B-Meson Mixing and Lifetimes:

Transcription

1 EAUTY th International Conerence on -Phyic at Haron Machine Aii (Perugia, Italy. June 0-4, 005 -Meon Mixing an Lietie: Mixing Paraeter:, With Dierence: Γ, Γ CP-Violation Paraeter: q / p, Lietie Ratio: + τ ( / τ (, τ ( / τ (, τ ( Λb / τ ( Cecilia Tarantino Univerità Roa Tre an INFN Sezione i Roa III

2 aic Forali Phyical Obervable

3 1. Mixing, Phenoenological iportance (UTA Theoretical input

4 Unitarity Triangle Analyi 1 = 0.50(7 p. [HFAG 005] > 14.4 p 1 (95% C. L

5 Extracting Extracting V V t t : : 0 0 ˆ ( 6 ˆ ( 6 t t W F t t W F x S V G x S V G η π ξ η π = = OPE Doinant top contribution : hort-itance phyic, ro Perturbation Theory (% [at NLO, ura et al.: Nucl.Phy.347 (1990] : non-perturbative QCD eect, ro Lattice QCD : lattice uncertaintie cancel ( 0 t x S η, ˆ ξ ξ, ( W t = ˆ ˆ ξ

6 -Phyic on the Lattice ab <<1 L L >>1 M π MULTISCALE PROLEM / a 50 (coputational cot liit HQET, NRQCD, FeriLab approach, extrapolation in the heavy quark a Extrapolation in the light quark a uing ChPT Lattice QCD Action: Wilon/O(a-iprove Wilon: proble at light ae (exceptional quenche coniguration Twite a: no exceptional coniguration, eaier iproving, but ore expenive Staggere: light ae, but 4 tate (ourth root trick Doain-wall/Overlap: light ae, but the ot expenive Accurate quenche tuie + recent N=, N=+1 calculation

7 -Meon Decay Contant ro Lattice QCD Quenche Siulation High level o accuracy; Goo agreeent aong ierent approache; Continnu extrapolation; [De Divitii et al.(003, ALPHA(003] Unquenche Siulation N= tuie [JLQCD(003: high tatitic an O(a-iprove action]; N=+1 preliinary value [Wingate at al. (003: taggere action]; 0 bγ γ = ip µ µ 5 FNAL NRQCD NRQCD NRQCD FNAL RELAT. With the preent accuracy: ea quark eect ee at O(10%-15%: ut continuu caling or other yteatic (NP-ren., FV eect, i. ICHEP 004: action not copletely invetigate = 30 ± 30 MeV

8 -Meon Decay Contant ro Lattice QCD Delicate Iue: Chiral Extrapolation Pion Loop coul be igniicant [Kronel-Ryan(00, O(15%] 0 bγ γ = ip µ µ (1 + 3g 4 π (4π log µ π (1 + 3g 1.8 With With the the preent accuracy: Chiral Log Eect roughly etiate [JLQCDJLQCD (N =, q / >0.5 +HPQCD (N =+1, q / >0.] ore tatitic an an lighter quark ae till till neee ICHEP 004: = Final Chiral Loop Eect: O(5%

9 - Mixing on the Lattice q 8 ( µ ( µ b γ L q b γ L q q = q ˆ q q 3 With With the the preent accuracy: Negligible ea quark eect!! Conitent with iagnoi euce ro QChPT veru ChPT: [ooth95,sharpe,zhang96] ˆ ˆ (, 1.017(16 ( ˆ 1.87( = = 17 [JLQCD(003, N =] JLQCD(003: N = & NRQCD

10 - Mixing on the Lattice Chiral ChiralLoop Loopnot not a proble or or ˆ They They are are expecte expecte all allro ChPT q 8 ( µ ( µ b γ L q b γ L q q = q ˆ q q 3 Lattice ata are conitent with a contant.

11 Mixing ro Lattice QCD (MeV EAUTY 005 ICHEP 00 (Lellouch (ICHEP 004, Hahioto 03(7( (7 ˆ (MeV / (MeV ξ 38(31 30(30 76(38 6( (4( ( (4( (6 Now Now average inclue rough ``etiate o o chiral log log ( ( q / q / >0. an an unquenche eect (N (N =+1

12 Mixing ro QCD Su Rule 1. Equating phenoenological an theoretical pectral unction;. Deterination o theoretical pectral unction by calculating two or three-point correlator in perturbative QCD, incluing correction ro the OPE. O(α recently calculate O(α coplete but non-actoriable contribution iportant Proble: any paraeter, looely contraine!

