BEAUTY 2005 10th International Conference on B-Physics at Hadron Machines

BEAUTY 200510th International Conference on B-Physics at Hadron Machines

Assisi (Perugia), Italy. June 20-24, 2005

•Mixing Parameters:

•Width Differences:

•CP-Violation Parameters:

•Lifetime Ratios:

Cecilia TarantinoUniversità Roma Tre and INFN Sezione di Roma III

)(/)(),(/)(),(/)( dbdsd BBBBB

sd BB ,

B-Meson Mixing and Lifetimes:

sdBpq

,|/|

sd mm ,

Basic FormalismBasic Formalism

Physical Physical ObservablesObservables

1.1. Mixing Mixing mmdd, , mmss

• Phenomenological importance (UTA)Phenomenological importance (UTA)• Theoretical inputsTheoretical inputs

Unitarity Triangle Analysis 1)7(502.0 psmd

.).%95(4.14 1 LCpsms

[HFAG 2005]

Extracting |VExtracting |Vtdtd|:|:

20

2

2

22

2

2

0

2

2

22

ˆ)(6

ˆ)(

6

BsBtBtsBWF

s

BsBtBtdB

WFd

fBxSVmmG

m

fBxSVm

mGm

ss

s

d

•OPE•Dominant top contribution • : short-distance physics, from Perturbation Theory (2%) [at NLO, Buras et al.: Nucl.Phys.B347 (1990)] • : non-perturbative QCD effects, from Lattice QCD

• : lattice uncertainties cancel

)(0 tB xS

22 ,ˆ ss BB fB

2

),( Wt mm

2

22

ˆ

ˆ

dd

ss

BB

BB

fB

fB

B-Physics on the Lattice

MULTISCALE PROBLEM

(computational cost limit)

1bam HQET, NRQCD, FermiLab approach, extrapolation in the heavy quark mass

1LM Extrapolation in the light quark mass using ChPT

Accurate “quenched” studies + recent Nf=2, Nf=2+1 calculations

50/ aL

Lattice QCD Actions:•Wilson/O(a)-improved Wilson: problem at light masses (exceptional quenched configurations)•Twisted mass: no exceptional configurations, easier improving, but more expensive•Staggered: light masses, but 4 tastes (fourth root trick)•Domain-wall/Overlap: light masses, but the most expensive

• sea quark effects seem at O(10%-15%):• But continuum scaling or other

systematics (NP-ren., FV effects, diff. actions …) not completely investigated 230 30 MeV

sBf

50ss Bs B i fb p

With the present accuracy:

NRQCD

FNAL

RELAT.

FNAL NRQCD

ICHEP 2004:ICHEP 2004:

NRQCD

Bs-Meson Decay Constant from Lattice QCD

•High level of accuracy;•Good agreement among different approaches;•Continnum extrapolation;[De Divitiis et al.(2003), ALPHA(2003)]

Quenched SimulationsQuenched Simulations

•Nf=2 studies [JLQCD(2003): high statistics and O(a)-improved action];•Nf=2+1 preliminary values [Wingate at al. (2003): staggered action];

Unquenched SimulationsUnquenched Simulations

s s

d d

B B

B B

f m

f m

0.050.061.22sB

B

f

f

50dd BB ip fb d

ICHEP 2004:ICHEP 2004:

• Chiral Log Effects roughly estimated [JLQCDJLQCD (Nf=2, mq/ms>0.5) +HPQCDHPQCD (Nf=2+1, mq/ms>0.2)]

With the present accuracy:With the present accuracy:

more statistics and lighter quark masses

still needed

more statistics and lighter quark masses

still needed Final Chiral Loop Effects: O(5%)

Bd-Meson Decay Constant from Lattice QCD

•Pion Loops could be significant [Kronfeld-Ryan(2002), O(15%)]

Delicate Issue: Chiral ExtrapolationDelicate Issue: Chiral Extrapolation

8.1)31(

log)4(4

)31(31

2

2

2

2

22

g

m

f

mg

mf

mf

dd

ss

BB

BB

[JLQCD(2003), N[JLQCD(2003), Nff=2]=2]

• Negligible sea quark effects!!Negligible sea quark effects!!• Consistent with diagnosis deduced Consistent with diagnosis deduced

from QChPT versus ChPTfrom QChPT versus ChPT: : [[Booth95,Sharpe,Zhang96]

With the present accuracy:With the present accuracy:

JLQCD(2003): NJLQCD(2003): Nff=2 & NRQCD=2 & NRQCD

B-B Mixing on the Lattice

qqq BBBqLLq BfmBqbqbB ˆ

3

8 22

5617

8695 )16(017.1

ˆ

ˆ ,)42(287.1ˆ

d

s

d

B

BB

B

BB

Lattice data are consistent with a constant.

Chiral Loops not a problem for

They are expected small from ChPT

Chiral Loops not a problem for

They are expected small from ChPT

B-B Mixing on the Lattice

qqq BBBqLLq BfmBqbqbB ˆ

3

8 22

dBB̂

ICHEP 2002 (Lellouch)BEAUTY 2005

(ICHEP 2004, Hashimoto)

203(27)(+0-20) 189(27)

238(31) 230(30)

276(38) 262(35)

1.18(4)(+12-0) 1.22(+5-6)

1.18(4)(+12-0) 1.23(6)

ˆ (MeV)s sB Bf B

Now averages include rough ``estimates’’ of chiral logs (mq/ms>0.2) and unquenched effects (Nf=2+1)

Now averages include rough ``estimates’’ of chiral logs (mq/ms>0.2) and unquenched effects (Nf=2+1)

B Mixing from Lattice QCD

)(MeVdBf

(MeV)sBf

ds BB ff /

fB O(s2) recently calculated

BB O(s) completed but non-factorisable contributions important

B Mixing from QCD Sum Rules

1. Equating phenomenological and theoretical spectral functions;2. Determination of theoretical spectral functions by calculating two or three-point correlators in perturbative QCD, including corrections from the OPE.

