Challenges of non-leptonic weak decays on the lattice

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Challenges of non-leptonic weak decays on the
lattice

• Amarjit Soni
• HET,BNL
• (soni_at_bnl.gov,adlersoni_at_gmail.com)

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Outline

• Introduction Motivation
• Recapitulate Crutches are unavoidable
• Key idea -gt common path to several crutches
• Lattice considerations
• HLChPT its implications
• Outlook

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Introduction Motivation

• Via the UT, Lattice Weak Matrix Elements
• effort played a pivotal role in attaining a
  milestone in our understanding of CPV phenomena
• For the future,though, exceedingly limited menu
  is/should be a very serious concern

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Youngjoon Kwon
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Youngjoon Kwon
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Past performance future prospects

• Some gloating over the past is justified.
• Note, though, that program all initiated in 80s
• Refinements therein are certainly useful
• But expt/phenom needs are NOT frozen in
• time.moves often speedily (esp.expt)

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Focus on B-gtDM
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ILLUSTRATES power of B decays

• For 2 or more common modes of D0 ,
• \bar D0 both weak and strong phases
• can be extracted
• 2 modes mean 4 observables versus
• 4 unknowns rBM ,wk phase ?,dstrong (mode1),
• dstrong (mode2). Thus FOR THE FIRST TIME
• a data driven method is able to tame DIRECT CPV.
• Availablity of dozens of FS allows for
• numerous similar useful applications

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M K, K, pi, rho. For charged and neutral B are
of interest
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Special note Br(B-gt\barD0 M),is very difficult
to measureexperimentally due to
technical(exptal) complications
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Crutches are unavoidable

• I. Infinite volume.lessons learned via
• D-gtK piBernard, Simone,A.S.90
• Abada et al, 90
• Maiani Testa,90
• Ciuchini,Franco,Martinelli,Silvestrini,96
• II. Finite volume (K).Lellouch, Luscher,00
• Lin,Martinelli,Sachrajda,Testa,01
• Christ, Kim, Yamazaki ,06
• Kim, Sachrajda, Sharpe,06

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Useful crutches

• QCDF
• pQCD
• SCET
• HLChpt
• .

Key idea common to all these crutches is that

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Application of HLChPT to BgtDM(Christopher Aubin
A.S)

• For HL mesons, (following WiseDonoghueBurdman)
  marry HQET ChPT.Now U(2m) spin-flavor symmetry
  on
• the HQ side and standard SU(n)LXSU(n)R
• for m heavy and n light flavors.
• For definiteness m2 n3
• For now, just to provide a concrete,though crude,
  0th order step use LO HLChPT.NLO clearly highly
• desirable (i.e need a good student!)
• Meantime

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Weak NL Decays of Q(path analogous now to
BDSPW85)
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For B-gtD only the scalar piece is relevant in
LO leads to the very simple (expected) relation
Similar relations in LO for the B-gt \bar D
case. An important diference is that for p -gt
K B0 -gt BS
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B-gtD (M) decays -gt New B-parameters to avoid
confusion call B1-params (for decays)
Qi from Heff ?B1, b-gtcu l OR b-gtu bar-c l
D0
B,BS
For MK , use BS also i1,2 Vac Sat leads to
(e.g. for MK) 1(or 1/3) MBs f Bs MD f D
contrast with (8/3)M2 f2 for the ?B 2
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Some Lattice Considerations

• Relevant important decays involve no
• quark loops, no mixing with LDO -gt less
  worrysome even with mixed action approaches
• However, partial cancellationa la GL74
  AM74 between contributions of Q1 Q 2 puts
  more demand on accuracy.
• B1s are simultaneously (along with the usual
  Bs) accessible represent basically a new
  application

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Hand-waving estimate

• Sqrt(rBM) Vub /(Vcb Vus) 0.4/Neff
• THUS what is relevant for (L)QCD
• is a precise determination of Neff in
• the above.
• . Neff c2 (c1/N)/ (c2/N) c1

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How well are rBM currently known?

• Sqrt(rBK ) (VS) 0.16 - 0.08 CRUDE GUESS
  ( Large N partial cancellation)
• Direct experimental determination (so far)has
  gotten the 1-s error on rBK to be 130 , i.e rBK
  0.012-0.015 (See hep-ex/0607065 /or HFAG07)
• Since of central interest is ratio which
• scales as 1/N (in amplitude), concern
• reg. HLChpt may be addrssed by varying
• the momentum of M and/or lattice masses

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Possible Impact

• Lattice determination of Neff can help
• in improving constraint on ? (using input
• value of Vub )
• Of course,eventually,experimentalist will
  simultaneously extract both ? rBK , as is
• guaranteed by the method, then with input
• from the lattice of Neff , exptal knowledge of
  rBK allows a new way to determine Vub /(Vcb Vus)

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Summary OUTLOOK

• .Non-leptonic weak decays continue to
• be challengingHUGE POTENTIAL
• Specific example B-gtD0 (\bar D0) K very useful
  for UT phase ? and also for Vub possibly
  providing a new (NL) avenue to Vub
• HLChPT provides a starting point LOChPT
• gives all relevant decay ?B1 amplitudes in
  terms of charcteristic two fig. 8 (B1) parameters
• . Simulateously accessible along with usual
  mixing ( ?B2) B-parameters
• Numerous continuum ideas and tons of available
  data should provide useful bridges.