Measurements of f D + and f Ds

Measurements of f D + and f Ds Jim Libby (University of Oxford) With thanks to S. Stone, L. Zhang and D. Asner 1

Outline Introduction and motivation f D + determination at CLEO-c f Ds determinations at: CLEO-c with D s µν and D s τ(πν)ν CLEO-c with D s τ(eνν)ν Belle with D s µν BABAR with D s µν Conclusions and outlook

Leptonic Decays: D l + ν _ c and q can annihilate, probability is proportional to wave function overlap Standard Model decay diagram: gluons V cd or cs In general for all pseudoscalars: + 1 m ν GF fpm M + l l l P V Qq 8π MP Γ(P ) = 1 Calculate, or measure f D if V Qq is known, here take V cd =V us = 0.56, V cs =V ud = 0.974 (s) (s) 3

Relationship to CKM Only a few measurements are independent of strong interaction calculations CP violation where we interfere one decay diagram with a mixing diagram (B o J/ψ K o ) Many important quantities measured in CKM are combinations of strong and weak parameters Interpreting B and B S mixing in terms of CKM parameters requires knowledge of f B /f s B Extracting V ub requires knowledge of absolute value of form-factors for B π(ρ)lν at least at one value of q 4

New Unquenched Lattice Calc Follana et al HPQCD & UKQCD collaborations (PRL 100, 0600 (008)) New predictions of f D += 07±4 MeV f Ds = 41±3 MeV Older unquenched from FNAL+MILC +HPQCD are: f D += 01±3±17 MeV f Ds = 49±3±16 MeV (Aubin et al., PRL 95, 100 (005)) 5

Beyond the SM sensitivity Besides the obvious interest in comparing with lattice & other calculations of f D there are NP possibilities CLEO s previous measurement of f Ds + Belle s (see Rosner & Stone arxiv:080.1043) give f Ds =74±10 MeV as compared with 41±3 MeV +1 unquenched lattice QCD calculation of Follana et.al (PRL 100, 0600 (008)) Dobrescu & Kronfeld (arxiv:0803.051) argue that this can well be the effect of NP, either charged Higgs (their own model) or leptoquarks CLEOs previous measurement of f D + was too inaccurate to challenge Follana et al., theory 07±4 versus 3±17 MeV (CLEO) 6

Situation Prior To FPCP 008 Experiment f Ds : CLEO measures both µ + ν & τ + ν, & Belle measures µ + ν. Average is 3.3 σ away, could be a fluctuation D + too inaccurate to say anything Updates to both CLEO measurements 7

> Favoured methods at CLEO-c Two-body production e + e DD Double tags at 3770 MeV: fully reconstruct one D 0 or D +, then one can either fully reconstruct the other D for absolute branching ratios and quantum correlations or look for events with one missing particle in leptonic decays, semileptonic decays or hadronic K L decays Similarly, double tags at 4170 MeV: here look for a D S or a D S * Some measurements also done using single tags e K > > > > + - D > D > π e 8

Basic Technique for D + µ + ν 1. Fully reconstruct a D ±, and count total # of tags. Seek events with only one additional oppositely charged track within cosθ <0.9 & no additional photons > 50 MeV (to veto D + π + π o ) 3. Charged track must deposit only minimum energy (from ionization) in calorimeter, E < 300 MeV True for 98.8% of muons Rejects 45% of π s 4. Compute missing-mass squared (MM ). If close to zero then almost certainly we have a µ + ν decay. MM = ( E E ) ( p p ) D + + + + We know that E D + =E beam and p D + = p D - l D l 9

Tags mbc = Ebeam p i i Particle ID from RICH & de/dx Total of 460,000 tags Background 89,400 10

The MM Distribution K o π + peak µ + ν peak τ + ν, τ + π + ν region 11

MM Signal Shapes MM = ( E E ) ( p p ) Beam + + l D l Events/0.01 GeV 400 300 00 Check with shape of K o π + peak, fit with double- Gaussian 100-0.10-0.05 0 0.05 0.10 MM (GeV ) Monte Carlo Signal µν Monte Carlo Signal τν, τ πν 1

