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Puzzles in B physics Recent development in PQCD, QCDF, SCET Hsiang-nan Li Academia Sinica, Taiwan presented at Whepp9 Bhubaneswar Jan. 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 amplitudes in power of the Wolfenstein parameter » 0.22 It is not a power counting from any rigorous theory Amplitude» (CKM) (Wilson coefficient) Induced by O 2 =(su)(ub) / C 2,s

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CKM matrix elements Wilson coefficients | -i |¼ 0.4 a 1 =C 2 +C 1 /N c a 2 =C 1 +C 2 /N c

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Quark amplitudes b u s u Color-allowed tree TColor-suppressed tree C QCD penguin PElectroweak penguin P ew s u u s u u s u u g Z W

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parameterization (C 4 /C 2 )(V td V tb /V ud V ub )/1» ( 2 /1)( 3 / 4 )» Tree-dominant

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B(B 0 ! 0 0 ) P, C, and P ew in 0 0 are all subleading. We should have Br( 0 0 )¼ O( 2 )Br( + - ) Data show Br( 0 0 )¼ O( )Br( + - ) The B! puzzle! Large P and/or C?

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K parameterization (C 2 /C 4 )(V us V ub /V ts V tb )» (1/ 2 )( 5 / 2 )»

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Direct CP in B! K K + - and K + 0 differ by subleading amplitudes, P ew /P » C/T». Their CP are expected to be similar. Their data differ by more than 3 !

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sin 2 1 /sin 2 1 decay amplitude, f CP =exp(-2i 1 ) Measure S f CP / Im f CP ) measure sin(2 1 ) Either pure-tree or pure-penguin modes serve the purpose Tree-dominant B! J/ K S, penguin pollution: P/T» (C 4 /C 2 )(V ts V tb /V cs V cb )» 2 » 5% Penguin-dominant b! s, tree pollution: C’/P’ » 2 » 5%

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4S 0 by about 1 A 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 s 0 1 dx/x (end-point singularity) in collinear factorization nonperturbative perturbative

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Hard kernels T I comes from vertex corrections T II comes from spectator diagrams Magnetic penguin O 8g q 1 x

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End-point singularity Singularity appears at O(1/m b ), twist-3 spectator and annihilation amplitudes, parameterized as X=(1+ e i )ln(m b / ) For QCDF to be predictive, O(1/m b ) corrections are better to be small ¼ FA. Data show important O(1/m b ). 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” k T factorization (Li and Sterman 92) Parton k T smear the singularity Same singularity in form factor is also smeared No free parameters

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Factorization picture Sudakov factors S, summation of s ln 2 (m b /k T ) to all orders, describe parton distribution in k T k T accumulates after infinitely many gluon exchanges, similar to DGLAP evolution up to k T ~Q Large k T Small b Always collinear gluons g g

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SCET I Two scales in B decays: m b and m b 2 Full theory! SCET I : integrate out the lines off-shell by m b 2 C( )J (0) ( )! C( ) ( ) J (0) Hard-collinear gluon, mass O(m b ) T( 0 )J (1) ( 0 ) b W mb2mb2 Wilson coeff of SCET I 22 1/m b suppressed current g

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SCET II SCET I ! SCET II : integrate out the lines off- shell by m b Compared to QCDF, T II ! T( 0 )J( 0, ) J( 0, )O( ) 22 Jet=Wilson coeff of SCET II ! T( 0 )J( 0, ) M ( ) B ( )

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B! K direct CP

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Large strong phase A CP (K + - )¼ -0.115 implies sizable » 15 o between T and P (PQCD, 00) T exp(i 3 ) P T exp(-i 3 ) T exp(i 3 ) P T exp(-i 3 ) If T =0 Br Br = Br If T =0 Br = Br Direct CP

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Explanation 1 How to understand the small A CP (K + 0 )? Large P EW to rotate P (Buras et al.; Yoshikawa; Gronau and Rosner; Ciuchini et al., Kundu and Nandi) ) new physics? (Hou’s talk) T exp(i 3 ) P T exp(-i 3 ) P EW Br¼ Br

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Explanation 2 Large C to rotate T (Charng and Li; He and McKellar) ) mechanism missed in naïve power counting? C is subleading by itself. Try NLO PQCD. (T+C) exp(i 3 ) (T+C) exp(-i 3 ) T exp(i 3) P Br¼ Br

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NLO PQCD (Li, Mishima, Sanda 05) LO: all pieces at LO LO NLOWC : 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/ a 2, and makes it almost imaginary. Without vertex correction Re, with vertex correction Im, with vertex correction Is 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’)=-80 o C’ is still subleading. T, P’ ew are almost unchanged.

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PQCD results Hadronic uncertainty

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QCDF T has a wrong sign in QCDF. C makes the situation worse. (T+C) exp(i 3 ) (T+C) exp(-i 3 ) T exp(i 3) P Br = Br

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SCET C/T is real in leading SCET, and large from the data. C can not reduce A CP (K + 0 ) (hep-ph/0510241). (T+C) exp(i 3 ) (T+C) exp(-i 3 ) T exp(i 3) 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 PQCD. The B! puzzle, large B( 0 0 ), remains. B( 0 0 ) 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 0 0 <1.1 <1.1 B! L L in NLO PQCD (Li, Mishima) LO NLOWC +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 0 0 0.35 0.81 0.41 0.25 0.72 NLO has saturated the 0 0 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 » m b h »(m b ) 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 A CP ( + K - ) 4 -3.5 -4.1 A CP ( 0 K + ) -11.5 -4.1 -3.9 Tendency is not favored ! Also overshoot the data Data (£ 10 -6 ) S4+LO jet S4+NLO jet B( 0 0 ) < 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 gave consistent results, and small uncertainty. C (tree pollution) remains small even with NLO Promising new physics signal, if data stand.

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Conclusion Many puzzles in B-factory data A CP (K + 0 ) much differs from A CP (K + - ). new physics in P EW ? New mechanism in C? A CP (B + ) are sensitive to NLO QCD B( 0 0 ) remains as a puzzle. Wait until Babar and Belle settle down. S penguin much different from S ccs is a promising new physics signal. If we are lucky, new physics may be right at the corner, but….

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