H. Kawamura, “QCD for B physics” QCD for B Physics KEK Theory meeting “Toward the New Era of Particle Physics ” Dec Hiroyuki Kawamura (RIKEN)

H. Kawamura, “QCD for B physics” B Physics NP search by (over)constraining “unitarity triangle” Flavor mixing + CP violation via weak interaction HFAG: LP07

H. Kawamura, “QCD for B physics” ex. (semi-leptonic decay) QCD for B Physics Extraction of |V CKM | and φ CP from hadronic weak decays requires a good understanding of QCD effects. QCD effects are even necessary for “direct CP violation” — phase is detected through quantum interference + ex. (hadronic decay) T (tree)P (penguin)

H. Kawamura, “QCD for B physics” Theoretical tools Light flavor symmetry: isospin, SU(3) symmetry, … Heavy quark effective theory (HQET) Λ/m b expansion ↔ separation of scales (factorization) ex. isospin analysis for B → ππ etc. QCD factorization for inclusive semi-leptonic decay Lattice simulation Light-cone sum rule (quark hadron duality, spectral function,OPE,…) This talk Mw mbmb Λ μ Soft-Collinear effective theory QCD factorization for exclusive hadronic decay M NP perturbative

H. Kawamura, “QCD for B physics” HQET Can be described by an effective field theory which includes only soft modes of “large component “of Q + soft quarks + soft gluon Heavy-light meson system HQET field: Perturbative matching with full QCD (α s (m b ) small) : Wilson coeff. Leading term : SU(2N f ) Spin-Flavor symmetry mbmb Λ MwMw μ QCD HQET

H. Kawamura, “QCD for B physics” Meson spectrum

H. Kawamura, “QCD for B physics” Exclusive semi-leptonic decays heavy-heavy form factor Isgur-Wise function At the “zero-recoil limit” :

H. Kawamura, “QCD for B physics” Experimental result LP07 ⇓ Extrapolation of the data to ω= WA

H. Kawamura, “QCD for B physics” Inclusive semi-leptonic decays total rate OPE (short distance expansion) ⇒ propagator 1 ↔

H. Kawamura, “QCD for B physics” Moments vs. |V cb | & HQET parameters Moment → Vcb & HQET parameters (kinetic energy) ⇓ Buchmuller & Flacher (‘05)

H. Kawamura, “QCD for B physics” differential rate B→ X u lν kinematical cuts to avoid X c background. ex. propagator → outgoing jet has low virtuality (sensitive to soft physics) scale of outgoing jet : non-local for b-quark residual momentum: shape function Factorization Korchemsky, Sterman (’94)

H. Kawamura, “QCD for B physics” Shape function: new non-perturbative object Strategies for extracting |V ub | from B → X u lν — ME of Light-cone non-local operator (similar to parton distribution) 1. Fit S(ω) from B → Xsγ, use it for B → X u lν 2. Use “shape-function free ” relation between B → Xsγand B → πlν Lange, Neubert,Paz (’05) ex. Lange, Neubert,Paz (’05) : weight function (calculated at 2-loop) : residual hadronic power corrections Leibovich,Low,Rothstein (‘99) B→ X u lν

H. Kawamura, “QCD for B physics” LLR: Leibovich,Low,Rothstein (’99) ↔ 1-loop, without rhc LNP: Lange, Neubert,Paz (’05) |V ub | from BaBar data ”SF free” analysis by Golubev, Skovpen, Luth : hep-ph/ v2 error: exp.(X u lν) +exp. (X s γ) + th.

H. Kawamura, “QCD for B physics” Exclusive hadronic decays Effective Hamiltonian Naïve factorization 4-fermi operators QCD factorization holds for decays in which the spectator quark is absorbed into the final heavy meson. from “color transparency” argument, but no μ dependence B D π T 0,8 ФπФπ FB→πFB→π Beneke, Buchalla, Neubert, Sachrajda (’00)

H. Kawamura, “QCD for B physics” B→Dπ What must be shown? — gluon exchange between (B,D) and π Soft div. cancel among diagrams Collinear div. absorbed into universal pion wave function — shown up to 2-loop by BBNS (’00) All-order proof was given using SCET : Bauer et al. (‘01) SCET (Soft-Collinear effective theory) HQET (soft) + collinear modes of quark & gluon + … — systematic expansion in — soft mode decouple with col. modes from power counting → Factorization proved at the leading power in operator language light-like vector

