# Presentation: 556907

## 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**

**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 **

## 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**

## Basic Muon g-2 

## The BNL Storage Ring 

**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)

***B***

## 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**
******a********(expt-thy) = (295±88) x 10****-11**** (3.4 ******** **

**Rep.Prog.Phys. 70, 795 (2007).**

## g ≠ 2 because of virtual loops, many of which can be calculated very precisely

## 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**

## 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”

**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:  ****m****0****, m****1/2****, sgn(********), tan********, 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 ********a******** from 88 to 39 in 10****-11**** units.  For a “legacy” effort, it will be somewhat smaller.**

## Consider the physics message carried by                         a(expt – thy) ~ 300 x 10-11 at present (E821: 88 x 10-11 ) and future (E969: 39 x 10-11 ) 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:**
**http://www.ippp.dur.ac.uk/~georg/sps/sps.html**

**10****-11**** units**

**293**
**318**
**16.5**
**135**
**490**
**86**
**169**
**237**
**173**
**-90**

**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:**
**http://www.ippp.dur.ac.uk/~georg/sps/sps.html**

******* 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 **10.22 ± 9.1.

## Typical CMSSM 2D space showing g-2 effect(note: NOT an exclusion plot)

**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******

**2******

**With new experimental and theoretical precision and same ********a******

**Present:**
******a****** = 295 ± 88 x 10-11

**Future**
******a****** = 295 ± 39 x 10-11

**Topical Review: D. St****ö****ckinger hep-ph/0609168v1**

**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**
**Requires Nova type upgrades, beam manipulations and ~4x10****20**** p**
**Can do in **_***pre Project X era***_
**Phase 2****:  ********-**** measurement to 0.1 ppm (or lower)**
**Requires many more protons due to xsection for ********-**
**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***_

**E821 final error:**
**± ****0.48 ppm statistical**
**± ****0.27 ppm systematic**

## E821 used a “forward” decay beam, with p 1.7% above pmagic to provide a separation at K3/K4

**Near side**

**Far side**

**E821 used a “forward” decay beam, with p******** 1.7% above p****magic ****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)**
******P/P of ********s tiny due to bkg**
**FODO transmission not optimized**
**Inflector ends scatter ********s**

## Superconducting storage ring with quads, kicker, etc.

**Superconducting storage ring with quads, kicker, etc.**

## At BNL, here is the current working plan

**Segmented detectors**

**Open inflector**

**Improve kicker**

**Part of Original Proposal**

**Quad doubling**

## MAR:   Muon Accumulator Ring – the BNL idea

**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 *****NP*****2**** increased by factor of ~12 or more**
**Fast “Switcher” magnets required**

## 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...**

## Booster-era Beam Transfer Scheme

**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 ...

- 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

## A complementary method of determining a is to plot Energy versus Time

## 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..***

## 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)**

## Systematic errors on ωa  (ppm)

| σsystematic | 1999 |  2000 |  2001 | Future |
| --- | --- | --- | --- | --- |
| Pile-up | 0.13 | 0.13 | 0.08 | 0.04 |
| AGS Background | 0.10 | 0.10 | 0.015* |  |
| Lost Muons | 0.10 | 0.10 | 0.09 | 0.04 |
| Timing Shifts | 0.10 | 0.02 | 0.02 |  |
| E-Field, Pitch | 0.08 | 0.03 | 0.06* | 0.05 |
| Fitting/Binning | 0.07 | 0.06 | 0.06* |  |
| CBO | 0.05 | 0.21 | 0.07 | 0.04 |
| Beam Debunching | 0.04 | 0.04 | 0.04* |  |
| Gain Change | 0.02 | 0.13 | 0.13 | 0.03 |
| total | 0.3 | 0.31 | 0.21 | ~0.09 |

**Σ***** = 0.11**

## E821 ωp 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 2nd-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.  

**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.****  **