Changes in EvtGen for Bs J

1
Changes in EvtGen for Bs? J/? ?

• Tristan du Pree Gerhard Raven
• NIKHEF

2
25/10 2006 PTM

• This talk also appropriate for
• Production and decay models (subject)
• PTM WG (channel ??, good time measurement
  needed)
• CP WG (CP violation in this channel)
• 02/11 PDM less physics (mail 10/10)
• 09/11 My first talk _at_ CPWG?

3
Outline

• About Bs ? J/? ?
• DaVinci studies
• New EvtGen model
• Checks using Gauss
• A working and tested generation of J/? ?

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Introduction

• Bs ? J/? ? has a lot of benefits, but for best
  results (??, ?s)
• Full angular time-dependent fit will give optimal
  information
• Mixed CP-even and CP-odd final state has 4
  observables
• lifetime and three angles
• Anyhow we have to perform time-dependent angular
  analysis

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One slide on the theory

• CP-even (Light) and CP-odd (Heavy) final state
  components show different behaviour
• CP-even lives shorter
• 16 of the initial state is CP-odd
• Angular distributions differ (here integrated
  over 2 angles)
• Definition
• FLIPPING ? for larger time the CP-odd behaviour
  should become dominant, especially for large ??

6
RooFit toy-MC

• We already have a working, full-angular
  time-dependent simulation. For example
• Since ?Hgt?L we see more CP-odd as time increases
• This flipping behaviour will appear handy for
  simple check

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II. DaVinci

• Since we need a good time and angular resolution
  and efficiency, we study the influence of the
  detector and reconstruction on our channel
• use DaVinci
• DaVinci is a program in the Gaudi-framework which
  fully simulates the detector response and
  reconstruction and with which you can compare
  mc-truth and reconstructed particles

8
DaVinci fit

• Full-angular time-dependent fit

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Problems in DaVinci (1)

• Lifetimes not fitted right (should be ?Hgt?L)
• Contrary to toy-mc in DaVinci angle appears not
  to flip
• Even with a large lifetime difference (large ??)
  we do not see the expected flip appear

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Problems in DaVinci (2)

• When testing time dependence with large ??
• Not the expected crossing double exponent
  encountered
• The largest component has the largest lifetime
  here (also wrong)
• So probably time dependence generation not right
• Test EvtGen standalone in Gauss (no Pythia and
  Geant)

log
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III. EvtGen

• EvtGen is the generator used in Gauss to generate
  B decays.
• Why use it to test?
• Can adjust and make new simulations very fast
• At the core of the generation
• Possible decay-files models in EvtGen to generate
  the time-dependent decay of Bs ? J/? ?
• SVVHelAmp The one used so far. Correct for ??0,
  but does not generate the right time-dependence.
  Generates only mixing, which is irrelevant here.
• SVVCPLH The one people advised to use instead.
  But also had wrong time-dependence (as we will
  see).

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EvtGen with SVVCPLH
TransAmp ? transversity amplitude HelAmp ?
helicity amplitude SVV ? scalar vector
vector CPLH ? CP light heavy
We call decaymodel SVVCPLH
EvtGengenDec EvtParticledecay()
EvtIncoherentMixing Generates t mixing
EvtDecayAmp Accepts HelAmp(t) (or not)
EvtSVVCPLH Sets envelope ? (exp.
weight) Generates t again TransAmps(t)?HelAmps
EvtSVVHelAmp
Bs decays with t from CPLH
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Signal generation with hit/miss(Bfys, PTM)

• First generate a random number 0ltxlt1
• Blindly throw darts below the blue line, keep
  all the xs
• t-log(x)/?H
• This gives a start for the right distribution
  the envelope
• We dont want to keep all of this exponent
  (because a part of distribution has ?L)

x
envelope
exp(-t/?H)
8
t
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What are we gonna throw away?(Bfys, PTM)

• For given t calculate A0,?exp(-??t)
  exp(-?Ht), A??exp(-?Ht)
• Then throw random number within exp(-?Ht)
• (so blindly throw darts below red line)
• Hit if random number(t) lt rate(t) ? keep
• Miss if number above blue line ? start over

miss
hit
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Mistakes in EvtSVVCPLH

• Time dependence made with ?B instead of ?H
• Hit/miss rejects/accepts within envelope, so
  envelope should be longest lifetime (?H), to be
  able to take into account ?? later
• Wrong all lifetimes smaller than in reality
• But most important
• Amplitudes calculated wrongly
• CP-even lived longest (thats why we didnt see
  crossing)
• Lifetime difference wrong
• Calculation TransAmp?HelAmp not correct
• (using standard definitions, e.g. hep-ph/9804253)

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Solutions with EvtPVVCPLH (new)

• Time dependence (for the third time) made in
  CPLH, now correct with ?H as envelope
• After that the amplitudes calculated correctly ?
  gives also ?L
• This recovers
• The flipping
• The right double exponent
• (New model, P stands for Pseudoscalar)

