Fermilab, June 26th 2001

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Fermilab, June 26th 2001
Thoughts on the fitting procedure for
the ?c lifetime with the ?????? channel
Gianluigi Boca
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Outline
Explanation of the fitting procedure Some check
s to show it works Try to answer to the 3 major
issues of the lifetime Committee Discussion
about Eduardos method of treating the double
solutions
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Peculiarity of the ?????? channel existence of
two solutions for the kink
(??)
Selection cuts ?? ?? linked, at least 3 chmbrs,
no m no REME L/s gt 7 Primary in target region
and ZXc lt 2.3 ISO2lt 0.001 s t lt 70 fs For the
Wobs(K) lt Wobs(p) 2 For the ???n?? channel
only from kink not belenging to a Vee
with 0.485 lt M(K)lt0.515 For the ???p?0
channel only proton from not linked and
Wobs(p)ltWobs(p) 5 Double solution
treatment Two solutions for the kink ? two ?c
effective mass ( m1, m2) If two solutions
survive the physics cuts accept them both with
weight 1 unless d(m) m1 m2 lt 30 MeV in
which case accept them both with weight 0.5
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Peculiarity of the ?????? channel cntd
MC plots from 6,000,000 ???n?? and 6,000,000
???p?0 events
Long tails of Xc signal, due to kink double
solutions, contaminate the sidebands. Extractio
n of background reduced proper time (t) plot,
used for lifetime fit, from Sidebands, is
slightly trickier than usual
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Two approaches to solve the problem
a) Modify the fitting procedure such that it can
work with any double solution treatment (my
method) b) try to eliminate tails in sidebands
by proper choices of one of the two double
solutions (Eduardos method)
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Description of my method

• Based on two assumptions
• MC reproduces correctly mass
• shape and t evolution of Xc
• events
• The t evolution of Xc signal
• in the sideband region is the
• same as the one in the peak
• region and it is proportional
• to

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Description of my method, contd

• Combined fit of
• Diplot of the t vs ?????? mass in
• peak region (from 2.445 to 2.485)

b) ?????? mass in the OUTER region
Each mass bin content in the outer region is
predicted
Outer region
Outer region
Peak region
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Likelihood function
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Likelihood, cntd Outer region
mass plot predicted entries


g(i) taken from MC and normalized A, C0, C1
fit parameters mi mass in the center of ith
bin
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Diplot t vs mass in peak region predicted
entries
Ag(j)?
(C0C1)?
Bk
?
)


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Extraction of the Bk from sidebands
Sidebands definition from 2.39 to 2.44 and
from 2.49 to 2.54
Bk
(1-Y)?
Y?
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Checking the method with Lc
?c ? ? (p ?0) ? ?? sample (courtesy of
Cristina)
PDG average 0.206 ? 0.012 ps
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Results for the Xc? ??????
all the sample
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A consistency check Xc lifetime varying
the doubles weighting scheme
Standard if two solutions survive the physics
cuts accept them both with weight 1 Unless d(m)
m1 m2 lt 30 MeV in which case accept them
both with weight 0.5
Variation 1 if two solutions survive the
discard the event Variation 2 if two solutions
survive accept both with w 1 Variation 3 if
two solutions survive accept both with w
0.5 Variation 4 if two solutions survive accept
only solution 1 Variation 5 if two solutions
survive accept only solution 2 Variation 6 (the
mad mans scheme) if two solutions survive
accept only
solution 2 with
w5. Variation 7 (similar to Eduardos scheme)
if two solutions survive accept
solution 1 if solution 2 is not in the 2.45
2.5 range, else discard the event
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A consistency check Xc lifetime varying
the doubles weighting scheme, cntd
Method is robust against different doubles
treatment
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The Xc lifetime Committee 3 major issues
on this fitting method
LOOK AT THE MC, ALL SAMPLE
ratio
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3 major issues, cntd
2) Is it true that B(tk) is independent of mass
and the values of A, C0 , C1 are
independent on tk ?
IN OTHER WORDS IS
TRUE ?
Yes, B(tk) is independent of mass since it is
extracted from sidebands and in all E687-E831
lifetime analysis we always have assumed that the
sidebands represent well the background under
the peak region (if no nasty reflections are
present like in the D0 case). If it represents
the bckgrnd under the peak, there are no reasons
to doubt that it represent the bckgrnd also in
any particular mass bin of the mass region!
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3 major issues, cntd
3) Can the Xc ? X-p?? and Xc ? ??????
samples be merged in one lifetime fit ?
Yes, just multiply the likelihood for the two
samples together and make A fit with 8 parameters
( t , the 4 parameters for the backgrounds of
the Xc ? X-p?? channel (type1, type2, kink,
MultiVee) and A, C0 , C1 for the Xc ? ??????
channel.
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Eduardos method
Reduces long tails in sidebands caused by wrong
kink solution
His double treatment (I hope this summary is
accurate) apply all the physics cuts and, for
the events with both solutions surviving the
cuts if (?m lt 30 MeV ) then choose
solution 1 else if ( m2 NOT in the
2.45 to 2.5 range ) then choose solution 1
else discard the event end if
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Eduardos method, cntd
MC, kink2, doubles selected solution
MC, kink4, doubles selected solution
works well with kink4 signal shape, but
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but, I have 2 questions
1)
Consider the background (non Xc events) having
both solutions passing the physical cuts
Toy model montecarlo, 10,000,000 entries
and apply Eduardos algorithm
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The artificial peak stems from the ?m lt 30 MeV
case. One can remove it and use condition
if (NOT 2.45lt m2 lt 2.5 ) then choose
solution 1 else discard the event
Price to pay some loss of Xc events
before
after
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Second question
2)
What about the events for which only one
solution passed the physical cuts ?
Option 1 ACCEPT IT
Tails remain !
Option 2 REMEMBER (or recalculate) OTHER
SOLUTION AND APPLY AGAIN
EDUARDOS CRITERION
Advantages for the kink4 fixes the tail
problem Disadvantages a) loose more
statistics b)
discarded solutions reenters from backdoor after
being
discarded previously by physical cuts
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Conclusions
I demonstrated (I hope) my fitting method works
with any kind of double soulution scheme for
the kink I addressed the three issues of the
Committee of the lifetime paper I think it
is the preferable method to be usde in the ?c
lifetime calculation for ?????? channel