muon g 2 Brendan Casey PIC 2014 September 17 2014 Sept 11 2014 muon g2 experimental hall Outline What is g and how do we predict its value How we measure it for muons ID: 800370
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Slide1
e+e- hadronic cross section andmuon g-2
Brendan CaseyPIC 2014September 17, 2014
Sept 11, 2014 muon g-2 experimental hall
Slide2OutlineWhat is g and how do we predict its valueHow we measure it for muonsWhere things stand and where they are goingMost numbers are from a snowmass white paper edited by Lee Roberts arXiv:1211.21989/17/14B. Casey, muon g-22/29
Slide3What is g?9/17/14B. Casey, muon g-23/29
Gyromagnetic ratio = magnetic dipole moment / angular momentum
m, q
v
r
Magnetic dipole moment
Angular momentum
Classical gyromagnetic
ratio
Quantum
g-factor
Bohr
magneton
g-factor nominally 1
Slide4Counting degrees of freedom9/17/14B. Casey, muon g-24/29Byproduct of the Dirac equation is extra degrees of freedom of the electron associated with spin
If we take the non-relativistic limit and try and recover the Pauli equation we get an extra factor of 2
With the extra degrees of freedom,
g = 2
(
Bjorken
,
Drell
)
Slide5Self energy9/17/14B. Casey, muon g-25/29Also need to include the corrections due to self interactions of the muon with its own field
(Schwinger term)
Predicting g now becomes a question of determining radiative corrections to the required precision
Slide6QED out to 10th order9/17/14B. Casey, muon g-26/29Calculated analytically to 6th order (72) diagrams
Calculated numerically to 10th order (12672) diagramsLargest 12th order terms estimated
Aoyama, Hayakawa, Kinoshita, Nio PRL 109, 111808 (2012)+ prelim update 7/14
Uncertainty dominated by fine structure constant
Slide7Electroweak contribution9/17/14B. Casey, muon g-27/29Gnendiger, Stockinger, Stockinger-Kim PRD 88, 053005 (2013)
(G = longitudinal component of gauge boson)
Calculated analytically to 2nd order and estimated out to 4th order
Recently updated to included measured value of the Higgs mass
This is 10
-9
and the leading term is 10
-3
so we call this a ppm correction
Very convenient way of thinking about different contributions:
New physics with weak scale masses and weak scale couplings naively gives a ppm level correction to
muon
g-2
Slide8Leading hadronic contribution9/17/14B. Casey, muon g-28/29
Hadronic vacuum polarizationUse analyticity to convert into a dispersion relationUse optical theorem in reverse to convert to a cross section
Figs from T. Teubner
Dominant term:
e
g
e
p
+
p
-
t
W
p
+
p
0
n
Use CVC and
isospin
to convert to
m(
p
+
p
0
) in
t
decays
Slide9R-scan data9/17/14B. Casey, muon g-29/29Most relevant R-scan data for muon g-2 comes from the SND and CMD-II detectors at the Novosibirsk VEPP-2M collider
Scans from 1992-2000~1% determination of the hadronic contribution to muon g-2This is a major effort
Slide10Radiative return9/17/14B. Casey, muon g-210/29
eg
e
p +
p
-
R-scan: vary beam energy to scan
Long and dedicated run time
e
g
e
p
+
p
-
Radiative
return: sit on a resonance and probe lower energies through ISR
Ideal for the era of high luminosity factories sitting at the
f, t
/c, and
U
(4S) resonances where it becomes a parasitic measurement
g
Slide11R-scan + radiative return9/17/14B. Casey, muon g-211/29KLOE
BaBarAddition of enormous radiative return data sets really doesn’t shrink the error since error is now dominated by disagreement between experiments
Slide12Higher order QCD9/17/14B. Casey, muon g-212/29Most relevant term is hadronic light by light scattering
Current knowledge is based on combinations of several model dependent calculations with error derived from the spread in the results
Slide13Current problemsTwo most precise data-based determinations of leading order QCD contributions do not agree.The e+e- determination does not agree with the t determinationGrowing evidence that this is due to unaccounted for isospin breaking effects but jury is still outIt is difficult to quantify the error in the hadronic light-by-light contributionMany people are worried that it is underestimatedEach of these effects is roughly the size of the quoted uncertainty and cloud the interpretation of the comparison between data and predictionWithout a program to address these, many people feel an upgraded muon g-2 experiment doesn’t make sense
9/17/14B. Casey, muon g-213/29
