QCD, Factorization, and the Soft-Collinear Effective Theory

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1 QCD Factorization and the Soft-Collinear Effective Theory Iain W. Stewart MIT The 9th International Conference on B Physics at Hadron Machines Oct (Beauty 2003) Iain Stewart p.1

2 Outline Motiviation QCD Expansion Parameters Analogy with HQET What is the Soft-Collinear Effective Theory (SCET)? Degrees of freedom Physical picture Symmetries -Physics Applications: ( ) Color-Suppressed Decays ( Heavy-to-Light Form factors Status of Outlook and Issues decays ( Summary from Beauty-SCET Workshop ) ) Iain Stewart p.2

3 Iain Stewart p.3 Motivation b-hadrons: Laboratory for EW new physics & QCD s decay weakly to many channnels The lightest ) (Repeat for Need to understand (elliminate) hadronic uncertainties from QCD

4 Scales quarks u d s c b t mass } light } heavy QCD resolution non-perturbative long distance perturbative short distance In full QCD usually we can not predict amplitudes with small uncertainties in a model independent way Need Expansion Parameters (If we use a model then we can not even estimate the uncertainties reliably) Iain Stewart p.4

5 Use Effective Field Theories Use Effective Field Theories: Separate physics at different momentum scales Expansion Parameters (1) Electroweak Hamiltonian (2) Heavy Quark Effective Theory (HQET) (3) SU(3) Chiral Perturbation Theory (4) Soft-Collinear Effective Theory (SCET) Depending on the observable one or more of these may be necessary (5) Lattice QCD Iain Stewart p.5

6 ) ( Electroweak Hamiltonian ): ( 1) Integrating out the b u b u d W d u u d b W u u d b d b u g uc u $ #!" u u %&! d b b d Operators come with different CKM elements Iain Stewart p.6

7 & & & HQET: Inclusive Decay: OPE in No At is free quark decay corrections have dependence on corrections computable HQET gives 0 at this order defined in HQET #%$ "! HQET is simpler than QCD Uncertainties suppressed by Spin-Flavor Symmetry Iain Stewart p.7

8 HQET: Inclusive Decay: OPE in Fit moments to simultaneously extract ( ) Example: CLEO I I I I I I I I I I 1 (GeV2 ) st Moment of Lepton Energy 1 Total Experimental Ellipse 0 th Moment of Lepton Energy 1 st Hadronic Mass Moment (GeV) I st Moment of Photon Energy (b s ) & & & from S.Stone at EPS Iain Stewart p.7

9 Soft-Collinear Effective Theory Many processes have energetic hadrons not apply where HQET does Iain Stewart p.8

10 Soft-Collinear Effective Theory C. Bauer S. Fleming M. Luke hep-ph/ (PRD) C. Bauer S. Fleming D. Pirjol I.S. hep-ph/ (PRD) C. Bauer I.S. hep-ph/ (PLB) C. Bauer D. Pirjol I.S. hep-ph/ (PRD) Builds on earlier work: Hard Exclusive: Brodsky Lepage Jet physics: Collins Soper Sterman Korchemsky B-physics Factorization: Dugan Grinstein Beneke Buchalla Neubert Sachrajda Iain Stewart p.8

11 Soft-Collinear Effective Theory Introduce fields for infrared degrees of freedom (in operators) modes fields collinear soft usoft Offshell modes with are integrated out (in coefficients) Iain Stewart p.8

12 Soft-Collinear Effective Theory Introduce fields for infrared degrees of freedom (in operators) modes fields collinear soft usoft eg. B D π Pion has: pion in rest frame has constituent momenta: boosting gives collinear constituents: Iain Stewart p.8

13 Soft-Collinear Effective Theory Introduce fields for infrared degrees of freedom (in operators) modes fields collinear soft usoft B D π are soft collinear Factorization if Iain Stewart p.8

14 Soft-Collinear Effective Theory Introduce fields for infrared degrees of freedom (in operators) fields modes collinear soft usoft jets usoft collinear Typically either: SCET soft collinear SCET exclusive Iain Stewart p.8

15 Soft-Collinear Effective Theory Introduce fields for infrared degrees of freedom (in operators) Symmetries modes collinear soft usoft 1) Gauge Symmetry Collinear Soft Usoft 2) Helicity Spinor Reduction 3) Reparameterization Invariance 4) CPT in different sectors fields Iain Stewart p.8

