A 1 ppm measurement of the positive muon lifetimeQinzeng PengAdvisor: Robert CareyBoston UniversityOctober 28, 2010

MuLan collaboration at BU:Robert Carey, James Miller, Lee Roberts, Kevin Lynch, Justin Phllips, William EarleInstitutes:BU, UIUC, Univ. of Kentucky, JMU

Outline Motivation and theoryMuLan experimental set up2006 data analysisSystematic errorsFinal results

Input parameters to the standard model and their precision measurementsThe CKM mixing matrixThe masses of fermions and Higgs boson3 parameters to determine the strength of the interaction and the masses of the weak gauge bosonsFine structure constant Z-boson mass MZFermi constant GF0.71 ppb23 ppm8.6 ppm

Fermi Constant and gContains all weak interaction loop corrections

Fermi Constant and Radiative corrections (maily QEC)Contact interaction from Fermi theoryIn 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in GF from theory to < 0.3 ppm (it was the dominant error before)

A Graphical History of the Muon Lifetime Measurements

Experimental Concept Traditional method: 1 muon decay each time MuLan method: n muons decay each cycle need pulsed muon beam kicker-12.5 kV+12.5 kVAccumulation periodMeasurement period

Experimental Setup beam line kicker detector ball WFD DAQ monitoring devices

Kicker 2 sets of parallel plates inside the vacuum pipe high voltage at +/- 12.5 KeV fast transition time (60 ns)

TargetFerromagnetic target to dephase muons polarization during accumulation period. Polarization is both depolarized and dephased.Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron)0.5 T internal magnetic fieldMuons arrive randomly during 5 us accumulation periodMuons precess by 0 to 350 revolutions

Muon CorridorErrant muons => vacuum pipeAK-3 Target inside the pipeAK3 liner

Entrance Muon Counter to monitor beam profile

MuLan Detector Ball170 detector pairs = 20 hexagons + 12 pentagons

Detector elements

Waveform digitizer2 Analog PulsesWFD 1WFD 2Anlog signal => Digitized samples ( ampitude and time)

More than 1012 muon decays in 2006 run >1 x 1012 coincidence pulses in 2006 data set >65 TBytes raw data

Data analysis3-parameter fit4-parameter fitArtificial pile-up construction

Systematic studiesEarly to late stability during 22 s measuring periodKicker stabilityBackground stabilityTiming stability Gain stability

Timing stability with laser systemNeed reference time, Laser pulse is narrower than normal pulseReference PMT is NOT contaminated with experimental background

Laser system setup

Laser runs24 tile laser channels3305 laser runs in 2006 => 5E6 hits per channelCombine the runs to study dt vs. time => 1.6E6 hits needed for 0.5 ppm error.

dt vs. run stabilitythe scale of change is about 0.02 clock ticks In single run sigma of dt=0.13 clock ticks (in next slide)

Multi peaks combination

dT vs. time, single channel

dT vs. time, 24 channelsMean = -5E-9 c.t. per clock tick is close to 0 RMS = 6E-8 c.t. per clock tick as the timing shiftTiming shift error: 0.06 ppm c.t per c.t.

Timing stabilityTiming is pretty stable for MuLan experiment, at 0.1 ppm level

Gain stabilityGain shift == threshold shiftGain shift => number vs. time shift vs. time is studied

Gain shift to lifetime shift

Run selection

big fluctuation from run 33282 to 54318(index 1 to 225)slight change (10 ADC) from run 54330 to 55428 (index 225 to 400)Sigma of amplitude of single run is 10 -15 ADCBetter region

Ratio methodRatio of amplitude of tile pulse to amplitude of the reference PMTRatio of amplitude of time bin I to amplitude of the last time bin

d(amp)/amp = (108-98)/98=0.1d(amp_ratio)/amp_ratio = (0.68-0.655)/0.655 = 0.0382

Slope of ratio_bin_i vs. run flat distribution

vs. time

24 channels combinedd(dG/G)/dt = 5E-5 per tau

Counts shift due to threshold changedN/N 3 x 10-4 for 1 ADC change in threshold

conclusionAmp vs. time < 1 ppm

WFD Pulse Fitter Algorithm

Foucs on neighboring pulses

Test of PFAPile on effect, signal region and pedestal region

Effect of small pile on

Effect of pile on near threshold

Change vs. amplitude of pile on

Estimated pull of timing

MuSR effectMuSR rotation results in an oscillation of the measurement probability for a given detector.

B = 34 G

MuSR relaxation results in a reduction of the polarization magnitude.

