Puzzles in B physics Recent development in PQCD, QCDF, SCET
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Puzzles in B physicsRecent development in PQCD, QCDF, SCET
Hsiang-nan LiAcademia Sinica, Taiwan
presented at Whepp9BhubaneswarJan. 07, 2006
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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
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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.
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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
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• CKM matrix elements
• Wilson coefficients
|-i|¼ 0.4
a1=C2+C1/Nc
a2=C1+C2/Nc
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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
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parameterization
(C4/C2)(VtdVtb/VudVub)/1» (2/1)(3/4)»
Tree-dominant
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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?
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K parameterization
(C2/C4)(VusVub/VtsVtb)» (1/2)(5/2)»
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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!
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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%
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4S0 by
about 1A puzzle?
Penguin-dominated
Tree-dominated
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QCD-improved Factorization(Beneke, Buchalla, Neubert, Sachrajda)
Perturbative QCD(Keum, Li, Sanda)
Soft-collinear Effective Theory(Bauer, Pirjol, Rothstein, Stewart)
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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
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Hard kernels • TI comes from vertex corrections
• TII comes from spectator diagramsMagnetic penguin O8g
q1
x
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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.
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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
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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
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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
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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()
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B! K direct CP
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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
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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
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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
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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%
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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!
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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.
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PQCD results Hadronicuncertainty
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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
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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
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SCET inputs
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SCET predictions
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B! branching ratios
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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.
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SCET inputs
Not a resolution
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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.
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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
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B!in QCDF/SCET • Branching ratios
• Beneke and Jager 05
Parameter sets
With NLO jet
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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
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Mixing-induced CP in b! s
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All approaches gaveconsistent results,and small uncertainty.C (tree pollution) remainssmall even with NLOPromising new physics signal, if data stand.
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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….