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

We are all here because of the following argument n LHC: direct search for new particles u But, what new physics will they reveal? n Precision measurements: u Lepton flavor violation u Electric dipole moments u Rare decays u Unitarity tests u Muon g-2 Consider a post-LHC world with many new mass states found SUSY Extra Dimensions The future a  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 Here is an example, related to g-2 UED SUSY

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

The BNL Storage Ring

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

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

g ≠ 2 because of virtual loops, many of which can be calculated very precisely B    QED Z Weak Had LbL  Had VP    KEY REGION 2006 plot

g ≠ 2 because of virtual loops, many of which can be calculated very precisely B    QED Z Weak  Had VP  Had LbL  Had VP  Had LbL 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

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

Sidebar: There are LOTs of “SUSYs” n General MSSM has > 100 free parameters. u Advantage: Well, we don’t know them  open minded. u Disadvantage: Not predictive, but experiments can “restrict” parts of this multi-dimensional space u Beware of claims of “Ruling Out SUSY” ! n CMSSM – “constrained” and, related but even more constrained, MSUGRA, … and others u These models assume many degeneracies in masses and couplings in order to restrict parameters.  Typically: m 0, m 1/2, sgn(  ), tan , A (or even fewer) n Then there is R parity – is sparticle number conserved? n 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  a  from 88 to 39 in units. For a “legacy” effort, it will be somewhat smaller.

Consider the physics message carried by  a  (expt – thy) ~ 300 x at present (E821: 88 x ) and future (E969: 39 x ) uncertainties in  a  Example 1: MSSM general parameter scan

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 * Snowmass Points and Slopes: units Compare to present  a  =295 Compare uncertainty to   a  ~ ±35

Suppose the MSSM reference point SPS1a* is realized and parameters determined by global fit (from LHC results)  sgn(  ) can’t be obtained from the collider  tan  can’t be pinned down by collider Possible future “blue band” plot, where tan β is determined from a μ to < 20% or better D. Stockinger * Snowmass Points and Slopes: * SPS1a is a ``Typical '' mSUGRA point with intermediate tan  = 10 Tan  “blue band” plot based on present a μ. With these SUSY parameters, LHC gets tan  of ± 9.1.

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

Experimental Issues Discussion: Three Phases for FNAL implementation Phase 1:  + measurement to 0.1 ppm statistical u Requires Nova type upgrades, beam manipulations and ~4x10 20 p u Can do in pre Project X era Phase 2:  - measurement to 0.1 ppm (or lower)  Requires many more protons due to xsection for  - u Would benefit from Project X n Phase 3: All “integrating” with much higher proton beam and restricted storage ring acceptance to lower systematics u Requires Project X E821 final error: ± 0.48 ppm statistical ± 0.27 ppm systematic

Near sideFar side E821 used a “forward” decay beam, with p  1.7% above p magic to provide a separation at K3/K GeV/c Decay GeV/c About 40% decay Flux down by momentum mismatch (~ 2 – 4)  P/P of  s tiny due to bkg FODO transmission not optimized Inflector ends scatter  s

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

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

MAR: Muon Accumulator Ring – the BNL idea n Catch most muons in first 2 turns. u Although spin precesses, it’s okay n Rest of turns just reduce pions by decay time Figure of Merit NP 2 increased by factor of ~12 or more n Fast “Switcher” magnets required     Fluxes and Figure of Merit Number of turns in racetrack

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

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

Bill’s marching orders … n Make these experiments a compelling part of Fermilab future from physics point of view n Demonstrate power of doing it at Fermilab u 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. n Demonstrate realistic scenario for making it work u No showstoppers identified nor any “tricky” bits n Demonstrate a scaling strategy u Pre-x era: Can do a 40 week run to 0.1 ppm u Post-X era: Can do negatives and an “all integrating” effort  See next picture

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

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

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

B. Lee Roberts, KEK – 10 January 2008 Systematic errors on ω a (ppm) σ systematic Future Pile-up AGS Background * Lost Muons Timing Shifts E-Field, Pitch *0.05 Fitting/Binning * CBO Beam Debunching * Gain Change total ~0.09 Σ* = 0.11

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

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

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