The sum cancels muSR effectsthe difference accentuates the effect.SumDifference/SumBcounts arb.counts arb.counts arb.

conclusionsTiming shift => 0.1 ppmGain shift => < 1 ppmPFA => < 0.1 ppm

Hello everybody, thank you for coming here to listen to my talk. Its been a long time for me to finally settle down the department seminar about my thesis.Ok. Lets go to the topic. My topic for todays talk is to measure the muon lifetime with high precision, the goal is 1 PPM, the worlds best result as time being.My advisor, Robert Carey, help me a lot during my thesis work. Our group, also name MuLan, includes 4 universities, BU, UIUC, U of Kentucky and JMU. In BU, we have 3 professors, 1 post doctor, 1 engineering professional, and 2 graduates. I joined the program since 2003 and took part in the experiment from 2004 to 2007, at PSI in North of Switzerland, and doing analysis work from 2004 up to last year. Today I will talk about 5 topics : theory, exp. 2006 data analysis, mainly on systematic errors like detector gain stability and timing stability, and then the final result, including some of the systematic uncertainty.The purpose of Muon lifetime measurement at high precision is related to the standard model. the standard model is regarded as a most reliable theory in high energy physics. Elementary particles: Fermions, charge (color, electric)Force carriers: BosonsCKM ? Why mixed, observed?Masses3 constants

GF and gThe difference between GF and g?The strength of Fermi's interaction is given by the Fermi coupling constant GF 4 leptons via contact interaction -> Fermi theory4 leptons via W boson -> Feyman diagram -> GF = sqrt(2)/8 g^2/M^2All interaction loops added -> correction of delta r -> why b t loop? The most massive one

GF and tau ?The muon lifetime measurement is such important that during the last decades many different experiments were done, to reach a better precission. The MuLan 2004 result is good at 18ppm and currently 2006 result is at 1ppm

MuLan used pulsed beam which was fulfilled by the kicker. during 5 microseconds accumulation period, about 20 muons were collected in the target from the DC beam. Then during the 20 microseconds measurement period, incoming muons were blocked by the kicker and the muons in the target start to decay.Proton => pion => muon, surface muon beamKicker fulfilled the MuLan method.170 detector pairs symmetrically around the target, key: polarization cancellation from opposite pair ; PU subtractionWFD: pulse amplitude and timing, for systematic study

Kicker, 2 platesHigh vacuum and high voltage, fast transit time

Moun beam is high polarized, which would result in non-symmetric decays. The time spectrum on single detector is decay modulated by g-2 oscillation, but if opposite pairs added together, such modulation will be canceled with each other, provided the distribution is symmetric.AK3 will dephase muon polariazion, muon will process during accumulation period and bundle of muons will have average of spin 0Errant muons : muons that stopped before coming to the target, their timing and distribution both hurt muon lifetime spectrum. Minimization is to use helium bag in 2004 and switch to vaccum pipe during 2006 and 2007

Why AK3 liner? Stopped muon under dephasing too?Beam monitor, make sure the beam is centered to the target center.Segmentation, PU minimized;symmetric, polarization modulation can be canceled by combination of opposite pairs

WFD: both have amplitude and time recorded. Amplitude can be used for systematic study. Timing, after good fit with template, will give better precision than TDCBasic 3 par fitPU term added => 4 par fitThe best way to fit is to artificial build up pile up term. => need one slide to talk about APU?Early to late is the universal concern during the MuLan experiment, 22 microseconds.Main topic is timing and gain stability, with the utility of laser pulses for timing.= (1+ ) = (dT(t2) dT(t1))/(t2-t1) slope of dT vs. timedT = t_measure t_real = t_Tile t_RefReference PMT as real time and tile PMT as measured timeReference PMT has no beam contamination so it gives us exact time. Also the reference PMT is much better on timing than tile PMT (dt sigma)

error = RMS/sqrt(N) = sigma/sqrt(N) for each time bin (one lifetime)=0.5ppm d(T) = 0.5ppm*2.2us = 1.1 ps in one lifetime= 1.1ps/(2.2ns/clk) = 0.5E-3 Clock ticks in one lifetime(bin).d(T) vs. time time bin = one life time error 0.06 ppm for this exampleGain stability can be separated by two parts:Gain shift == threshold shift => counts vs. time shift counts vs. time => lifetime shift Amplitude vs. run is not stable, so simply combine runs may introduce uncerntainty.Method 1: use Reference PMT and make ratio => no goodMethod 2: use ratio of time bin I to time bin last => betterTop: simply vs runBottom: vs. run => better but still some shiftin each run, divide 22us to 10 time binsin each time bin, get mean value from amplitude distribution -> _bin_i make ratio of _bin_i to _bin_last = ratio_bin_iplot ratio vs. time ( ratio_bin_i vs. time bin i) and fit by po1 to get p0 and p1(slope)plot ratio slope vs. run ( p1 vs. run) to see if it's flat (shown in this picture)Combine 400 runs to get mean value of ratio_bin_i for each time bin (ratio_bin_i -1) = plot vs. time and fit by po1 to get p0 and p1(slope)

Mean < error => use error as error.1E-4 per tau5E-5 +/- 1.8E-4 per taud(dN/N)/dt = n/N*h_Th*(d(dG/G)/dt) = 3E-4 per ADC * 60 ADC * 5E-5 per tau = 0.9 ppm per tau