Paolo Gambino Beach 2006 Lancaster 1 |V xb | from semileptonic B decays Paolo Gambino INFN Torino.

Paolo Gambino Beach 2006 Lancaster 1

|V|Vxbxb| from semileptonic| from semileptonicB decaysB decays

Paolo Gambino INFN Torino


A set of interdependent measurements

b→c l ν treeBR~10

%|Vcb|

b→u l ν tree ~10-3 |Vub|

b→s loop ~3 10-4 new physics, |Vts|

b→d loop ~ 10-6 new physics, |Vtd|

Not only BR are relevant: various asymmetries,

spectra etc


What do they have in common?

INCLUSIVE EXCLUSIVE

OPE: non-pert physics described by B matrix elemnts of local operators can be extracted by exp suppressed by 1/mb

2

Form factors: in general computed by non pert methods (lattice, sum rules,...) symmetry can provide

normalization

Simplicity: ew or em currents probe the B dynamics

B

X

Simplicity is almost always destroyed in practical situations...


EXCLUSIVE

Determination of ADetermination of A

VCKM

A can be determined using |Vcb| or |Vts|

Two roads to |Vcb|

INCLUSIVE


|Vcb| from BD*l

At zero recoil, where rate vanishes.Despite extrapolation, exp error ~ 2%

Main problem is form factor F(1)

The non-pert quantities relevant for excl decays cannot be experimentally determined

Must be calculated but HQET helps.

Lattice QCD: F(1) = 0.91+0.03-0.04

Sum rules give consistent resultsNeeds unquenching (under way)Even slope may be calculable...

FB→D*(1) = ηA [1 - O(1/mb,1/mc)2]

BDl gives consistent but less precise results; lattice control is better

δVcb/Vcb~ 5% and agrees with inclusive det, despite contradictory exps

THE NON-PERT UNKNOWNSMUST BE CALCULATED,CANNOT BE MEASURED

B D*b c

d

l

v


F(1)BD =1.074(18)(16) first unquenched result Fermilab/MILC


far reaching consequences

• New Babar BD*lv

|Vcb|excl = 3.76 (3)stat(13)syst(18)th x10-2

2 away from previous result! and far from inclusive

next WA will likely be lower than it was but higher than this

• Reduction of systematics for lept endpoint |Vub|

extraction (better understanding of background)


The advantage of being The advantage of being inclusiveinclusive

ΛQCD«mb : inclusive decays admit systematic expansion in

ΛQCD/mb Non-pert corrections are generally small and can be controlled

Hadronization probability =1 because we sum over all statesApproximately insensitive to details of meson structure as ΛQCD«mb

(as long as one is far from perturbative singularities)

02

2

dqdqdE

d

l

can be expressed as double series in ααs s and and ΛQCD/mb

(OPE) with parton model as leading term No 1/mb

correction!


HQE = Heavy Quark Expansion

A double expansionA double expansion can be expressed in terms of structure

functions related to Im of0

2

2

dqdqdE

d

l

GbbcbDbcbbcJxJT 3

2

21)0()(OPE (HQE):

The leading term is parton model, ci are series in αs

New operators have non-vanishing expection values in B and are suppressed by powers of the energy released, Er~ mb-mc

No 1/mb correction! OPE predictions can be compared to exp only after SMEARING

and away from endpoints: they have no LOCAL meaning


Leptonic and hadronic spectra

Total rate gives CKM elmnts; global shape parameterstells us about B structure


heavy quark massesmust be carefully defined:short distance, low scale

State of the artKnown corrections up to 1/mb

3: OPE/HQE predictions are only functions of possible cuts and of

1,2

O(1/mb2): mean

kin.energy of b in B

BbDibB

MB

|)(|2

1 22




1,2Gremm,Kapustin...1,2

33 , LSD

O(1/mb2): mean

kin.energy of b in B

BbDibB

MB

|)(|2

1 22


3

3

43

3

32

2

22

2

10

2

3

52

)()()()(1192 b

LS

b

D

b

G

bewcb

bFcl m

ram

ram

ram

rarzAVmG

Perturbative Corrections: full O(αs) and O(β0 αs2) available

For hadronic moments thanks to NEW calculations Trott Aquila,PG,Ridolfi,Uraltsev

Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG



1,2Gremm,Kapustin...1,2

33 , LSD


Using moments to extract HQE parameters

432222 1.064.052.16.44.03.1 GeVmmMM DcbXX

Central moments can be VERY sensitive to HQE parameters

Experiments at Υ(4s) require a CUT on the lepton energy El>0.6-1.5 GeV.