13 . Decay: With Dierence Γ q ( = 1 Γ, Γ CP-Violation Paraeter Lietie Ratio Γ q ( = 11 q / p, 0 + τ ( / τ (, τ ( / τ (, τ ( Λb / τ (

14 HQE >> Λ ( b QCD Large energy releae contact interaction SPECTATOR EFFECTS Scale eparation q c r k (µ : hort-itance (perturbative r 0 q = 0 ( q O µ : long-itance (non-perturbative k q

15 Wilon Coeicient ro P.T. Lietie Ratio O (1 O α ( GF Vcb Γ = 3 19π (M (1996 [M. Neubert an C.T. Sachraja] (00 [E. Franco, V. Lubicz, F. Mecia an C.T.] [M. eneke, G. uchalla, C. Greub, A. Lenz an U. Nierte] 5 b c (3 b b + c (5 g b b σ µν G µν b 96π + 3 b k c (6 k O (6 k ck + (7 b O (7 k O( 1/ b (004 [F. Gabbiani, A. I. Onihchenko an A. A. Petrov] With Dierence an CP O α ( (003 [M. Ciuchini, E. Franco, V. Lubicz, F. Mecia an C.T.] [M. eneke, G. uchalla, A. Lenz an U. Nierte] O( 1/ b (1996 [M. eneke, G. uchalla an I. Dunietz] Γ G F b * 1 = ( VcbVc 1π (M [ G Q + G Q + δ ] S S 1/ b

16 Matrix Eleent: = Operator Leaing contribution O(1/ 3 b 1 q, q Fro the lattice (with ierent etho or QCD -u rule [J.G. Korner et al., 003] 4 Subleaing contribution O(1/ b q q q q 4 operator R, R, R, R : R q, R q 1 4 q q R, R3 ( : relate, through Fierz an eq. o otion, to operator copute on the lattice : ro the VSA

17 HQET NRQCD 1, q q on the lattice [V. Gienez an J. Reye, 000] [Hi-KEK (S. Hahioto et al., 000] unquenche NRQCD [JLQCD (S. Aoki et al., ] QCD [APE (D. ecirevic et al., 000] QCD +HQET [APE (D. ecirevic et al., 001]

18 So ar, the approach ha been only applie in the quenche cae

19 Matrix Eleent: = 0 Operator 3 Leaing pectator eect contribution O(1/ b (not copute (not copute Λ b -paraeter: :copute in lattice-hqet, evolve at the LO

20 + -paraeter Lattice-HQET [M. Di Pierro an C.T. Sachraja, 1998] Lattice-QCD [APE (D. ecirevic et al., 001] Su Rule, in HQET [M.S. aek et al., 1998] 4 Subleaing pectator eect contribution O(1/ 8 operator, ro the VSA (-eon or the quark-iquark oel (baryon b

21 With Dierence 4 Theoretical preiction at the NLO + contribution o O (1 / : b Experiental eaureent:

22 Γ Γ = [CDF, 004] Γ 0.5 = ± 0.01 σ Γ = [D0, CKM005] Γ Γ = 0.1 [( ( ] (0 (1 (0 (1 c + c O + c + c O + * / {( ( } b (preliinary LO 6% Fact δ c 1 << c [THEORY] 4 LO+ O(1/ 16% b NLO 18% 4 NLO+ O(1/ 7% b c c (1 = (0 7% (large cancellation at the NLO c δ 1/ O b = 55% 4 (large cancellation at O(1/ b

23 CP-Violation Paraeter Theoretical preiction at the NLO: Experiental eaureent: (q/p 1 = ± [HFAG, 005] Iportance o ore accurate eaureent UTA

24 Lietie Ratio LO NLO τ ( + τ ( τ ( τ ( τ ( Λ τ ( b

25 τ ( τ ( + τ ( τ ( LO 1.01(3 1.00(1 0.93(4 τ ( Λ τ ( b NLO 1.06(3 1.00(1 0.90(5 NLO+ 1.06( 1.00(1 0.88(5 O(1/ 4 b 4 Theoretical preiction at the NLO + contribution o O(1/ : b Experiental eaureent: 4 Goo agreeent at the NLO an O(1/ ( τ ( Λ b / τ ( at 1σ b

26 Concluion, MIXING: Phenoenological iportance o in the UTA Theoretical input at 5-15% ro Lattice QCD DECAY: Iportance o NLO correction in QCD 4 an O(1/ in the HQE [CDF, 004] Γ = Γ ± 0.01 b With Dierence [D0, Lattice005] Γ Γ = 0.1 CP-Violation Paraeter Iportance o ore accurate eaureent Lietie Ratio τ σ τ Λ b / ( at 1 ( (preliinary Γ Γ [THEORY] = 0.07 ± 0.03 UTA