B. Golob, Ljubljana Univ.Results from B factories 1HQP School, Dubna, Aug 2008 Boštjan Golob University of Ljubljana, Jožef Stefan Institute & Belle Collaboration

B. Golob, Ljubljana Univ. Results from B factories 1 HQP School, Dubna, Aug 2008

Boštjan GolobUniversity of Ljubljana, Jožef Stefan Institute & Belle Collaboration

Beauty and charm results from B factories

University of Ljubljana

“Jožef Stefan” Institute

Helmholtz International Summer School “Heavy Quark Physics”Bogoliubov Laboratory of Theoretical Physics,

Dubna, Russia, August 11-21, 2008

JINR


Outline

Part of B-factories lectures with A.J. Bevan; division by topics, not by experiments

Lecture 1 Beauty

1. Introduction2. B Oscillations3. (Mostly) rare B decays leptonic semileptonic b →sg b →sll

Lecture 2Charm and others

4. D0 mixing and CPV decays to CP states WS decays t-dependent Dalitz 5. Ds leptonic decays6. Spectroscopy exotic states

It is a curious fact that people are never so trivial as when they take themselves seriously.

O. Wilde (1854 - 1900)

exp. resultswith some commentson phenomenology


Introduction

Experiments

s(c c) 1.3 nb (~109 XcYc pairs)

continuum production g* c

c

on resonance productione+e- → U(4S) → B0B0, B+B- s(BB) 1.1 nb (~0.9x109 BB pairs)

e+e- → y(3770) → D0D0, D+D- (coherent C=-1 state); ~800 pb-1 of data available at y(3770); 2.8x106 D0D0

3.5 fb-1 on tapes(D0; pt>5.5 GeV,|y|<1)≈≈13 mb50x109 D0’s

very diverse exp. conditionsWe all live with the objective of being happy; our lives are all different and yet the same.

Anne Frank (1929 -1945)


B oscillations

diagonal elem.: P0 P0 (including decays)non-diagonal elem.: P0 P0

P0q1

q2 q1

P0q2

P0 = K0, Bd0, Bs

0 and D0

Time evolution (also lectures by U. Nierste, A. Pivovarov) flavour states ≠ Heff eigenstates: (defined flavour) (defined m1,2 and G1,2)

002,1 PqPpP

eigenvalues:

q

p

q

p

iMiM

iMiM

2,1*12*

12

1212

22

22

),(2 1212

2,12,12,1

Mfim

)(4

2||4

2*1212

2

12212

22

Mm

Mm2121 , mmm

more


)sin(2)sinh(2

)cos()cosh(

)(1

**

22

22

0

xtAAp

qytAA

p

q

xtAp

qAytA

p

qA

dt

fPd

e

ffff

ffff

t

B oscillations Time evolution

;2

; 2121

ymm

x

for easier notation: Gt → t

U(4S) →B0B0: B meson pairin quantum coherent state;before 1st B decay: B0B0

1st B decay: tag B0/B0; mixing clock start, t →Dt

decay rates:

Decay time distribution of experimentally accessible states P0, P0

sensitive to mixing parameters x and y, depending on final state

D. Kirkby, Y. Nir, CPV in Meson Decays, in RPP

P1,2 evolve in time according to m1,2 and G1,2: )0()( 2,12,12,1 tPetP ti

002,1 PqPpP |P0(t)>, |P0(t)>

more


B oscillations Time evolution

visually unobservabledeviation from pure exponential

~ Bs0

more difficult to observeoscillations within t

probab. to observe an initially produced X0 as X0 after time tprobab. to observe an initially produced X0 as X0 after time t

~ D0


B oscillations Method similar to CPV, reconstruct flavor specific final states

Bsig

Btag

J/y

K*0

m+

m-

p-

K+

K-l-

fully reconstruct decayto flavor specific final state

tag flavorof other B from chargesof typicaldecay products

Dt=Dz/bgc

determine time between decays

U(4

S)

determinedB0(B0)