Provided cut is not too severe (~1.3GeV)the cut moments give additional info

We do know something on HQE par.need to check consistency.

•MB*-MB fixes G2= 0.35±0.03

•Sum rules: G2 2, ρD

3 -ρ3

LS...

BUT: OPE accuracy deteriorates for higher moments (getting sensitive to local effects)

Variance of mass distribution


Global fit to |Vcb|, BRsl,HQE Buchmuller & Flacher 06

Based on Gambino & Uraltsev,Benson et al


Bauer, Manohar, Ligeti, Luke, Trott 2005

Results in the 1S scheme

There are several differences• perturbative quark mass scheme• expansion in inverse powers of mc

• use of HQET relations• handling of higher orders• estimate of th errors...

mc(mc)= 1.224 ± 0.017exp±0.054th GeV


+unquenching+unquenching


Theoretical uncertainties

1. Missing higher power corrections 2. Missing perturbative effects in the Wilson

coefficients: O(s2), O(αs/mb

2) etc

3. Intrinsic charm Bigi, Uraltsev, Zwicky

4. Duality violations

How can we estimate all this?Different recipes for 1+3, results for |Vcb| unchanged


Testing parton-hadron Testing parton-hadron dualityduality

What is it?What is it? For all practical purposes: the OPE. No OPE, no duality

Do we expect violations?Do we expect violations? Yes, problems prevalently arise because OPE must be continued analytically. there are effects that cannot be described by the OPE, like hadronic thresholds. Expected small in semileptonic decays

Can we constrain them effectively?Can we constrain them effectively? in a self-consistent way: just check the OPE predictions. E.g. leptonic vs hadronic moments. Models may also give hints of how it

works

Caveats?Caveats? HQE depends on many parameters and we know only a few terms of the double expansion in αs and Λ/mb.


It is not just Vcb ...

HQE parameters describe universal properties of the B meson and of the quarks

• c and b masses can be determined with competitive accuracy (likely better than 70 and 50 MeV) mb-mc is already measured to better than 30 MeV: a benchmark for lattice QCD etc?

• It tests the foundations for inclusive measurements

• most Vub incl. determinations are sensitive to a shape function, whose moments are related to μ

2 etc,

• Bounds on , the slope of IW function (BD* form factor) that are perfectly satisfied by new measurement

• ...Need precision measurements to probe limits of HQE & test

our th. framework |Vcb| can be measured to 1%


Precision studies need

• Moments with higher cuts, eg Elcut>1.5 GeV

• High hadronic moments, eg <MX6>

• Modified Hadron moments <NXn> with NX

2= MX2-2 Λ EX +Λ2

need <EXn MX

2m>

• q2 moments, to constrain IC

• QED effects (also for background in b u)

• Moments in b→u, especially q2 moments with a cut

on El not above 1.5 GeV

• from theory: Wilson coefficients at O(s2),O(s/mb

2)


|V|Vubub| is now the priority | is now the priority

ρ = 0.197 ± 0.031

η = 0.351 ± 0.020

http://www.utfit.org


Strictly tree level


In detail

Bona et al


Really an inclusive problem?


b→ulv exclusive

There is NO normalization of form f.s from HQ symmetry

New first unquenched resultslattice errors still ~11-15%

Sum rules good at low q2

lattice at high q2: complementeach other

q2 extrapolation from theory bounds plus data: FF normaliza-

tion at 1 point is sufficient Ball-Zwicky, Becher-Hill etc

Lattice (distant) goal is 5-6%

New strategy using combinationof rare B,D decays Grinstein& Pirjol


|Vub| from B l

FF calculation Vub [10-3] Ball-Zwicky q2 < 16 3.36 § 0.15 +0.55-0.37

HPQCD q2 > 16 4.20 § 0.29 +0.63-0.43

FNAL q2 > 16 3.75 § 0.26 +0.65-0.43

APE q2 > 16 3.78 § 0.26 +1.45-0.67

full range

Unquenched results probably notyet mature: handle with care


|Vub| inclusive

Buchmuller & Flacher fit:

but life is not that easy!