Model of K o π + Tail Use double tag D 0 D 0 events, where both D 0 K π ± K π ± K π ± π o Make loose cuts on nd D 0 so as not to bias distribution: require only 4 charged tracks in the event Compute MM ignoring K ± Expectation from residual π + π (1.1 events) Gives an excellent description of shape of low mass tail Extra 1.3 event background in signal region 13

Additional floating backgrounds Background cocktail composed of three-body modes τ + decays: ρ + ν and µ + νν Semileptonic decays: π 0 µ + ν (check with e + ) Hadronic decays: ρ + π 0 We only use the shape in MM, not the absolute number 14

Fit MM to sum of signal & bkgrd Case(i) E< 300 MeV where τ + ν/µ + ν is fixed to SM ratio 149.7±1.0 µν 8.5 τν Case(i) E< 300 MeV where τ + ν/µ + ν is allowed to float 153.9±13.5 µν 13.5±15.3 τν π + π ο µν Background cocktail K o π τν, τ πν 15

Residual Backgrounds for µυ Monte Carlo of continuum, D o, radiative return and other D + modes, in µν signal region This we subtract off the fitted yields 16

Background Check Use case (ii) E>300 MeV Fix τν & µν from case (i) µν. Consider signal region MM <0.05 GeV. Expect 1.7 µν + 5.4 π + π ο + 4.0 τν = 11.1 Find 11 events Additional background 0.1±3.3 events π + π ο Background cocktail K o π τν, τ πν µν 17

Systematic Errors Source of Error % Finding the µ + track 0.7 Minimum ionization of µ + in EM cal 1.0 Particle identification of µ + 1.0 MM width 0. Extra showers in event > 50 MeV 0.4 Background 0.7 Number of single tag D + 0.6 Total. 18

Branching Fractions & f D + Fix τν/µν at SM ratio of.65 PRD 78, 05003 (008) BF(D + µ + ν)= (3.8±0.3±0.09)x10-4 f D +=(05.8±8.5±.5) MeV This is best number in context of SM Float τν/µυ BF(D + µ + ν)= (3.93±0.35±0.10)x10-4 f D +=(07.6±9.3±.5) MeV This is best number for use with BSM models These numbers have been radiatively corrected by 1% in the branching ratio for D + γd* + γµ + ν Also, limits on BF(D + e + ν), BF(D + τ + ν) and A CP (D + µ + ν) All agree with SM expectation 19

CLEO-c s improved measurement of f Ds CLEO has two methods of measuring f Ds Measure µ + ν & τ + ν, τ + π + ν using similar MM technique used for D +. Update result using new analysis & 30% more data (~400 pb 1 ) Updated 008 Measure τ + e + νν by using missing energy. This result has not been updated (~300 pb 1 ) PRL 100, 161801 (008) 0

Use e + e - D S D S * at 4170 MeV Presence of D S * causes analysis changes: Reconstruct D S Find the γ from the D S * & compute MM* from D S & γ MM * = ( E E E ) ( p p ) CM - - D γ D γ Select combinations consistent with a missing D S + & count the number Find MM from candidate muon for (i) E< 300 MeV in Ecal, (ii) E>300 MeV or (iii) e - cand. MM = ( E E E E ) ( p p p ) CM - - D γ µ D γ µ 1

D S - Tags: Invariant Mass 1000 10000 8000 6000 4000 000 K + K - π 00 000 K S K - 900 ηπ 1800 800 1600 700 1400 600 100 500 1000 400 800 600 300 400 00 00 100 Events / ( 0.00 GeV ) 500 400 300 00 100 η'π η' π π + η 14000 1000 10000 8000 6000 4000 000 7000 6000 5000 K + K - π π ο 4000 π π π + 3000 000 1000 3000 500 K* o K* - 3500 3000 500 000 1500 1000 500 000 1500 1000 η ρ 000 1500 1000 η'π η' ργ 500 500 500 1.94 1.96 1.98 1.9 1.94 1.96 1.98.0 1.94 1.96 1.98 LHCb Presentation July, 008 1.9 1.94 1.96 1.98.0 1.94 1.96 1.98 1.9 1.94 1.96 1.98.0 M(D s) (GeV)