Slide14The Program I: New R-scan dataNew Novosibirsk R-scanUpgraded higher luminosity machineMajor detector upgradesData taking began in 2009 and already have data sets on tape comparable to BaBarAfter complete R-scan up to 2 GeV, machine will sit at N N-bar threshold and collect radiative return dataRadiative return measurements now integral part of all the factory programs (BES III, Belle II, KLOE)Not to mention enormous t data sets Now have 2 high statistics measurements, by the end of the decade we expect 8Projection is for a factor of 2 reduction in the uncertainty on muon g-2
9/17/14B. Casey, muon g-214/29
Slide15The Program II: Data driven light-by-lightNew detectors installed in KLOE-II to measure outgoing e+e- in two photon collisionsCan measure transition form factors down to unprecedented q2This data can be used to verify the models used to calculate hadronic light-by-lightRecent workshop held in Mianz produced a draft roadmap for a data driven approach to hLbL (arXiv:1407.4021)Projections for future improvement do not assume a reduction in uncertainty. Only a more robust uncertainty. 9/17/14B. Casey, muon g-2
15/29
Slide16The Program III: Lattice QCD First principles calculation of hadronic contributions becoming a fairly significant thrust in lattice QCD11 papers presented at Lattice-2014HVP and hLbL, alternate techniques, fitting biases, strange and charm quark contributions, disconnected diagrams…..9/17/14B. Casey, muon g-216/29
LatticeprecisiontimescalebenchmarkHVP1-2%Few yearst -- e+e- discrepancyHVP
sub-%This decadeCompetitive w/ e+e-
hLbLany
soon
Course
Verification
of
models
hLbL
~30%
3-5 years
Competitive
with models
hLbL
~10%
Ultimate goal
Replace models
Slide1717Measuring muon g-2Produce polarized muons and inject them into a storage ring with vertical B fieldB field is mapped using NMR probesMuon spin precesses around the B fieldPositrons decay along spin direction so precession frequency is measured by counting positrons
Slide18Magic momentumNeed to focus the muons to store them. Done using electrostatic quadropolesAdds a motional B field term to the precession frequency For (g-2)/2 = 0.1% and g = 29.3, the above term cancelsCERN II, III, Brookhaven and Fermilab experiments are all magic momentum experiments with p = 3.094 GeV 9/17/14B. Casey, muon g-2
18/29
Slide19Frequency measurementWeak decay sopositron direction follows muon spin
Highest energy positrons occur when
muon
spin and momentum are aligned
# high energy positrons versus time
momentum
spin
e
+
(R)
ν
e
(L)
ν
μ
(R)
μ
+
19
/29
B. Casey, muon g-2
9/17/14
Slide20Brookhaven result9/17/14B. Casey, muon g-220/29
0.54 ppm uncertainty
0.42 ppm uncertainty
2.5 ppm difference
Big effect, needs confirmation
Slide21The Program IV: A new experiment at FermilabPhilosophy:Re-use the BNL storage ring It is one continuous conductor and has sub-ppm level uniformity averaged around the ring Move the ring to FermilabHigher rate, higher polarization, higher purity than at BNLFactor of 20 increase in statistics per yearRebuild (almost) all instrumentation from scratchUse of modern detector technology reduces systematic uncertainties to keep pace with the reduced statistical uncertaintyGoal: 140 ppb9/17/14B. Casey, muon g-2
21/29
Slide22Disassembly storage ring at the end of the last experiment22/29B. Casey, muon g-29/17/14
Slide23Disassembly Summer 2011
23/29B. Casey, muon g-29/17/14
Slide24The big move249/17/14B. Casey, muon g-2
Slide25reassembly9/17/14B. Casey, muon g-225/29
Slide26MilestonesSubmitted proposal to Fermilab Nov 2009Ring disassembly began Summer 2011Ring shipped to Fermilab Summer 2013Ring moved into new building Summer 2014Ring cold Spring 2015 and shimming beginsDetectors installed and accelerator work complete in 2016First large data set in 2017Significant results in 20189/17/14B. Casey, muon g-2
26/29
Slide27The Program V: A new experiment at JPARC Experiment also planned for JPARCWill use MRI magnet (x10 better local uniformity)Not at magic momentum, muons not stored9/17/14B. Casey, muon g-227/29T. Mibe
Slide28The Program at the end of the decade9/17/14B. Casey, muon g-228/29Minimum outcome
Have an independent measurement of muon g-2Have a much more robust understanding of the uncertainty in the predictionMaximum outcomeIf discrepancies in prediction are resolved and experimental value is confirmed, we will have an 8 sigma result
Slide29ConclusionsThere is a worldwide program underway to drastically improve our understanding of muon g-2Results on all fronts are expected this decadeExtremely challenging but also extremely exciting and hopefully extremely rewarding9/17/14B. Casey, muon g-229/29