# 1 “Courses cooking in Semileptonic B Decays” or “Adding High Accuracy to High Sensitivity” Ikaros Bigi Notre Dame du Lac 10/’03 The Menu  |V(cb)|, |V(ub)|

## Presentation on theme: "1 “Courses cooking in Semileptonic B Decays” or “Adding High Accuracy to High Sensitivity” Ikaros Bigi Notre Dame du Lac 10/’03 The Menu  |V(cb)|, |V(ub)|"— Presentation transcript:

1 “Courses cooking in Semileptonic B Decays” or “Adding High Accuracy to High Sensitivity” Ikaros Bigi Notre Dame du Lac 10/’03 The Menu  |V(cb)|, |V(ub)| [|V(td)|] m supporting measurements q moments, experim. cuts  g spectrum m quality control q higher moments q B d vs. B u vs. B s q D J resonances & SR  New Physics & B Æ tn D

2 I |V(cb)| (1.1) The golden way: G (B Æ l n X c ) `inclusive’ G (B Æ l n X c ) =F(V(cb),HQP:m Q, m p 2,…) ± 1- 2%,th. limiting factor: perturb. correct. to nonpert. contrib. Caveat: do not rely on expansion in 1/m ch ! å do not impose constraint m b -m c = - +m p 2 (1/2m ch -1/2m b )+nonlocal op. can check it a posteriori energy/had. mass moments Æ HQP  |V(cb)/0.042| = 1-0.65[m b - 4.6 GeV] - 0.61(m c -1.15 GeV) + 0.06( m G 2 -0.35 GeV 2 ) - 0.013( m p 2 -0.4 GeV 2 ) - 0.1 ( r D 3 -0.12 GeV 3 )- 0.01 ( r LS 3 +0.15 GeV 3 ) Benson,Mannel,Ural tsev,IB,Nucl.Phys.B 665,367

3 2 need higher moments M 1 (E l ) = G -1 Ú dE l E l d G /d E l M n (E l ) = G -1 Ú dE l [E l - M 1 (E l )] n d G /d E l, n > 1 M 1 (M X ) = G -1 Ú dM X 2 (M X 2 - M D 2 )d G /dM X 2 M n (M X ) = G -1 Ú dM X 2 (M X 2 - ) n d G /dM X 2, n > 1

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5  |V(cb)/0.042| = 1-0.65[m b - 4.6 GeV] - 0.61(m c -1.15 GeV) + 0.06( m G 2 -0.35 GeV 2 ) - 0.013( m p 2 -0.4 GeV 2 ) - 0.1 ( r D 3 -0.12 GeV 3 )- 0.01 ( r LS 3 +0.15 GeV 3 ) |V cb |=0.0416 ¥ (1 ± 0.017| exp ± 0.010|  (B) ± 0.015| HQP ) Achille us vs. “ d m b ~ 2% implying  |V cb | > 5%”??? low moments depend on ~ same comb. of HQP! G SL & low mom.=F(m b -0.65m c ) reflects  parton µ m b 2 (m b -m c ) 3 |V(cb)/0.042| = 1- 1.71 [ -1.38 GeV]- 0.06 (m c -1.15 GeV) + 0.08 ( m G 2 -0.35 GeV 2 ) - 0.07( m p 2 -0.4 GeV 2 ) - 0.05( r D 3 -0.12 GeV 3 )- 0.005 ( r LS 3 +0.15 GeV 3 )

6 caveat: relation {moments  HQP} has not been scrutinized yet to same degree as relation { G SL (B)  HQP} (s.later) (1.2) The gold-plated way: B Æ l n D* at zero recoil -- `exclusive’ measure rate of B -> l n D*  extrapolate to zero recoil & extract |V(cb) F D* (0) | F D* (0) = 1 + O (1/m Q 2 ) +O(a s ) normalized holds automatically for m b = m c  expansion in 1/m c !

7 0.89±0.08[0.05] Uraltsev etal.:O(1/m Q 2 ) 0.913±0.042 BaBar Book not a consensus F D* (0) = (dubious procedure)! 0.935 ± 0.03 first prelim. lattice: Hashimoto, Kronf. et al. 0.913 +0.024 -0.017 +0.017 -0.030 2nd quenched lattice: HashKro et al. O(1/m Q 3 ) [~ 0.89 at O(1/m Q 2 )] caveat: relies on expansion in 1/m c ! will use: F D* (0) = 0.90 ± 0.05 for convenience |F D* (0)V(cb)| = 0.0367 ± 0.0013  |V(cb)| excl =0.0408 ¥ (1 ± 0.035| exp ±0.06| theor ) vs. full agreement with diff. systematics!  theor. “brickwall”: expansion in 1/m c ! |V cb |=0.0416 ¥ (1 ± 0.017| exp ± 0.010|  (B) ± 0.015| HQP )