) ) ) ) ) ) ) ) ) MM* Distributions From D S + γ Events / ( 0.01 GeV Events / ( 0.01 GeV 500 000 1500 1000 500 350 K + K - π 500 K 300 S K - ηπ 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 180 160 140 10 100 80 60 40 0 η'π η' π π + η Multi γ bkgrnd Sideband bkgrnd 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) Events / ( 0.01 GeV Events / ( 0.01 GeV 400 300 00 100 4000 3500 3000 500 000 1500 1000 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 500 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) Events / ( 0.01 GeV Events / ( 0.01 GeV 50 00 150 100 000 1800 K + K - π π ο π π π + 50 1600 1400 100 1000 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 800 600 400 00 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) Events / ( 0.01 GeV 600 500 400 300 1000 K* o K* - η ρ Events / ( 0.01 GeV 800 600 Events / ( 0.01 GeV 800 700 600 500 400 η'π η' ργ 00 100 400 00 300 00 100 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 0 3.5 3.6 3.7 3.8 3.9 4 4.1 4. MM* (GeV ) 3

MM data for D S Total of 30848±695 tags 98.% of µ + ν in E < 300 MeV 55%/45% split of τ + ν, τ + π + ν in two cases Events/ 0.01 GeV 30 0 10 0 16 8 0 case (i) case (ii) E < 300 MeV E > 300 MeV K o π, ηπ region Track consistent with electron Small e - background 0 0.00 0.5 0.50 MM (GeV ) 4

Fit to signal & background 60 Case (i) + Case(ii) Events / ( 0.0 GeV ) 50 40 30 0 10 µ + ν τ + ν -0.1 0 0.1 0. MM (GeV ) Background D S sidebands Extra background from real D S+, mainly 3-body LHCb Presentation July, 008 5

Systematic Errors Source of Error % Finding the µ + track 0.7 Particle identification of µ + 1.0 MM width 0. Extra showers in event > 300 MeV 0.4 Background 0.5 Number of single tag D - S 3.0 Total 3.3 6

Branching Ratio & f Ds (preliminary) Mode BF (%) f D (MeV) (1) µν+τν (fix SM ratio) BF eff (D s µν) = (0.613±0.044±0.00) () µν only BF(D s µν) = (0.600±0.054±0.00) (3) τν, τ πν BF(D s τν) = (6.1±0.9±0.) s 68.±9.6±4.4 65.4±11.9±4.4 71±0±4 7

CLEO: D S+ τ + ν, τ + e + νν BF(D S+ τ + ν) BF(τ + e + νν) 1.3% is significant compared with expected BF(D S+ Xe + ν) 8% Search for events opposite a tag with one electron and very little additional energy Opt to use only a subset of the cleanest tags 8

Measuring D S+ τ + ν, τ + e + νν Technique is to find events with an e + opposite D S- tags & no other tracks, with Σ calorimeter energy < 400 MeV No need to find γ from D S * BF(D S+ τ + ν) =(6.17±0.71±0.36)% f Ds =73±16±8 MeV 400 MeV PRL 100, 161801 (008) 9

Branching Ratio & f Ds (preliminary) Mode BF (%) f D (MeV) (1) µν+τν (fix SM ratio) BF eff (D s µν) = (0.613±0.044±0.00) () µν only BF(D s µν) = (0.600±0.054±0.00) (3) τν, τ πν BF(D s τν) = (6.1±0.9±0.) (4) τν, τ eνν BF(D s τν) = (6.17±0.71±0.36) CLEO Average of (1) & (4) Rad. corr. s 68.±9.6±4.4 65.4±11.9±4.4 71±0±4 73±16±8 69.4±8.±3.9 67.9±8.±3.9 30

Belle: D S+ µ + ν Look for e + e - DKXγ(D S ), where X=nπ & the D S is not observed but inferred from calculating the MM Then add a candidate µ + and compute MM BF(D S+ µ + ν) = (0.644±0.076±0.057)% f Ds =75±16±1 MeV Results stable as a function of final state multiplicity 548 fb 1 PRL 100, 41801 (008) 31

