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1 Measurement of f D + via D + + Sheldon Stone, Syracuse University D o D o, D o K - + K-K- K+K+ ++ K-K- K+K+ “I charm you, by my once-commended beauty” Julius Cæsar, Act II, Scene I

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2 Importance of Measuring f D + and f D u We can compare theoretical calculations of f D to our measurements and gain confidence in theory to predict f B u f B is necessary to translate measurement of B o -B o mixing into value for |V td |. If we B + + was measured, then we would have a measurement of the product of |V ub | f B. Knowing f B gives V ub u Similarly, can check f Ds /f D to learn about f Bs /f B _ + s

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3 Leptonic Decays: D + Introduction: Pseudoscalar decay constants Q and q can annihilate, probability is to wave function overlap Example - : _ In general for all pseudoscalars: Calculate, or measure if V Qq is known V Qq

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4 Expected B for P + + decays u We know: f = 131.73±0.15 MeV f K = 160.6±1.3 MeV u The D s has the largest B, the µ + rate is ~0.5% u f Ds Measured by several groups, best CLEO II, but still poorly known For D + also use µ + +

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5 CLEO-c Detector u Upgrade of CLEO II. Kept CsI EM calorimeter, magnet & muon system u New charged particle tracking u New particle id via RICH u New inner wire chamber u B now 1 T, lowered from 1.5T ¼ section vertex wire chamber

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6 Kinematical Niceties Ease of B measurements using "double tags“ B A = # of A/# of D's u Possible because relatively large B (many %), u multiplicities typically small = ~2.5, ~ 1.2, u enough luminosity u Reconstruct D mesons using: System is over constrained if all particles are observed: p i 3, E tot 1, m D =m D 1

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7 D + K - + + & D - K + - - 377 events D+K-++D+K-++ Single tags Double Tags D + K - + + or D - K + - -, 15,120 events 57 pb -1 of data, we now have 280 pb -1

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8 Leptonic Decays u Ease of leptonic decays using double tags & MM 2 technique We know E D =E beam, p D = - p D u Search for peak near MM 2 =0 Since resolution ~ M o, reject extra particles with calorimeter & tracking u Note that this method is used to evaluate systematic errors on the tracking efficiency, simply by using double tags with one missing track 2

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9 Technique for D + + u Fully reconstruct one D Seek events with only one additional charged track and no additional photons > 250 MeV to veto D + + o u Charged track must deposit only minimum ionization in calorimeter u Compute MM 2 If close to zero then almost certainly we have a decay. u Can identify electrons to check background level Expect resolution of ~M o If MM 2 > 0, candidate for , but this is difficult 2 ±

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10 Single Tag Sample u From 280 pb -1

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11 Problem: how many events? u Fits to Asymmetric signal function (Crystal Ball shape) plus smooth background shape (ARGUS function) – error in tags ±0.3%

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12 MM 2 resolution MM 2 from K S - from data & MC =0.0222±0.0005 GeV 2 =0.0233±0.0009 GeV 2 Consistent now, for 1 st analysis data was 15% larger

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13 Backgrounds: D + + o u We don’t specifically identify muons, only reject hadronic interactions in the crystals. This mode has a B =(0.13±0.02)% Eliminate by requiring muon candidate be in good barrel region & reject events with an extra with E > 250 MeV. Residual effect is 0.3 events in 57 pb -1 and 1.4 events for 280 pb -1.

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14 Backgrounds: D + + + + Because D + is nearly at rest can get some very fast +. B is 2.65 x B (D + + u Background is calculated via MC with small error, 0.2 events for 57 pb -1 and 1.08 events for 280 pb -1

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15 Backgrounds: tail of D + K o + u Two methods u Monte Carlo: Simulation gives 0.44±0.22 events for 280 fb -1 u Measurement using double tag events with one D o K - + gives 0.44±0.44 events for 280 fb -1 1 bkgrd

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16 Other Backgrounds u Simulate: u Continuum sample 540 pb -1 gives 0 events u D o D o sample 540 pb -1 gives 0 events u D + D - 1700 pb -1 gives 0 events, other than the 3 modes we have already considered.

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17 One D + + Candidate

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18 Measurement of f D + MC Expectations from 1.7 fb -1, 30 X this sample Data show 8 events in the signal region in 57 pb -1

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19 Deriving a Value for f D + u Tags are 28,575 events, = 69.9% B ( D + + =(3.5±1.4±0.6)x10 -4 u f D + = (202±41±17) MeV No D + e + events seen Backgrounds Mode B (%) # Events +0+0 0.13±0.020.31±0.04 ++ 2.77±0.180.06±0.05 2.64* B (D + + ) 0.30 ±0.07 0 0.25 ±0.15negligible Continuum(old estimate) 0.33 ± 0.23 Total 1.00±0.25 For 57 pb -1

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20 Comparison to Theory u CLEO-c measurement – 8 events u BES measurement based on 2.67±1.74 events u Current Lattice measurement (unquenched light flavors) is consistent u But errors on theory & data are still large

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21 Systematic Errors (Current) Much smaller than statistical errors

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22 New Data u Now have ~50 events in peak around MM 2 =0 u New value will be announced at Lepton- Photon conference in Artuso’s talk. Error will be ±16 MeV u New Unquenched Lattice result to also appear u Thus we will have an interesting comparison +9 -7

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