A determination of the formation rate of muonic hydrogen molecules from the MuCap experiment
Sara Anita [email protected]
Final ExamJune 25th, 2012
Outline
• The MuCap experiment• Motivation for the measurement of ΛS
• Muon kinetics• Molecular (ppμ) state
• A measurement of the molecular formation rate, λppμ • The experiment
• Event selection • Analysis of the decay electron time spectrum
• Systematic effects• Results• Fit stability
• Analysis of the capture neutron time spectrum• Consistency check
• Conclusions
Muon capture in the Standard Model
• Weak force interaction
• Sensitive to the hadronic environment• spectator quarks
• Described in field theories• χPT
p n
The hadronic form factors
• Theory gS(q2) , gT(q2) 0
• Experiment gV(q2), gM(q2), gA(q2)• GF and Vud also known
• Leaves gP(q2=-0.88mm2 ) less well
determined experimentally
• Muon capture on the proton
• gP(q2=-0.88mm2)=8.36(23) from
χPT to NLO
A measurement of the singlet μp state capture rate, ΛS, determines the pseudoscalar form factor gP
First MuCap result
The lifetime method – the MuCap experiment • Muon decay
• μ- e- νμνe • BR=O(1)
• Capture• μ-+p n+ν• BR=O(1.5x10-3)
• Molecular state effects• μp+H2[(ppμ)pe]++e-
λ- = λ+ + ΛS - Δppμ
• λ+ 1 ppm relative precision – • MuLan - Phys. Rev. Lett. 106, 041803 (2011)
• ΛS 1% relative precision• λ- 10 ppm relative precision
A muon stopping in hydrogen
mpSinglet
m=455170.2(5) s-1
mpTriplet
m
3/4
1/4
S=711.5 s-1
T=12 s-1
• Enters the n≈14 quantum state
• Prompt (≈10 ns) cascade into singlet state
• Radiative transitions, Coulomb de-excitation, and Auger interactions
Irreversibly de-excites to the singlet state under thermal conditions.
The ppμ molecular state
• Collisional process - ppm=φλppm
• Dominant mode of formation• Electric dipole transition• J=1 “ortho” state• Normalized rate of λppμ=1.8 (9) x 106 s-1
• J=0 “para” state formation is suppressed • λpf=7.5 x 103 s-1
J=1
J=0
Molecular state kinetics
mpSinglet
ppmOrtho
m=455170.2(5) s-1
op=6.6(3.4) x104 s-1
mpTriplet
m ppm=φλppm
ppmPara
S=711.5 s-1
m
m
P=213.6 s-1
O=541.5 s-1
3/4
1/4
pf=φλpf
Ambiguity of ΛS Interpretation due to the molecular state kinetics
• Measurements of gP
• liquid hydrogen target• Sensitive to op
• The MuCap result is less sensitive to this knowledge
• Gaseous hydrogen at 10 bar
f = 1 (Liquid)R
el. P
opul
atio
n
Time after mp Formation
f = 0.01 (~10 bar gas)
Time after mp Formation
Rel
. Pop
ulat
ion
Relative population of mp, ppm-o and ppm-p states vs. time (0-20000 ns)
Placing the hydrogen gas under 10 bar at room temperature minimizes the formation of molecular states and their effect on the S extraction
Systematic error for the MuCap measurement
Source of uncertainty First MuCap result Final
- Statistical error 12.5 s-1 5.4 s-1
- Systematic error 8.4 s-1 5.0 s-1
Correction for Δppm
(<ppm>=2.3(5) x106 s-1) (λop)23.5 4.3 3.9 s-1 < 2 s-1
The improved precision of the final MuCap result requires an improved determination of λppm
The current uncertainty of λppm
• Historical variation of results and conditions
• Systematic < 2 s-1 < 10 % relative precision
• <ppm>=2.3(5) x 106 s-1
• Bystritskii et al. Soviet Physics 43(4), 606 (1976)
• Hydrogen gas doped to 30 ppm (atomic) with Xe
• Impurity elements introduce competing processes involving the muon
Liquid
Solid
Gas
Muon kinetics in an argon-doped hydrogen gas
mpSinglet
ppm
mmAr
ppm=φλppμ
≈2.2 x104 s-1
pAr=φcArλpAr
≈4.5 x104 s-1
≈20 ppm (atomic)
Ar≈1.3 x106 s-1
m
m=0.455170 x106 s-1
nμAr(t), nμp(t) and nppμ(t)
Muon kinetics with Z>1 elements• Muon Transfer – collisional process
• Scales approximately Z2
• Muon Capture
• Remnant (Z-1) nucleus remains.