BABAR: D S+ µ + ν PRL 98, 141801 (007) Look for events with a tag D 0, D ±, D * or D s with both a µ and aγ consitant to be from D s * decay in the rest of the event Approximate neutrino 4-mom to (E miss, p miss ) Compute M = M ( µνγ ) M ( µν ) Subtract background using sidebands and electron sample Remaining background from mis- IDed muons in ccbar and misreconstructed signal Fit M distribution to extract signal f Ds =(83±17(stat)±7(syst)±14(D s φπ)) MeV 30 fb 1 3

f D & f / f + s Ds D Weighted Average of absolute measurements from CLEO + Belle: f Ds =70.4±7.3±3.7 MeV, the systematic uncertainty is uncorrelated between the measurements Using f D + = (05.8±8.5±.5) MeV f Ds /f D + = 1.31±0.06±0.0 larger than LQCD predictions Γ(D S+ τ + ν)/γ (D S+ µ + ν)=10.3±1.1 SM=9.7 Consistent with lepton universality 33

Conclusions More data required to see if experiment and theory are significantly inconsistent 06(9) 68(9) 34

Future datasets CLEO will further update f Ds using at total of ~600 pb -1 50% increase in data for µν 100% increase in data for τν, τ eνν Improved D s tag systematic to 3% % f D + will not see any major improvements until BES Also for f Ds can run at 4030 MeV for D s D s production only Reduce tag yield systematic < 1% B-factories plans: BABAR: absolute measurement with full set Belle: update with final 0.9-1.0 ab 1 data set 35

Backup 36

Case(i) With τ + ν/µ + ν Floating Fixed 149.7±1.0 µυ 8.5 τν Floating 153.9±13.5 µυ 13.5±15.3 τν LHCb Presentation July, 008 37

Upper limits on τ + ν & e + ν Fit both case(i) & case(ii) constraining the relative τν yield to the pion acceptance ratio 55:45. case (i) E<300 MeV case (ii) E> 300 MeV Find BF(D + τ + ν) < 1.x10-3, @ 90% c.l. BF(D + τ + ν)/.65bf(d + µ + ν) < 1. @ 90% c. l. Also BF(D + e + ν)< 8.8x10-6, @ 90% c.l. 38

CP Violation D + tags 8,945±551 D - tags 31,107±55 µ ν events 64.8±8.1 µ + ν events 76.0±8.6 A CP + + Γ( D µ ν ) Γ( D µ ν ) = 0.08 ± 0.08 + + Γ( D µ ν ) + Γ( D µ ν ) -0.05<A CP <0.1 @ 90% c. l. Consistent with SM expectation of no direct CP violation 39

µν Signal Shape Checked K o π + data K o π + MC Data σ=0.047±0.001 GeV MC σ=0.035±0.0007 GeV Both average of double Gaussians 40

Other Non-absolute Measurements Exp. mode BF BF(D S φπ) f Ds (MeV) (%) See arxiv:080.1043 for references 41

Possibilities Pick your favorite of the three: Experiment will eventually converge on SM predicted value If LQCD predictions of f Ds /f D + do not agree with the data, why should we believe f Bs /f B from theory? What does this do to the CKM fits? If there is New Physics affecting leptonic D S decays, how does it affect B S mixing and other B S decays? (See A. Kundu & S. Nandi, R-parity violating supersymmetry, B S mixing, & D S+ l + ν [arxiv:0803.1898]) 4

If there is a Shift.. If increases the radius of the m d / m s constraint increases Red arrow indicates a shift of ~10% in f Bs /f B 43

New Physics Possibilities Ratio of leptonic decays could be modified e.g. in Standard Model + + τ ν m / m τ µ m 1 m 1 + + τ µ µ ν MP MP Γ(P ) = Γ(P ) If H ± couple proportional to M no effect See Hewett [hepph/950546] & Hou, PRD 48, 34 (1993). 44

New Physics Possibilities III Leptonic decay rate is modified by H ± Can calculate in SUSY as function of m q /m c, In HDM predicted decay width is x by tan β m q rq = 1 M D M ± H m c + m q Corrected M D 1 rq = 1 + mc mq tan mc + m q M ± H See Akeryod [hep-ph/030860] Since m d is ~0, effect can be seen only in D S ( β ) = meas rate/sm rate From Akeroyd tan β/m H 45