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Ikaros Bigi, Notre Dame du Lac

WIN ‘05. On the Theoretical Treatment of Semileptonic B Decays. Ikaros Bigi, Notre Dame du Lac. SM with CKM structure has scored novel & quantitatively impressive successes can not count on massive intervention of New Physics in B decays

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Ikaros Bigi, Notre Dame du Lac

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  1. WIN ‘05 On the Theoretical Treatment of Semileptonic B Decays Ikaros Bigi, Notre Dame du Lac • SM with CKM structure has scored • novel & quantitatively impressive successes • cannot count on massive intervention of New Physics in B decays • need numerical precision in SM/CKM predictions • requiresaccurate & reliablevalues for |V(cb)|,|V(ub)| Can we answer the ~ % level accuracy challenge?

  2. Status ‘04 mb(1 GeV) = (4.61 ± 0.068) GeV 1.5 % mc(1 GeV) = (1.18 ± 0.092) GeV 7.8 % mb(1 GeV) - 0.74 mc(1 GeV) = (3.74 ± 0.017) GeV 0.5 % |V(cb)| = (41.390 ± 0.870)x10-32.1 % vs. |V(us)|KTeV = 0.2252 ± 0.0022 1.1 %

  3. Essential role of O(perator)P(roduct)E(xpansion) e+ e+ q q g g g g q q e- e- s µlmnÚd4xe-iQx<0|{Jmhad (x)Jnhad (0)}T|0> Jmhad Jnhad optical thm Sifi(x)Oi(0) as Q Æ¥ l l n n Sifi(x)Oi(0) as mbÆ¥ b b B B G µlmnÚd4xe-iQx<B|{Jmhad (x)Jnhad (0)}T|B> optical thm

  4. Novel symbiosis between different theoretical technologies for heavy flavour nonperturbative dynamics -- in particular between HQE and LQCD observables = Sici(CKM,mQ,aS) <HQ|Oi|HQ> HQP HQE LQCD • it enhances the power of and confidence in both technologies by • increasing the range of applications & • providing more benchmarks • duality ≠additional ad-hoc assumption • duality violation inGSL(B) < 0.5 %! IB & N.Uraltsev,Int.J.Mod.Phys.A16(01)5201,`Vademecum … ‘ (48 p!)

  5. The Menu I A Case Study in Accuracy: Extracting V(cb), mb etc. II Lessons fromB ÆgX III Lessons forB Æ lnXu IV B ÆtnX, B ÆtnD andNew Physics V CP in t Decays VI Summary

  6. I A Case Study in Accuracy: Extracting V(cb), mb etc. B Æ lnXc • 2 step procedure for quantitative results • express observable in terms of HQPthrough explicit OPE Benson,ibi,Uraltsev Bauer,Ligeti,Luke,Manohar • determine HQP from independentobservable both with commensurate accuracy & reliability! Gambino,Uraltsev Trott; Bauer,Ligeti,Luke,Manohar

  7. 3.1 Master Formulae for SL Width GSL(B) = G0(b) {f(z)[1-(2/3)(aS/p)(g(z)/f(z))+c2aS2+c3aS3+..]¥[1-(mp2(m)-mG2(m) )/2mb2] -2(1-z)4 mG2(m)/mb2 +[d(z)rD3(m)+l(z) rLS3(m)]/ mb3 +O(1/mb4)} G0(b) = GF2mb5(m) |V(cb)|2/192p3 f(z), g(z),d(z),l(z): phase space function of z=mc2/mb2 c2: BLMaS2b0+ estimate for non-BLM, b0= 11NC/3 - 2Nf/3 = 9 c3: BLMaS3b02, [BLM known to all ordersaSnb0n-1] m p2(m)= <B|b(iD)2b|B>|m/2MB kinetic energy mG2(m) = <B|b(i/2)smnGmnb|B>|m/2MB chromomagn. moment rD3(m) = <B|b(-1/2D∑E)b|B>|m/2MB Darwin term rLS3(m)= <B|b(s∑E¥p)b|B>|m/2MB LS term Benson et al., Nucl.Phys.B665(‘03)367

