# Presentation: 449853

## “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)|]
-  supporting measurements
-    moments, experim. cuts
-    g spectrum
-  quality control
-    higher moments
-    Bd vs. Bu vs. Bs
-     DJ resonances & SR
-   New Physics &  B Æ tn D

## I  |V(cb)|

- (1.1) The golden way: G(B Æ l n Xc)  `inclusive’

- G(B Æ ln Xc) =F(V(cb),HQP:mQ, mp2,...) ±1-2%,th.

- limiting factor: perturb. correct. to nonpert. contrib.

- Caveat: do not rely on expansion in 1/mch!
-    do not impose constraint
- mb-mc= <MB> - <MD>+mp2(1/2mch-1/2mb)+nonlocal op.
- can check it *a posteriori*

- energy/had. mass moments Æ  HQP

-  |V(cb)/0.042| =
- 1-0.65[mb- 4.6 GeV] - 0.61(mc-1.15 GeV)
- + 0.06(mG2 -0.35 GeV2) - 0.013(mp2 -0.4 GeV2)
- - 0.1(rD3 -0.12 GeV3)- 0.01 (rLS3 +0.15 GeV3)

- Benson,Mannel,Uraltsev,IB,Nucl.Phys.B665,367

##   need higher moments

-   need higher moments

- M1(El) = G-1ÚdEl El d G/d El
- Mn(El) = G-1ÚdEl [El- M1(El)]nd G/d El  , n > 1
- M1(MX) = G-1ÚdMX2(MX2- MD2)d G/dMX2
- Mn(MX) = G-1ÚdMX2(MX2- <MX2>)nd G/dMX2 , n > 1

## Slide 4

##  |V(cb)/0.042| = 

-  |V(cb)/0.042| =
- 1-0.65[mb- 4.6 GeV] - 0.61(mc-1.15 GeV)
- + 0.06(mG2 -0.35 GeV2) - 0.013(mp2 -0.4 GeV2)
- - 0.1(rD3 -0.12 GeV3)- 0.01 (rLS3 +0.15 GeV3)

- |Vcb|=0.0416¥(1±0.017|exp±0.010|(B)±0.015|HQP)

- Achille

- us

-     vs. “dmb ~ 2% implying  |Vcb|  > 5%”???
- low moments depend on ~ same comb. of HQP!
- GSL& low mom.=F(mb-0.65mc)  reflects partonμmb2(mb-mc)3
- |V(cb)/0.042| =
- 1- 1.71 [<El>-1.38 GeV]- 0.06 (mc-1.15 GeV)
- + 0.08 (mG2 -0.35 GeV2) - 0.07(mp2 -0.4 GeV2)
- - 0.05(rD3 -0.12 GeV3)- 0.005 (r LS3 +0.15 GeV3)

## caveat: 

- caveat:
- relation    {moments  HQP}
- has not been scrutinized yet to same degree as
- relation      {GSL(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) FD* (0) |
-    FD* (0) = 1 + *O *(1/mQ2) +*O*(as) normalized
-    holds automatically for mb = mc
-    expansion in 1/mc!

##                    0.89±0.08[0.05]  Uraltsev etal.:O(1/mQ2)

-                    0.89±0.08[0.05]  Uraltsev etal.:*O*(1/mQ2)
-                    0.913±0.042        BaBar Book
-                                                not a consensus
- FD* (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/mQ3)
-                                              [~  0.89 at *O*(1/mQ2)]
-                               caveat: relies on expansion in 1/mc!
-      will use:     FD* (0)  = 0.90 ± 0.05  for convenience
- |FD* (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/mc!

- |Vcb|=0.0416¥(1±0.017|exp±0.010|(B)±0.015|HQP)

## (1.3) A `Cinderella’ story in the making? 

- (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 *
-  FBÆD(0) has 1/mc term -- unlike for FBÆD*(0)
-  FBÆD(0) -- unlike FBÆD*(0) -- not normalized to
-    unity in the heavy quark limit
- another `cinderella’ story in the making?
- BPS limit as `good fairy’
- if 2=G2: ********|B>=0, 2=3/4
-  FF  f-(q2)= -(MB-MD)/(MB+MD) f+(q2) modified
-    by pert. corr.,unaffect. by power corrections
- in real QCD 2 - G2 << 2, 2 3/4
- expansion in =[3(2-3/4)]1/2 = 3 [n|(n)1/2|2]1/2
- irreducibledf+(0) ~ exp(-2mc/had) ~ few %

## Program:

- extract |V(cb)| from B Æ l n D
- compare with `true’ |V(cb)|** **
- if successful,use it for B Æ t n D (2nd FF!)
- check for New Physics (Higgs-X !)

- II  |V(ub)|

- Inclusive method
-   expansion in 1/mb better
-   purely perturb. contributions better known
-   need mb rather than mb - 0.65 mc
-   no HQS in final state, no SV Sum Rules
-   experimentally much harder

## partially integrat. had. recoil mass spectrum

** **Ú dMXds/dMX (B Æ  l n X) with  MX,max< MD
- least reliable part theoretically:
- low q2 (q = lepton pair momentum)
-   cut low q2                              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 (?)

## III  |V(td)|

- differentiate between
- B** ****Æ g****  **Xd and B** ****Æ g****  **Xs
-       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[-cQ/mhad]
-    missed in usual OPE expressions
-   quite irrelevant for Q >> mhad
-   yet relevant for Q  ~ mhad!

## for B Æ g Xq:  Q = mb - 2 Ecut

- for B **Æ** g Xq:  Q = mb - 2 Ecut
-                                 e.g.: for Ecut~ 2 GeV, Q ~ 1 GeV
- Pilot study  (Uraltsev, IB)

##   encouraging, yet more work needed

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

##      prod. of diff. D(sq)    ́          HQP 

- V  Quality Control

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

##   rigorous inequalities + experim. constraints 

-   rigorous inequalities + experim. constraints

-    r2(m) - 1/4  = Sn |t 1/2 (n) |2 + 2 Sm |t 3/2 (m) |2
-              1/2        = - 2 Sn |t 1/2 (n) |2 +   Sm |t 3/2 (m) |2
-   L(m) = 2 ( Sn en |t 1/2 (n) |2 + 2 Sm em |t 3/2 (m) |2)
-   m2p(m)/3=  Sn en2 |t 1/2 (n) |2 + 2 Sm em2|t 3/2 (m) |2
-    m2G(m)/3= -2 Sn en2 |t 1/2 (n) |2 + 2Sm em2|t3/2(m) |2
-    ......
- where: t1/2 & t3/2 denote transition amplitudes for
- B Æ l  D(sq = 1/2 or 3/2)
- with excitation energy ek = M(B)-M(Dk), ek £ m

- SV SR strongly suggested broad D(sq=3/2) to lie below 2400 MeV -- contrary to usual interpretation of data.
- BaBar’s discovery of DsJ reopened issue!

##  extract CKM parameters separately for 

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

## VI  Outlook

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

## Slide 18

## Slide 19