Part I: Muon g-2 theory update / motivation Part II: Possibilities for FNAL experiment at 0.1 ppm

1. Part I: Muon g-2 theory update / motivationPart II: Possibilities for FNAL experiment at 0.1 ppm David Hertzog University of Illinois at Urbana-Champaign • The theory situation • Stronger motivation now compared to 2004 • The basic experimental requirements • The BNL plan • The (exciting) possibilities for moving g-2 to FNAL • Bill’s questions … briefly 2nd Project X Workshop / Jan 25, 2008

2. UED Here is an example, related to g-2 SUSY SUSY Extra Dimensions The future am measurement will separate the two models by more than 7 standard deviations and thus allow for a clear decision in favor of one of them We are all here because of the following argument • LHC: direct search for new particles • But, what new physics will they reveal? • Precision measurements: • Lepton flavor violation • Electric dipole moments • Rare decays • Unitarity tests • Muon g-2 Consider a post-LHC world with many new mass states found

3. e Momentum Spin Final report: Bennett et al, PRD 73, 072003 (2006) Basic Muon g-2

4. The BNL Storage Ring

5. wa 1 ppm contours Muon g-2 is determined by a ratio of two precision measurements:waand B(and some knowledge of the muon orbit) B

6. TIME Compare K. Hagiwara, A.D. Martin, Daisuke Nomura, T. Teubner Arguably, strongest experimental evidence of Physics Beyond Standard Model The Standard Model theory has improved in the last year and will continue to sharpen. • Key points: • Theory: 0.48 ppm • Experimental 0.54 ppm • Dam(expt-thy) = (295±88) x 10-11 (3.4 s) Rep.Prog.Phys. 70, 795 (2007).

7. p p g m Z m p p B Weak Had LbL Had VP Had VP QED 2006 plot KEY REGION g ≠ 2 because of virtual loops, many of which can be calculated very precisely

8. g m Z m p p p p B Weak Had LbL Had LbL QED Had VP Had VP g ≠ 2 because of virtual loops, many of which can be calculated very precisely • Hadronic Light by Light has a 36% relative uncertainty !! ~ 0.34 ppm • Leading contribution must be positive • But, then we need a hadronic model • Many constraints, but can we achieve 15% relative error ? • New efforts include • A Dyson-Schwinger calculation • Two independent lattice efforts

9. New physics enters through loops … e.g., SUSY R-parity conserving Supersymmetry (vertices have pairs) And the diagrams are amplified by powers of tanb(here linearly)

10. Sidebar: There are LOTs of “SUSYs” • General MSSM has > 100 free parameters. • Advantage: Well, we don’t know them  open minded. • Disadvantage: Not predictive, but experiments can “restrict” parts of this multi-dimensional space • Beware of claims of “Ruling Out SUSY” ! • CMSSM – “constrained” and, related but even more constrained, MSUGRA, … and others • These models assume many degeneracies in masses and couplings in order to restrict parameters. • Typically: m0, m1/2, sgn(m), tanb, A (or even fewer) • Then there is R parity – is sparticle number conserved? • And, many ways to describe EW symmetry breaking Note: in some plots that follow, we use an improvement in Experiment and Theory, which reduces the present uncertainty in Dam from 88 to 39 in 10-11 units. For a “legacy” effort, it will be somewhat smaller.

11. Consider the physics message carried by Dam(expt – thy) ~ 300 x 10-11 at present (E821: 88 x 10-11 ) and future (E969: 39 x 10-11 ) uncertainties in Dam Example 1: MSSM general parameter scan

12. The Snowmass Points and Slopes is an attempt to assemble some reasonable SUSY benchmark tests.Muon g-2, like other precision measurements, has powerful discriminating input 10-11 units Compare to present Dam =295 293 318 16.5 135 490 86 169 237 173 -90 Compare uncertainty to dDam ~ ±35 *Snowmass Points and Slopes: http://www.ippp.dur.ac.uk/~georg/sps/sps.html

13. Suppose the MSSM reference point SPS1a* is realized and parameters determined by global fit (from LHC results) • sgn(m) can’t be obtained from the collider • tanbcan’t be pinned down by collider With these SUSY parameters, LHC gets tan b of 10.22 ± 9.1. Tan b “blue band” plot based on present aμ. Possible future “blue band” plot, where tan β is determined from aμ to < 20% or better D. Stockinger * SPS1a is a ``Typical '' mSUGRA point with intermediate tanb = 10 *Snowmass Points and Slopes: http://www.ippp.dur.ac.uk/~georg/sps/sps.html

14. Typical CMSSM 2D space showing g-2 effect(note: NOT an exclusion plot) Future Dam = 295 ± 39 x 10-11 Present: Dam = 295 ± 88 x 10-11 Here, neutralino accounts for the WMAP implied dark matter density scalar mass 2s 1s Excluded for neutral dark matter gaugino mass With new experimental and theoretical precision and same Dam This CMSSM calculation: Ellis, Olive, Santoso, Spanos. Plot update: K. Olive Topical Review: D. Stöckinger hep-ph/0609168v1

