Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 1 ⁫● 03:44:44 PM Aart Heijboer University of Pennsylvania.

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Presentation transcript:

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 1 ⁫● 03:44:44 PM Aart Heijboer University of Pennsylvania previous result:PRL 97, (2006) current result: PRL 97, (2006) PRD in preparation outline: motivation what do we look for / previous results the measurement and how we improved it the observation Observation of B s oscillations at CDF

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 2 ⁫● 03:44:44 PM Introduction & motivation

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 3 ⁫● 03:44:44 PM What do we measure? M H = M +  M/2 M L = M -  M/2  M = 2M 12 There is a diagram which allows a B s meson to transform into its own anti-particle time

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 4 ⁫● 03:44:44 PM mass difference M H = M +  M/2 M L = M -  M/2 Because of a coupling between the two states, we get: two separate mass eigenstates oscillation between B s and B s

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 5 ⁫● 03:44:44 PM classical version test Energy eigenstates (normal modes) time By measuring the frequency, we are measuring the strength of the coupling

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 6 ⁫● 03:44:44 PM motivation most uncertain parameters  and  To get at V td : measure  m d (B d oscillations) hard to calculate (lattice QCD). uncertainty: 10% 1.21  0.05 q=s or d If we measure  m s, we can form the ratio which allows for much more accurate measurement of V ts /V td (hep-lat/ ) pretty well known parameterization assuming unitarity

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 7 ⁫● 03:44:44 PM motivation 2005 Limit on  m s was already helping to measure CKM matrix... Plot Combines many different measurements to constrain  and . Check that all measurements are consistent: i.e. that CKM matrix is unitary. V td =A 3 (1-  -i  )

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 8 ⁫● 03:44:44 PM motivation Effect of measuring  m s to the level of a few % => shrinking the orange band Plot Combines many different measurements to constrain  and . Check that all measurements are consistent: i.e. that CKM matrix is unitary. V td =A 3 (1-  -i  )

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 9 ⁫● 03:44:44 PM motivation Effect of measuring  m s to the level of a few % => shrinking the orange band Plot Combines many different measurements to constrain  and . Check that all measurements are consistent: i.e. that CKM matrix is unitary. V td =A 3 (1-  -i  ) Turn the argument around: standard model prediction: Go measure if SM is right. If the answer is no.....

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 10 ⁫● 03:44:44 PM motivation: new physics New particles can enhance the B s B s transition harnik et al. hep-ph/ supersymmetry with large mixing between squarks  m s is sensitive to new physics Phys.Lett.B596: ,2004 Z'

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 11 ⁫● 03:44:44 PM history UA1 result PLB 186 (1997) UA1: neutral B-mesons mix Argus measures fraction of B d mesons that mix (  ~18%) => ~half of the Bs mesons must mix =>  ms is large compared to the decay time => need to resolve rapid oscillations: hard! == 1 1+ (  m) fraction of mixed events Bs case:  =0.5 -> no handle on  ms

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 12 ⁫● 03:44:44 PM time How do we look for mixing? Make a B s meson and measure its flavor when it decays Identify the flavor at production (tagging) Look at oscillation probability vs proper decay time. Bs/BsBs/Bs time Fourier component of asymmetry: Mixing amplitude asymmetry =N unminx -N mix /N mixing frequency

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 13 ⁫● 03:44:44 PM history-II: looking for oscillations LEP, SLD, CDF RUN-I have tried, but have not seen a convincing signal: lower limits on  m s 2005 world average: compatible with mixing but not significant enough We know Bs mixes, now try to search for the right frequency  m s

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 14 ⁫● 03:44:44 PM history: recent results D0 result large amplitude around  m s = 19 ps -1 CDF's previous result amplitude compatible with 1 around 17.3

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 15 ⁫● 03:44:44 PM history: recent results D0 result A double sided 90% confidence level interval. (17-20 ps -1 ) p-value = 5% (now 8%) CDF's previous result p-value = 0.2% (3  ) linguistics “under the assumption that this is signal, we measure:” When are we sure we are not seeing a fluctuation? convention: 5  : p-value = 5.7 x => ~no doubt => publish “Observation” PRL 97, (2006)