  8. GSL(B Æ lnXc)= F(HQP) ± 1%|pert± 2.4%|hWc± 0.8%|hpc± 1.4%|IC = • F(HQP) ± 3%|th |V(cb)|/0.0417 = (1+dth) x [1+0.30(aS(mb) -0.22)] x [1-0.66x(mb(1 GeV) -4.6 GeV) + 0.39x(mc(1 GeV) -1.15 GeV) + +0.013x(mp2 -0.4 GeV2) + 0.05x(mG2 -0.35 GeV2) + +0.09x(rD3 -0.2 GeV3) + 0.01x(rLS3 +0.15 GeV3)]; dth=± 0.5 %|pert± 1.2%|hWc± 0.4%|hpc± 0.7%|IC

  9. Heavy Quark Parameters need definitions of HQP that can pass muster by quantum field theory! through O(1/mQ3): 6 HQP • 2 different classes of HQP • mb, mc -- external to QCD, i.e. canneverbe calculated by LQCD without experimental input caveat: quark masses depend on renorm. scheme & scale • mp2, mG2, rD3, rLS3, … internal to QCD, i.e. canbe calculated by LQCD without experimental input caveat: mp2 ≠ -l1, mG2 ≠ -l2

  10. U(4S) Æ bb: before 2002 • 4.56 ±0.06 GeV MeYe • mb,kin(1 GeV) = 4.57 ±0.05 GeV Ho • 4.59 ±0.06 GeV BeSi • 4.58 ±0.05 GeV KuSt • <mb,kin(1 GeV)>|bb = 4.57 ±0.08 GeV chromomagnetic moment mG2 mG2 = <HQ|Qi/2smnGmnQ| HQ>/2M(HQ) = (3/2) [M2(VQ) - M2(PQ)] for b = Q:mG2 ª0.35 + 0.03- 0.02 GeV2 kinetic energymp2 mp2 = <HQ|Qp2Q| HQ>/2M(HQ)ª - l1+ 0.18 GeV2to one-loop SV SR:mp2 > mG2; `QCD’ SR:mp2 =0.45 ±0.1GeV2

  11. Extracting Heavy Quark Parameters determine HQP without compromising advantages of OPE • V(cb) & HQP GSL(B Æ lnXc), i.e. integrated spectrum • V(cb) & HQP shape of (El&MX) spectrum • normalizedmomentsshape of spectrum • normalizedmoments HQP Lepton energy and hadronic mass moments: M1(El) = G-1ÚdEl El d G/d El Mn(El) = G-1ÚdEl [El- M1(El)]nd G/d El , n > 1 M1(MX) = G-1ÚdMX2(MX2- MD2)d G/dMX2 Mn(MX) = G-1ÚdMX2(MX2- <MX2>)nd G/dMX2 , n > 1 • aim for overconstraints

  12. short comment on history: • CLEO did lots of pioneering work -- also on moments measured originally 2 lepton energy moments in B Æ lnXc & photon energy moment in B Æ gXcwith severelower cuts on El & Eg. • Analysis by Battaglia et al. on DELPHI data in 2002 was the first to establish the present working paradigm: • measure 3 lepton energy and 3 hadronic mass moments in B Æ lnXc with acceptance over the full range of El.

  13. BABAR DELPHI

  14. excellent description of large set of data points in terms of 6 or even merely 4 parameters: mb, mc,mp2, rD3, (mG2, rLS3) • a priori free fit parameters assume values obeying various theoretical constraints and knowledge! mb(1 GeV) = (4.61 ± 0.068) GeV mb,kin(1 GeV)|bb=4.57±0.08 GeV mc(1 GeV) =(1.18 ± 0.092)GeV mb(1 GeV)-mc(1 GeV)=(3.436±0.032)GeV mb(1 GeV)-mc(1 GeV)|MB-MD=(3.48±0.02± ?) GeV mb(1 GeV) - 0.74mc(1 GeV) =(3.737 ± 0.017) GeV challengeforLQCD! mG2(1 GeV) =(0.267 ± 0.067) GeV2 mG2|HFª0.35 ±0.03 GeV2 mp2(1 GeV) =(0.447 ± 0.053) GeV2mp2|QCDSR=0.45 ±0.1GeV2 rD3(1 GeV) =(0.195 ± 0.029) GeV3 rD3(1 GeV)~ 0.1 GeV3

