B V P h r P u I ( D P k y P P i c I t Z w a - PDF document

e t e t i m m o C g ) P i n P r P e I t e m s P a B → V γ P h r P u I ( D ✧ P ✧ k y P P i c I t Z w a n s a m i c s R o h y P r u o v l a F

• B-physics CKM-matrix generalities • Exclusive decays H e ff • Hadronic matrix elements – Distribution Amplitudes • Overview of our activities • Focus B → V γ beyond QCD factorization • Particular focus on time dep. CP-asymmetry

V us s u    δ 3  δ V ud V us V ub 1 δ 2 V cd V cs V cb δ 1 hierarchy : δ ∼ 0 . 2  ∼    H ∆ S =1 W δ 3 δ 2 V td V ts V tb 1 absolute values • V arbitrary unitary matrix 9 parameters (5=6-1 absorbed in phases of quarks) ⇒ 4 parameters ∼ 3 rotation & 1 complex pahse • ( CP ) L weak ( CP ) † = L weak ⇔ V αβ = V ∗ αβ CP-violation • unitarity V V † = 1, 9 conditions among B 0 d triangle V du V ∗ ub + V dc V ∗ cb + V dt V ∗ tb = 0 s and K 0 triangles too flat) known as the CKM-triangle ( B 0 • CP violation ↔ non-zero area triangle • only established source of CP-viol SM (MNS neutrinos ?)

Results: 1. CKM mechanism works • triangle overconstrained • describes CP-viol. mesons quant. 2. Not enough Baryogenesis ( ∼ 10 10 ) → T.Underwood’s talk From Sides (CP-cons.) From Angles (CP-viol.)

Relate observables to fund. parameters (Hadronization) Γ ( B → π e ν ) , ∆ M s m b , V ub , V ts ↔ A few simple examples • A CP ( B → J/ Ψ K s ) ∼ sin(2 β ) sin( ∆ Mt ) Bigi & Sanda 81 • | V ub | − 2 ∼ dq 2 | f + ( q 2 ) | 2 � one single form factor !

B → X Y ↔ � XY | H e ff | B � remark type H e ff (¯ B → π e ν bu ) V − tree − level semileptonic A (¯ ¯ b σ · Fs ) V + A + . . . FCNC semileptonic B → K ∗ γ (¯ A ( ¯ bu ) V − du ) V − tree − level non − leptonic B → ππ A � M W Λ QCD Λ m b m b new Exploit hierarchy Physics ? of scales 5 80GeV 1 0 . 2 • M W to m b described pert. QCD ⇒ concretely apply Wilsonian picture � H e ff = C i ( µ ) O i ( µ ) � �� � � �� � UV IR Q i operators (above), µ ∼ m b factorisation scale . . . steps: 1. matching scale M W (initial condition) 2. RNG-running scale C i ∼ L γ i . . . γ i anomal. dim → calc. 3. evaluate � XY | Q i ( µ ) B � d f ” i i ” t o a o e e s e m n x p r

• Parametrize matrix element grounds Lorentz-covariane 0 < q 2 < ( m B − m π ) 2 � π ( p ) | ¯ b γ µ (1 − γ 5 ) q | B � = 2 p µ f + ( q 2 ) Heavy-light (no sym. light-light or heavy-heavy) ⇒ non-pert object Methods : 1. Light-Cone Sum Rules small q 2 ↔ E π large, pion LC 2. Lattice-QCD large q 2 ↔ E π small, pion o/w not resolved by lattice are complementary • LCSR are QCD sum-rules OPE ↔ LC − OPE Cond : � ¯ qq � ↔ DistributionAmplitudes : φ π ( u ) • Leading part the form factor in LCSR f B → π ∼ f π (1 + O (1) a 2 ( π ) . . . ) + . . . + a 2 moment DA

• relevant exclusive processes at large momentum transfer (LC) • most important DA ↔ minimal number of partons � e iupx φ π ( u ) + O ( x 2 , m 2 � π ( p ) | ¯ q ( x ) γ µ γ 5 q (0) | 0 � = if π p µ π ) – called twist-2, twist = dim - spin = 3 -1 correction: higher Fock states, dev. from LC – variable u : col. momentum fraction of corr. quark in meson • QCD e.o.m. di ff erent DA related � 1 q ( x ) x α gG α µ ( vx ) γ µ s ( − x ) − ( m s + m q )¯ ∂ µ ¯ q ( x ) γ µ s ( − x ) = − i dv v ¯ q ( x ) i ( γ 5 ) s ( − x ) − 1 Wilson lines omitted, take matrix elements • what to do φ π ( u ) ?