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 16 ⁫● 03:44:44 PM Upgrading the analysis signal selection use neural network use particle-ID on kaon-candidates add partially reconstructed decays add some trigger paths tagging kinematic information same side tagger combine opposite side taggers optimally Previous analysis had: precise measurement of  m s, but the significance was not enough (0.2%). Goal for new analysis: remove all doubt and go for the conclusive, final, 'Observation' reblind the analysis & improve until we have a chance to see 5  most likely contain 90% of experiments previous result

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 17 ⁫● 03:44:44 PM 1) Getting the signals

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 18 ⁫● 03:44:44 PM The Tevatron 1.2 fb -1 collected, 1 fb -1 in 'good' runs ~2/3 of the data collected in 2005 no new data added since previous result both are 1 fb -1

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 19 ⁫● 03:44:44 PM The CDF detector

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 20 ⁫● 03:44:44 PM The CDF detector momentum & dE/dx decay time PID

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 21 ⁫● 03:44:44 PM The signals we are looking for Semileptonic Hadronic B s Momentum is measured B s mass used for good S/N Small branching ratio: low yield Missing momentum ( ) Need to rely on D s mass Large branching ratio: high yield Bs/BsBs/Bs 

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 22 ⁫● 03:44:44 PM A typical B event at a hadron collider => look for displaced tracks Trigger on events with two displaced (d>120  m) tracks d very fast reconstruction of silicon data at L2 (20  s latency) by dedicated hardware: SVT cdf d (  ) Displaced track trigger

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 23 ⁫● 03:44:44 PM Hadronic signals Added partially reconstructed modes in the Ds->  mode. Bs/BsBs/Bs  undetected particles have small momentum => decay is almost fully reconstructed

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 24 ⁫● 03:44:44 PM Hadronic signals reflection of less severe because we check that the PID of the kaon. Allows looser veto based on M KK  - M D + Added one new decay mode B s -> six pions

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 25 ⁫● 03:44:44 PM hadronic signal selection signal selection previously done using cuts on kinematic variables, vertex displacement, fit quality.... select signal using NN inputs: O(30) variables including all of the above & P T of tracks, D s 's  's, K*, PID particle-ID likelihoods use measurement of time-of-flight and dE/dx in the COT to distinguish kaons from pions. careful to make sure NN is not trained to select mass. (e.g.  R not used as input variable) gain signal lose only background

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 26 ⁫● 03:44:44 PM hadronic yields 8700 signal events (was 3700) improved S/B too equivalent to an increase in sample size of a factor 2.5

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 27 ⁫● 03:44:44 PM Semileptonic signals improvements: using particle ID to identify kaons reduces combinatorial background eliminates need for explicit D + rejection 62k Bs signal events (was 37k)

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 28 ⁫● 03:44:44 PM Proper decay time and resolution

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 29 ⁫● 03:44:44 PM Proper time reconstruction: hadronic  Hadronic: ●  ct 0 : ~ 30  m (100 fs) ●  p /p < 1%  Semileptonic ●  ct 0 : ~ 50  m (167 fs) ●  p /p ~ 15% (K factor) Bs/BsBs/Bs LxyLxy piece of cake! Bs mass from the PDG, PT from adding up the moment of all the decay tracks

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 30 ⁫● 03:44:44 PM Proper time: semileptonic  Hadronic: ●  ct 0 : ~ 30  m (100 fs) ●  p /p < 1%  Semileptonic ●  ct 0 : ~ 50  m (167 fs) ●  p /p ~ 15% (K factor) Bs/BsBs/Bs LxyLxy ● k-factor PDF obtained from Monte Carlo ● Take advantage of variation with l D s mass. ● high m lDs means small missing p T ) ● can not measure p T for semileptonic ● large uncertainty in ct for high Lxy ● correct for missing p T on average:

