Ikaros%20Bigi,%20Notre%20Dame%20du%20Lac

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
• requires accurate reliable values 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)x10-3
2.1 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
e-
q
e-
s µlmnÚd4xe-iQxlt0Jmhad (x)Jnhad (0)T0gt
Jmhad
Jnhad
optical thm
Sifi(x)Oi(0) as Q Æ
l
l
n
n
Sifi(x)Oi(0) as mb Æ
b
b
B
B
G µlmnÚd4xe-iQxltBJmhad (x)Jnhad (0)TBgt
optical thm
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Novel symbiosis between different theoretical
technologies for heavy flavour nonperturbative
dynamics -- in particular between HQE and
LQCD observables Si ci(CKM,mQ,aS) ltHQOiHQgt
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 in GSL(B) lt 0.5 !

IB N.Uraltsev,Int.J.Mod.Phys.A16(01)5201,Vademe
cum (48 p!)
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The Menu
I A Case Study in Accuracy Extracting V(cb), mb
etc.
II Lessons from B Æ gX
III Lessons for B Æ lnXu
IV B Æ tnX, B Æ tnD and New Physics
V CP in t Decays
VI Summary
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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 HQP through
  explicit OPE
• Benson,ibi,Uraltsev
  Bauer,Ligeti,Luke,Manohar
• determine HQP from independent observable
• both with commensurate accuracy
  reliability!
• Gambino,Uraltsev Trott
  Bauer,Ligeti,Luke,Manohar

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3.1 Master Formulae for SL Width
GSL(B) G0(b) f(z)1-(2/3)(aS/p)(g(z)/f(z))c2aS
2c3aS3..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 zmc2/mb2 c2 BLM aS2b0 estimate for non-BLM,
b0 11NC/3 - 2Nf/3 9 c3 BLM aS3b02,
BLM known to all orders aSnb0n-1 m p2(m)
ltBb(iD)2bBgtm/2MB kinetic
energy mG2(m) ltBb(i/2)smnGmnbBgtm/2MB
chromomagn. moment rD3(m) ltBb(-1/2D?E)bBgtm
/2MB Darwin term rLS3(m) ltBb(s?Ep)bBgtm/2
MB LS term
Benson et al., Nucl.Phys.B665(03)367

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• GSL(B Æ lnXc)
• F(HQP) 1pert 2.4hWc 0.8hpc 1.4IC
• F(HQP) 3th

V(cb)/0.0417 (1dth) x 10.30(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
1.2hWc 0.4hpc 0.7IC
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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. can never be
  calculated
• by LQCD without experimental input
• caveat quark masses depend on renorm. scheme
  scale
• mp2, mG2, rD3, rLS3, internal to QCD, i.e.
  can be calculated
• by LQCD without experimental input
• caveat mp2 ? -l1, mG2 ? -l2

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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
• ltmb,kin(1 GeV)gtbb 4.57 0.08 GeV

chromomagnetic moment mG2 mG2 ltHQQi/2smnGmnQ
HQgt/2M(HQ) (3/2) M2(VQ) - M2(PQ) for
b Q mG2 ª 0.35 0.03- 0.02 GeV2
kinetic energy mp2 mp2 ltHQQp2Q HQgt/2M(HQ)ª -
l1 0.18 GeV2 to one-loop SV SR
mp2 gt mG2 QCD SR mp2 0.45 0.1 GeV2
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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 (ElMX) spectrum
• normalized moments shape of spectrum
• normalized moments 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 gt 1 M1(MX)
G-1ÚdMX2(MX2- MD2)d G/dMX2 Mn(MX) G-1ÚdMX2(MX2-
ltMX2gt)nd G/dMX2 , n gt 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 gXc with severe
  lower 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.

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BABAR
DELPHI
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• 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)bb4.570.08 GeV mc(1 GeV) (1.18
0.092)GeV mb(1 GeV)-mc(1 GeV)(3.4360.032)GeV
mb(1 GeV)-mc(1
GeV)MB-MD(3.480.02 ?) GeV mb(1 GeV) -
0.74mc(1 GeV) (3.737 0.017) GeV

challenge for LQCD! mG2(1 GeV) (0.267 0.067)
GeV2 mG2HFª 0.35 0.03 GeV2 mp2(1 GeV)
(0.447 0.053) GeV2 mp2QCDSR 0.45 0.1
GeV2 rD3(1 GeV) (0.195 0.029) GeV3
rD3(1 GeV) 0.1 GeV3
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mb(1 GeV )B Æ lnXc 4.61 0.068 GeV
BaBar mb(1 GeV)Hb Æ lnXc
4.5750.0690.0430.005 GeV DELPHI mb(1
GeV)U(4S)Æbb 4.570.08 GeV mc(1 GeV) )B Æ
lnXc 1.18 0.092 GeV
BaBar mc(1 GeV)Hb Æ lnXc
1.1440.1060.0710.020 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 3.4360.032 GeV BaBar mb(1
GeV)-mc(1 GeV )Hb Æ lnXc 3.431 ? GeV
DELPHI mb(1 GeV)-mc(1 GeV)MB-MD
3.480.02 ? GeV mp2(1 GeV)B Æ lnXc 0.447
0.053 GeV2 BaBar
mp2(1 GeV)Hb Æ lnXc 0.3990.0470.0390.020
GeV2 DELPHI mp2(1 GeV)QCDSR 0.45 0.1
GeV2 mG2(1 GeV)HF 0.35 0.03 GeV2
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for Patricia
Uraltsev
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• CLEO DELPHI
• BABAR 04
• V(cb)incl(41.390 0.870) x 10-341.390x(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!
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B Æ lnD

• measure rate of B -gt 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!

