more details in http://ific.uv.es/~babar/Azzolini-2008_Vub_Valencia.pdf

Virginia Azzolini, Universitat de Valencia - 2008

Measurement of

Partial Branching fraction for B  Xul decays and

determination of |Vub|

[PRL 100, 171802 (2008)]

Vub is the smallest element of the CKM-matrix, yet, for the

Standard Model to describe CP violation, it has to be nonzero.

Our group studies semileptonic decays of the B going to a

hadronic system Xu, containing the light u quark.

This process is sensitive to |Vub|, but is 1000 times

less common than transitions to Xc , containing instead a heavy c quark.

We have determined partial branching fractions in 3 limited regions of phase space:

MX < 1.55 GeV/c2, P+ < 0.66 GeV/c), and MX < 1.7 GeV/c2, q2 > 8 GeV2/c4.

Corresponding values of |Vub| are extracted using several theoretical calculations

in 5 min:

[Theory]

[BLNP]

[DGE]

[BLNP]

[DGE]

[BLNP]

[DGE]

[BLL]

DB(B→Xul n)

D ( stat. sys. th. )

MX < 1.55 GeV/c2 1.18 ± 0.09 ± 0.07 ± 0.01

P+< 0.66 GeV/c2 0.95 ± 0.10 ± 0.08 ± 0.01

MX < 1.7 GeV/c2 & 0.81 ± 0.08 ± 0.07 ± 0.02

q2 >8.0 GeV2/c2

|Vub| (10-3)

D ( stat. sys. th. )

4.27 ± 0.16 ± 0.13 ± 0.30

4.56 ± 0.17 ± 0.14 ± 0.32

3.88 ± 0.19 ± 0.16 ± 0.28

3.99 ± 0.20 ± 0.16 ± 0.24

4.57 ± 0.22 ± 0.19 ± 0.30

4.64 ± 0.23 ± 0.19 ± 0.25

4.93 ± 0.24 ± 0.20 ± 0.36

Kinematic region

Partial Branching Fraction

The left side over-constrain the Triangle is more difficult

. Uncertainty is dominated by the errors on |Vub| ~ 8%

→ precision is improving (it was 18% in 2004), but still not enough

→ next GOAL: Measure |Vub| with < 5%

Why study Vub and Vcb ?

. Tree level semileptonic decays provide an excellent laboratory because free of NP contributions

. Theoretically simple at parton level

. leptonic and hadronic currents factor out cleanly,

thus one can probe strong interactions in B mesons

.. Explore structure of B meson

.. Allow test of e.g. Lattice QCD

. Rate depends directly on CKM elements |Vub|, |Vcb|, the quark masses mb and mc

. Experimentally branching fractions are prominent

10.5 % for semi-electronic and semi- muon

Semileptonic B decays

hadronic

effects

free

b

ℓ-

u,c

W -

nℓ

parton level

B

Xu,Xc

Vxb

nℓ

ℓ-

Hadron level

Answer: redundant and precise measurements of the Unitary Triangle are needed.

The dimensions of the triangle are infact tightly connected to CP violation research.

The angle  and right-side measured

better than 5%

. orthogonal constraints

→ Anchor the (r,h) apex

Not to scale!

No detector

resolution!

q2 = momentum transfer squared = (pB-pX)2 = (pl+pn)2

mX = mass of the hadronic system

P+ = EX-|pX| = light-cone component of X momentum

free quark decay

perturbative

corrections

(known to O(as2))

Non-perturbative

power corrections

(suppressed by 1/mb2)

Inclusive b →u l n measurement

G(b ® u l n) |Vub|2 1

G(b ® c l n) |Vcb|2 50

 

. Heavy Quark Expansion gives G(B ® Xu l n) = GF2 mb5/192 p3 |Vub|2 [1+Aew ]Apert Anonpert

. Unfortunately :

. kinematic cuts needed

to suppress the dominant

b → c l n background

. Smaller acceptances increase theory uncertainties

. OPE breaks down

. “shape function” to resum non-perturbative physics

. Measure partial Branching Fraction DB(B → Xulνn) in a region where

. the signal/background is good, and

. the partial rate ΔΓu is reliably calculable

. To reduce systematic uncertainties, we measure first a ratio of partial BF

. Get partial rate prediction z(DF) from theory

BLNP - HFAG

|Vub|= (3.98 ± 0.15exp ± 0.30mb+theory) x 10-3

Total Error: 8.3 % total

= Exp. 3.9%

±1.8bc model ±1.1bu model

±2.0stat ±2.5exp

= Theory 8.1%

±0.7sub SF ±3.6matching ±1.4WA

±6.3HQE param ±0.4SF form

Exclusive

Inclusive

BLNP

analytic coupling

DGE

BLL

Current Inclusive |Vub| Measurements

BNLP + only b→ c l n moments

subdivided into:

. supersedes our 2004 PRL

. reduces the relative uncertainty of a 40%

. is compatible with all the other inclusive measurements

. is compatible with the exclusive charmless semileptonic

decays measurements [PDG]

(read further about this compatibility on the right → )

Our BaBar result, based on hadronic mass spectrum

|Vub|= (4.27 ± 0.16stat ± 0.13exp± 0.30theory) x 10-3 (BABAR)

|Vub|= (3.74 ± 0.18exp ± 0.31mb+theory) x 10-3 (HFAG*)

CKM consistency

* HFAG results are rescaled to common HQE inputs: mb(SF)=4.707+0.059/-0.053 GeV , μπ2=0.216+0.054/-0.076 GeV2

Indirect determination from global UT fit (plot bands)

|Vub| from exclusive decays = (3.33 0.21+0.58-0.38)x10-3

directly measured values (points/symbols)

|Vub| from exclusive decays = (3.33  0.21+0.58-0.38)x10-3

.	|Vub| from inclusive decays = (3.98  0.15  0.30)x10-3

and single theoretical framework inclusive measurements

Recently a lot of work in the inclusive decays has been done but still

there is some “tension”, some distance between the central values

Open questions: is it due to New Physics? is it going to disappear in the future?

are we possibly just doing something wrong?