8 (1.3) A `Cinderella’ story in the making? B Æ l n D -- `exclusive’ B Æ l n D seen as `poor relative’ of B Æ l n D *  F B Æ D (0) has 1/m c term -- unlike for F B Æ D* (0)  F B Æ D (0) -- unlike F B Æ D* (0) -- not normalized to unity in the heavy quark limit another `cinderella’ story in the making? BPS limit as `good fairy’ if   2 =  G 2 :  |B>=0,  2 =3/4  FF f - (q 2 )= -(M B -M D )/(M B +M D ) f + (q 2 ) modified by pert. corr.,unaffect. by power corrections in real QCD   2 -  G 2 <<   2,  2  3/4 expansion in  =[3(  2 -3/4 )] 1/2 = 3 [  n |  (n) 1/2 | 2 ] 1/2 irreducible  d f + (0) ~ exp(-2m c /  had ) ~ few %

9 Program:  extract |V(cb)| from B Æ l n D Ëcompare with `true’ |V(cb)|  if successful,use it for B Æ t n D (2nd FF!) Ícheck for New Physics (Higgs-X !) II |V(ub)| Inclusive method expansion in 1/m b better purely perturb. contributions better known  need m b rather than m b - 0.65 m c  no HQS in final state, no SV Sum Rules  experimentally much harder

10 partially integrat. had. recoil mass spectrum Ú dM X d s /dM X (B Æ l n X) with M X,max < M D least reliable part theoretically: low q 2 (q = lepton pair momentum) 2 cut low q 2 Bauer et al.  lose constraints due to Sum Rules  retain < 50 % of rate -- duality viol.?  infer from recoil mass spectrum in B Æ g X Uraltsev & IB  need photon spectrum below 2 GeV -- say 1.8 GeV < E g < 2 GeV  d |V(ub)| ~ 5 % attainable (?)

11 III |V(td)| differentiate between B Æ g X d and B Æ g X s to extract |V(td)/V(ts)| IV Impact of Experim. Cuts Experimental cuts on energy etc. typically applied for practical reasons yet they degrade `hardness’ Q of transition  `exponential’ contributions exp[-c Q / m had ] missed in usual OPE expressions  quite irrelevant for Q >> m had  yet relevant for Q ~ m had !

12 for B Æ g X q : Q = m b - 2 E cut e.g.: for E cut ~ 2 GeV, Q ~ 1 GeV Pilot study (Uraltsev, IB)

13 å encouraging, yet more work needed Lessons: q keep the cuts as low as possible q bias in the meas. moments induced by cuts + can be corrected for + not a pretext for inflating theor. uncert. q moments measured as function of cuts provide important cross check!

14 V Quality Control Overconstraints most powerful protection against ignorance Lenin’s dictum: “Trust is good -- control is better!” m measure higher (2nd and 3rd) moments m of different types m keep energy cuts as low as possible m yet analyze moments as function of (reasonable) cuts  final states in B Æ l D(s q = 1/2 or 3/2) prod. of diff. D(s q ) ´ HQP SSV sum rules

15  rigorous inequalities + experim. constraints  r 2 ( m ) - 1/4 = S n | t 1/2 (n) | 2 + 2 S m | t 3/2 (m) | 2  1/2 = - 2 S n | t 1/2 (n) | 2 + S m | t 3/2 (m) | 2  L ( m ) = 2 ( S n e n | t 1/2 (n) | 2 + 2 S m e m | t 3/2 (m) | 2 )  m 2 p ( m )/3= S n e n 2 | t 1/2 (n) | 2 + 2 S m e m 2 | t 3/2 (m) | 2  m 2 G ( m )/3= -2 S n e n 2 | t 1/2 (n) | 2 + 2 S m e m 2 | t 3/2 (m) | 2  …… where: t 1/2 & t 3/2 denote transition amplitudes for B Æ l D(s q = 1/2 or 3/2) with excitation energy e k = M(B)-M(D k ), e k £ m SV SR strongly suggested broad D(s q =3/2) to lie below 2400 MeV -- contrary to usual interpretation of data. BaBar’s discovery of D sJ reopened issue!

16 m extract CKM parameters separately for SL B u vs. B d vs. B s decays as a check on quark-hadron duality nearby & narrow resonance could modify rate b Æ c: would affect B d & B u equally (isospin); B s Æ l n D s (*), G SL (B s ) would provide test! Not doable at had.coll.(?) b Æ u: B d & B u already different

17 VI Outlook We are witnessing B Physics adding high accuracy to high sensitivity due to q magnificent experim. facilities coupled with q powerful theoretical technologies can we answer the “1 % challenge”? predict measure observables with ~O(1%) uncert. interprete diagnose

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