• The rate ΛZ scales with Zeff4
• # of protons• Wavefunction overlap
The decay electron time spectrum analysis
• Four kinetic rates dominate • λμ, Λppμ, ΛpAr and ΛAr
rppm m
rmp m+ ppm+pAr
rmAr m+Ar
Cppm= ppm/(ppm+pAr)
Cmp= pAr Ar /((ppm+pAr)(ppm+ pAr- Ar))
CmAr= pAr/(ppm+pAr- Ar)
• O(108) events
• Known muon decay rate λμ
• Determine Λppμ, ΛpAr and ΛAr
• to %-level precision.
Capture neutron time spectrum
• Dominated by capture form μAr state
• 7% of all muon stop events
• Can obtain O(106) events
• Extract rμp and rμAr
• Internal consistency check
The MuCap experimental setup
• Muon beam
• Entrance detectors, μSC• Muon timing, tμ
• Time projection chamber (TPC)
• Decay electron detectors• ePC chambers (tracking)• eSC hodoscope (te - timing)
• Eight liquid scintillator neutron detectors
• Neutron timing, tn
Muon beamKicke
r
Separator
Quadrupoles
MuCap detector
TPC
Slit
pE3 beamline
• Delivers 7x104 muon/s• p≈32.6 MeV/c • ≈5 MeV
• Electrostatic kicker• Reduces beam rate by 100
• With μSC implements a single muon event structure
• Pileup protection
The time projection chamber target
• 80 anode wires, z axis• 35 strips cathode strips, x axis• Time to digital converter readout
• 2-D unit pixel • EL, EH, EVH thresholds
2.0 kV/cm drift field
Vdrift of 5.5 mm/μs
• The hydrogen gas is both a target and an active detection volume
Selecting a muon decay event• Stop Location
• EH and EL pixels
• Fiducial volume criteria
• Particle track criteria• Straight-line fits • χ2, total length l
• Time coincident electron information
• Decay time: tdecay=te-tμ
• Same criteria used for the main analysis• Documented extensively
Time relative to muon entrance, tμ
y
z
y
x
Neutron detectors
• Liquid organic scintillator detectors
• FADC (analog) readout of pulses
• Sensitive to fast neutrons (MeV-scale energy) • Gamma rays and electrons
• Different pulse shapes from neutron and gamma ray hits
• pulse shape discrimination, PSD.
• Determines time of the neutron tn
Selection of capture neutron events
• Requires a good muon stop• a coincident neutron hit (±35000 ns)
• tcapture=tn-tμ
• Electron veto:• coincident electron hits• within 0 - 20000 ns of muon entrance
• Charge deposition in the capture process
Typical capture event in the TPC
Another observable for muon capture
y
z
y
x
Summary of data taken with the argon-doped hydrogen gas
• Decay electron time spectrum• 4.9x108 analysis-selected events.• 40 ns binning
• Capture neutron time spectrum • 1x106 analysis-selected events• 60 ns binning
• Capture recoil time spectrum• 200 ns binning• Not presented further
Atomic systematic effects
mpSinglet
ppm
hm
m
mAr
m
m
ppm
pAr
f
1-f
Ar
• Prompt formation of the μAr state• Direct stops• Excited-state transfer - μp cascade• f=4.95(99)x10-4
• Bound μAr state decay rate effect• Relativistic orbit - time dilation• Phase-space suppressed• h=0.985(3)
• Relative efficiency• Nuclear charge• eAr=0.9956(25)
mAr decay electrons detected with (relative) efficiency eAr
μAr, μp, free
Full kinetics model
mpSinglet
ppmOrtho
hm
op
mAr
m
ppm
pAr
efficiency eAr
f
1-f
Ar
ppmPara
S
m
m
O
P
m
Λpf
Description of the time spectrum
• Differential equations, initial conditions, full time spectrum.