Problem: many parameters, loosely constrained!

2. 2. Decay:Decay:

sd BB ,

sdBpq

,|/|

)(/)(),(/)(),(/)( dbdsd BBBBB

•Width Differences

•CP-Violation Parameters

•Lifetime Ratios

)0( 11 Bq

)2( 21 Bq

HQE )( QCDbm Large energy release contact interaction

SPECTATOR EFFECTS

Scale separation

• : short-distance (perturbative)• : long-distance (non-perturbative)

)(qkc

020 )( q

Bqkq BOB

•Lifetime Ratios (1996) [M. Neubert and C.T. Sachrajda]

(2002)•[E. Franco, V. Lubicz, F. Mescia and C.T.]•[M. Beneke, G. Buchalla, C. Greub, A. Lenz and U. Nierste]

(2004)•[F. Gabbiani, A. I. Onishchenko and A. A. Petrov]

•Width Differences and CP (2003)•[M. Ciuchini, E. Franco, V. Lubicz, F. Mescia and C.T.]•[M. Beneke, G. Buchalla, A. Lenz and U. Nierste]

(1996) •[M. Beneke, G. Buchalla and I. Dunietz]

)( sO

)/1( bmO

)/1( bmO

)( sO

)1(O

kk

b

kkk

bb

s

B

bcbF Om

cOc

mbGb

m

gcbbc

M

mVG )7()7(

)6()6(3

2

2)5()3(

3

522 96

)2(192

b

s

mSScscbB

bFs QGQGVVM

mG/1

2*22

21 )()2(12

Wilson Coefficients from P.T.

Matrix Elements: Operators2B

)/1( 3bmOLeading contribution

21 , qq BB From the lattice (with different methods) or QCD -sum rules [J.G. Korner et al., 2003]

Subleading contribution )/1( 4bmO

4 operators :),,,( 4321qqqq RRRR

qq RR 41 ,

qq RR 32 ,

• : related, through Fierz and eq. of motion, to operators computed on the lattice

• : from the VSA

21 , qq BB on the lattice•HQET

•NRQCD

•unquenched NRQCD

•QCD

•QCD +HQET

[V. Gimenez and J. Reyes, 2000]

[Hi-KEK (S. Hashimoto et al.), 2000]

[JLQCD (S. Aoki et al.), 2001-2003]

[APE (D. Becirevic et al.), 2000]

[APE (D. Becirevic et al.), 2001]

• So far, the approach has been only applied in the quenched case

Matrix Elements: Operators0BLeading spectator effect contribution )/1( 3

bmO

(not computed)

(not computed)

B-parameters:b• :computed in lattice-HQET, evolved at the LO

BBB sd B-parameters

•Lattice-HQET

•Lattice-QCD

•Sum Rules, in HQET

Subleading spectator effect contribution )/1( 4bmO

8 operators, from the VSA (B-mesons) or the quark-diquark model (baryon)

[M. Di Pierro and C.T. Sachrajda, 1998]

[APE (D. Becirevic et al.), 2001]

[M.S. Baek et al., 1998]

Width Differences

Experimental measurements:

Theoretical predictions at the NLO + contribution of :)/1( 4bmO

LO 26%

LO+ 16%

NLO 18%

NLO+ 7%)/1( 4bmO

2 01.065.0 25.033.0

s

s

[CDF, 2004] 21.0 27.0

40.0

s

s

[D0, CKM2005]

(preliminary)

097.0)064.0240.0()014.0018.0(

)()(* /12)1(

2)0(

21)1(

1)0(

1

bm

ss

s

s OccOccFact )/1( 4bmO

21 cc

%27)0(

2

)1(2 c

c

%5522

/1 s

m

Ocb

(large cancellations at the NLO)

(large cancellations at ))/1( 4bmO

[THEORY]

CP-Violation Parameters

Theoretical predictions at the NLO:

Experimental measurement:

•Importance of more accurate measurements UTA

0034.00013.01(q/p)d [HFAG, 2005]

Lifetime Ratios

LO NLO

)(

)(

dB

B

)(

)(

d

s

B

B

)(

)(

d

b

B

Theoretical predictions at the NLO + contribution of : )/1( 4bmO

Experimental measurements:

•Good agreement at the NLO and )1at )(/)(( db B)/1( 4bmO

LO 1.01(3) 1.00(1) 0.93(4)

NLO 1.06(3) 1.00(1) 0.90(5)

NLO+ 1.06(2) 1.00(1) 0.88(5)

)(

)(

dB

B

)(

)(

d

s

B

B

)(

)(

d

b

B

)/1( 4bmO

Conclusions

DECAY: Importance of NLO corrections in QCD and in the HQE

Lifetime Ratios 1at )(/)( db B

Width Differences

)/1( 4bmO

[CDF, 2004]

01.065.0 25.033.0

s

s

Importance of more accurate measurements UTA

CP-Violation Parameters

21.0 27.040.0

s

s

[D0, Lattice2005]

(preliminary)

03.007.0

s

s

[THEORY]

MIXING: Phenomenological importance of in the UTA Theoretical inputs at 5-15% from Lattice QCD

sd mm ,