B0 or B0

22 )()2(

iCM

bc

pE

M

2CMi EEE

signal

signal


B oscillations Method reconstructed flavour specific decays

Belle, PRD71, 072003 (2005), 140 fb-1

DE signal region

measure Dt distribution

more

Method Dt distribution Af=0, |y|<<1

)()]cos()21(1[)(1

)()]cos()21(1[)(1

0

2

0

2

tRetxwtd

fPd

A

tRetxwtd

fPd

A

t

f

t

f

t

f

t

f

etxtd

fPd

A

etxtd

fPd

A

)]cos(1[)(1

)]cos(1[)(1

0

2

0

2

t

f

t

f

etxwtd

fPd

A

etxwtd

fPd

A

)]cos()21(1[)(1

)]cos()21(1[)(1

0

2

0

2

w: wrong tag probability (reduces ampl. of oscillations)R(Dt): resolution function - intrinsic detector resolution on position of both B vertices - smearing due to non-primary tracks - smearing due to B meson CMS momentumsaver(Dt)=1.43 ps

more


B oscillations Results flavour asymmetry

)()cos()21(

/)(/)(

/)(/)(00

0

tRtxw

tdfBdtdfBd

tdfBdtdfBd

Belle, PRD71, 072003 (2005), 140 fb-1

Dmd=(0.511±0.005±0.006) ps-1

HFAG, http://www.slac.stanford.edu/xorg/hfag/

Dmd=(0.507±0.005) ps-1

x=DmdtBd= 0.776±0.008

largest syst.: D** bkg.


B oscillations

if mi = mj due to CKM unitarity: no mixing

d

b

b

d

u, c, t

u, c, t

W+ W-B0 B0

d

b

b

d

u, c, t u, c, t

W+

W-

B0 B0

Vid

Vjd

Vjb*

Vib*

Phenomenology (see also lectures by U. Nierste) P0-P0 transition → box diagram at quark level

),,( 2

,,,

22**

00

jtcuji

iWjbjdidib

wk

mmmVVVV

BHB

F

P0: any pseudo-scalar meson;specific example of Bd

0

jtcuji

ijbjdidibwk mmVVVVBHB

,,,

**00

considering CKM values and q masses: largest contribution from t quark

loop int., CKM unitarity

more


B oscillations

calculate M12, G12 frombox diagram; from that calculate Dm, DG

must be calculated to determine Vij; theor. uncertainty (LQCD)

q: d (Bd) or s (Bs);and Dms also measured...

Phenomenology

2*2'22

12

2*2202

222

12

)(8

))(/(12

tbtqBqBqBqBbF

tbtqWtBqBqBqBWF

VVfBmmG

VVmmSfBmmG

M

A.J. Buras et al., Nucl.Phys.B245, 369 (1984)

BBq: bag parameter, <Bq0|bgm(1-g5)q|Bq

0>fBq: decay constanthB

(‘): QCD corr. O(1)S0(xt): known kinematic function

|)|/|(|)1(||2)1(||2

1)/(|~|/||

1212

12

12

221212

M

MmmmOM tb

O

2

2

2

2

td

ts

BdBdBd

BsBsBs

d

s

V

V

fBm

fBm

m

m

reduced theor.

uncertainty in ratio

035.0047.0210.1

M. Okamoto, hep-lat/0510113x2


B oscillations

Bs

amplitude method: instead of Dms

fit A at different values of Dms;

A=1 oscillations at this Dms value t

f

etxwtd

fPPd

A

)]cos()21(1[

))((1 00

2 A

CDF, PRL97, 242003 (2006)

A

Dms=(17.77±0.10±0.07) ps-1

x=DmstBs= 25.5±0.6 Dms /Dmd

uncertainties on (r2+h2): Dmd constraint ±13% Dmd ±1%

fBdBBd ±12% Dms /Dmd constraint ±6% Dms /Dmd ±1.5% x ±5%


Leptonic B decays

B → tn

Q

q

P+

l+

n

fP

VQq

2

2222

2

18

)(

PPPQq

F

m

mmmfV

G

P

G(B+ → t+n): G(B+ → m+n): G(B+ → e+n)=1:4x10-3:10-7

fP → meas. VQq; H±;

W+

Method fully reconstruct Btag in hadronic decays (K+p-p+p-p+); search for 1/3 tracks from Bsig→tn (e-); no additional energy in EM calorim. (from p0, g, ...); signal at EECL~0

B → tncandidate event

EM calorim.

(H+)


BaBar, PRD77, 011107 (2008), 346 fb-1

Leptonic B decays

Results

Belle, PRL97, 251802 (2006), 414 fb-1

signal

bkg.