|Vub| (not so much) inclusive

|Vub| from total BR(bul) almost exactly like incl |Vcb| but we need kinematic cuts to avoid the ~100x larger bcl background:

mX < MD El > (MB2-MD

2)/2MB q2 > (MB-MD)2 ...

or combined (mX,q2) cuts

The cuts destroy convergenceof the OPE, supposed to workonly away from pert singularities

Rate becomes sensitive to “local”b-quark wave function properties like Fermi motion

at leading in 1/mb SHAPE FUNCTION f(k+)


Luke, CKM workshop 2005


Each strategy has pros and cons

Luke, CKM workshop 2005


What do we know about the SF?

• Its moments can be expressed in terms of m.e. of local operators, those extracted from the b->c moments

• It can be extracted from b→s

• It can also be studied in b→ulv spectra

• It gets renormalized and we have learned how (delicate interplay with pert contributions)

• Various subleading SFs appear in bulv


Weak annihilation

Σq

q

b

u

coefficient of Darwin operator

adding 1loop corrections

-dep of WA sets natural scale of non-factorizable flavor-singlet contributions to BWA see PG,Ossola,Uraltsev

BAD: WA ≤3% in rate but gets enhanced in phase space cornersGOOD: WA small but can be experimentally constrained,not only in B+/B0


Vub inclusive results

Intense theoretical activity:

subleading shape functionsoptimization of cuts (P+,P- etc)weak annihilation contribs.Resum. pert. effectsrelation to bs spectrum (SF free relations, see eg Lange 05) SCET insight

REQUIRES MANY COMPLEMENTARY MEASUREMENTS (affected by different uncert.)

There is no Best Method

Need triple diff rate. Currently 2 groups haveprovided HFAG the necessary technology:

BLNP (Bosch,Lange,Neubert,Paz) & DGE (Andersen,Gardi)

A lot can be learned from exp

(on shape function from bs, WA, indirect constraints on s.f., subleading effects from cut dependence,...)


BLNP

Paolo Gambino Beach 2006 Lancaster 41large 2 mostly driven by tension in the exp data

4% th error!!


Comments on BLNP & DGE

• BNLP: the 3 scales are very close, does resummation really improve at NLO, NNLO necessary? SF modelling and uncertainty estimates under control? transition to OPE region?

• DGE: difficult to swallow that 1 parameter (mb) works better than an infinity... BUT iff it fits data there may be a lesson to learn. Can systematically include error from subl SFs and other power corrections: there are assumptions but it’s not a model. Check error estimates.

• nice agreement so far. Both need full NNLO pQCD & other competitors

• Ultimately data decide: use them effectively, to scrutinize DGE & BLNP, any info on b u spectra is essential

and get as far from thresholds as possible!


Cutting the cuts...New exp analyses basedon fully reconstructed events allow high discrimination of charmed final states

2004

Unfolded MX spectrumBabar measured MX

moments. Results can beimproved by cutting in amilder way than usual

It’s time to start using b->u data to constrain SF !

Truncated moments are useful to validate theory and constrain f(k+) & WA: q2

moments and hadronic moments even at low cuts

PG,Ossola,Uraltsev


Summary of main theory limitations

processquantity

Th error

needs goal

B→D*lv |Vcb| ~4% New lattice results

1%

B→Xclv |Vcb|~1.5%

New pert calculations

<1%

B→π lv |Vub| ~12% Lattice developments

5-6%

B→Xulv |Vub| ~6%More data,checks,synergy th/exp

<5%

Paolo Gambino Beach 2006 Lancaster 1 |V xb | from semileptonic B decays Paolo Gambino INFN Torino.

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