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 31 ⁫● 03:44:44 PM Proper time resolution Effect of non-zero ct error asymmetry: attenuation of the oscillation Smearing of decay time causes attenuation of asymmetry signal: Have to know  ct to measure the mixing amplitude How to measure  ct ? 2 2 )( t t m eD     

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 32 ⁫● 03:44:44 PM Measuring the proper time resolution Cannot measure the ct resolution directly on data (no prompt peak in the B s signal due to trigger) Solution: construct events that look like a B but are known to come from the PV.. real D some pion from the underlying event (i.e. from PV) True must be zero; compare error with predicted error from the vertex fit. And study dependence on kinematic variables, isolation,  2 of fit etc..

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 33 ⁫● 03:44:44 PM proper time resolution period for  m s = 18 ps -1 ● partially reconstructed hadronic almost as good as the fully rec. ● time resolution = ¼ oscillation period

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 34 ⁫● 03:44:44 PM 3) Flavour tagging

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 35 ⁫● 03:44:44 PM Flavor tagging Bs/BsBs/Bs L xy We need to know the flavor of the B s at production. Opposite side tag: look at the decay products of the other b quark in the event: Lepton Kaon Charge of the b-'jet' the two b quarks fragment independently: can calibrate opposite side taggers with B d & B u other B often outside acceptance Same side kaon tag: look at particles produced in B meson formation (K in case of Bs) Very powerful (high acceptance) but cannot calibrate on B d & B u Need to rely on MC K e/  K

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 36 ⁫● 03:44:44 PM A tagger is characterized by  : efficiency D: dilution = 1-2 x mistag rate (large dilution is good) Dampens asymmetry: Effective statistical power / figure of merit =  D 2 x D We must know what D is to measure A D<1 dampens the oscillation signal Flavor tagging II

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 37 ⁫● 03:44:44 PM OST: improvement previous analysis: In case multiple tagger gave a decision, used the best one new analysis combine all tagger decision, per-event predicted dilutions and kinematic variables into a single Neural Network, producing tag decision & dilution.

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 38 ⁫● 03:44:44 PM ● Fragmentation into B s tends to produce an additional kaon. ● Charge of K identifies B s flavor at production ● B 0 and B + mostly accompanied by pions ● Use combined likelihood from time-of-flight detector and dE/dx in COT identify Kaons Same side kaon tagging

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 39 ⁫● 03:44:44 PM Same side kaon tagging tagger not optimized for these modes, but valuable check that MC predicts the right dilution

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 40 ⁫● 03:44:44 PM Same side kaon: improvements Previously based only on particle ID Kinematic variables can also be used for for selecting the tagging track Combine in Neural network PID likelihood,  R, p T p T rel, p L rel,... improvement in  D 2 based on predicted dilutions for events: semileptonic data: +8% hadronic data : +0% monte carlo : +6% %OST 3.7(4.8)% D2D2 SST Tag final tagger performance

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 41 ⁫● 03:44:44 PM Blind Amplitude Scan (July 25) With all the improvements:  A < 0.2 → good chance of seeing 5 . unblind! (old value: 0.28)

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 42 ⁫● 03:44:44 PM Results

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 43 ⁫● 03:44:44 PM Results

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 44 ⁫● 03:44:44 PM Results depth of likelihood dip= what is the significance of such a dip? old value

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 45 ⁫● 03:44:44 PM significance “Observation” Randomize the tagger decisions of the data events and repeat the likelihood scan many many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many times

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 46 ⁫● 03:44:44 PM comparing taggers Opposite side tagger Same side kaon tagger Both taggers see the oscillations

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 47 ⁫● 03:44:44 PM Comparing datasets partially reconstructed hadronic modes semileptonic modes fully reconstructed hadronic modes all see the signal!