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Get it working

• We needed to plug the rightly calculated,
  time-dependent amplitudes into EvtSVVHelAmp
• How to implement such a new decay model within
  LHCb/Gauss context?
• In Gauss.opts include dkfile, in which you tell
  EvtGen
• Decay model (call PVV_CPLH)
• Particles
• Branching ratio
• Arguments
• And register the new model
• In Gen/EvtGen/../src/EvtModelReg.cpp
• Include EvtPVVCPLH.hh, register EvtPVVCPLH
• The transformation of the amplitudes to a real
  decay are taken care of by EvtSVVHelAmp and the
  rest of the framework of EvtGen

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IV. The correct fits

• Now lets have a look at the fits!
• Note (if not mentioned different)
• 4 observables (3 angles, time)
• 42 variables (3 coupled amps lifetimes)
• 14k events generated by Gauss

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Angular check (?? 0)

• Time-dependent, full angular fit
• (only time-component and fit-values shown)
• Fit returns input values amplitudes and phase

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Double lifetime check (?? large)

• Very large lifetime difference
• So now we do see two, crossing exponents
• (note here only lifetime fitted)

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Full angle check (?? large)

• Time-integrated flat
  Large t (tgt4) convex
• Now we do see flipping
• The full angular fit returns the right values

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Standard values (amps B?J/? K)

• Fit can also return standard values with 14k
  events
• Input a0 0.6, a? 0.16, ? ?2.50?? , ?H
  1.54, ?L 1.39

(large t)
(Large t)
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Summary corrections

• Minor correction ?ms removed as argument
• (could get defined twice useless and dangerous)
• Lifetime generation with correct ?H
• General ?? (also negative)
• Formulas transversity amplitudes
• Transformation from TransAmp to HelAmp

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Conclusions EvtPVVCPLH

• We now have a working event generation of
  Bs?J/??
• Outlook
• DC06 will have right properties for Bs ? J/? ? as
  soon as this is included
• We can then properly test resolution, acceptance,
  background, etcetera with DaVinci
• Hopefully this version will also replace the
  EvtGen version, not only the LHCb version

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BACKUP

• About Bs?J/?f
• DaVinci resolutions/acceptances
• Most important code changes

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Pros and cons

• Advantages
• Branching ratio (93)10-4 relatively large
• 2008 a lot of Bs-mesons
• Bs L sbb b?Bs 51032cm-2/s 500µb 10
  1011y-1
• Bs (Bs?J/?f) (J/??µµ-) (f?KK-)
• gt 1011 10-3 6 50 gt millions per
  year! (2x incl Bsbar)
• Theoretically clean
• No SM pollution (penguins suppressed), small
  uncertainty
• SM-phase very small gt new processes involved
  easy to recognize
• But especially J/?f?µµ-KK- easy to
  reconstruct
• Oscillations should be no problem to measure
• DISADVANTAGE
• Mixture of different CP-eigenstates (large
  statistics, angular res/eff needed)
• Study angular distribution ( angular res/eff)

Bs?J/? ?
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Bs?J/?f

• Feynman diagram similar to Bd?J/?Ks
• (used for sin2ß)
• CP-asymmetry in interference mixing and decay
• Final state is CP-eigenstate
• ACP
• 
  
• 
  
  
• Advantage J/?f direct decay in two charged
  leptons
• Disadvantage endproducts both vector mesons, so
  mixture of CP-eigenstates
• G(Bs ? f) - G(Bsbar ? f) ACP?(angles)
  fraction ? as function of spatial angles
• Angular analysis like B?J/?K

2
2
-
cc

sin2? sin?mst
? ?SM ?NP
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Angular distribution
e.g. hep-ph/9804253

• Bs?J/?f is P ?VV
• spin Bs 0, so two daughters in B-frame equal
  (but opposite) helicities
• spin J/?, f 1
• f ? KK- spin 0s,
• J/? ? µµ- no a0
• Decay amplitude
• Angular distribution
• Now take all possible combinations and just fill
  in

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Transversity frame

• CP(J/?KK-)(-1)?(J/?)1
• Transversity t(J/?KK-) ?(J/?) spin projection
  on z
• For Bsbar some signs flip (especially terms with
  ?)

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Reco decay topology boosts
?
K

• Lorentz transformations do not form a group
• Lx,Ly-iRz ?? L(v3 ) RL(v2)L(v3)
• So always boost via Bs!

Bs
J/?
?
1cm
Bs-frame
?-
K-
J/?-frame
?
is rotated!
lab
?
Bs
L boost R rotation
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DaVinci

• Can study mc-particles and reconstructed
  simulation
• From sharp peak reco we can already see very good
  resolution
• Propertime resolution
• double Gaussian, s 0.03 ps

reco
mc
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Angular resolution

• Problem angles boosted in labframe
• Advantage boost everything in detector
• Maybe disadvantage for angular analysis
• sphi 6, 31 mrad spsi
  19 mrad stheta
  6, 24 mrad
• Wrong because of error in macro
• Even less than one tenth of these red lines

phi
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DaVinci acceptances
All practically straight (as hoped)
Binning effect?
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Code EvtPVVCPLH (vs SVVCPLH)
Calls this
wrong
Old, did not take into account tauH
if(mixed) mother-gtsetLifetime(t)
The new one does
General for positive and negative ???
Its an amplitude, not a rate!
Now the right exponents
And the right conversion
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Negative ??

• Right values
• tauHlttauL
• Component CP-odd smaller