Fermilab, June 26th 2001

Thoughts on the fitting procedure for the c

+ lifetime with the channel

Gianluigi Boca

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 Eduardo’s method of treating the double solutions

Peculiarity of the channel : existence of two solutions for the kink ()

Selection cuts

linked, at least 3 chmbrs, no no REMEL/ > 7Primary in target region and Zc < 2.3ISO2< 0.001 t < 70 fsFor the : Wobs(K) < Wobs –2For the n channel only : from kink not belenging to a Vee with 0.485 < M(K)<0.515For the p0 channel only : proton from not linked and Wobs(p)<Wobs – 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 unlessm) = | m1 – m2 | < 30 MeV in which case accept them both with weight 0.5

Peculiarity of the channel … cntd

Long tails of c+ signal, due to kink double solutions, ‘contaminate’ the sidebands.

Extraction of background reduced proper time (t’) plot, used for lifetime fit, fromSidebands, is slightly trickier than usual

MC plots from 6,000,000 n and 6,000,000 p0 events

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 (Eduardo’s method)

Description of my method

Based on two assumptions

1) MC reproduces correctly mass shape and t’ evolution of c events2) The t’ evolution of c signal in the sideband region is the same as the one in the peak region and it is proportional to

Description of my method, contd

Combined fit of

a) Diplot of the t’ vs massin peak region (from 2.445 to 2.485)

b) massin the OUTER region

Peak region

Each bin content is predicted Each mass bin content inthe outer region is predicted

Outer region

Outer region

Likelihood function

Likelihood, cntdOuter region mass plot predicted entries

g(i) taken from MC and normalizedA, C0, C1 = fit parametersmi = mass in the center of ith bin

= +

Diplot t’ vs mass in peak region predicted entries

=Ag(j) +(C0+C1) Bk

= + )

Extraction of the Bk from sidebandsSidebands definition : from 2.39 to 2.44 and from 2.49 to 2.54

+

+ (1-Y)= YBk

Checking the method with c

c+ + (p 0) + sample (courtesy of Cristina)

SelectionsNo stubsl/ > 5CLD > 0.03Picon > 6p from kink not lnkd

psdof

PDG average = ps

Results for the c+

all the sample

ps dof

A consistency check : c+ lifetime varying

the doubles weighting scheme

Standard : if two solutions survive the physics cuts accept them both with weight 1Unless m) = | m1 – m2 | < 30 MeV in which case accept them both with weight 0.5

Variation 1 : if two solutions survive the discard the eventVariation 2 : if two solutions survive accept both with w =1Variation 3 : if two solutions survive accept both with w = 0.5Variation 4 : if two solutions survive accept only solution 1Variation 5 : if two solutions survive accept only solution 2Variation 6 (the mad man’s scheme) : if two solutions survive accept only solution 2 with w=5.Variation 7 (similar to Eduardo’s scheme) : if two solutions survive accept solution 1 if solution 2 is not in the 2.45 – 2.5 range, else discard the event

A consistency check : c+ lifetime varying

the doubles weighting scheme, cntd

Method is robust against different doubles treatment

The c+ lifetime Committee 3 major issues

on this fitting method1) “Is it true the c

+ signal present in the sideband region have the

same t’ distribution as the c+ signal in the peak ?”

LOOK AT THE MC,ALL SAMPLE

ratio

3 major issues, cntd

2) “Is it true that B(t’k) is independent of mass and the values of A, C0 , C1 are independent on t’k ?”

IN OTHER WORDS : IS TRUE ?

Yes, B(t’k) is independent of mass since it is extracted from sidebands and in allE687-E831 lifetime analysis we always have assumed that the sidebands represent well the background under the peak region (if no nasty reflections are present likein the D0 case). If it represents the bckgrnd under the peak, there are no reasons todoubt that it represent the bckgrnd also in any particular mass bin of the massregion!

3 major issues, cntd

3) “Can the c +

and c +

samples be merged in one lifetime fit ?“

Yes, just multiply the likelihood for the two samples together and makeA fit with 8 parameters (, the 4 parameters for the backgrounds of the c

+ channel (type1, type2, kink, MultiVee) and A, C0 , C1

for the c +

channel.

Eduardo’s 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 solutionssurviving the cuts

if (m < 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

Eduardo’s method, cntd

works well with kink4 signal shape, but …

MC, kink2, doublesselected solution

MC, kink4, doublesselected solution

… but, I have 2 questions

Consider the background (non c + events) having both solutions

passing the physical cuts

Toy model montecarlo, 10,000,000 entries

and apply Eduardo’s algorithm

artificial bump created inlifetime analysis one needs todetermine the amount of background actually presentunder the peak

1)

The artificial peak stems from the m < 30 MeV case.One can remove it and use condition :

if (NOT 2.45< m2 < 2.5 ) then choose solution 1else discard the event

Price to pay :some loss of c +events

before after

Second question :What about the events for which only one solution passed the physical cuts ?

Option 1 : ACCEPT IT

Option 2 : REMEMBER (or recalculate) OTHER SOLUTION AND APPLY AGAIN EDUARDO’S CRITERION

Advantages : for the kink4 fixes the tail problemDisadvantages : a) loose more statistics b) discarded solutions reenters from backdoor after being discarded previously by physical cuts

2)

Tails remain !

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