1. 1 Semileptonic physics in FOCUS D  K  0 l form factor measurement –Motivation –Method and Signals D   l form factor measurement –Motivation –Signals D  K l non-parametric f(q 2 ) dependence –Motivation –Algorithm –Resolution functions –Anticipated measurement power

2. 2 Form factors as tests of LGT Quark Models LGT Models  Data Provides incisive tests of Quark models and Lattice Gauge calculations. Similar LGT calculations are important in CPV studies of B. Experimental data is self-consistent and is more accurate than present LGT calculations. - Much more accurate w/ FOCUS

3. 3 Measuring form factors R 2 and R v E791 muons 3034±595 events E687 875 ±44 events FOCUS FOCUS has ~80 x E687 and ~10 x E791 sample with “clean” cuts  l gon e

4. 4 Fit technique (Las Vegas weighting) Bin data in kinematic variables and fit K* yield in each bin Vary R 2 and R V in MC to minimize  2 between predict and obs yields –Generate MC once to get correct smearing and efficiency Impractical to generate complete MC for each fit iteration. –Re-weight the points for each R 2 and R V iteration to get predicted yield in each bin. Weighting for R 2, R V =.75,1.85 (bubble size proportional to weight) Weighting for R 2, R V = 0, 0.5

5. 5 Fitting the data cos(  v )  cos(   )  Background level and shape is very bin dependent! D*  , D  K  ? ? Subtract fitted WS K* yield in each bin

6. 6 Some Insidious Backgrounds Events from MC K*0  absent black is right sign red is wrong sign Two problems:  thought to be   really from D* Very easy to remove!

7. 7 Measuring R 2 and R v for  l  R2 Results are different from LGT predictions. Apparent unexpected inconsistency between measured form factors for: Data shows a 2  discrepancy between  l and K * l R 2 form factor – Unexpected in most models QMLGTData

8. 8  l Signals E687 127   events E791 144  e events E791 Expect comparable yield in  e ~70 x E687 ~20 x E791 FOCUS

9. 9 D 0  K l  q 2 dependence Form factor ratios are typically measured at low q 2 but predicted at q max 2 (Quark and LG) A pole form f ( q 2 ) is used to connect theory and experiment. Pole expected at D s * but appears lower experimentally BUT is the pole form valid? Here are 3 forms with similar slope but different extrapolations into D 0   l Which is right?? theory Data

10. 10 Direct Measurement of Allows a more incisive comparison of LGT with FF Limited q 2 resolution due to neutrino reconstruction Use a deconvolution to account for resolution:

11. 11 Testing Q 2 Resolution function K  K  Black - data Red - MC But can we trust the MC resolution function? Depends on details of the primary vertex properties and reconstruction. Use fully reconstructed K  and K . Blank one pion to act as the missing neutrino. Then compare “observed” resolution function in data to that predicted by MC. MC models bias and width very well!

12. 12 What Can We Expect to See in FOCUS ? Based on an simple Monte Carlo study, assuming a pole form 4 bins8 bins Pole (solid), Exponential (dash), Linear (dot) Even over limited K l range, the 3 forms can be easily distinguished. Parameterization free comparisons of f ( q 2 ) near q max 2 with theory should be possible!

13. 13 Summary FOCUS collected a huge data set with a totally rebuilt muon system and electromagnetic calorimetry. K  l –Anticipate ~80x more data than E687 and ~10x more than E791 –Incisive test of LGT model (Required for disentangling CPV in B) –Best signal to develop fit technique  l –Anticipate ~70x more data than E687 and ~20x more than E791 –Resolve long standing discrepancy between K  l and  l FF?? Kl –Measure f ( q 2 ) in a parameterization free way –Required to connect theory with experiment

14. 14 Finding the Neutrino’s Momentum Consider two daughters: Boost to “*” reference frame –Boost along D’s line of flight, given by primary and secondary vertices –Boost so that Pc is perpendicular to the D line of flight –Find the energy of the neutrino in this frame – –If is too large, the decay is “unphysical” –Normally there are two solutions Traditional solution P  balance E balance

15. 15 Two-fold Ambiguity and Unphysical Decays Which of the two solutions should we pick, the forward (high momentum) or backward one? The traditional choice is the backward one, which is justified here. Our acceptance is better for this topology K  K3K3 forward backward Often (about 40% of the time) Here we move the primary vertex the least distance necessary, just onto the cone of allowed primary vertex locations.