Current Methods of determining Vub

I. Endpoint of the inclusive lepton spectrum II. Exclusive decays

Methods of determining Vub with small theoretical errors

1) Inclusive: low hadronic mass region2)Inclusive: endpoint of the q2 spectrum 3)Exclusive: lattice

Calibration with charm semileptonic decays Rate and slope in Bl

Precision determination of Vub at an e+e- B factory

Jik Lee & Ian Shipsey Purdue University

Snowmass July 2001

lepton endpoint, beyond the kinematic limit for b c

1% of lepton spectrum, (CLEO’93) Measures |Vub/Vcb|

I. Endpoint Determination of Vub

Challenges: Large b to c bkgdLimited understanding of decay spectrum/form factorsLarge extrapolation (5-20%bu in endpoint)endpoint dominated by several exclusivemodes, so models must be usedlimited by theoretical error

clb ulb

Non-resonant bkgd

02.008.0||

||

cb

ub

V

V

thycb

ub

V

V016.0008.0076.0

||

||exp

Endpoint useful as reality check of more precise methods

to reduce theory error by X2 need to know: how much of the rate is in acceptance ? ~10% the overall normalization?~ 15% 2 solutions: theory provides an absolute normalization point (as in bc) minimise extrapolation i.e. maximize acceptance and test theory

Vub method II :Exclusive decays

* Method 2: exclusive reconstruction require neutrino consistency.* To keep bkgd tractable work in endpoint

* Measures Vub * Drawback: extracted Vub relies on poorly known form factors* Model dependence dominates

%20ub

ub

V

V

321.029.0

433.046.0

10)55.014.025.3(

10)41.029.057.2()(

ubV

lBBR (Averaged with published CLEO Bl)

stat sys model

CLEO PRD 61 0520013.3 x 10 6

BB

Beginning to probe distribution but little discriminating power between models at high lepton energy (where the measurement is performed)

no easy way to choose between models hard to quantify systematic error associated with a model although experimental statistical errors on Vub will tend to zero with large data sets dominant uncertainties are

theoretical

Exclusive Decays and Vub

2dq

d

2q

2q

To make major experimental progress in Vub need powerful suppression of b cl provided by full reconstruction of companion B

B tagging efficiency CLEO II/II.V is ~ 2.1 x 10 -3 (2.85 x 10-3 in BaBar book, use this number)

technique impractical for (most) analyses with pre-B factory samples, but will be used extensively in future Assume 1% systematic error in lepton ID, 2% systematic error in tracking.

New Inclusive Methods for Vub

ulBnDB )((*)

To distinguish bu from bc theoretically: better betterq2 spectrum > mhad spectrum > Elepton spectrum

But experimental difficulty is in opposite order

),( KBB

select b u with mx< mD (~90% acceptance for b u )

require: Q(event) =0, 1 lepton/event, missing mass consistent with neutrino

just look at mhad< 1.7 , cut with largest acceptance and hence least theoretical uncertainty, keep bkgd small with p(lepton)>1.4 GeV

Inclusive: Hadronic mass spectrum

clb

ulb

2m

hadmGeV7.14.1

TRKSIM CLEO III FAST MC

-1ab1

~100 b ulv events/30 fb-1 : Method attractive with large data samples

Systematic error is dominated by charm leakage into signal region.

Depends on S/B ratio & B. Assume B = 0.1 B @ 100 fb-1. S/B can be improved by vertexing. B can be reduced as Br(B [D*/D**/D/D ] l) and the form factors in these decays become better measured. B

can also be reduced through better knowledge of D branching ratios. Assume these improvements lead to B = 0.05 B @ 500 fb-1 or higher Ldt. Then the systematic error dominates for Ldt 1000 fb -1 . Br(b ulv) ~ 3.4% , Vub~1.7% Recall theoretical error is ~ 10%

Inclusive: Hadronic mass spectrum

year Ldt # bul #b cl Vub Vub Vub (stat) (sys) (expt)2002 100 fb-1 335 127 3.2% 2.2% 3.9%2005 500 fb-1 1675 635 1.5% 1.5% 2.1%2010 2000 fb-1 6700 2540 0.7% 1.5% 1.7%

Inclusive q2 endpoint, lose statistics, gain in theoretical certainty ~40 b ulv events/30 fb-1 Method attractive with VERY large data

samples.

Inclusive: endpoint q2spectrum

clb

ulb

)( 22 GeVq 10.8 11.6S/B: 4/1 18/1

look at q2 > 11.6 , and 10.8 keep bkgd small with p(lepton)>1.4 GeVOne experimental advantage compared to mhad is that S/B is more favorable

TRKSIM CLEO III FAST MC

-1ab1

Systematic error is dominated by charm leakage into signal region for q2>10.8 (S/B ratio & B, same issues as mhad) .

