Conventions for CPV in EvtGen and PVVfit: complex stuff

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Conventions for CPV in EvtGen and
PVVfitcomplex stuff

• Tristan du Pree, Nikhef
• 25 October, TPTM

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Introduction

• Cause of this talk mailing list discussion
• So today
• Signs names of frames phis
• Formulas with all conventions
• Goal one convention documentation
• For PVVfit model and EvtGen

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Unitarity relations
Bd

• VCKMVCKM1

Bs
Same under d?s
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Root of confusion about fs
In SM both positive
Related by d?s and complex conjugation
Not same scale
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NB

• Sometimes ßs different
• Sometimes conjugated
• Sometimes fake ßs/?/df
• e.g. ?TDR ßs
• Different matrix product including Vts defines
  different angle
• Only for show
• Physically not sensible/exact
• But to first order the same

Footnote from Silva (hep-ph/0410351)
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JpsiPhi vs JpsiK

2nd terms
1st terms
3rd term
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fs vs fd

• is phase Bbar-gtB mixing
• So

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So whats (almost) in EvtGen?Amplitudes

• In (next version?) EvtGen

For Bbar ?-1
beta 0.02 phi_s -0.04
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Latest improvements EvtPVVCPLH

• Repaired sign beta_s in formula
• Now input beta_s0.02 gives phi_s-0.04
• Corrected some higher order terms
• Now consistent with formulas from this talk
• Fit with PVVfit (next slide)
• Signs strong phases correct
• Reconstruction angles consistent with fit
• Sign phis correct (correction EvtGen)
• Old fit/data in backup, opposite oscillation

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Comparing old new

• New
• Old
• So sign beta wrong
• Underestimated half of the terms by factor
  ei?Gt
• In amplitudes squared
• sinfs terms times e?Gt
• cosfs terms not existing
• Bottom line
• old version correct for leading orders of ?G and
  fs

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PVVFit Amplitudes squared

• Actual formulae
• As programmed in PVVfit
• Using phi_q is more symmetric

Only difference JpsiPhi vs JpsiK
dGamma.setVal(0)
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Frames

• Very good explanation TJampens thesis
• https//oraweb.slac.stanford.edu/pls/slacquery/BAB
  AR_DOCUMENTS.DetailedIndex?P_BP_ID3629
• Conventions Dunietz vs TJampens
• Both right handed
• Only difference definition of x-axis

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CLEO (Dunietz et al)
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Babar/DESY (TJampens)
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Angular functions
Dunietz et al

• Of course reconstruct and fit in same frame
• Advice from experience ?

Transformations Dunietz ?Tjampens
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Our other conventions

• ?m mH-mL
• ?G GL - GH gt 0
• Names angles cpsi, ctheta, phi
• Easier to program with
• Consistent with Dunietz names
• Name CP-phase phi_q (qs,d)
• Since same sign JpsiPhi and JpsiK easier to
  generalize software
• Note actually you fit /-2beta(_s)

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Final formulae in PVVfit

• Frame functions two slides back
• Amplitude functions

JpsiK(Kspi0) dG0 JpsiK(Kpi-) also phiq0
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Usable notes

• Total explanation
• Thesis TJampens
• Very good, but not convention discussed today
• Amplitudes
• 2001 Dunietz for amplitudes (all orders)
• Angular functions
• E.g. 1995/1998 Dunietz
• But watch out for df approximation in amplitudes
  and negative dG convention
• Kmumu transversity
• Ahmed Ali Salim Safir (DESY Tjampens
  convention)

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References

• JpsiK
• Babar
• Hep-ex/0107049
• Hep-ex/0411016
• Thesis TJampens
• JpsiPhi
• Dunietz
• hep-ph/9511363
• hep-ph/9804253
• hep-ph/0012219
• Clarke/McClean/Osorio
• LHCb/internal/lhcb-2007-101
• Ball et al
• Hep-ph/0003238
• Kmumu
• DESY
• hep-ph/0205254

TJampens convention
Angle formulas (but be careful)
Full time-dependent amplitudes
Full time-dep. amplitude functions. (But current
version TJampens-frame and Dunietz-formulas)
Full time dep, but different frame
TJampens convention
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Be careful

• In general definitions of ßs/?/df can differ
• Babar notes/articles follow Tjampens angle
  convention
• Babar physics book (p218)
• angular functions contain sign typos
• Dunietz et al 98
  Amplitudes in terms of their
  df2ßs, only up to first order. Very confusing
  convention anyway.
• Dunietz et al 95
• ?G GH GL lt 0
• Ball et al angles angular functions different
• Overall watch out frame conventions
• f ? f, ?tr ? ?

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Benefit of chatroom

• One document this talk
• Hopefully one convention
• But maybe in near future TJampens-LHCb article?

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Conclusions

• It is very important to know the used conventions
• Especially watch out for
• Definition of ßs
• Definition of the frames
• We have this talk for JpsiX with
• All formulas
• All the conventions
• The formulas of PVVFit and EvtGen
• EvtGen improved
• Sign phi_s higher order terms

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BACKUP
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Signs?
20K events
Old EvtGen wrong sign phis Wrong reconstruction
angles wrong signs strong phases
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Beta vs beta_s

• So sign difference in phases ß and ßs
• Since by construction ß and ßs gt 0
• BTW
• arg(Vtd) -ß
• arg(Vts) ßs p
• beta_s0.02

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Code PVVFit

• ERASMUS???
• PhysFit/PVVFit?