16 SCET gives a systematic expansion in QCD model independent description of power corrections can estimate uncertainties make symmetries explicit understand factorization in a universal way Determine quantities that are short and long distance calculate short distance coefficients Proof of Factorization means Known to be Model Independent once hadronic parameters are determined has hard coefficients lines W has jet coefficients with with Wilson Wilson lines Iain Stewart p.9

17 # % $ # 4. % 35 6 % 6 % Hadronic Parameters Define universal hadronic parameters exploit symmetries ) Non-Pert. functions Process Degrees of Freedom ( ) ) s ( c ( ) ) c ( ) s ( c ( & ) ) us ( c ( "! (*) "! /. - + ) ) c ( ) s ( c ( ( ) ) ) us ( 0+ c ( (*) % /. + ) ) c ( ) s ( c ( / ) ) c ( ) s ( c ( ! &:9 8! &7 ) c ( 6 ; ) ) s ( c ( 6? > 0> ) ) s ( c ( = < < 2 Iain Stewart p.10

18 Hadronic Parameters SCET Authors (in no particular order): S.Mantry C.Bauer D.Pirjol I.S. S.Fleming M.Luke I.Rothstein M.Beneke T.Feldmann M.Diehl A.Chapovsky Descotes-Genon J.Chay C.Kim G.Buchalla C.Sachrajda E.Lunghi D.Wyler S.Bosch R.Hill B.Lange M.Neubert T.Becher M.Wise A.Manohar T.Mehen A.Leibovich Z.Ligeti Iain Stewart p.10

19 ! $? 4 Hadronic Parameters Example: where / - - #" - & /!?! =. /.10 - % ( % *+? )( % &% graphs LO = 2 corrections will be Example 2: 587 : shape function Iain Stewart p.10

20 phenomenology Type Decay Br Decay Br I III II I III II PDG or abcd=cleo b=belle New BaBar numbers (hep-ex/ yesterday): Iain Stewart p.11

21 phenomenology Type Decay Br Decay Br I III II I III II decays agree within errors small as expected (0 at LO) 20-30% power corrections for )/ ) Nonzero strong phase 9 Iain Stewart p.11

22 # "Tree" "Color suppressed" "Exchange" b c π D π c u d ud B D u d b d u u b c d u d B B D π u d - not very predictive: Large Iain Stewart p.12

23 # "Tree" "Color suppressed" "Exchange" b c π D π c u d ud B D u d b d u u b c d u d B B D π u d Naive Factorization - too small: Iain Stewart p.12

24 # "Tree" "Color suppressed" "Exchange" b c π D π c u d ud B D u d b d u u b c d u d B B D π u d is non-factorizable channel BBNS QCDF - Keum et.al. pqcd - predicted with expansion in Iain Stewart p.12

25 Factorization for Color-Suppressed Decays Mantry Pirjol I.S. SCET factorization mechanism for color suppressed channels still predictive Iain Stewart p.13

26 ! Factorization for Color-Suppressed Decays Mantry Pirjol I.S. "Tree" "Color suppressed" "Exchange" b c π D c D B d u b u u d ud d u d B b c d B D π u π u d / 8 8 " 8 / " 8 "! 8 Iain Stewart p.13

27 5 5? 7 7 # $ Take operators Mediated by a single class of (a) (b) c c b b u d u d d u d u d u d u we find a factorization formula When matched onto ( ): : two new non-perturbative soft functions 5 # and same for )* + )( &% #! #"! Iain Stewart p.14

28 + + % ( & # "! $ ( & 0 " # $ Results and Predictions relative to suppressed by and Find both is complex gives non-perturbative strong phase which is independent of and choice of vs. % Predict equal strong phases equal amplitudes corrections to this are Expt (pdg average):.- + *) +%$ % + " % " /. ( 1 " + ) +%$ % + " % " Iain Stewart p.15

29 + * $ $ * ( * ( % * ( ( arg Iain Stewart p.16 Test and Predictions 0.8 π π = D = D* R I 3 A 00 2 A0 _ 0.2 φ δ Also predict (not post-dict): + #" % & + " %

30 + * Test and Predictions 0.8 π π = D = D* 0.6 * ( 0.4 * ( % * ( ( arg R I 3 A 00 2 A0 _ 0.2 φ δ Also predict (not post-dict): Iain Stewart p.16