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 48 ⁫● 03:44:44 PM measurement of  m s and |V td |/|V ts | uncertainty of length scale of detector limited by theory error

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 49 ⁫● 03:44:44 PM asymmetry mt PP PP A mixumix mixumix     cos asymmetry time stack all oscillation periods on top of each other and fit for A in bins of proper decay time... data are well described by the expected cosine curve. hadronic data only

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 50 ⁫● 03:44:44 PM asymmetry

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 51 ⁫● 03:44:44 PM conclusions We have 'Observed' Bs mixing p-value = 8x10 -8, significance is 5.4   We measure

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 52 ⁫● 03:44:44 PM

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 53 ⁫● 03:44:44 PM World average back in 1999 just for fun Abbaneo & Boix: JHEP 08(1999)004 “p-value = 3%”

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 54 ⁫● 03:44:44 PM all data before 2004 LEP + SLD World average before Tevatron run II Amplitude scan: fix  m s and measure the amplitude of the corresponding frequency component (Fourier) Recent D0 result ● 17 <  ms <21 ps-1 at 90% CL ● p-value = 5% previous results

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 55 ⁫● 03:44:44 PM likelihood and amplitude scan Amplitude: quantity constructed so that A=1 if the data (i.e. the likelihood) consistent with mixing A=0 everywhere else Amplitude is 'easy' to understand, but we use the likelihood to make the measurement, namely: signature of a signal signature of a signal

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 56 ⁫● 03:44:44 PM ● resolution ~ 100 ps ● separates kaons from pions up to 1.5 GeV ● crucial for SSKT Time of flight detector

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 57 ⁫● 03:44:44 PM Expected CDF Sensitivity With L00 Without L00 95% CL sensitivity 3  sensitivity  ms AA

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 58 ⁫● 03:44:44 PM cdf-II error at 15.0/ps : 0.2

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 59 ⁫● 03:44:44 PM likelihood definition the probability to measure an event as (un)mixed as a function of the measured decay time: the probability that an event mixes (does not mix) as a function of the true decay time: goodness of flavor tagger (dilution) time resolution (sketch of) -log likelihood of all events: If the data are compatible with oscillations, -log(L) has a dip at the right value of  ms

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 60 ⁫● 03:44:44 PM The big questions How accurately can we measure  m s ? determined by shape of the likelihood at minimum How sure are we that what we are seeing is not just a random fluctuation? formally: What is the probability that an apparent signal at least as significant as the one we see in data would occur at any value of  m s in case there is no signal in reality? probability that a dip so deep would come from random fluctuation = 0.2 %

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 61 ⁫● 03:44:44 PM Opposite side taggers Measure opposite side tagger dilutions Simultaneous fit to lD +, lD 0 and lD* modes predicted dilution dilution scale factor Dilution predicted on event-by-event basis (based on P T rel, lepton-id etc). how to check/calibrate the prediction is correct?

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 62 ⁫● 03:44:44 PM Amplitude scan in sideband

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 63 ⁫● 03:44:44 PM A nice event

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 64 ⁫● 03:44:44 PM systematics on amplitude

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 65 ⁫● 03:44:44 PM systematics on  m s

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 66 ⁫● 03:44:44 PM likelihood definition the probability to measure an event as (un)mixed as a function of the measured decay time: the probability that an event mixes (does not mix) as a function of the true decay time: goodness of flavor tagger (dilution) time resolution (sketch of) -log likelihood of all events: If the data are compatible with oscillations, -log(L) has a dip at the right value of  ms

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 67 ⁫● 03:44:44 PM  and cpv sigma(deltagamma) sigma(phi)

Aart Heijboer ⁫● Observation of Bs oscilations ⁫●⁫ Nikhef special seminar ⁫⁫● 01/08/07 ⁫● slide 68 ⁫● 03:44:44 PM likelihood definition the probability to measure an event as (un)mixed as a function of the measured decay time: the probability that an event mixes (does not mix) as a function of the true decay time: goodness of flavor tagger (dilution) time resolution (sketch of) -log likelihood of all events: If the data are compatible with oscillations, -log(L) has a dip at the right value of  ms