D hh ν. Four-body charm semileptonic decay. Jim Wiss University of Illinois

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1 Four-body charm semeptonc decay Jm Wss Unversty of Inos D hh ν 1 1. ector domnance. Expected decay ntensty 3. SU(3) apped to D s φν 4. Anaytc forms for form factors 5. Non-parametrc form factors 6. Future drectons 1

2 ery heavy domnated by vector resonances D Kπν D s KKν D ππν Premnary A K*? A φ? A ρ? M(Kπ) M(ππ) M(KK) Decay descrbed by 3 hecty form factors. One for each vector hecty component A χ (1 cos ) sn e χ = (1 cos ) sn e 8 sn cos Intensty gven by 3 nterferng amptudes

3 ecty form factors wrtten n terms of axa and vector form factors A ± = A A 1 Form of the hecty form factors Cauchy Theorem Im{ s} α 1 β ( m ) D K * = γ δ Spectroscopc approach (SPD) Anaytcty provdes nsght nto ( ) and A ( ) m = { } Re s poe R m 1 π cut ( m *) D K s { f s) } Im ( 1, gnores cut ntegra competey 1, Under SPD, just two numbers descrbe anguar dstrbuton 3 ds ε () A () = A = 1 /.1 1 /.5 R D K* ν dγ dcos dcos dχ d v ( os v,co s, χ, ;, ) Fc R R () = and R = A A A 1 1 ()

4 R R FOCUS FOCUS BEAT BEAT Exampe of SPD approach years of fts to D K*ν 1.66±.6 E791 tme E791 E ±.55 E687 E653 E653 E691 E691 R R Juy 6 D s φν Od resuts ndcated a probem wth SU(3) symmetry whch s now appears resoved But we know SPD doesn t work for D Kν ow can t work for D K* ν?? 4

5 Two SPD remedes Modfed poe forms = m D* R { f s } 1 Im π md K s ds ε Becrevc & Kadaov wrte ntegra as effectve poe wth m f D D* QET&SCET f = c m = m D* D γ md* γ m eff D* αγ cm D* Res & Poe α =1/ γ f = ( 1 / md* )( 1α / md* ) The effectve poe adds one new parameter α α s SPD voaton Fajfer and Kamenk (5) extended modfed poes to vector decays transformaton pane Z pane R.J. makes a compex mappng that pushes the cut snguartes far from the physca regon. physca cut R.J. hep-ph/663 (FPCP6) Form factors are then gven by a smpe Tayor seres for z << 1 a a1 P() t φ( t) f z = z Do we need these remedes n vector semeptonc decays? 5

6 Averagng over acopanarty χ we have: A cosl Projectng out the hecty form factors ((1 cos )sn ) ( ) = ( ) cos (1 cos )sn ( ) sn cos FF products are soutons = D f m f m ( ) m f ( ) ( ) and wrtten as f ( ) = P Each term has a characterstc pattern n the 9 bns that we use to dsentange to D () = P D: M M- M m vectors (anguar bn ) where the projecton vectors are just: 1 P m m m m m m m P = m m mm mm m P mm mm mm m The hecty form factors are projected out based on anguar bn popuatons () ( ) P D D obtaned from weghted hstogram 6

7 Same approach can be used for hadronc decay D KKπ FOCUS used ths technue to project out the S wave, P wave, and SP nterference peces of the Kπ amptudes n D KKπ decay. SKπ ( ) P S ( K π ) PKπ ( ) K*(143)? K*(89)???? M(Kπ) 7

8 An S-wave D Κπ μν component Athough Kπ ne shape s a great match to pure BW FOCUS () observed a cos decay asymmetry A ((1 cos )sn ) 1 ((1 cos )sn ) = 8 ( sn cos ) 8sn cos Re BW BW BW δ ( ) h o { Ae BW } Same hecty nterference survves dχ We ncude the nterference term by addng a 4th projector for h pece. 1 P m m m m m m m mi m P = m m m m m m m mi m P mm mm mm m m I m mim m I P I m mim mimi mi We can measure h ( ) neary as we as ( ), Snce nterference term has odd party and s orthogona to other projectors. 8

9 Non-parametrc D K π e ν Form Factors (81 pb 1 ) We pot ntensty contrbutons Mutpy the FF products by CL = 4% SPD mode CL = 4% α β ( ) ( ) CL = 59% h( ) CL =.% As : Upper pots ; Lower pots 1 (normazaton) Apart from s-wave nterference, the CL to the SPD mode are good. (Ge /c ) 9

