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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