410)79.1()(51.046.0

49.056.0 BBr

Nsig=17 ± 5 3.5 s signif. (-2lnL0/Lmax)

largest syst. from signal and bkg. shapesemileptonic tag added

BaBar:hadronic decays for Btag;

combined with semil. decays:

more

410)4.04.02.1()( BBr

BaBar, PRD76, 052002 (2007), 346 fb-1

expected signalBr=3x10-3


410)43.041.1()( BBr

Belle, ICHEP08, 600 fb-1

410)65.1()(37.035.0

37.038.0 BBr

410)37.043.1()( BBr


Leptonic B decays

Phenomenology using fB=(216 ± 22) MeV, |Vub|=(3.9 ± 0.5)x10-3, tB

BrSM(B+ →tn) = (1.25 ± 0.41)x10-4

new physics:

to make predictions/measure |Vub| → fB (from LQCD) needed;

validate LQCD in charm sector (better exp. precision) → to be addressed later;

established method for decays with large Emiss; to be exploited at SuperB (B→Knn, dark matter)

222

2

)tan1()()( H

BSM

m

mBB

HPQCD, PRL95, 212001 (2005)

51.013.1)tan1( 222

2

H

B

m

m

410)43.041.1()(

BBr

SuperB50 ab-1

b

u

B-

t

n

H+

more


Semileptonic B decays

P →Pln

))(())(()()(

)()()1(2

122

122

111222

21

111222531

ppqfppqfpMJpMppq

pMJpMvuVG

qqF

Mq1 q3

n

l+

M1

q2

M2

q2

in G suppressed by ml2/mM1

2

negligible for e,m; not for t P →Vln 3 form f. for e,m; 4 for t HQS: relations among f.f.’s; can be tested; for suppressed f.f.’s only by t

W±,H±

H± exchange modified SM Br’s for t; in P→ V only helicity=0 V possible

more

more measurement challenging due to multiple n’s;

skip



B0 →D*-t+nt method: D* reconstruction; t →enn, pn Bsig: D* and e/p Btag: rest of event control sample: Bsig →D*p , check Btag reconstruction signal sample: requirements on Xmis, Evis

method: excl. Btag reconstruction t →enn, mnn Bsig: D/D* and e/m mmis

2=pmis2

MCdata

Bsig →D*p

20

2/* /)( BbeameDmismis mEppEX

related to missing mass (>0 for several n);Evis < m(U(4S))

D*

Bsig

e/p

nn

Btag

Belle, PRL99, 191807 (2007), 480 fb-1

)( /* eDtageemis ppppp

BaBar, PRL100, 021801 (2008), 209 fb-1

missing mass (>0 for several n);

t



B0 →D*-t+nt results bkg. from B0 →D*en (peaking) t →rn

Nsig=60 ±12

6.7 s signif. (-2lnL0/Lmax)

)%37.002.2()*(37.040.00 DBBr

main systematics:from signal and bkg shape (MC)Btag reconstr. eff. (control sample)

Belle, PRL99, 191807 (2007), 480 fb-1

BaBar, PRL100, 021801 (2008), 209 fb-1

)%05.010.031.062.1()*( DBBr

)%06.011.024.086.0()( DBBr D*-t+nt

D-t+nt

D-l+n

D*-l+n

last uncertainty: normaliz. modes (Dln , D*ln)main systematics:from signal and bkg shape (MC)D** contrib.



B →D(*)tn phenomenology limits on H±;

inclusive B →Xctn predicted Br: (2.30 ±0.25)% sum of D*tn, Dtn: (2.59 ±0.39)%

M. Tanaka, Z.Phys.C67, 321 (1995)

Ba/lle average(assuming no correl.and 100% long. polariz.)

BaBar

A.F.Falk et al., PLB326, 145 (1994)

G(B

→D

* lon

g.tn

)G

(B →

D*m

n)|

SM

more


b → sg

Motivation FCNC process; sensitive to NP in loop; parton level: Eg ≈ mb/2; determ. of mb, Fermi motion → needed for Vub determ. from inclusive semil. B decays;

Difficulties theory: parameter extraction from partial Br(Eg>Ecut) → extrapolation needed;

experiment: measure low Eg

huge bkg.

b sW±

u, c, tVqb Vqs

g

b s

u, c, tX Y

H±

g

c±

b s

X Y

tcu ~,~,~g

more

signal

continuump0

Your background and environment is with you for life. No question about that.