Possible answers: it is unlikely NP, possibly it is due to a statistical fluctuation,

certainly we still are affected by problems with theoretical calculation and/or

estimation of the uncertainties

Still Experimental and Theoretical work is

needed to understand current results

PRD72:073006(2005)

. Formula used

. Several theoretical calculations available:

.. DFN (De Fazio,Neubert) → HQE with ad-hoc inclusion of SF

.. BLNP(Bosch,Lange,Neubert,Paz) → HQE with systematic incorporation of SF

.. BLL (Bauer,Ligeti,Luke) → HQE for mX< mD and q2>8 (‘non SF region’)

to minimize SF effect

.. DGE (Anderson,Gardi) → use “Dressed Gluon Exponentiation” to

convert on-shell b quark calculation

into meson decay spectra

Getting |Vub| from the partial rate

z(DF): theoretical acceptance,

computed by

different theo. frameworks

DF : global fit (mbSF,mp2 SF) param.,

Buchmüller & Flächer,

PRD73:073008

JHEP9906:017(1999)

PRD64:113004(2001)

JHEP0601:097(2006)

Ldata ~ 348 fb-1 ≣ 383· 106

Kinematic variables distributions:

Same spectra, background subtracted and rebinned to show the actual variable shape:

(note: measured distributions, not efficiency corrected)

Because we have 1 single database and we perform 3 calculations,

we evaluate the statistical correlation between them

65% between MX and combined (MX,q2)

67% between MX and P+

38% between (MX,q2) and P+

Entries

Nu = 803 ± 60

Nu = 633 ± 63

Nu = 562 ± 55

Entries

q2, MX<1.7 GeV/c2

b→ u l n IN

b→ u l n crossfeed

b→ c l n + oth

data

P+

MX

In theoretical framework, (BLNP e.g.)

. all errors are correlated

Statistical: 3.8%

Systematic: 3.0%

Theory: 7 % (SF errors dominate, mb) it is still the dominant error

. experimental correlation evaluated

agreement at 1 σ level for the MX and combined (MX,q2)

P+ differs from the two others at a 2.5 σ level

Even if we publish all the 7 |Vub| measurements, we elect as the best one

the MX method analysis method because

. it maps out the largest portion of phase space

. it gives the most precise determination of |Vub|

Crossing the different theoretical framework BLNP and DGE give consistent results,

within the theoretical uncertainty

Dominant systematic errors

. MC stat (4.0%)

. detector effects (3.2%)

. complex fitting technique (mES fits) 4.3%

. modeling of signal and background contributions

Recoil Analysis technique

Breco

- SemiLeptonic selection:

. presence of charged lepton: Pl > 1 GeV

. system X reconstructed using charged tracks and photons

. neutrino momentum inferred Pmiss = Pϒ -PBreco – Pl -PX

- Signal selection:

. require 1 charged lepton Pl > 1 GeV

. Charge Conservation:	Qtot = 0

. Charge Correlation:(correct for B0 mixing) Ql Qreco < 0

. Missing Mass Squared:	Mmiss2< 0.5GeV2

. veto on K±, KS and on B0 → D* l n events

Brecoil

e-

D*



e+

Breco

Brecoil

Xu

l



Y(4S)

Υ(4S) →BB events are tagged by the full reconstruction of a hadronic decay

of one of the B mesons (Breco).

The semileptonic decay of the second B meson (Brecoil) is identified

by the presence of an electron or a muon.

This technique results in a low event selection efficiency but

allows the determination of the momentum, charge, and flavor of the B mesons.

- Full reconstruction of tag B: B  D(*) Y

D: charm meson (D0, D+,D*0,D*+)

Y: hadrons (,0,K,KS0,0) collection of charge 1

- Kinematic consistency is checked with

. beam energy-substituted mass:

. energy difference:

Gx≡ G(b  xln)  |Vxb|2

Exclusive vs Inclusive measurements

Exclusive Decays:	hadronic final states Xu reconstructed

→Low signal rate, better bkg reduction and

kinematic constraints

Need Form Factor F(q2) to describe the

hadronization process u  pπ rρ …

Measurement as function of q2

Inclusive Decays: select lepton and

look at the rest of the event inclusively

→Large signal rate, high b  cℓn bkg

“Easy” to calculate (OPE/HQE)

Need Shape Function (that describes

b-quark motion inside B meson)

Constrain SF param. mb, mp2

with b  sg or b  cℓnν

MX < MD

q2 > (MB - MD)2

P+ < mD2 / mB

“optimized

cuts”

~ 80 %

~ 70 %

~ 30 %

~ 45 %

lots of rate

- still lost of rate

- relation to radiative

decays simplest

insensitive to f(k+)

insensitive to f(k+)

depends on f(k+)

(and subleading)

depends on f(k+)

(and subleading)

- very sensitive to mb

- substantail WA corrections

- effective expansion param.

QCD/mc

- still “only” 45% of rate

- less rate than MX cut,

& more complicate to measure

Kinematic variables: Problems and Triumph

phase rate(%) Pros Cons

space

... and |Vub| results

The B Factory Detector

Toyoko Orimoto

2004-10-01T21:59:29