0.890.080.05 Uraltsev et al.
O(1/mQ2) FD (0) 0.9130.042 BaBar
Book par ordre de Mufti 0.913
0.024-0.0170.017-0.030 2nd quenched latticeH,K
et al. O(1/mQ3)

0.89 at O(1/mQ2)
use FD (0) 0.90 0.05 for convenience

• V(cb)excl 0.0416 (1 0.022exp
  0.06theor)

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Unorthodoxy B Æ e/m n D
Uraltsev BPS expansion if mp2mG2 s pBgt0,
r23/4 in real QCD mp2 - mG2 ltlt mp2, r2 3/4
expansion in b3(r2-3/4)1/2 3
Snt(n)1/221/2 irreducible df(0)
exp(-2mc/mhad) few

• Program
• extract V(cb) from B Æ e/m n D
• compare with true V(cb) from GSL(B)
• to validate BPS expansion
• if successful -- see later

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on the power of the OPE rate(HQ Æ f) Si
ci(f)ltHQQQHQgt
once extracted from GSL(B Æ lnXc) can be used in
all transitions -- in particular B Æ lnXu, B Æ
gXq
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II Lessons from B Æ gX
Issue of biases due to experimental cuts

• Experimental cuts on energy etc. 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 gtgt mhad
• yet relevant for Q mhad!
• Test case B Æ g Xq

for B Æ g Xq Q mb - 2 Ecut
e.g. for Ecut 2 GeV, Q 1 GeV !
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• noted before usual OPE expression for B Æ g Xq
  somewhat indifferent to impact of experimental
  cuts
• early CLEO analyses showed a systematic shift
  in values of HQP extracted from B Æ g Xq

Pilot study (Uraltsev, IB, PL B 579 (04) 340)
Detailed study Benson,Uraltsev, IB,
Nucl.Phys.B710(05)371
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(No Transcript)
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bias corrections depend on values of HQP for
BABARs central values of the HQP we get
ltEggt1.8biased2.305 GeV Æ
ltEggt1.8corr2.312 GeV
ltEggt1.8BELLE2.2920.0260.034
GeV ltEggt1.9biased2.313 GeV Æ
ltEggt1.9corr2.325 GeV ltEggt2.0biased2.321 GeV
Æ ltEggt2.0corr2.342 GeV
ltEggt2.0CLEO2.3460.0320.011
GeV ltEggt2.1biased2.329 GeV Æ
ltEggt2.1corr2.364 GeV
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lt(Eg-ltEggt)2gt1.8bias0.0357 GeV2Ælt(Eg-ltEggt)2gt1.8c
orr0.0309 GeV2 lt(Eg-ltEggt)2gt1.8BELLE0
.03050.00740.0063 GeV2 lt(Eg-ltEggt)2gt1.9bias0.03
21 GeV2Ælt(Eg-ltEggt)2gt1.9corr0.0255 GeV2
lt(Eg-ltEggt)2gt2.0bias0.0293 GeV2Ælt(Eg-ltEggt)2gt2.0c
orr0.020 GeV2 lt(Eg-ltEggt)2gt2.0CLEO0.
02260.00660.0020 GeV2 lt(Eg-ltEggt)2gt2.1bias0.027
1 GeV2Ælt(Eg-ltEggt)2gt2.1corr0.0145 GeV2
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from O. Buchmueller
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defensible ? --
moment
usual OPE expression OPE with bias correc.
Ecut
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• Lessons
• keep the cuts as low as possible
• bias in 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 important
  cross check!

• Personal plea to BELLE/BABAR
• Please tell us what you measure for
• ltEggt, lt Eg2 - ltEggt2gt
• with Ecut 1.8, 1.9, 2.0, 2.1, 2.2 GeV!!

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III Lessons for B 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 Æ gX
• 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

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IV B Æ tnX, B Æ tnD and New Physics

• analyze B Æ ln D extract V(cb)
• validate it with V(cb) from B Æ ln X
• if successful, measure B Æ tn D - 2nd FF f-
  can be measured!
• compare with SM prediction for known V(cb)
• discrepancy could be interpreted in terms of
  charged Higgs
• repeat analysis for B Æ tn X

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V CP in t Decays
SM forbidden t decays
t Æ m/e g

• Æ 3 l

if New Physics in b Æ sss New Physics in t Æ
mmm then BR(t Æ mmm) 10-8
need to find CP in leptodynamics to complete CP
paradigm
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CP in t decays

• most promising channels t Æ nK p
• most sensitive to Higgs dynamics
• CP asymmetries possible also in final state
  distributions
• rather than integrated rates
• unique opportunity for ee- Æ tt-
• pair produced with spins aligned
• 1 t decays can tag the spin of the other
• can probe spin-dependent CP with unpolarized
  beams!
• confidently predicted CP from known dynamics
• 0.0033 in G(tÆ nKS p ) vs. G(t-Æ nKS p -)
• -- due to KSs preference for antimatter

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VI Summary

• Extracting CKM parameters with accuracy seemingly
  
• unrealistic less than 10 years ago --
• with detailed defensible error budgets from
  theorists!
• dV(cb) 2 now, 1 soon
• dV(ub) 5 conceivable
• without new theoretical breakthrough
• Progress based on two key elements
• robust theory subjected to the challenges of
• high quality data
• precision, i.e. small defensible uncertainties

overconstraints