S. Connery (1930)


b → sg

Inclusive measurement (see also lectures by U. Heisch) only g reconstructed;

bkg. treatment subtract lumin. scaled off-data from on-data (continuum bkg.);

veto p0, h → ;gg

rest bkg. from MC (control samples);

timing info for EM calorim. clusters (overlapping evts.: hadronic + Bhabha)

inclusive B→ p0X, hX samples reconstructed in data (off- data subtraction) and MC; 5%-10% correction to MC bkg. normaliz.

onoff

onscaled off

subtracted80% of remaining bkg. from p0, h → gg

after vetoing p0, h → gg

Belle, arXiv:0804.1580,605 fb-1

more


b → sg

Inclusive measurement Eg spectrum

Br(B →Xsg) deconvolution of Eg

(Egmeas → Eg

true; using radiative di-muon evts); boost to B rest frame; b →dg contrib. (4%);

consistent with 0 aboveB decaythreshold

mb1S/2~2.3 GeV

410)01.037.019.031.3()8.27.1;( GeVEXBBr s last uncertainty due to boost;largest system.: corr. factors in off-data subtraction;bkg. g’s from B (other than p0, h)

222 )0012.00214.00156.00396.0(

)002.0053.0032.0281.2(

GeVEE

GeVE

Belle, arXiv:0804.1580,605 fb-1


b → sg

Seminclusive measurement B reconstructed; (see also lectures by B. Pecjak) sum of exclusive decay modes Xs: no S-wave states in B→Xsg 22 final states K-(0)+(1-4)p 10 K-(0)+h+(0-2)p 6 3K-(0)+(0-1)p

g + Xs B

(better resol.)

bgk.: p0, h veto, NN from topological variables for continuum;

not all final states reconstructed →corr. for missing fraction (from MC, checked with data in various final state categories)

BaBar, PRD72, 052004, 82 fb-1

B

XsB

M

MME

2

22

peaking bkg.: missing final statesreconstructed as one of signal decays; signal decays with some particles exchanged with other B

25% at low M(Xs) from KL

at high M(Xs) from K+ 5p


b → sg

Seminclusive measurement fit in bins of M(Xs) Br(M(Xs));

Eg spectrum (Eg>1.9 GeV);

moments of dG/dEg also determined;

mb (and other QCD parameters)

determined for use in b →uln; e.g.

BaBar, PRD72, 052004, 82 fb-1

K*(892)

410)18.027.3(

)9.1;(

12.004.0

40.055.0

GeVEXBBr s

main systematics: from missing final states

GeVGeVmb )08.004.067.4()1( more details at


more


b → sg

Phenomenology average of results:

comparison with limits from B →tn:

95% C.L. lower limit on m(H±), all tanb

M. Misiak et al., PRL98, 022002 (2007)

410)09.023.052.3(

)6.1;(

GeVEXBBr s HFAG, winter 08, http://www.slac.stanford.edu/xorg/hfag/

first error: stat.+syst.second error: Eg spectrum (extrapol.)

Belle, PRL97, 251802 (2006), 414 fb-1

m(H±)=300 GeV

For my part I know nothing with any certainty, but the sight of the stars makes me dream.

V. van Gogh (1853 - 1890)


b → sll Motivation (see also lectures by E. Lunghi) FCNC process; M expressed in terms C7,9,10; Wilson coeff.’s

NP modifies C7,9,10 or/and adds new operators

Wilson coeff.’s independent of final state (C7 same for b→ sg and b→ sll);

|C7 |2 constrained by Br(B→ Xsg); sign not known;

b→ sll: interference of amplitudes additional information (also sign) on C7,9,10

b sW±

u, c, tVqb Vqs

g

b s

g

=VqbV*qs C7 x

=

perturbative (dependence on MW, mt, MNP) non-perturbative

more


b → sll

exclusive B →K*ll qK distrib. fraction of long. polarized K* (FL);

ql distrib. lepton

forward-backward asymmetry (AFB);

prediction for AFB:

q2=m2(l+l-)

B l+l-

p

K*

K

qK

)cos1)(1(4

3cos

2

3 22KLKL FF

B

l-

K*ql

l+

lll cos)cos1)(1(8

3)cos1(

4

3 22FBLL AFF

q2

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

low q2 high q2veto

veto


b → sll

reconstruction e+e-, m+m-; K* →Kp, Kp0, Ksp; Mbc fit combinatorial bkg.: e+m-; misid. hadrons: h+m-; peaking bkg.: D(→K*p)p ( mm sample only, veto on m(K*p)); signal fraction

qK fit FL free parameter;

ql fit AFB free parameter;

