Puzzles in B physicsRecent development in PQCD, QCDF, SCET

Hsiang-nan LiAcademia Sinica, Taiwan

presented at Whepp9BhubaneswarJan. 07, 2006

Outlines• Introduction

• QCDF, PQCD, and SCET

• B! VV polarizations

• B! K direct CP asymmetries

• B! branching ratios

• Mixing-induced CP asymmetries in b! s penguin

• Conclusion

Introduction• Missions of B factories:

Constrain standard-model parameters

Explore heavy quark dynamics

Search for new physics

• Entering the era of precision measurement, puzzles have appeared.

• Critical examination of QCD effects is necessary for confirming new physics.

Naïve power counting• Estimate order of magnitude of B decay amplitud

es in power of the Wolfenstein parameter » 0.22

• It is not a power counting from any rigorous theory

• Amplitude» (CKM) (Wilson coefficient)

Induced by O2=(su)(ub)

/ C2

,s

• CKM matrix elements

• Wilson coefficients

|-i|¼ 0.4

a1=C2+C1/Nc

a2=C1+C2/Nc

Quark amplitudes

b

u

s

u

Color-allowed tree T Color-suppressed tree C

QCD penguin P Electroweak penguin Pew

s

u

u

s

u

u

s

u

ug Z

W

parameterization

(C4/C2)(VtdVtb/VudVub)/1» (2/1)(3/4)»

Tree-dominant

B(B0! 00)• P, C, and Pew in 00 are all subleading.

• We should have Br(00)¼ O(2)Br(+-)

• Data show Br(00)¼ O()Br(+-)

• The B! puzzle!

• Large P and/or C?

K parameterization

(C2/C4)(VusVub/VtsVtb)» (1/2)(5/2)»

Direct CP in B! K • K+- and K+0 differ by subleading amplitud

es, Pew/P » C/T» . Their CP are expected to be similar.

• Their data differ by more than 3!

sin 21/sin 2• 1 decay amplitude, fCP

=exp(-2i1)

• Measure SfCP/ ImfCP

) measure sin(21)

• Either pure-tree or pure-penguin modes serve the purpose

• Tree-dominant B! J/ KS, penguin pollution:

P/T» (C4/C2)(VtsVtb/VcsVcb)» 2» 5%• Penguin-dominant b! s, tree pollution:

C’/P’ » 2 » 5%

4S0 by

about 1A puzzle?

Penguin-dominated

Tree-dominated

QCD-improved Factorization(Beneke, Buchalla, Neubert, Sachrajda)

Perturbative QCD(Keum, Li, Sanda)

Soft-collinear Effective Theory(Bauer, Pirjol, Rothstein, Stewart)

QCDF • Based on collinear factorization (Brodsky

and Lepage 80).

• Compute correction to naïve factorization (NF), ie., the heavy-quark limit.

• Divergent like s01 dx/x (end-point singularit

y) in collinear factorization

nonperturbative

perturbative

Hard kernels • TI comes from vertex corrections

• TII comes from spectator diagramsMagnetic penguin O8g

q1

x

End-point singularity • Singularity appears at O(1/mb), twist-3 spec

tator and annihilation amplitudes, parameterized as X=(1+ ei)ln(mb/)

• For QCDF to be predictive, O(1/mb) corrections are better to be small ¼ FA.

• Data show important O(1/mb). Different free (,) must be chosen for B! PP, PV, VP.

PQCD• End-point singularity means breakdown of

collinear factorization

• Use more “conservative” kT factorization (Li and Sterman 92)

• Parton kT smear the singularity

• Same singularity in form factor is also smeared

• No free parameters

2210

1

BT mkxdx

b

BF

Factorization picture

Sudakov factors S,summation of sln2(mb/k

T)

to all orders, describe parton distribution in kT

kT accumulates after infinitely many gluon exchanges, similar to DGLAP evolution up to kT~Q

Large kT

Small b

Always collinear gluons

gg

SCETI

• Two scales in B decays: mb and mb2

• Full theory! SCETI: integrate out the lines off-shell by mb

2

C()J(0)()! C()()J(0)

Hard-collineargluon, mass O(mb)

T(0)J(1)(0)

b

W

mb2

Wilson coeff of SCETI

2

1/mb suppressedcurrent

g

SCETII

• SCETI! SCETII: integrate out the lines off-shell by mb

• Compared to QCDF, TII! T(0)J(0,)

J(0,)O()

2

Jet=Wilson coeff of SCETII

! T(0)J(0,)M()B()

B! K direct CP

Large strong phase

• ACP(K+-)¼ -0.115 implies sizable » 15o

between T and P (PQCD, 00)

T exp(i3)

P

T exp(-i3)

T exp(i3)

P

T exp(-i3)

If T=0

Br

Br = Br

If T=0

Br = BrDirect CP

Explanation 1• How to understand the small ACP(K+0)?

