A determination of the formation rate of muonic hydrogen molecules from the MuCap experiment

Sara Anita Knaacksknaack@illinois.edu

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