Future of CP violation in. a sl. Matthew Kirk. Toward the Ultimate Precision in Flavour Physics Warwick 17 April 2018

Transcription

1 Future of CP violation in Matthew Kirk Toward the Ultimate Precision in Flavour Physics Warwick 17 April

2 Im ( Γ 12 ) M 12 Ratio is nice for calculation major uncertainty in both ( f B ) cancels out Theory: Exp: Γ(B f ) Γ(B f ) Γ(B f )+Γ(B f ) a s sl =2.22± a s sl =(170±300) 10 5 a d sl =( 47±6) 10 5 a d sl =( 150±170)

3 B s Mixing 3

4 What are the limits on? Unknown matrix elements of dimension 7 operators Being done by lattice (e.g. HPQCD soon) Also calculable via sum rules (Kirk, Lenz, Rauh ) NNLO QCD O(α s 2 ) In , some corrections calculated 4

5 Duality Violation? theory calculation depends on assumption of quark-hadron duality How can we test this? Γ 12 Calculation of sum over intermediate shared decay states of B and B mesons Is quark level sum same? 5

6 Phenomenological study On the ultimate precision of meson mixing observables ( ) Phenomenological study of duality violation in mixing By quark-hadron duality we mean validity of HQE So e.g. exp( m b /Λ) term goes to zero in HQE could be source of daulity violation in some full solution of QCD. 6

7 Possible source of duality violation Expansion parameter is really Λ M i 2 M f 2 Different in different decay channels 7

8 GIM suppression broken with duality violation Γ 12 Break up using CKM unitarity Γ 12 cc = Γ 12 M ~ 2 λ u Γ M 12 λ ~ t cc uc Γ 12 M 12 See GIM suppression in action λ 2 u λ t 2 Γ cc 12 2 Γ uc uu 12 +Γ 12 ~ M 12 Break duality differently in each channel large effects 8

9 Limits on from duality violation 9

10 Limits on from duality violation 10

11 Limits on from duality violation These limits come from bounds on Δ Γs Δ M s =Re ( Γ 12 M 12 ) Currently ~ 15-20% precision from theory Main uncertainties in this calculation come from matrix elements of dimension 7 operators, scale variation 11

12 Limits on from duality violation In we did a forward looking / aggressive calculation what if the dimension 7 matrix elements were known to 20% accuracy? Reduce the theory error by almost 1/3 Is this a plausible scenario? 12

13 Sum rules for In we used sum rules to calculate bag parameters For dimension 6 operators, errors of ~ 10-15% achieved Comparable with latest lattice 13

14 Sum rules for In we used sum rules to calculate bag parameters For dimension 6 operators, errors of ~ 10-15% achieved Comparable with latest lattice 14

15 15

16 Sum rules for Calculation for dimension 7 operators should be doable in the same way Hopefully provide a timely comparison with upcoming lattice results But issues with calculation (pole cancellation) 16

17 NNLO QCD Corrections In , O(α 2 s N f ) corrections calculated Steps towards full NNLO calculation Expected to take ~ 5-10 years Also NLO QCD for dimension 7 operators has been studied but issues with uncancelled divergences 17

18 Future knowledge of If similar accuracy as dimension 6 possible, and higher order corrections calculated, can achieve high precision 18

19 Future knowledge of If similar accuracy as dimension 6 possible, and higher order corrections calculated, can achieve high precision 19

20 s,d is well known from theory Summary But if we question an underlying assumption (quark-hadron duality violation) then uncertainty is much larger Lattice / sum rule calculation of dimension 7 matrix elements will improve SM prediction and allow to test quark-hadron duality NP might then be much more clearly seen 20