A. models obeying theor. & exp. constraints B. expand in Eigenfunction of evolution kernel � a n ( µ, π ) C 3 / 2 φ π ( u, µ ) = 6 u (1 − u )(1 + (2 u − 1)) n n ≥ 1 – a n Gegenbauer moments – C n Gegenbauer pol. rep. collinear SL (2 , R ) ∈ S 0(4 , 2) conformal – asymptotic part 6 u (1 − u ) exact from perturbative QCD • Why good expansion ? � 1. convolution smooth kernel duT ( u ) C n ( u ) decreasing ( C n n nodes) 2. det. of a n indicate a 0 ≡ 1 > | a 1 | > | a 2 | . . . ”consistent” with γ n +1 > γ n conformal hierarchy • Determination ? a. fit to experiment .. (contam. other hadr. uncert.) b. calculate from local matrix element (Fourier inversion) ∗ QCD sum rules ∗ lattice QCD (new e ff orts)

1. calculation of all weak and penguin form factors B → ( P, V ) from LCSR PRD 71, 14015 and PRD 71, 14029 2005 Ball RZ | V ub | HFAG = 3 . 38 ± 0 . 12 +0 . 56 − 0 . 37 10 − 3 BZ Open parenthesis (NP ?) | V ub | CKM − fit = 3 . 5 ± 0 . 18 10 − 3 | V ub | DGE = 4 . 46 ± 0 . 2 ± 0 . 2 10 − 3 incl 2. Kaon DA K, K ∗ , � , K ∗ , ⊥ emph. SU(3)-break. PLB 633,289 2006, JHEP 0602:034 2006 Ball RZ a � 1 ( K ∗ ) = 0 . 03 ± 0 . 02 , a ⊥ 1 ( K ∗ ) = 0 . 04 ± 0 . 03 . a 1 ( K ) = 0 . 06 ± 0 . 03 , Later QCDSF/HPQCD & QCDSF same values advert. smaller uncert. 3. apply these results B → V γ JHEP 0604:046,2006, PLB B642:478 RZ Ball all new hep-ph/0612081 Ball Jones RZ topic rest

B → V γ beyond QCD Factorisation • whole zoo: B → ( ρ (0 , +) , ω , K ∗ , (0 , +) ) and B s → ( ¯ K ∗ , φ ) • FCNC new physics hidden loops ? • B ( b → X s γ ) incl no hints NP • history 1993 B → K ∗ γ CLEO 2005 B → ργ Belle (BaBar 2006) 200x B s → ( ¯ K ∗ , φ ) γ LHCb

  = G F � � H ( d,s ) λ ( d,s )  + BSM  C 1 Q 1 + C 2 Q 2 + C i Q i √ e ff U 2 � �� � U = u,c i =3 ,..., 8 CKM E ff ective Hamiltonian (OPE-description), CKM-factors λ s t = V bt V ∗ ts U = (¯ s i U j ) V − A ( ¯ sU ) V − A ( ¯ U =(¯ Q 1 U j b i ) V − A Q 2 Ub ) V − A � � Q 3 =(¯ sb ) V − A (¯ qq ) V − A Q 4 = (¯ s i b j ) V − A (¯ q j q i ) V − A q q � � Q 5 =(¯ sb ) V − A (¯ qq ) V + A Q 6 = (¯ s i b j ) V − A (¯ q j q i ) V + A q q Q 7 = e g s i σ µ ν (1 + γ 5 ) b i F µ ν s i σ µ ν (1 + γ 5 ) T a ij b j G a 8 π 2 m b ¯ Q 8 = 8 π 2 m b ¯ µ ν • C i Wilson Coe ff . NLO α s (NNLO first estimate) from “inclusive people” • C 7 leading 1 /m b and α s b → ( d, s ) γ , add O ( m s )-part later • C 2 1 /m b (power)-correction in b → ( d, s ) γ , but C 2 ∼ C 7 • Q 2 U -flavour sensitive, discr. final state