15. Experimental Issues E821 final error: ± 0.48 ppm statistical ± 0.27 ppm systematic Discussion: Three Phases for FNAL implementation • Phase 1: m+ measurement to 0.1 ppm statistical • Requires Nova type upgrades, beam manipulations and ~4x1020 p • Can do in pre Project X era • Phase 2: m- measurement to 0.1 ppm (or lower) • Requires many more protons due to xsection for p- • Would benefit from Project X • Phase 3: All “integrating” with much higher proton beam and restricted storage ring acceptance to lower systematics • Requires Project X

16. E821 used a “forward” decay beam, with pp 1.7% above pmagic to provide a separation at K3/K4 Pions @ 3.115 GeV/c Decay muons @ 3.094 GeV/c About 40% decay Flux down by momentum mismatch (~ 2 – 4) DP/P of ps tiny due to bkg FODO transmission not optimized Inflector ends scatter ms Near side Far side

17. incoming muons Quads Superconducting storage ring with quads, kicker, etc.

18. Muon Pre-Accumulator Ring MuPAR can get up 15 – 20 times more beam (on paper) At BNL, here is the current working plan Part of Original Proposal Open inflector Quad doubling Segmented detectors Improve kicker

19. Catch most muons in first 2 turns. Although spin precesses, it’s okay Rest of turns just reduce pions by decay time Figure of Merit NP2 increased by factor of ~12 or more Fast “Switcher” magnets required p/m Fluxes and Figure of Merit p/m m p 0 1 2 3 4 5 6 7 8 Number of turns in racetrack MAR: Muon Accumulator Ring – the BNL idea

20. For FNAL, we’d like a single long beamline and a shot rate of > 50 bunches / sec with width ~25 ns Removed pions Got muons Ideal…

21. Booster-era Beam Transfer Scheme Ankenbrandt and Popovic, Fermilab m->e g-2 Rare Kaon Decays m Test Facility Alternative ? Question: Is Decay line “too short” ? 21

22. Bill’s marching orders … • Make these experiments a compelling part of Fermilab future from physics point of view • • Demonstrate power of doing it at Fermilab • Clear advantages from beam bunch deliver perspective and running of high-intensity protons (they do not exist at BNL anymore without ~12 M upgrades to AGS. The multi-bunching at BNL is only an idea. The “more muons” requires a new ring and kickers to be competitive with FNAL. • • Demonstrate realistic scenario for making it work • No showstoppers identified nor any “tricky” bits • • Demonstrate a scaling strategy • Pre-x era: Can do a 40 week run to 0.1 ppm • Post-X era: Can do negatives and an “all integrating” effort • See next picture

23. Geant simulation using new detector schemes Event Method Same GEANT simulation Energy Method A complementary method of determining wa is to plot Energy versus Time

24. Bill’s questions … • Is it superior to BNL, JPARC? Yes • What is scaling of sensitivity with pulse rate? TBD • On what time scale can the theory be improved … • See slides plus Babar, KLOE and VEPP-2000 and Belle to come • Lattice efforts for HLbL • • Can the systematic uncertainties be reduced? • Yes: Many related to flash and rate uncertainties. These are just scaled to expected statistics in future. We need “quiet” fills. • Field has long list of natural reductions that only require people and time (but not much money) • • What are the uncertainties in the pion flux? ~20% ? MiniBooNe • • What is total downside risk on performance? TBD • • How does the g-2 approach to new physics compare/contrast with the K decay case, e.g. for supersymmetry search? • Probably Bill Marciano can tell us but g-2 is VERY sensitive to SUSY..

25. Additional experimental considerations • Ring mass / stable floor / cryogenic • New calorimeter system (in development now) • And associated electronics / daq • Upgraded internal kickers and probably electrostatic quads • Other physics outcomes • Muon EDM improvement • Lorentz violation / CPT test with sidereal day comparison • See: arXiv:0709.4670 (PRL accepted 2008)

26. Systematic errors on ωa (ppm) Σ* = 0.11 B. Lee Roberts, KEK – 10 January 2008

27. E821 ωpsystematic errors (ppm) Future (i) *higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time-varying stray fields. B. Lee Roberts, KEK – 10 January 2008

28. a(had) from hadronic t decay? • Assume: CVC, no 2nd-class currents, isospin breaking corrections. • e+e- goes through neutral r • while t-decay goes through charged r • n.b. t decay has no isoscalar piece, e+e- does • The inconsistencies in comparison of e+e- and t decay now seem to be resolved.

29. The most important consequence of this work is indirect and confirms the known 3.3s discrepancy between the direct BNL measurement of the muon anomalous moment and its theoretical estimate relying on e+e- data.