beauty and charm results from b factories

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

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

(c c) 1.3 nb (~109 XcYc pairs) continuum production * c

c

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

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

3.5 fb-1 on tape(D0; pt>5.5 GeV,|y|<1)≈≈13 b50x109 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 1,2)

002,1 PqPpP

eigenvalues:

qp

qp

iMiM

iMiM2,1*

12*12

1212

22

22

),(2 1212

2,12,12,1

Mfim

)(42

||42

*1212

2122

12

22

Mm

Mm2121 , mmm

more


)sin(2)sinh(2

)cos()cosh(

)(1

**

22

22

0

xtAApqytAA

pq

xtApqAytA

pqA

dtfPd

e

ffff

ffff

t

B oscillations Time evolution

;2

; 2121

ymmx

for easier notation: t → t

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

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

decay rates:

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

P1,2 evolve in time according to m1,2 and 1,2: )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

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/

K*0

+

-

-

K+

K-l-

fully reconstruct decayto flavor specific final state

tag flavorof other B from chargesof typicaldecay products

t=z/c

determine time between decays

(4

S)

determinedB0(B0)

B0 or B0

22 )()2(

iCM

bc

pEM

2CMi EEE

signal

signal


B oscillations Method reconstructed flavour specific decays

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

E signal region

measure t distribution

more

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

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

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

0

2

0

2

tRetxwtdfPd

A

tRetxwtdfPd

A

t

f

t

f

t

f

t

f

etxtdfPd

A

etxtdfPd

A

)]cos(1[)(1

)]cos(1[)(1

0

2

0

2

t

f

t

f

etxwtdfPd

A

etxwtdfPd

A

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

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

0

2

0

2

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

more


B oscillations Results flavour asymmetry

)()cos()21(

/)(/)(/)(/)(

00

0

tRtxw

tdfBdtdfBdtdfBdtdfBd

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

md=(0.511±0.005±0.006) ps-1

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

md=(0.507±0.005) ps-1

x=mdBd= 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, tW+

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

mmmVVVVBHB

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, 12 frombox diagram; from that calculate m,

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

q: d (Bd) or s (Bs);and ms 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|b(1-5)q|Bq

0>fBq: decay constantB

(‘): 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

VfBmfBm

mm

reduced theor.

uncertainty in ratio

035.0047.0210.1

M. Okamoto, hep-lat/05101132


B oscillations

Bs

amplitude method: instead of ms

fit A at different values of ms; A=1 oscillations at this ms value

t

f

etxwtd

fPPd

A

)]cos()21(1[))((1 00

2 A

CDF, PRL97, 242003 (2006)

A

ms=(17.77±0.10±0.07) ps-1

x=msBs= 25.5±0.6 ms/md

uncertainties on (2+2): md constraint ±13% md ±1%

fBdBBd ±12% ms/md constraint ±6% ms /md ±1.5% ±5%


Leptonic B decays B →

Q

q

P+l+

fP

VQq

2

22222

18

)(

PPPQq

F

mmmmfVG

P

(B+ →): (B+ →): (B+ →e+)=1:4x10-3:10-7

fP → meas. VQq; H±;

W+

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

B → candidate 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 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, B

BrSM(B+ →) = (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→K, dark matter)

222

2

)tan1()()( H

BSM

mmBB

HPQCD, PRL95, 212001 (2005)

51.013.1)tan1( 222

2

H

B

mm

410)43.041.1()(

BBr

SuperB50 ab-1

b

uB-

H+

more


Semileptonic B decays

P →Pl

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

)()()1(2

122

122

111222

21

111222531

ppqfppqfpMJpMppq

pMJpMvuVGqq

F

Mq1 q3

l+

M1

q2

M2

q2

in suppressed by ml2/mM1

2

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

W±,H±

H± exchange modified SM Br’s for ; in P→ V only helicity=0 V possible

more

more measurement challenging due to multiple ’s;

skip



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

method: excl. Btag reconstruction →e, Bsig: D/D* and e/ mmis

2=pmis2

MCdata

Bsig →D*

20

2/* /)( BbeameDmismis mEppEX

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

D*

Bsige/

Btag

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

)( /* eDtageemis ppppp

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

missing mass (>0 for several );



B0 →D*-+ results bkg. from B0 →D*e (peaking) →

Nsig=60 ±12

6.7 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*-+

D-+

D-l+

D*-l+

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



B →D(*) phenomenology limits on H±;

inclusive B →Xc predicted Br: (2.30 ±0.25)% sum of D*, D: (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)

(B

→D

* long

.)