  15. mb(1 GeV )|B Æ lnXc= 4.61 ± 0.068 GeV BaBar mb(1 GeV)|Hb Æ lnXc= 4.575±0.069±0.043±0.005 GeV DELPHI mb(1 GeV)|U(4S)Æbb =4.57±0.08 GeV mc(1 GeV) )|B Æ lnXc = 1.18 ± 0.092 GeV BaBar mc(1 GeV)|Hb Æ lnXc= 1.144±0.106±0.071±0.020 GeV DELPHI mc(1 GeV) )|cc SR = 1.19 ± 0.11 GeV mc(1 GeV) )|cc SR = 1.30 ± 0.03 GeV mb(1 GeV)-mc(1 GeV )|B Æ lnXc = 3.436±0.032 GeV BaBar mb(1 GeV)-mc(1 GeV )|Hb Æ lnXc= 3.431 ± ? GeV DELPHI mb(1 GeV)-mc(1 GeV)|MB-MD = 3.48±0.02± ? GeV mp2(1 GeV)|B Æ lnXc = 0.447 ± 0.053 GeV2 BaBar mp2(1 GeV)|Hb Æ lnXc= 0.399±0.047±0.039±0.020 GeV2 DELPHI mp2(1 GeV)|QCDSR = 0.45 ±0.1GeV2 mG2(1 GeV)|HF =0.35 ±0.03 GeV2

  16. for Patricia Uraltsev

  17. … CLEO … DELPHI … BABAR ‘04: V(cb)|incl=(41.390 ±0.870) x 10-3=41.390x(1 ±0.021) x 10-3 DELPHI ‘04 preliminary V(cb)|incl=(42.1 ± 1.1) x 10-3 =42.1x(1 ± 0.025) x 10-3 analysis by Bauer et al. yields very similar numbers (though I do not understand their error analysis) Comment: impressive consistency of all measured moments yields best bounds on b Æ c being purely left-handed!

  18. B Æ lnD* • measure rate ofB -> l n D* • extrapolate to zero recoil & extract |V(cb) FD* (0)| • FD* (0)= 1 + O (1/mQ2) +O(as) normalized • holds automatically for mb = mc • expansion in 1/mc! 0.89±0.08[0.05] Uraltsev et al.: O(1/mQ2) FD* (0)= 0.913±0.042 BaBar Book `par ordre de Mufti’ 0.913 +0.024-0.017+0.017-0.0302ndquenched lattice:H,K et al. O(1/mQ3) [~ 0.89 at O(1/mQ2)] use: FD* (0) = 0.90 ± 0.05for convenience • |V(cb)|excl= 0.0416 ¥(1 ± 0.022|exp ± 0.06|theor)

  19. Unorthodoxy: B Æ e/mn D Uraltsev: BPS expansion ifmp2=mG2:s · p|B>=0,r2=3/4 in real QCD:mp2 -mG2 <<mp2,r2 »3/4 expansion inb=[3(r2-3/4)]1/2 = 3 [Sn|t(n)1/2|2]1/2 irreducibledf+(0) ~ exp(-2mc/mhad) ~ few % Program: • extract |V(cb)| from BÆe/mn D • compare with`true’ |V(cb)|from GSL(B) to validate BPS expansion if successful -- see later

  20. on the power of the OPE: rate(HQÆ f) = Si ci(f)<HQ|Q…Q|HQ> once extracted from GSL(B Æ lnXc)can be used in all transitions -- in particular B Æ lnXu, B Æ gXq

  21. II Lessons fromB ÆgX Issue of `biases’ due to experimental cuts • Experimental cuts on energyetc. applied for practical reasons • yet they degrade`hardness’ Q of transition • `exponential’ contributions exp[-cQ/mhad]missed in usual OPE expressions • quite irrelevant for Q >> mhad • yet relevant for Q ~ mhad! Test case: B Æg Xq for B Æg Xq: Q = mb - 2 Ecut e.g.: for Ecut~ 2 GeV, Q ~ 1 GeV !

