David Hertzog University of Illinois at Urbana-Champaign Our piece of the PhiPsi08 poster n Motivation n The theory situation n The basic experimental requirements n Specifics Measurement of Muon (g-2) and Future Prospects

The quest for new physics understanding requires different tools n LHC: direct search for new particles u But, what new physics will they reveal? n Precision measurements:  Lepton flavor violation (  ) u EDMs of e, n, atoms, etc. u Rare decays  0  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

The Standard Model theory has improved. Hopefully at this Workshop we will learn even more n Key points: u Theory: 0.48 ppm u Experimental 0.54 ppm (0.46 ppm stat; 0.31 ppm syst.)  a  (expt-thy) = (297±88) x (3.4  Arguably, strongest experimental evidence of Physics Beyond Standard Model K. Hagiwara, A.D. Martin, Daisuke Nomura, T. Teubner Compare TIME deRafael, Glasgow MDM

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 A key discussion point at this Workshop, so I will defer to the experts

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 ? At Glasgow, we learned of several new efforts A Dyson-Schwinger calculation (C. Fischer) Two independent lattice efforts (Hayakawa et al; Rakow for QCDSF) THIS IS THE QUESTION WE GET ASKED ALL THE TIME BY FUNDING COMMITTEES

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)

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  = 297 ± 88 x Future  a  = 297 ± 39 x Topical Review: D. Stöckinger hep-ph/ v1 Here, neutralino accounts for the WMAP implied dark matter density

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

The Snowmass Points and Slopes give reasonable benchmarks to test observables with model predictions Muon g-2 is a powerful discriminator no matter where the final value lands!! Model Version Expt Future? SPS Definitions

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  exp = 25 x 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.

 a  improvement requires both experimental and theoretical progress Combined Error Theory Error Experimental Error Actual path ? units: x This would get to ~9 

Considerations to aim at ~15 x experimental precision Momentum Spin e Final report: Bennett et al, PRD 73, (2006)

The BNL storage ring will remain the central element

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 Improving here requires greater statistics … x 25 (to be discussed) And, reducing background and controlling fit parameters from beam motions Improving here requires more uniform field – shimming, and in the delicate procedure to calibrate and measure the field – using pNMR

An “event” is an isolated electron above a threshold. e+e+ 2.5 ns samples N A NA 2 =0.4 Higher rate exacerbates pileup & gain stability issues Lab Frame N, A and NA 2

Improve kicker Open inflector Quad doubling More muons are available, even in the existing experimental setup Segmented detectors 4 Then, to accept the higher rate, changes in the experiment are required; e.g.,

Pedestal vs. Time Near inflector Far side It is instructive to understand the muon production, first with the standard “forward-decay” beam 3.15 GeV/c Decay GeV/c The hadronic flash background limits fit start time Survive momentum selection The FLASH is a limiting factor to just “turning up the rate” for any new expt.

Muon Accumulator Ring MAR   How to get more muons AND avoid the flash 1. Take the 0-degree forward muons u High polarization, highest yield u Long beamline to remove flash by pion decay 1. “Recycle” by muon accumulator ring (MAR) 2. Very long beamline 2. Take 180-degree “backward” muons 1. High polarization (reversed), slightly smaller yield 2. Intrinsically, no flash because of  momentum difference

MAR: Muon Accumulator Ring 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 n Figure of Merit NP 2 increased by factor of ~12 or more n Fast “Switcher” magnet required to flick beam straight (default is stay in ring to avoid background)     Fluxes and Figure of Merit Number of turns in racetrack

Alternatively, consider a single long beamline Got muons Removed pions Ideal…

Ideal conditions at FNAL using 8 GeV p  ->e g-2  Test Facility Rare Kaon Decays or along TeV ring g-2 Long beamline possible; more , less flash n High repetition rate of muon fills in ring u 84 fills / 1.4 sec (x 14.5 compared to BNL)  x 25 stats in ~1 year

For JPARC, high-intensity, 30 GeV p beam, and tight space suggests backward decay beam 5.4 GeV/c pions 3.15 GeV/c pions GeV/c muons

Can inject wider  P/P pions beam into decay channel to increase flux 2 nd -order achromat to inject pions into channel

In the backward decay beam, large difference in  momentum eliminates pion flash. Lorentz boos limits yield GeV/c Decay GeV/c  P/P opened up here to catch more flux No hadron-induced prompt flash Both Sides Expected

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

I did not discuss the equally important issue of systematic error improvements … n Magnetic field u Make it more uniform u Keep muons better centered u Improve precision of the calibration probe interpolation, which implies position precision n Precession signal u Detector gain stability monitoring improvements u Pileup reduction u Muon loss reduction (better kicker) u Alternative methods of analysis (Q and T)

Conclusions n A next-generation experiment is likely to happen. u My remarks: n Motivation sharp with respect to LHC era physics search n A few theory clarifications will go a long way to give the project higher priority u Resolution of tau vs ee problem in HVP u Confirmation of VEPP-2M ee result from KLOE and BaBar u Progress (or at least a believable path) toward improved HLbL

SPS points and slopes n SPS 1a: ``Typical '' mSUGRA point with intermediate value of tan_beta. n SPS 1b: ``Typical '' mSUGRA point with relatively high tan_beta; tau- rich neutralino and chargino decays. n 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 n SPS 3: mSUGRA scenario with model line into ``co-annihilation region''; very small slepton-neutralino mass difference n 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 n SPS 5: mSUGRA scenario with relatively light scalar top quark; relatively low tan_beta n SPS 6: mSUGRA-like scenario with non-unified gaugino masses n SPS 7: GMSB scenario with stau NLSP n SPS 8: GMSB scenario with neutralino NLSP n SPS 9: AMSB scenario SPS PLOT