A proposal to measure the muon anomalous magnetic moment to 0.14 ppm precision The New g-2 Collaboration

Is the science compelling? Is Fermilab the right place? Is the experiment well designed? Is it cost effective?

Momentum

Spin

e

D. Hertzog and L. Roberts – PAC Fermilab – March 6, 2009

Built on the foundation of E821, with important new strength added

@ 20 Institutions

a

List does not include the many PDRAs and Students who will join an approved effort

a = (g – 2)/2 is non-zero because of virtual loops, which can be calculated very precisely

B

QED

Z

Weak Had LbL

Had VP

Had VP

Known well Theoretical work ongoing

a = 51 x 10-11

arXiv:0809.3085 Eduardo De Rafael (CPT)

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)

Where we are and where we are going

Leads to a(Expt – Thy) = 295 ± 81 x 10-11 3.6

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 a 0.21 0.07

Theory uncertainty: 51 30 x 10-11

(If xx remains 295, the deviation from zero would be close to 9)

Future: a(Expt – Thy) = xx ± 34 x 10-11

Precise knowledge of a will aid in discrimination between a wide variety of standard model extensions

UED models (1D) typically predict “tiny” effects Incompatible with a a of ~ 300 x 10-11

SUSY models – there are many – predict a contributions of about the observed magnitude for a

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

SUSY: Muon g-2 is very sensitive through loops, which are amplified by tan

See full Topical Review: D. Stöckinger J.Phys. G34 (2007) R45-R92

2

SUSY -11μ

SUSY

100 GeVa ≈130×10 tanβ sign μM

Difficult to obtain at the LHC

The Snowmass Points and Slopes are 10 representative SUSY models with typical parameters for MSUSY masses and tan, etc. They serve as test points to indicate the discrimination power of experiments.

Muon g-2 is a powerful discriminator no matter where the final value lands

SPSDefinitions

Universal Extra Dimensions 1D

Illustration of “resolving power”

among SUSY models

Model

UED

Future?

PresentPresent

Models

Suppose the MSSM reference point SPS1a* is realized and parameters are determined by global fit from full LHC data

sign() difficult to obtain from the collider tan poorly determined by collider

* SPS1a is a ``Typical '' mSUGRA point with intermediate tan = 10

LHC (Sfitter)

Old g-2

New g-2

g-2 is complementary to the LHC

Connection between a, EDM and the charged Lepton Flavor Violating transition moment → e

→ e a (real) EDM (imaginary)

SUSY slepton mixing

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

(1) Precession frequency

(2) Muon distribution

(3) Magnetic field map

The measurement involves determining 3 quantities to high precision

B

g 2

1 2 3

TIME

Double Blind Analysis

a

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

4 key elements of the g-2 measurement

1. Polarized muonsforward decays, captured in FODO, ~97% polarized source

2. Precession proportional to (g-2)

3. P magic momentum = 3.094 GeV/cE field doesn’t affect muon spin when = 29.3

4. Parity violation in the decay gives average spin direction

µ

EaBa

mce

a

1

12

ee

2

2a spin cyclotron

g eB

mc

Booster/Linac

Extraction from RR

Injection to RR

NEW TRANSFER LINE

A3 lineA2 line

Main Injector

F0P1 line

MI-52

MI-30

p

Recycler

_p

MI-10

Pbar

AP0

P2 line

Accelerator Overview

INJ8GeV

Polarized muons delivered and stored in the ring at the magic momentum, 3.094 GeV/c

Uses 6/20 batches* parasitic to program

Proton plan up to AP0 target is almost the 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*Can use all 20 if MI program is off

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)

Stored Muons / POT

Flash compared to BNL

parameter FNAL/BNL

p / fill 0.25

/ p 0.4

survive to ring 0.01

at magic P 50

Net 0.05

The Storage Ring exists and will be moved to FNAL

incoming muons

Quads

Power supplies

Quads

Vacuum system

Fiber harps

Kickers

Into the ring Beamline “stub”

Design for FNAL

Open-end inflector*x2 increase in transmission

Kicker deflects beam onto orbitImprovements planned for pulse shape / magnitude

AP-3

Existing Proposed

*This was built at one-third length, tested, but final design had closed ends

stub

An “event” is an isolated electron above a threshold.

e+

2.5 ns samples

N

A

NA2

<A>=0.4

An “event” is an isolated electron above a threshold.

