1. FRAGMENTAION UNCERTAINTIES IN THE EXTRACTION OF FROM THE SEMI-INCLUSIVE MEASUREMENT OF B  X d  Tim Beck, Bruce Schumm Radiative Penguin Meeting April 17, 2008

2. Measured quantity: R obs = Electroweak quantity R EW = How well can we determine  ?

3. Breakdown of Measured/Unmeasured Width Nominal Signal MC M had #  0 # bodies MEASURED UNMEASURED ( , ,K * ) 1.0 < M had < 1.81.8 < M had XSXS XdXd

4. Goal: Estimate systematic error on correction factor  in M had < 1.8 GeV region (extrapolation to full mass region a separate systematic) with X d,S M the white measured fraction in the diagram on the previous page For estimation of systematic effects, assume M had < 1.0 GeV region is a fixed 10% contribution (K*/rho/omega dominant  largely model-independent)

5. Alternative 0: Nominal Model X S,d mass distribution from KN465. Fragmentation of X S,d system via “phase space” (switch within JETSET). Nominal (1 < M had < 1.8) Measured % X d (X s ) Unmeasured % X d (X s ) 2, 3, and 4 Bodies 19.2 (17.2)11.2 (22.8) 5+ Bodies11.9 ( 3.4) Total19.2 (17.2)23.1 (26.1)  = 0.94 Again,  is the factor that multiplies the observed BF ratio to give the EW observable  (b  d  )/  (b  s  )

6. Alternative I: Reweight to Measured Fragmentation Fragmentation has been measured for X s  ; reweight nominal model to agree with measurements. Apply same weights to both X s  and X d  Keep low-mass (M had < 1.0) region at 10% of width; again, calculate  for region 0 < M had < 1.8 only. Reweight X d,X s (1 < M had < 1.8) Measured % X d (X s ) Unmeasured % X d (X s ) 2, 3, and 4 Bodies 9.3 (12.6)16.6 (35.9) 5+ Bodies16.1 (6.5) Total 9.3 (12.6)32.7 (30.8)  = 1.18 Measured fraction drops more for X d than X s ; differences picked up about equally between 2/3/4 and 5+ bodies

7. Alternative II: 50% Resonances (B  X R  ); 50% Weighted X R S is equal amounts of K1(1270), K1(1400), K*(1410), K*2(1430), K*(1680) X R d equal amounts of h 1 0 (1170), b 1 0 (1235), b 1 + (1235), a 1 0 (1260), a 1 + (1260), f 2 0 (1270), f 1 0 (1285), a 2 0 (1320), a 2 + (1320) 50% Resonant (1 < M had < 1.8) Measured % X d (X s ) Unmeasured % X d (X s ) 2, 3, and 4 Bodies 28.0 (25.3)27.7 (35.9) 5+ Bodies10.7 (3.4) Total 28.0 (25.3)38.4 (39.3)  = 0.93 Similar, larger measured fraction for both X S and X d ; 5 bodies almost gone for X S.

8. Alternative III: Reduced X d 5+ Bodies Reweighted X d is about 40% 5+ bodies while reweighted X S is about 15%. Due to presence of X R h and X R h h decays of X d ; not observed for X s (plus slightly higher multiplicity decays of X R for X d case). Reduce X d 5+ bodies to 15% Measured % X d (X s ) Unmeasured % X d (X s ) 2, 3, and 4 Bodies 12.9 (12.6)22.9 (35.9) 5+ Bodies 6.3 (6.5) Total 12.9 (12.6)29.2(30.8)  = 0.99 Reduction of X d 5+ bodies increases measured fraction accordingly.

9. Alternative IV: Reweight X S Only MC suggests that X S and X d fragmentation is governed by different principles (resonance characteristics rather than parton strings). Not clear that they should be trated equivalently Reweight X d,X s (1 < M had < 1.8) Measured % X d (X s ) Unmeasured % X d (X s ) 2, 3, and 4 Bodies 19.2 (12.6)11.2 (35.9) 5+ Bodies11.9 (6.5) Total 19.2 (12.6)23.1 (30.8)  = 0.78 Shifts a lot of X S into unmeasured region without corresponding shift for X d.

10. SUMMARY Model  Nominal0.94 Reweight Both1.18 Reweight X S Only0.78 50% Resonances0.93 X d 15% 5+ Body0.99 Overall range is between 0.78 and 1.18, with a concentration close to 1.0. One idea is to take average of largest and smallest:  = 0.98  0.20 Note: Does not include systematics from efficiency vs. multiplicity for measured modes, or for extrapolating beyond M=1.8 GeV