H. Kawamura, “QCD for B physics” Key point: B → π form factor — end-point singularity ↔ soft nature of spectator quarks — “hard-collinear scale” asymptotic form 3 formalisms have been developed in recent years (1) QCDF (BBNS:’99 - ) end-point singularity included in the form factor. proof given by SCET. power corrections partly included (parameterized) NLO calculation completed B → M 1 M 2 B→ππ, Kπ

H. Kawamura, “QCD for B physics” (2) SCET (BPSR ’04-) Bauer, Pirjol, Stewart, Rothstein end-point singularity included in the form factor hard-collinear scale distinguished. → different formula from (1) power correction neglected modest → large number of fitted input (3) PQCD (’01-) Li, Kuem, Sanda, Kurimoto, Mishima, Nagashima,,, k T factorization + Sudakov →end-point suppressed power counting different from (1) & (2). more predictive power NLO calculation has started b:impact parameter B→ππ, Kπ

H. Kawamura, “QCD for B physics” Theory (QCDF) vs. Data Beneke (Beauty06) Good agreement with B → PP, PV data except “πK puzzle” and large direct CP of π+π- (input set S4: Beneke &Neubert (’03)) BPRS, PQCD are also good. How can different formalism can give similar prediction?

H. Kawamura, “QCD for B physics” CKM phase from data Average: UT fit Beneke (Beauty06)

H. Kawamura, “QCD for B physics” B meson LCWF Operator definition light-cone vector: momentum rep. momentum of light quark (at tree level) Complicated object which contains soft + “hard” dynamics In SCET soft fields col. fields Hard radiative tail

H. Kawamura, “QCD for B physics” Operator relations Kodaira, Tanaka, Qiao, HK (’01) HQ symmetry + EOM → 3-body ops. “Solution” “Wandzura-Wilczek approx.” — “Twist = Dimension - Spin” is not a good quantum number — Higher dim. operators appear in IR region (at large tΛ) “enhanced power correction” Lee,Neubert,Paz (’06) Shape Function

H. Kawamura, “QCD for B physics” Radiative corrections Lange & Neubert (’03), Braun et al,(03), Li & Liao (’04), Lee & Neubert (’05) Cusp singularity non-analytic at t=0 → hard radiative tail 1-loop UV & IR structure different!

H. Kawamura, “QCD for B physics” Evolution equation Consistent with Lange & Neubert (’03)

H. Kawamura, “QCD for B physics” Operator product expansion Separation of UV & IR behavior ⇒ OPE Interpolate B meson LCWF to HQET parameters RG evolution for LCWF RG evolution for local ops. many higher-dim. ops expansion parameter 1-loop matching

H. Kawamura, “QCD for B physics” Lee & Neubert PRD72(’05) : Cut-off scheme up to dim-4 ops. Operator product expansion (cont’d) Our calculation (HK & K.Tanaka) → OPE + exponential ansatz “hybrid model” MS-bar scheme up to dim-5 ops. +

H. Kawamura, “QCD for B physics” Calculation 2-point + 3-point functions with non-local operators Operator identification calculation in x-space Keep gauge invariance explicitly background method + Fock-Schwinger gauge → decouple from Wilson line

H. Kawamura, “QCD for B physics” dim.3 dim.4 dim.5 Result

H. Kawamura, “QCD for B physics” Matrix elements dim.3 dim.4 dim.5 (covariant tensor formalism) “Chromo-electronic” “Chromo-magnetic” : decay constant

H. Kawamura, “QCD for B physics” LCWF from OPE Dim.3&4 terms reproduce the results in cut-off scheme by Lee & Neubert (’05) dim.3 dim.4 dim.5 Represented by HQET parameter: ↔ Lattice, QCD sum rule Evolution & phenomenological studies underway!

H. Kawamura, “QCD for B physics” Summary Understanding of QCD effects in B physics has been largely improved in recent years. B meson wave function for exclusive B decay is quite different from pion wave function. OPE for bilocal operator for B meson LCWF to dim.5 → expressed by 3 HQET parameters different UV & IR structures Model-independent study of B meson LCWF is underway. Similar analysis for shape function is ongoing.