e+

2.5 ns samples

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

Traditional method of determining a is to plot Number vs. Time

Event Method

Geant simulation using new detector schemes

N

A

NA2

<A>=0.4

Here, Asym is the average asymmetry of events above energy threshold cut

A complementary (integrating) method of determining a is to plot Energy vs. Time

Event Method

Geant simulation using new detector schemes

Energy Method

Same GEANT simulationPotential method for Project X rates

The magnet will be carefully shimmed and precisely mapped

Continuously monitored using 366 fixed probes mounted above and below the storage region

Measured in situ using an NMR trolley

1 ppm contours ppm

0.05

0.09

0.05

0.07

0.10

0.17

(Final BNL)

g-2 budget estimate, contingencies included(assumed protons are delivered to AP0 at 15 Hz operation of booster)

Ring relocation

NSF Nucl.+ International

Relatively standard beamline elements

Mu2e & g-2common

g-2 & Mu2e need RF

PROTONs

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

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.

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

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 a 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

Analyticity and the optical theorem: Back

contributionerror2

(from F. Jegerlehner)

• 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

|F|2 from KLOE, CMD2 and SND agree well Back

weighted contribution

recall that:

Suppose the hadronic contribution increased to remove the difference?

• A similar dispersion integral enters elsewhere

• Increasing (s) to remove the (g-2) difference lowers the Higgs mass limit PRD 78, 013009 (2008)

• This cross section is important for a and for any precision EW physics.

• Future work continues in Frascati and Novosibirsk. Belle is also beginning to explore this possibility.

Back

Note, with a = 295 x 10-11 … If HLBL is the source of the difference with SM, it would need to increase by 11 ....

Back

arXiv:0901.0306v1

Dynamical models with QCD behavior

The 0 (Goldstone) contribution fixes sign of the contribution From pt 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:

Back

How general is the UED “tiny effects” prediction?

UED models (1D) typically predict “tiny” effects Incompatible with a a 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)

Back

Sfitter LHC global fit(Alexander, Kreiss, Lafaye, Plehn, Rauch, Zerwas; Les Houches 2007, Physics at TeV Colliders)

With g-2, many are improved, some significantly

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.

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

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

www.ippp.dur.ac.uk/~georg/sps/sps.htmlSPS PLOT

Back

Parasitic Muon EDM Measurement using straw tube arrays

The EDM tips the precession plane, producing an up-down oscillation with time (out of phase with a)

Measure upward-going vs. downward-going decay electrons vs. time with straw tube arrays

E821 straw-tube array

BackarXiv:0811.1207v1

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

(g-2) signal: # Tracks vs time, modulo g-2 period, in phase.

EDM Signal: Average vertical angle modulo g-2 period. Out-of-phase by 90° from g-2; this is the EDM signal

Back

(g-2) EDM

The new idea imagines in-vacuum straws, matched with out-of-vacuum pre-calorimeter straws (used also for shower impact)

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

Out-of-vacuum straws / impact detector

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

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

Back

Next

(g-2)

a Systematic Error SummaryBack

What drives the detector choice? Compact based on fixed space Non-magnetic to avoid field

perturbations Resolution is not critical for a

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,

Back

Conceptual idea for Si-PM readout of W/SciFi modules

Si PM Array W / SciFi BlockWinston cone Bundle fibers

Back

3 cm

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

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

Back

The “yellow” budget box is related to accelerator improvements for the intensity frontier in general

Assumed done

Must do for Mu2e, g-2 and any other expt.

see below

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

Back

Extraction Recycler to P1

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 ” 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 ) ring being explored with

muons from 3-GeV Booster. The idea is in its infancy. Possible future focus on small ring dedicated EDM effort

Back

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

Back

66 ms of a “batch”

1 2 3 4

11 ms

OptiM

MARS15

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

scal

ar m

ass

Excluded for neutral dark matter

2

Present:a = 295 ± 88 x 10-11

Topical Review: D. Stöckinger hep-ph/0609168v1

Here, neutralino accounts for the WMAP implied dark matter density

Back

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

scal

ar m

ass

Excluded for neutral dark matter

With new experimental and theoretical precision and same a

Futurea = 295 ± 34 x 10-11

Topical Review: D. Stöckinger hep-ph/0609168v1

Here, neutralino accounts for the WMAP implied dark matter density

Historically muon (g-2) has played an important role in restricting models of new physics.

It provides constraints that are independent and complementary to high-energy experiments.

Back