(B

→D

*)

| SM

more


b → s

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

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

experiment: measure low E

huge bkg.

b sW±

u, c, tVqb Vqs

b s

u, c, tX Y

H±

±

b sX Y

tcu ~,~,~

more

signal

continuum0

Your background and environment is with you for life. No question about that. S. Connery (1930)


b → s

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

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

veto 0, →

rest bkg. from MC (control samples);

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

inclusive B→ 0X, X samples reconstructed in data (off- data subtraction) and MC; 5%-10% correction to MC bkg. normaliz.

onoff

onscaled off

subtracted80% of remaining bkg. from 0, →

after vetoing 0, →

Belle, arXiv:0804.1580,605 fb-1

more


b → s

Inclusive measurement E spectrum

Br(B →Xs) deconvolution of E

(Emeas → E

true; using radiative di-muon evts); boost to B rest frame; b →d 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. ’s from B (other than 0, )

222 )0012.00214.00156.00396.0(

)002.0053.0032.0281.2(

GeVEE

GeVE

Belle, arXiv:0804.1580,605 fb-1


b → s

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

+ Xs B

(better resol.)

bgk.: 0, 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

MMME

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+ 5


b → s

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

E spectrum (E>1.9 GeV);

moments of d/dE also determined;

mb (and other QCD parameters) determined for use in b →ul; 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 → s

Phenomenology average of results:

comparison with limits from B →:

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

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: E 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→ s and b→ sll);

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

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

b sW±

u, c, tVqb Vqs

b s

=VqbV*qs C7 x

=

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

more


b → sll

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

l distrib. lepton forward-backward asymmetry (AFB);

prediction for AFB:

q2=m2(l+l-)

B l+l-

K*

K

K

)cos1)(1(43cos

23 22

KLKL FF

B

l-

K*l

l+

lll cos)cos1)(1(83)cos1(

43 22

FBLL 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-, +-; K* →K, K0, Ks; Mbc fit combinatorial bkg.: e+-; misid. hadrons: h+-; peaking bkg.: D(→K*) (sample only, veto on m(K*)); signal fraction

K fit FL free parameter;

l 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 );

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 →s; e+e-, +-; K-/Ks+(0-4) ~30% missing modes; charmonium sample provides cross-check of bkg.;

constraints on NP in Ci Br(B →Xs), Br(B →Xsll), Br(K → ) Br(Bs →), no Br(B →K*ll ) (large th. uncertainty)

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

Nsig=68 ±145.4 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

C9

C7C9

C10

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 1,2)

002,1 PqPpP

)(

)(

2)(

)(0

0

0

0

tP

tPitP

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:

qp

qp

iMiM

iMiM2,1*

12*12

1212

22

22

2

2**

,222 12

12

1212

22,1

2,112

122,1

iM

iM

pqimiM

pqiM

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

P1,2 evolve in time according to m1,2 and 1,2:

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



mimiMiM

mim

im

m

m

iMiMiMpq

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



)(42

||42

2)(

2||4

2)

2)(

2(4

*1212

2122

12

22

22*

1212

2122

12

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 mmmymmx

ttmietyixP

pqtyixPtP 2000

2sinh

2cosh)(

ttmietyixP

qptyixPtP 2000

2sinh

2cosh)(

210

210

21

,21

PPq

P

PPp

P

back


B oscillations more

)sin(2)sinh(2

)cos()cosh()(1

**

22

220

xtAApqytAA

pq

xtApqAytA

pqA

dtfPd

e

ffff

fffft

)sin(2)sinh(2

)cos()cosh()(1

**

22

220

xtAAqpytAA

qp

xtAqpAytA

qpA

dtfPd

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)(1 220

2

txty

txtytdfPd

eA

ff

fftf

)sin(2)sinh(2

)cos(1)cosh(1)(

)/(

1

**

220

2

txty

ttytdfPd

eAqp

ff

fftf

)sin(||1)(2

)cos(||1

)||1(

)(/)(/)(/)(/

22

2

00

00

txtx

fBtddfBtddfBtddfBtddA

f

f

f

f

CP

|f|≠1

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

I(f) ≠ 0 CPV in interf.