• Atomic physics parameters f, h, and eAr • relative contribution of μAr state decays
• The hydrogen kinetic rates, λμ, ΛS, λop, Λpf, ΛO, and ΛP • Directly affect the time distribution of events
• The fit function is A ne(t)+B
Fit to the decay electron time spectrum
• Basic fit results• Λppμ=2.208(65) x 104 s-1
• ΛpAr=4.529(15) x 104 s-1
• ΛAr=1.302(14) x 106 s-1
• χ2/Ndf=0.983(64)
• One external systematic correction
Summary of results
• Disappearance rate results
• rμp=0.52350(80) x 106 s-1 where rμp=λμ+Λppμ+ΛpAr+ΛS+Λpf
• rμAr=1.750(16) x 106 s-1 where rμAr=hλμ+ΛAr
• Statistics limited results
• Scrutiny of fit procedure
• Correlated and non-linear features
χ2 Map of the Λppμ, ΛpAr, and ΛAr parameter space
• Variation of the χ2 relative to the minimum value
• The Δχ2=1 contour is consistent with the ±1 σ of the fit results
• Reflects the correlation of these parameters
• The χ2 variation is controlled and smoothly varying
Fit reproducibility
• 104 pseudo data histograms• Fit function result• Same statistics as data
• Reliability of the central values
• As well as the reported fit errors
Capture Neutron Kinetics
mpSinglet
ppmOrtho
hm
op
mAr
m
ppm
pAr
• Relative efficiency, eH, of 5.2 MeV neutrons
• eH=1.833(80)
• ≈ 1-3 MeV neutrons
f
1-f
Ar
S
m
O
m
nn(t)=eH(Snmp(t)+OnOrtho(t))+ ArnmAr(t)
rmp= m+ppm+ pAr+S+ pf
rmAr= hm+ Ar
Timing calibration• 5.2 MeV neutron -> time-of-flight of ≈18 ns
• The time-of-arrival, tH, and the spread sH
• Extracted from the pure hydrogen data
• tH to ±2 ns precision• sH=15.5(5.9) ns
• 1-3 MeV neutrons from capture onto argon • Arrive ≈11 ns (2 MeV) later than tH
• Time window of ±8 ns
• No sharp transition feature • Physical energy distribution not well understood
• tAr=tH+11±8 ns• sAr=15.5(10.9) ns
566 mm
tn-tμ [ns]
tn-tμ [ns]
Neutron Time Spectrum
Neutron Time Spectrum
-100 100
0 20010000
Fit start-time scan and sensitivity to systematics
• Change in fit results: tAr is varied by ±8 and ±4 ns
• rμAr dominates in the first 1500 ns• Early time window data determines rate
• rμAr and rμp are correlated • variation in both rates with start-time
• The start-time of 600 ns minimizes sensitivity
• Allowed 1 σ limit of variation
• Stable result
Neutron time spectrum results
• Timing calibration• systematic uncertainties
• The rμAr result is “systematics limited”
• Well-understood corrections• Prompt μAr formation• Capture from hydrogen states• Relative efficiency of 5.2 MeV neutrons
• Comparable precision for rμp
Comparison of results• 1 and 2 σ contours of the electron and
neutron time spectrum analysis results
• 1 σ agreement for rμp
• 0.5 σ agreement for rμAr
• Consistent with statistics
• The neutron time spectrum - large systematic effects• Timing calibration• Background• Others
• The more precise results of the electron time spectrum are the main results of this work.
Normalized molecular formation rate result, λppμ
• Known gas density φ=0.0115(1)
• ≈3% relative precision
• Agrees well with theory• Faifman: 1.8(9) x 106 s-1
• Differs from Bystritskii et al. at 2.3 σ• Only comparable gaseous target
Solid
Liquid
Gas
Final MuCap result• Identical conditions as the λ-
measurement
• Exceeds 10% benchmark• < 2 s-1 uncertainty to Δppμ
• Clear interpretation of correction
A precision determination of s also determines the pseudoscalar coupling constant gp.
m- + p n +
m-
p n
q2 = -0.88mm2
• Most precise experimental determination of gp
• Test of chiral symmetries and low energy QCD
• The electron time spectrum is described with a single lifetime; reduced due to capture.
• MuCap measures S by comparing the m- decay rate in hydrogen to the muon lifetime.
• Recently measured to 1 ppm precision
Phys. Rev. Lett. 99, 032002 (2007) and Phys. Rev. Lett. 106, 041803 (2011)
In leading order:
Muons and the Weak Force
• Fundamental particle• mμ=105.7 MeV/c2
• Decays through the weak interaction• lifetime of τμ≈2.2 μs• decay rate λμ.
Measured to 1 ppm relative precision by the MuLan collaboration
λμ=455170.2(5) s-1
Also a significant update to the knowledge of the Fermi Constant GF
The Hadronic Form Factors
• G-Parity gS(q2) , gT(q2) 0.
• CVC + Electron scattering • gV(q2=-0.88mm) = 0.976 ± 0.001• gM(q2=-0.88mm) = 3.583 ± 0.003
• Neutron beta decay • gA(q2=-0.88mm ) = 1.247 ± 0.004
Leaves gP(q2=-0.88mm ) ill determined experimentally.
Muon Capture on the proton
gP(q2=-0.88mm )=8.36(23) from χPT to NLO
Decay Electron Event Selection
• 3-D tracking from ePC1 and ePC2
• Timing te, from eSC hodoscope
• 16 segments• two 0.5 mm thick layers• Four photo multiplier tubes (PMTs
• “Paired” - fourfold coincidence (±25 ns)
• tdecay=te-tμ
• Impact Parameter b • b ≤ 120 mm • Electron and muon stop data processed
separately at the raw stage of the analysis.