10 As Understandng the asymptotc forms, the eptons become conear As max, the W and K* are at rest and no hecty axs can be defned sotropy We thus expect - 1 Isotropy and observe: Natura ecty Unnatura ecty = ± const ( ) = ( ) ( ), - constant max constant (Ge ) (Ge ) 1

11 Can we test SPD? Poe Mass Senstvty n Data M =.1 M A =.5 ( ) α β ( ) Constant A & ( ) Data fts spectroscopc poes and constant form factors euay we. No evdence for or aganst SPD. 11

12 Confrmng the s-wave phase n D K π e ν Beow K* Above K* Focus () saw the cos asym ony beow the K* poe. Ths s due to Re δ { Ae BW } cos CLEO ony sees nterference beow the K* as we ( ) δ h Re{ Aexp( ) BW } mk ( π )<.896 mk ( π )>.896 CLEO-c (Ge / c ) BW Im δ A BW Re The dsappearance of the nterference above the K* and the (-) nterference beow mpes the above phase reatonshps between the BW and the s-wave amptude. δ 45 1

13 Add a D-wave projector Search for D-wave Kπ h D m < K * m > K * Guard aganst phase canceaton by showng above and beow the K* Ge 1 1 No evdence for h D( ) or h ( ) F 13

14 Premnary Z transform of K*e ν decay by Anayss of CLEO non-parametrc data by R.J. (prvate communcaton) P φ (z) The z range s 4 smaer n D K* ν, compared to D Kν (z) w be essentay constant CLEO data D K π e ν -z Indeed the - transformed data seems neary constant as a functon of Z 14

15 A Future: mass suppressed form factors For D K π μ ν we can study and T T χ (1 cos ) sn e 1 m (1 cos )sn χ = m e 8 sn ( cos A ) Perhaps t w ook ke the ( FOCUS) mode? μ sn sn sn cos cos χ e sn e cos t χ We get both h and T nterference sx form factor products. α β ( ) h T T Our prognoss for semmuonc decays ooks good! The best T nformaton w come from the T nterference term. Semmuonc decay shoud aso mprove knowedge other form factors aong wth addtona data 15

16 Summary 1. A studed 4 body SL decays are heavy domnated by ector ν * Mosty descrbed by just 3 hecty form factors. Recent Ds φ ν anayss of BaBar confrms that Ds aso fts the SPD mode for D K* ν to hgh precson. * A nce test of SU(3) symmetry! 3. Non-parametrc method for form factor extracton n D K* e ν a. Studes on the s-wave term n D Kπ e ν (non-resonant). ) Frst measurements of ths new form factor h( ) ) Confrms FOCUS s-wave phase of 45 degrees b. Present data consstent wth SPD mode (apart from s-wave?) c. Ltte senstvty to axa and vector poes w/ present data d. No evdence for d or f wave e. transform: (z) ooks fat n z f. Woud ke to extend studes to D Kπ μ ν 16

17 Queston sdes 17

18 18 Anguar dstrbutons A sn sn (1 cos ) sn sn sn 1 (1 cos )sn 8 cos cos sn cos cos t e e e m m e A χ χ χ μ χ = A (1 cos ) sn (1 cos ) sn 8 sn cos e e χ χ =

19 Cauchy Theorem Im{ s} ( m K) D Re{ s} Poe Domnance <Mpoe> s 5.1 σ ower than D s * D s * m D* f ( R ) = 1 md* f ( ) = D D* QET&SCET { f ( s) } Im ds ( m ) π D K s ε Becrevc & Kadaov wrte ntegra as effectve poe wth f c m = m m D* D γ md* eff D* αγ cm γ m D* Res & Poe α =1/ γ f ( 1 / md* )( 1α / md* ) = Fts to f m 1 poe α = 5. ± 4. Integra term s mportant BK expresson s a good ft to recent attce cacuatons (4) 19

20 R.J. s New Approach to f ( ) z makes a compex mappng that pushes the cut snguartes far from maxmum. physca Iustrate wth B πeν data [ (6)] f ( ) cut 1x Pφf (z) R.J. hep-ph/663 (FPCP6) Juy 6 Form factors are gven by a smpe Tayor seres for z << 1 -z.5x a a1 P() t φ( t) f z = z For B π: The cut s very cose to the maxmum and f ( ) as max After z mappng, the physca and cut regon are far apart. The f (z) data s we ft wth just a straght ne as a poynoma. Charm data??