31 % + % ) + More Predictions + * More predictions can be made if we expand in = constant = At tree level * ( + % ) + * ( % so get * ( Iain Stewart p.17

32 ) ) " 0 0 " ) ) 0 0 " & " " More Predictions More predictions can be made if we expand in = constant = At tree level ) so get ) then If! # *) "! ) ) ) = Also would predict that If we fit the complex from dim. analysis ie natural size Iain Stewart p.17

33 More Predictions naive factorization for color suppressed decays? Iain Stewart p.18

34 # & Heavy-to-Light Decays Large accessible on the Lattice ( For small ) and large energy factorization applies 300 Events / (1 GeV 2 /c 4 ) CLEO Events/2.2 GeV 2 /c BABAR Why is it interesting? q 2 (GeV 2 /c 4 ) Important ingredient for Phenomenology: (CP violation) q 2 (GeV 2 /c 4 ) Iain Stewart p.19

35 Heavy-to-Light Form Factors pseudoscalar: vector: ( Soft part Hard part Iain Stewart p.20

36 $ Form Factor Results Bauer Pirjol I.S. Beneke Feldmann Our result p 2 ~ Q 2 result at LO in all orders in where B M p 2 ~ 2 Λ Λ p 2 ~ Q p 2 ~ Λ 2 Iain Stewart p.21

37 Results Pirjol I.S. to pseudoscalar #"% "% #"$! Iain Stewart p.22

38 Results Pirjol I.S. Iain Stewart p.22 to vector

39 $ $ $ Implications and by helicity symmetry Burdman Hiller certain and combinations are goal is to identify processes besides same non-perturbative parameters egs. suppressed that depend on If lattice can get points in the low region they can read off important hadronic moments by fitting certain linear combinations eg. For ( SCET reduces the lattice problem to ) ( ) Maybe in the future we can get to ( ) ( ) ( ) Iain Stewart p.23

40 $ " + Form Factor Result More comments is observed might by an ( ) No suppression of expect In BBNS use Keum Li Sanda use (with a different definition) Luo Rosner Fit with f.f. models gives will eventually tell Data for us how compares with to this factorization + ) Theory Corrections are growing as gets smaller ) Iain Stewart p.24

41 & with eg. Measure ) ) ) ) & ) ) ) ) & & & T = tree P = penguin need information from QCD (or isospin analysis) P/T Iain Stewart p.25

42 ) ) In QCD Factorization π Beneke Buchalla Neubert Sachrajda π B ) π B π ) ) In SCET π p 2 ~ 2 Λ Chay Kim Bauer Pirjol Rothstein I.S. (in progress) p 2 ~ Q 2 involves ) B π p 2 ~ Λ2 p 2 ~ QΛ p 2 ~ 2 Λ Iain Stewart p.26

43 1 & & & Issues in 1) Factorization/Exponentiation of gluons beyond Chay Kim 2) Result if is not perturbative? 3) New Soft-Collinear messenger modes BecherHillNeubert Could spoil factorization in 4) Glauber Gluons beyond etc. (like Coulombic exchange) 5) Numerical stability and convergence chirally enhanced terms? 6) Error estimates could power corrections dominate? (since BBNS and pqcd disagree with new Belle and BaBar data) or is something else going on? Iain Stewart p.27

44 Workshop Issues Is it always true that the vacuum factorizes? Manohar Can SCET help to explain the cross section for? Fleming Could singularities forbid factorization below the scale? Feldmann Claim of a non-zero time ordered product in for -decays. Pirjol Claim soft-collinear modes exist and spoil factorization in some cases. Neubert A proposal for a new choice of fields for soft-collinear modes. and doubts about Chay Iain Stewart p.28

45 Outlook SCET gives operator definitions to universal hadronic parameters need to measure these with experiment Subfields: Jet Physics Physics Physics Allows power corrections to be addressed in a model independent way (even when we lack a rigorous OPE) Need to carefully examine expansion for each process and improve our understanding of power corrections to go beyond 20-30% accuracy for s SCET applies to many inclusive/exclusive processes A lot of theory and phenomenology left to study Iain Stewart p.29

46 Colors This is blue This is red This is brown This is magenta This is Dark Green This is Dark Blue This is Green This is Cyan Test how this color looks Test how this color looks Test how this color looks Test how this color looks Test how this color looks Iain Stewart p.30