  22. noted before: usual OPE expression for B Æg Xq somewhat indifferent to impact of experimental cuts • early CLEO analyses showed a systematic shift in values of HQP extracted from B Æg Xq Pilot study (Uraltsev, IB, PL B 579 (‘04) 340) Detailed study Benson,Uraltsev, IB, Nucl.Phys.B710(‘05)371

  23. bias corrections depend on values of HQP for BABAR’s central values of the HQP we get <Eg>|1.8biased=2.305 GeVÆ <Eg>|1.8corr=2.312 GeV <Eg>|1.8BELLE=2.292±0.026±0.034 GeV <Eg>|1.9biased=2.313 GeV Æ <Eg>|1.9corr=2.325 GeV <Eg>|2.0biased=2.321 GeVÆ <Eg>|2.0corr=2.342 GeV <Eg>|2.0CLEO=2.346±0.032±0.011 GeV <Eg>|2.1biased=2.329 GeVÆ <Eg>|2.1corr=2.364 GeV

  24. <(Eg-<Eg>)2>|1.8bias=0.0357 GeV2Æ<(Eg-<Eg>)2>|1.8corr=0.0309 GeV2 <(Eg-<Eg>)2>|1.8BELLE=0.0305±0.0074±0.0063 GeV2 <(Eg-<Eg>)2>|1.9bias=0.0321 GeV2Æ<(Eg-<Eg>)2>|1.9corr=0.0255 GeV2 <(Eg-<Eg>)2>|2.0bias=0.0293 GeV2Æ<(Eg-<Eg>)2>|2.0corr=0.020 GeV2 <(Eg-<Eg>)2>|2.0CLEO=0.0226±0.0066±0.0020 GeV2 <(Eg-<Eg>)2>|2.1bias=0.0271 GeV2Æ<(Eg-<Eg>)2>|2.1corr=0.0145 GeV2

  25. from O. Buchmueller

  26. `defensible’ ? -- `moment’ usual OPE expression OPE with bias correc. `Ecut’

  27. Lessons: • keep the cuts as low as possible • biasin the meas. moments induced by cuts • can be corrected for (within a certain range of cut values) • not a pretext for inflating theor. uncert. • moments meas. as fction of cuts:importantcross check! • Personal plea to BELLE/BABAR: • Please tell us what you measure for • <Eg>, < Eg2- <Eg>2> • with Ecut = 1.8, 1.9, 2.0, 2.1, 2.2 GeV!!

  28. III Lessons forB Æ lnXu no need to `re-invent the wheel’ -- for B Æ lnXu use the same values of the HQP as determined in B Æ lnXc Lepton energy endpoint spectrum ? • model dependent! • can get heavy quark distribution function from B ÆgX • but only to leading order in 1/mb • endpoint spectrum different for SL Bu and Bd decays (WA) Hadronic recoil mass spectrum ! • |V(ub)| within 10 % likely, 5 % possible

  29. IV B ÆtnX, B ÆtnD andNew Physics • analyze B Æ lnD & extract |V(cb)| • validate it with |V(cb)| from B Æ lnX • if successful, measure B Æ tnD - 2nd FF f-can be measured! • compare withSM predictionfor known |V(cb)| • discrepancy could be interpreted in terms of charged Higgs • repeat analysis for B Æ tnX

  30. V CP in t Decays SM forbidden t decays tÆm/e g • Æ 3 l if New Physics in b Æ sss≈ New Physics in tÆmmm thenBR(tÆmmm) ~ 10-8 need to find CP in leptodynamics to complete CP paradigm

  31. CP in t decays • most promising channels: tÆnK p • most sensitive to Higgs dynamics • CP asymmetries possible also in final statedistributions rather than integrated rates • unique opportunity for e+e-Æ t+t- pair producedwith spins aligned: 1 t decays can `tag’ the spin of the other • can probe spin-dependent CP with unpolarized beams! • confidently predicted CP fromknown dynamics: 0.0033 in G(t+ÆnKS p +) vs.G(t-ÆnKS p -) -- due to KS’s preference for antimatter

  32. VI Summary Extracting CKM parameters with accuracy seemingly unrealistic less than 10 years ago -- with detailed & defensible error budgetsfrom theorists! • dV(cb) ~ 2 % now, ~ 1 % soon • dV(ub) ~ 5 % conceivable without newtheoretical breakthrough • Progress based on two key elements: • robusttheory subjected to the challenges of • high qualitydata • precision, i.e. small defensible uncertainties overconstraints

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