Assume B = 1.0 B @ 100 fb-1, and B = 0.2 B @ 500 fb-1 or higher Ldt. For q2 > 11.6 (S/B = 18/1), systematic error (tracking and lepton ID) dominates @ Ldt 1000

fb-1

2000 fb-1 Br(b ulv) ~ 3.2% , Vub~1.6%. Recall theoretical uncertainty ~ (5 – 10) %

Inclusive: endpoint q2 spectrum

For q2 > 11.6:year Ldt # bul #b cl Vub Vub Vub (stat) (sys) (expt)2002 100 fb-1 127 7 4.6 % 3.0% 5.5%2005 500 fb-1 635 36 2.0 % 1.2% 2.3%2010 2000 fb-1 2538 144 1.0 % 1.2% 1.6%

Semileptonic B decays are used to determine the quark couplings Vub and Vcb as the strong interaction is confined to the lower vertex

In charm semileptonic decays, as Vcs (or Vcd) is known from three generation unitarity the hadronic current can be measured

D system provide a way to test ideas about hadronic physics needed to get Vub Vcb in B decays. Ideas-= HQS, lattice….

Charm Semileptonic Decay and Vub

HLVHJHlVM cscscs )0()1( 5

HLVHJHlVM ubbuub )0()1( 5

known

unitarity

modell

The complexity of the hadronic current depends on the spin of the initial and final state meson and the mass of the final state quark

Simplest case

at same pion energy:

form factor ratio equal by Heavy Quark Symmetry, corrections order 20% but little known about heavy to light transitions need q2 dependence in both B and D decay to assess the size of

the of 1/m corrections. Lattice also determines the form factors, in principle it may be most precise method. Will concentrate on this

method here...

l

B

D

l

lv

HQS

Charm Semileptonic Decays

22

22

)()(

)()(

/)(

/)(

DfspacephaseV

BfspacephaseV

dElDd

dElBd

cd

ub

The lattice is capable of predicting the absolute normalization of the form factor in Bl or D l to ~few%. Vub/Vub ~1-2%

But lattice must be calibrated!

Within the quenched approximation all systematic errors are accounted for and smaller than statistical errors

A comparison of lattice and expt. in D l can give an estimate of the size of the

effect of using the quenched approximation

compare lattice to data, if quenching is understood shape should be same

A lattice determination of Vub

STEP ONE: CALIBRATE LATTICE with D l

STEP TWO: MEASURE d/dp in Bl

STEP THREE: MEASURE (Bl) + lattice Vub

The best way to d/dq2 in D l is at a charm factory (e.g. CLEO-c) Kinematics at threshold cleanly separates signal from background

Charm Factory vs. B Factory

signal

eKDDD fs /, 00*

eKD0

eD f0

emf

Charm Factoryno background

B Factory S/B ~1.3 cf CLEO II S/B 1/3

CLEO II PRD 52 2656 (1995)

TRKSIM CLEO III FAST MC

missmiss PEU

eKD0

eD0

Measure :

Step I Calibrate Lattice: Dl

:

dp

eDd )( 0

compare to lattice prediction ex: hep-ph/0101023 El-KhadraNote: lattice error large ~15%on normalization but in future1-few % predicted

veDTaggedD 00 ,

TRKSIM CLEOIII FAST MC

-1fb1

Step II d(Bl)/dq2

compare to lattice predictionex: hep-ph/0101023 El-Khadra

dp

lBd )(

For the same as D l:

TRKSIM CLEO III FAST MC

lBnDB )((*)

TRKSIM CLEO III FAST MC

-1ab1

If data and lattice agree for 0.4 < p < 0.8 GeV, still need faith that lattice is correct for p > 0.8 GeV.

Lattice can compute rate to few %. How much data would we need to have a comparably small experimental error?

Assume S/B = 10/1 and B = 0.1 B

all p Such large data samples are beyond the reach of existing B factories

that expect accumulate ~2000 fb-1 by 2010. SBF !!!

Step III Vub

year Ldt # bul S/B Vub Vub Vub (%) (10/1) (stat) (sys) (expt)2008 1000 fb-1 590(29) 59(3) 4.3(9.8) 1.2 4.5(9.9) ? 10000 fb-1 5900(290) 590(30) 0.7(3.1) 1.2 1.4(3.3)

0.4 < p < 0.8

ub

ub

V

V

All possible theoretically clean measurements are very important, even if they are redundant within the standard model

Must pursue both CP violating and CP conserving measurements (i.e. Vub) to test SM and look for new physics

Inclusive methods will achieve Vub ~ few % (expt) ~ 5 -10% (theory) q2 endpoint is the method of choice.

The first test of CKM at the 10% level will come from this measurement and Vcb , sin2, and Vtd/Vts

If the lattice can reach the predicted accuracy (1-2%) it will become the method of choice for future measurements of Vub (and Vcb)

Lattice must be calibrated. A charm factory can provide crucial tests of lattice predictions. A ~10,000-20,000 fb-1 data sample is required to attain a total experimental error of 1-2% on Vub

commensurate with the lattice error.

Conclusions