is very powerful tool to discriminate between different new physics models. (D. Stockinger)

35. Back Sfitter LHC global fit (Alexander, Kreiss, Lafaye, Plehn, Rauch, Zerwas; Les Houches 2007, Physics at TeV Colliders) Confirmation of tanbeta measurement by comprehensive global fit. Improvement of tanbeta-error with current g-2: 4.5 -> 2.0 estimated improvement with future g-2: 4.5 -> 1.0 Result for the general MSSM parameter determination at the LHC in SPS1a. Flat theory errors (non-gaussian) are assumed. The fit is done with and without inclusion of the current measurement of g-2. With g-2, many are improved, some significantly

36. Back SPS points and slopes • SPS 1a: ``Typical '' mSUGRA point with intermediate value of tan_beta. • SPS 1b: ``Typical '' mSUGRA point with relatively high tan_beta; tau-rich neutralino and chargino decays. • SPS 2: ``Focus point '' scenario in mSUGRA; relatively heavy squarks and sleptons, charginos and neutralinos are fairly light; the gluino is lighter than the squarks • SPS 3: mSUGRA scenario with model line into ``co-annihilation region''; very small slepton-neutralino mass difference • SPS 4: mSUGRA scenario with large tan_beta; the couplings of A, H to b quarks and taus as well as the coupling of the charged Higgs to top and bottom are significantly enhanced in this scenario, resulting in particular in large associated production cross sections for the heavy Higgs bosons • SPS 5: mSUGRA scenario with relatively light scalar top quark; relatively low tan_beta • SPS 6: mSUGRA-like scenario with non-unified gaugino masses • SPS 7: GMSB scenario with stau NLSP • SPS 8: GMSB scenario with neutralino NLSP • SPS 9: AMSB scenario SPS PLOT www.ippp.dur.ac.uk/~georg/sps/sps.html

37. Parasitic Muon EDM Measurement using straw tube arrays Back arXiv:0811.1207v1 The EDM tips the precession plane, producing an up-down oscillation with time (out of phase with wa) E821 straw-tube array Measure upward-going vs. downward-going decay electrons vs. time with straw tube arrays

38. Back E821 Data:up-going/down-going tracks vs. time, (modulo the g-2 frequency): • BNL traceback measurement was entirely statistics limited • 1 station • Late turn-on time • Small acceptance • Ran 2 out of 3 years EDM (g-2) EDM Signal: Average vertical angle modulo g-2 period. Out-of-phase by 90° from g-2; this is the EDM signal (g-2) signal: # Tracks vs time, modulo g-2 period, in phase.

39. Back The new idea imagines in-vacuum straws, matched with out-of-vacuum pre-calorimeter straws (used also for shower impact) Out-of-vacuum straws / impact detector We are already studying at FNAL, in-vacuum straw chambers for “traceback” systems on many of the stations, which will serve as EDM measurement stations as well

40. Back How was event rate obtained? Proton complex parameters and plans Compared to achieved BNL stored muon per proton rate and detailed factors for beamline differences Monte Carlo and simple calculations This is the key factor. We have calculated 11.5 so far, so we have included a “100% contingency” in estimating the beam time request to allow for something to go wrong. MARS15 model of target, beamline simulation to capture / decay pions

41. Back The Precision Field: Systematic errors • Why is the error 0.11 ppm? • That’s with existing knowledge and experience • with R&D defined in proposal, it will get better Next (g-2)

42. Back wa Systematic Error Summary

43. Back What drives the detector choice? • Compact based on fixed space • Non-magnetic to avoid field perturbations • Resolution is not critical for dwa • Useful for pileup & gain monitoring • E821 “8%”; We propose 10% for tungsten-based calorimeter • Pileup depends on signal speed and shower separation • 4/5 events separated was goal • GEANT sim work in good shape Many more details and studies available. See also,

44. Back Conceptual idea for Si-PM readout of W/SciFi modules 3 cm Si PM Array Winston cone Bundle fibers W / SciFi Block

45. Back Benefits of a longer beamline • Reduced pions • Permits “forward” decays • Collects “all” muons • Eliminates “lost muon” systematic from muons born just prior to the ring

46. Back Ring relocation • Heavy-lift helicopters bring coils to a barge • Rest of magnet is a “kit” that can be trucked to and from the barge

47. Back The “yellow” budget box is related to accelerator improvements for the intensity frontier in general • Recycler Ring RF • For g-2: makes 4 mini bunches out of each Booster injection. Each is then extracted for g-2 as a whole to strike the target and create a pion/muon bunch • With value engineering, this cost could go down Assumed done see below Must do for Mu2e, g-2 and any other expt. Extraction Recycler to P1

48. Back P5 suggested we “determine the optimal path toward a next generation experiment” by examining JPARC and FNAL • Feb. 2008 • Technical note sent to P5 by collaboration outlining generic comparisons (and some rough cost considerations) • June 2008 • 2-day, joint Japan / US collaboration meeting held to examine technical possibilities at three labs (BNL, FNAL, JPARC). • Conclusions • It is challenging to stage the “magic g” experiment at JPARC. Real estate exists only for a short backward decay beamline. • Need bunch splitting to achieve h = 90 to reduce pileup • J-PARC regulations for cryogenics (probably) prohibit SC coil design from E821 to be used. Coils would have to be rebuilt at J-PARC • Single user mode only • Current thoughts for JPARC • Use of low-momentum (non-magic g) ring being explored with muons from 3-GeV Booster. The idea is in its infancy. • Possible future focus on small ring dedicated EDM effort

49. Back 1 2 3 4 11 ms 66 ms of a “batch” Beamline study – simplified • Up to proton batch in Recycler, same as Mu2e • RF in Recycler divides batch into 4 bunches of 1012 p/bunch • Pion production on existing target done with MARS15 • Acceptance computed into AP-2 line using OptiM • Pi-to-Mu calculation and captured muons simulated with Decay Turtle for various scenarios of quad lattice spacing • The rest of the study is based on a detailed comparison to BNL where hard numbers exist and ratios are well understood MARS15 OptiM

50. Back Typical CMSSM 2D space showing g-2 effect(note: NOT an exclusion plot) Present: Dam = 295 ± 88 x 10-11 Here, neutralino accounts for the WMAP implied dark matter density scalar mass 2s Excluded for neutral dark matter gaugino mass This CMSSM calculation: Ellis, Olive, Santoso, Spanos. Plot update: K. Olive Topical Review: D. Stöckinger hep-ph/0609168v1