• At O ( α 0 s ), LO 1 /m b only electric penguin � V γ | ¯ b σ · F (1+ γ 5 ) q | B � = kin.T 1 (0) FF from LCSR � �� � Q 7 • At O ( α s ), LO 1 /mb QCD factorization ( Bosch et al, Beneke et al, Ali et al 01): � 1 T I d ξ du φ B ( ξ ) φ V ⊥ ( u ) T II � V γ | Q i | B � = i F ( B → V ⊥ ) + i ( ξ , u ) + O ( Λ /m b ) 0 = # � V γ | Q 7 | B � + O ( Λ /m b ) Ex. hard-spectator, T II Ex. hard-vertex, T I

power supressed non-factorizable contribution c, u Q 2 Q 6 annihilation (drives isospin break.) c, u -loops (Time-dep CP asymmetry) • B ( B → V γ ) ∼ 20(30)% • Isospin asymmetries – ( ρ 0 , ρ + ) depend angle γ – ( K ∗ 0 , K ∗ + ) .. interesting 2 � � • R ≡ B ( B → ( ρ , ω ) γ ) � V td red. uncert. � � B ( B → K ∗ γ ) ∼ V ts � extract | V td /V ts | BJZ r = C 6 /C SM BaBar = 0 . 199(22)(14) 6 compare | V td /V ts | ∆ M s CDF = 0 . 206(8)

B 0 decay ( V − A )-int.produce predominantly left handed photons • Key idea ¯ Beyond SM anything possible .. enhanced m NP /m b • A CP = Γ ( ¯ B 0 ( t ) → ¯ K ∗ 0 γ ) − Γ ( B 0 ( t ) → K ∗ 0 γ ) K ∗ 0 γ ) + Γ ( B 0 ( t ) → K ∗ 0 γ ) = S sin( ∆ m B t ) − C cos( ∆ m B t ) , Γ ( ¯ B 0 ( t ) → ¯ • Gronau,Attwood & Soni 97 since LO operator e 7 + m s s σ µ ν (1 − γ 5 ) b ] F µ ν ≡ Q L Q R Q 7 = 8 π 2 [ m b ¯ s σ µ ν (1 + γ 5 ) b + m s ¯ 7 m b Time dependent CP asymmetry ( ∼ L · R/L 2 = − sin(2 β ) m s S SM ,s R (2 + O ( α s )) ∼ (2 − 3)% K ∗ γ m b – O ( α s )-correction calculable QCD-F – B ∼ ( L 2 + R 2 ) /L 2 right-handed ”not sizable” O ( m 2 s /m 2 b )

• Grinstein et al 04 futher contribution from soft gluon emission, c-loop from Q c 2 (QCD V-interaction) non-factorizable Q 2 Q 2 • SCET based analysis resorts to dimensional estimate of matrix element and obtain � � C 2 Λ QCD | S SM , soft gluons � � | = 2 sin(2 β ) ≈ 0 . 06 . � � K ∗ γ 3 C 7 m b � � reach conclusion: S SM K ∗ γ ∼ 10% with large uncertainties

• idea: on-shell photon, c-quark heavy perform a local OPE � d 4 xe iqx T { [¯ ie ∗ µ c ( x ) γ µ c ( x )] Q c Q F = 2 (0) } λ a 1 s γ ρ (1 − γ 5 ) g � ( D ρ F αβ )[¯ G a = − 2 b ] + . . . αβ 48 π 2 m 2 c • Remains calculate matrix element � K ∗ ( p, η ) γ ( q, e ) | Q F | B � = L kin 1 +˜ L kin 2 • use LCSR (generous uncertainty, 3-particle DA, 1 /m c -corrections) � � L − ˜ − C 2 L S SM , soft gluons = − 2 sin(2 β ) = 0 . 5 ± 1% K ∗ γ c T B → K ∗ C 7 36 m b m 2 (0) 1 ⇒ S SM = − 2 . 2 ± 1 . 2 +0 − 1 α s % (232 · 10 6 B ¯ S BaBar = − 21 ± 40 (stat) ± 5 (syst)% BaBar B pairs), (535 · 10 6 B ¯ = − 32 +36 S Belle − 33 (stat) ± 5 (syst)% Belle B pairs), and S HFAG = − 28 ± 26% waiting for BaBar update !