f

ff A

Apq

back


B oscillations more Method reconstructed flavour specific decays; D*l

=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, tW+

W-

B0 B0

Vid

Vjd

Vjb*

Vib*

Phenomenology

P0-P0 transition → box diagram at quark level

),,( 2

,,,

22**

00

jtcuji

iWjbjdidib

wk

mmmVVVVBHB

F

)(),,( 23

22

21

20

222 WjijiWjiW mOmmfmfmfmfmmmFsimplified 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- , D*0 →D00

back

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


Leptonic B decays more

Phenomenology additional Higgs doublet;

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

H± coupling ml same factor as helicity SM suppression

ratio independent ofH ± contribution:

back

moftindependen

H

BSM

mmBB 22

2

2

)tan1()()(

2

2222

2

18

)(B

BBubFSM

mmmmfVGB

2222

2221

22

21

21 )/1()/1()(/)(

Bl

Bl

l

lSMSM

mmmm

mmBB

ll

Type II Two Higgs Doublets Models(1 gives masses to d-type

and charged l; 2 gives masses to u-type; in Type I models 1 is decoupled and 2 generates all masses)W.S.Hou, PRD48, 2342 (1993)

if meas>SM H± contribution dominant


Semileptonic B decays more

Form factors P→P:

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

B(v) → D(v’): for mb, mc → same (HQS)

back

qqmmqfq

qmmppqf

ppqfppqfpDJp

ppq

pDJpvuVGcd

F

2

22

212

02

22

21

122

1

122

122

1122

21

11225

)())((

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

)()()1(2

M

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

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

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

'

'

vvvvvBbcvDmm

vvvvvBbbvBm

vvcb

vvb

)'(2

)2(0

1

2)(

21)2(1 vv

DmBmDmBmqf

DmBm

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* phenomenology amplitude for W exchange: M=±,0; =±; W=±,0; D*, , 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 →D phenomenology update of predictions:

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

mB2/mH

2 tan2 (in 2HDM-II)

back

measurement

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


b → smore

inclusive semil. B decays semil. width:

Operator Product Expansion to O(1/mb

2):

two parameters, 1, 2:

back

))1()()1((2

4

||||)(~)(

55

2

bcVGO

BOXspacephasedcb

cbF

sl

Xcslc

BbGgbBBM

BbiDbBBM

mmmc

mmmcbmcbVFG

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 → smore

inclusive semil. B decays Fermi motion:

new parameter

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

or E moments in b →s :

back

bmBmk

kbmpartondkfdkd

)()(

22,2

1,2

2,

)2(1)2(

BmBmBmBmf

nDms

dsdds

sln

DmsH

12

2122

EE

mE B

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

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


b → smore

off-data subtraction : lumin. ratio; hadronic,B→Xs

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

back


b → smore

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

semi-inclusive meas.: E from

(E) ~ 1-5 MeV;

back

B

XsB

MMME

2

22


b → sllmore 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

udMi

Mi

Mbc

udMq

Mq

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



rad. corr. to lowest order:

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

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

back

b c

d

uW

g

W

bs

W

bs M

mMm 22 lnln

jj

W

iiI ud

MqbcO )1(1)1( 5

225

(i,j: color indices)

0effHdd




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

Heff is thus

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

back

b c

d

uW

g

ij

W

jiII ud

MqbcO )1(1)1( 5

225

(changed color indices)

)()()()( IIIIIIeff OCOCH



b → sllmore OPE, Wilson coeff.

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

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

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

back

2

2

2

2

ln)(ln)(lnW

sb

sW

bs M

mMm

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

0effHdd

23/1223/6

, )()(

)()(

21)(

s

Ws

s

WsIII

MMC


b → sllmore OPE, Wilson coeff.

Br(b → sll ):

AFB, RPV SUSY contrib.:

back

2

2

ˆbmqs

|1i3’1i2’*|<4.7x10-5

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

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


b → sllmore

back

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

C7 = -C7SM

C9 C10 = -C9SM C10

SM

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

beauty and charm results from b factories

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