BaBar, arXiv:0804.4412, 350 fb-1

low q2 high q2

Ns=27.2 ±6.3

Ns=36.6 ±9.6


b → sll

results FL; consistent with SM and -C7

SM;

AFB; -C9

SM C10SM disfavored (>3 s);

stronger constraints;

BaBar, arXiv:0804.4412, 350 fb-1

SM

q2

average over interval

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

Belle, PRL96, 251801 (2006), 357 fb-1

C7 = -C7SM

more

Belle, ICHEP08, 600 fb-1


b → sll semi-inclusive similar as b →sg; e+e-, m+m-; K-/Ks+(0-4) ;p ~30% missing modes; charmonium sample provides cross-check of bkg.;

constraints on NP in Ci Br(B →Xsg), Br(B →Xsll), Br(K →pnn ) Br(Bs →mm),

no Br(B →K*ll ) (large th. uncertainty)

Belle PRD72, 092005 (2005), 140 fb-1

Nsig=68 ±145.4 s signif. (-2lnL0/Lmax)

6

6

10)3.15.16.5()(

10)83.011.4()(81.085.0

s

s

XBBr

XBBr Belle PRD72, 092005 (2005), 140 fb-1

BaBar PRL93, 081802 (2004), 82 fb-1

dC

9

dC7dC9

dC

10

J. Kamenik, arXiv:0805.2363


B oscillations more

Time evolution state initially produced as superposition (n.b.: a(0)/b(0) can be 0) will evolve in time as

if interested in a(t), b(t): effective Hamiltonian and t-dependent Schrödinger eq.:

eigenstates: (well defined m1,2 and G1,2)

002,1 PqPpP

)(

)(

2)(

)(0

0

0

0

tP

tPi

tP

tP

ti ΓM

00 )0()0()0( PbPat

1100 )()()()( ftcPtbPtat

D. Kirkby, Y. Nir, CPV in Meson Decays, in RPP

back


B oscillations more

Time evolution eigenvalues:

q

p

q

p

iMiM

iMiM

2,1*12*

12

1212

22

22

2

2*

*,

222 1212

1212

2

2,12,1

12122,1

iM

iM

p

qimiM

p

qiM

diagonal elem.: P0 P0 (including decays)non-diagonal elem.: P0 P0

P1,2 evolve in time according to m1,2 and G1,2:

)0()( 2,12,12,1 tPetP ti


B oscillations more


mimiMiM

mim

im

m

m

iMiMiMp

q

22

*12*

1212

12

222

21

2121212

2122

21

2121

212

212

22

2121

*12*

1212

1212

1221

2)

2)(

2(4

2)(

)()(2)()()()()(2

)()(2

)(2

),(

)2

)(2

(22

2


B oscillations more


)(4

2||4

2

2)(

2||4

2)

2)(

2(4

*1212

2

12212

22

22*

1212

2

12212

22

*12*

1212

12

Mm

Mm

mimMiM

mimiMiM

back


B oscillations more

Time evolution

taking into account

we arrive at time evolution of P0, P0:

2;

2;

2; 21212121 mm

mymm

x

ttmiet

yixP

p

qt

yixPtP 2000

2sinh

2cosh)(

ttmiet

yixP

q

pt

yixPtP 2000

2sinh

2cosh)(

210

210

2

1

,2

1

PPq

P

PPp

P

back


B oscillations more

)sin(2)sinh(2

)cos()cosh()(1

**

22

22

0

xtAAp

qytAA

p

q

xtAp

qAytA

p

qA

dt

fPd

e

ffff

fffft

)sin(2)sinh(2

)cos()cosh()(1

**

22

22

0

xtAAq

pytAA

q

p

xtAq

pAytA

q

pA

dt

fPd

e

ffff

fffft

Time evolutiondecay rates:

for CP conjugated states: Af → Af, Af → Af


B oscillations more CPV

|p/q|=1, y<<1 (well fulfilled for Bd)

)sin(2)sinh(2

)cos(1)cosh(1)(1 22

0

2

txty

txtytd

fPd

eA

ff

fft

f

)sin(2)sinh(2

)cos(1)cosh(1)(

)/(

1

**

220

2

txty

ttytd

fPd

eAqp

ff

fft

f

)sin(||1

)(2)cos(

||1

)||1(

)(/)(/

)(/)(/

22

2

00

00

txtx

fBtddfBtdd

fBtddfBtddA

f

f

f

f

CP

|lf|≠1

|Af/Af|≠1 CPV in decay |q/p| ≠1 CPV in mixing

I(lf) ≠ 0 CPV in interf.

f

ff A

A

p

q

back


B oscillations more Method reconstructed flavour specific decays;

D*ln

=0 known meas. known meas. known meas. meas.

total bkgD** bkg.