• Large PEW to rotate P (Buras et al.; Yoshikawa; Gronau and Rosner; Ciuchini et al., Kundu and Nandi)

) new physics? (Hou’s talk)T exp(i3)

P

T exp(-i3)PEWBr¼ Br

Explanation 2• Large C to rotate T (Charng and Li; He an

d McKellar)

) mechanism missed in naïve power counting?

• C is subleading by itself. Try NLO PQCD.

(T+C) exp(i3)

(T+C) exp(-i3)

T exp(i3)

P

Br¼ Br

NLO PQCD (Li, Mishima, Sanda 05)

• LO: all pieces at LO• LONLOWC: NLO Wilson coefficients• VC: vertex correction• QL: quark loops• MP: Magnetic penguin

• Corrections to form factors are not very relevant here.

decrease P by 10%

Vertex correction• Vertex correction enhances C/ a2, and

makes it almost imaginary.

Without vertex correction

Re, with vertex correction

Im, with vertex correctionIs negative. It rotates T!

Quark amplitudes at LO and NLO

C’ is enhanced by a factor of 3, Arg(C’/T’)=-80o

C’ is still subleading. T, P’ew are almost unchanged.

PQCD results Hadronicuncertainty

QCDF T has a wrong sign in QCDF. C makes t

he situation worse.

(T+C) exp(i3)

(T+C) exp(-i3)

T exp(i3)P

Br = Br

SCET• C/T is real in leading SCET, and large

from the data.

• C can not reduce ACP(K+0) (hep-ph/0510241).

(T+C) exp(i3)

(T+C) exp(-i3)

T exp(i3)

P

Br = Br

SCET inputs

SCET predictions

B! branching ratios

Remarks• It is natural to explain the K data in PQC

D.

• The B! puzzle, large B(00), remains.

• B(00) is an input of SCET, not a resolution

• Resolution was claimed in QCDF/SCET (Beneke and Yang 05).

• Any proposal for the puzzle must survive the constraint from other data.

SCET inputs

Not a resolution

B!in PQCD • Data BABAR Belle Average +- 30± 4± 5 30± 6

+0 22.5+5.7-5.4± 5.8 31.7±7 7.1+3.8

-6.7 26.4+6.1-6.4

00 <1.1 <1.1

• B!LL in NLO PQCD (Li, Mishima)• LONLOWC +VC     +QL  +MP +NLO   +- 24.29   23.43 24.76 24.12 23.67 +0  15.85   15.57 15.85 15.85 15.57   00  0.35     0.81   0.41  0.25   0.72

NLO has saturated the 00 bound the puzzle is confirmed.

QCDF• The mechanism to enhance C/ 2 comes

from the NLO jet function in SCET.• The QCDF formulas are modified:

• The enhancement from the jet function is about 30» 60%

Jet function

» mb

h»(mb)1/2

B!in QCDF/SCET • Branching ratios

• Beneke and Jager 05

Parameter sets

With NLO jet

Check B!K, • Large real C/T=0.72 !• Data S4+LO jet S4+NLO jet  

ACP(+K-) 4 -3.5   -4.1

ACP(0K+) -11.5  -4.1 -3.9

• Tendency is not favored !• Also overshoot the data

Data (£ 10-6) S4+LO jet S4+NLO jet

B(00)  < 1.1 0.87     1.68• Expected, because and factorization

formulas are almost identical  

Mixing-induced CP in b! s

All approaches gaveconsistent results,and small uncertainty.C (tree pollution) remainssmall even with NLOPromising new physics signal, if data stand.

Conclusion• Many puzzles in B-factory data• ACP(K+0) much differs from ACP(K+-). new p

hysics in PEW? New mechanism in C?• ACP(B+) are sensitive to NLO QCD• B(00) remains as a puzzle.• Wait until Babar and Belle settle down.• Spenguin much different from Sccs is a promisin

g new physics signal.• If we are lucky, new physics may be right at

the corner, but….