• Bulk data processing at NCSA
TDC Electronics: threshold discrimination• EL “low” threshold
• Muon track• 0.014 MeV
• EH “high” threshold• 0.060 MeV• Increased dE/dX as the μ- slows• Signature of a stop
• EVH “very high” threshold • 0.290 MeV• Recoiled pulse in muon capture
onto a Z>1 nucleus• Digitization applied at the clock boundary of 200 ns
sampling bins.
• 2-D coordinate for the TPC, • anode wire : time of a sample bin• pixel
• The cathode strips are read out in a similar way.
Selecting a muon decay event• Stop Location
• Down-stream most anode at EH: z• The time of first EH pixel, tStop, y
• via y=(tStop-tμ)/vdrift
• Coincident cathode strip pixels, x
• Fiducial volume criteria• Stop location and all EH – pixels
• “MuStop” fiducial volume.• All EL (or higher) pixels
• “Track” fiducial volume.
• Particle track criteria• Straight-line fit to EL pixels• χ2, total length l
• Decay time: tdecay=te-tμ
• MuCap criteria• Documented extensively
Time relative to muon entrance, tμ
y
z
y
x
Oxygen Impurity Correction
• Induce muon transfer and capture.• CO=0.23 ppm and CN=0.23 ppm
• Two sets of simulated time spectra• varying CO and CN
• Known N and O transfer and capture rates
• x105 more statistics than in the data
• Linear coefficient of variation, k
• Correction Δ=k CO
• CO =0.12(11) ppm
• Applied to Λppμ and ΛpAr
Fit start-time scan
• A sub-set of the data is chosen with start-time• moved back from 120 ns
• Fit stop-time fixed at 20000 ns
• Amplitude and background fixed• From “free” 120 – 20000 ns result
• Allowed 1 σ limit of variation
Pulse Waveform Analysis
• Resampling from 5.9 ns to 0.3 ns• Interpolation fit to rate data
• Peak time determines tn
• Slow, iS, and total, iΣ, integrals
• Discriminant rPSD=iS/iΣ
• Upper and lower limits• Vary with the total Integral• l = c + k/iΣ
• Specific to each detector
• A final 400 ADC bit ≤ iΣ≤ 5000 ADC bit
• 0.5 MeV - 5.0 MeV energy cut
Neutron Background• Paired eSC hit and
neutron coincident to same muon stop
• Prompt -150<te-tn<50 ns• “misidentified”
electron hits
• Separation of beam-correlated background
CPE Interference
• Fiducial volume conditions unstable• Early times, before 1000 ns• Rejected from the analysis
• pC=60.8(7.0)%
• Disconnected events, predominant after 2000 • pD=15.1(3.7)%
• CPE -> particle track in the analysis• pT=35.7(6.2)%
• Correction applied using the time spectrum of the disconnected “track” events
• fCPE=(pD-pC)/pT=1.28(31)
• Systematic errors • 3.1 x 102 s-1 for rμp
• 1.42 x 104 s-1 for rμAr
Connected
Disconnected
Fit start-time scan and sensitivity to systematics
• No systematic correction
• Prompt μAr formation
• μp state capture events
• Relative efficiency of μp state capture events
• Full result – correction for capture from the ortho-molecular sate
• Including the relative efficiency
• A start-time of 600 ns minimizes sensitivity to these systematics as well.
The capture neutron time spectrum nn(t)=eH(Snmp(t)+OnOrtho(t))+ ArnmAr(t)
nmp’(t) = -rmp nmp(t) nmAr’(t) = pAr nmp(t) -rmAr nAr’(t) nOrtho’(t)= ppmnmp(t)-(m+ O+ op)NOrtho(t)
Where nmp(0)=1-f and nmAr(0)= f,
rmp= m+ppm+ pAr+S+ pf
rmAr= h m+ Ar
• Results for rmp and rmAr respectively.
• Capture from the para-molecular state is neglected.
• Fit function: A nn(t) +B
Oxygen Impurity Correction
• Induce muon transfer and capture.• CO=0.23 ppm and CN=0.23 ppm
• Two sets of simulated time spectra• varying CO and CN
• λpN=0.34 x 1011 s-1 and ΛN=0.069 x 106 s-1
• λpO= 1.7 x 1011 s-1 and ΛO=0.102 x 106 s-1
• x105 more statistics than in the data
• Linear coefficient of variation, k• each of the kinetic rates
• Correction for each rate, Δ• Δ=k CO
• CO =0.12(11) ppm
• Δ=191(175) s-1 is applied to Λppμ
• Δ=27(24) s-1 is applied to ΛpAr
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