Belle, PRD71, 072003 (2005), 140 fb-1

back


B oscillations more Method tagging

q=+(-)1 B0(B0) r: tag quality

H. Kakuno et al., NIM A533, 516 (2004)


B oscillations more Method tagging

single r bin:

two r bins:

H. Kakuno et al., NIM A533, 516 (2004)

back


B oscillations more Method resolution function

H. Tajima et al., NIM A533, 370 (2004)

back

Rful: vtx of fully reconstructed B mesonRasc: vtx of tagging B mesonRnp: non-primary tracksRk: kinematic smearing


B oscillations more

if mi = mj due to CKM unitarity: no mixing

d

b

b

d

u, c, t

u, c, t

W+ W-B0 B0

d

b

b

d

u, c, t u, c, t

W+

W-

B0 B0

Vid

Vjd

Vjb*

Vib*

Phenomenology

P0-P0 transition → box diagram at quark level

),,( 2

,,,

22**

00

jtcuji

iWjbjdidib

wk

mmmVVVV

BHB

F

)(),,( 23

22

21

20

222 WjijiWjiW mOmmfmfmfmfmmmF

simplified treatment based on dimension: O. Nachtmann, Elem. Part. Phys., Springer-Verlag

A.J. Buras et al., Nucl.Phys.B245, 369 (1984)for serious treatment see e.g.:

P0: any pseudo-scalar meson;specific example of Bd

0

back


Leptonic B decays more

Systematic checks Bsig decay modes

check of EECL, double tagged decays,

Bsig- →D*0 l- n, D*0 →D0p0

back

Belle, PRL97, 251802 (2006), 414 fb-1


Leptonic B decays more

Phenomenology additional Higgs doublet;

tanb=v1/v2, ratio of vacuum expectation values;

H± coupling ml same factor as

helicity SM suppression

ratio independent ofH ± contribution:

back

moftindependen

H

BSM

m

mBB 22

2

2

)tan1()()(

2

2222

2

18

)(B

BBubFSM

m

mmmfV

GB

2222

2221

22

21

21 )/1(

)/1()(/)(

Bl

Bl

l

lSMSM

mm

mm

m

mBB

ll

Type II Two Higgs Doublets Models(f1 gives masses to d-type

and charged l; f2 gives masses to u-type; in Type I models f1 is decoupled and f2 generates all masses)W.S.Hou, PRD48, 2342 (1993)

if Gmeas>GSM H± contribution dominant


Semileptonic B decays more

Form factors P→P:

B(v) → B(v’): for mb → amplitude can only depend on g = v·v’; for v = v’ nothing happens, z(1)=1;

B(v) → D(v’): for mb, mc → same (HQS)

back

qq

mmqfq

q

mmppqf

ppqfppqf

pDJpppq

pDJpvuVG

cdF

2

22

212

02

22

21

122

1

122

122

1122

21

11225

)())((

))(())((

)()(

)()()1(2

M

z(v·v’): Isgur-Wise functionrelates two in principle independent form factors for P → P transition

)')('()(||)'(1

)')('()(||)'(1

'

'

vvvvvBbcvDmm

vvvvvBbbvBm

vv

cb

vvb

)'(2

)2(0

1

2)(

21)2(

1vv

DmB

mD

mB

mqf

Dm

Bm

qqf



Form factors P→V:

back

q2

one more f.f. if ml not small;

HQS: relations among f.f.’s for P→ P and P →V



B →D*tn phenomenology amplitude for W exchange: lM=±,0; lt=±; lW=±,0; D*, t, W helicity

amplitude for H± exchange:

relation among H ±, W exchange amplitudes:

H ± : no contribution of transversely polarized D* (HR,L

±=0) back

M. Tanaka, Z.Phys.C67, 321 (1995)



B →Dtn phenomenology update of predictions:

U. Nierste et al., PRD78, 015006 (2008)

mB2/mH

2 tan2b (in 2HDM-II)

back

measurement

BaBar, PRL100, 021801 (2008), 209 fb-1


b → s g more

inclusive semil. B decays semil. width:

Operator Product

Expansion to O(1/mb2):

two parameters, l1, l2:

back

))1()()1((2

4

||||)(~)(

55

2

bcVG

O

BOXspacephasedcb

cbF

sl

Xcslc

BbGg

bBB

M

BbiDbBB

M

mm

mc

mm

mcb

mcbV

FG

bb

c

bb

c

|2

|6

12

|2)(|2

11

6)(

2

31)(

3192

52||2

22

2221

1

222

*

1

4

)2

1)((

BB

DBDBcb

mm

mmmmmm

average p2 of b in B

hyperfine interaction


b → s g more

inclusive semil. B decays Fermi motion:

new parameter L

same parameters governing moments of various distributions, e.g. mass of hadronic system in semil. decays:

or Eg moments in b →s g:

back

bm

Bmk

kbm

partondkfdkd

)()(

22,

21,

2

2,

)2(1

)2(

Bm

Bm

BmB

mf

nD

msds

dds

sln

DmsH

12

21

22

EE

mE B

A.F.Falk, M.E.Luke, PRD57, 424 (1998)

A.Kapustin, Z. LigetiPLB355, 318 (1995)


b → s g more

off-data subtraction a: lumin. ratio; ehadronic,B→Xsg

ON,OFF: efficiency of hadronic, signal selection; FN,E: corr. factor due to lower mean E and multiplicity in off-data

back


b → s g more

Eg resolution inclusive meas.: Eg measured in EM calorim.; s(Eg;Eg=2 GeV) ~ 20 MeV;

semi-inclusive meas.: Eg from

s(Eg) ~ 1-5 MeV;

back

B

XsB

M

MME

2

22


b → sll more

OPE, Wilson coeff. example of b →cdu

almost point-like inter.:

series: product of currents expressed as series of local operators (OPE);

such expansion valid if q2/MW2<<1;

in this range an effective theory can be constructed, valid up to a cut-off, in the above case up to MW;

back

b c

d

uW

22

522

5 )1(1

)1(

WWb

W

MqMm

udMq

bc

udM

i

M

i

Mbc

udM

q

M

q

Mbc

WWW

WWW

)1()()(

11

)1(

)1(11

)1(

54

4

2

2

25

54

4

2

2

25

BaBar Physics Book, SLAC-R-504


b → sll more


rad. corr. to lowest order:

operators receive radiation corr. and must be renormalized; they become dependent on renormalization scale m;

physics must be independent of m operators receive m dependent coefficients in order for Heff to satisfy:

back

b c

d

uW

g

W

bs

W

bs M

m

M

m 22 lnln

jj

W

iiI ud

MqbcO )1(

1)1( 5

225

(i,j: color indices)

0effHd

d



b → sll more


under renormaliz. set of operators can be enlarged, for the example under consideration there is also

Heff is thus

Ci(m) are Wilson coeff., containing information on short distance physics down to (arbitrary) scale m; all heavy masses (M>>m) dependence (mt, MW, MNP) is contained in Ci(m)

back

b c

d

uW

g

ij

W

jiII ud

MqbcO )1(

1)1( 5

225

(changed color indices)

)()()()( IIIIIIeff OCOCH



b → sll more

OPE, Wilson coeff.

once Oi(m) dependence is calculated, Ci(m) follow from for b →cdu

division of energy scales between Ci(m) and local operators <f|Oi(m)|B> can be schematically viewed as

Wilson coeff. Ci(m) are independent of external states (f)

back

2

2

2

2

ln)(ln)(lnW

sb

sW

bs M

m

M

m

<f|Oi(m)|B> Ci(m)

0effHd

d

23/1223/6

, )(

)(

)(

)(

2

1)(

s

Ws

s

WsIII

MMC


b → sll more

OPE, Wilson coeff.

Br(b → sll ):

AFB, RPV SUSY contrib.:

back

2

2

ˆbm

qs

|l1i3’l1i2’*|<4.7x10-5

Y.-G. Xu et al., PRD74, 114019 (2006)

P. Gambino et al., PRL94, 061803 (2005)


b → sll more

back

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

Belle, PRL96, 251801 (2006), 357 fb-1

Documents

B. Golob, Ljubljana Univ.Results from B factories 1HQP School, Dubna, Aug 2008 Boštjan Golob University of Ljubljana, Jožef Stefan Institute & Belle Collaboration