14/06/11 Jet physics 1 Flavour fractions in di-jet system V.Kostyukhin C.Lapoire M.Lehmacher Bonn

$Page 1: 14/06/11 Jet physics 1 Flavour fractions in di-jet system V.Kostyukhin C.Lapoire M.Lehmacher Bonn$
14/06/11 Jet physics meeting V.Kostyukhin 1

Flavour fractions in di-jet system

V.Kostyukhin C.Lapoire

M.LehmacherBonn


Some theory

1) Heavy flavour pair creation

Heavy flavour production can be approximately described by 3 mechanisms

2) Flavour exitation heavy flavour from proton sea or alternatively from initial state showers

3) Gluon splitting gQQ in final state parton showers


Some theoryPYTHIA predictions for inclusive b-jet production (b-quark p>5GeV)

Similar picture for charm


Some theory Only flavour pair creation mechanism (1) makes back-to-back jet

pairs with identical (heavy) flavours . Mainly LO process. Flavour exitation (2) and gluon splitting (3) produce back-to-back

heavy+light jet pairs. NLO processes. Even flavour pair creation process contribute to heavy+light

back-to-back pair in NLO, see below

QQ pairs – LO dominantQ+light pairs – NLO dominant


Di-jet flavoursDi-jet (2 leading jets in event back-to-back) analysis

model includes 6 fractions (full set): UU (light+light) ~85% CC (charm+charm) ~1% BB (beaty+beaty) ~0.6% BC (beauty+charm) ~0.3% BU (beauty+light) ~4% CU (charm+light) ~10%

PYTHIA predictions


Di-jet flavours analysisTo distinguish flavours the kinematical variables from secondary vertices in jet are used. Many variables were considered. Optimisation included

• Highest sensitivity to jet flavour content• Minimal jet p dependence• Stability with respect to detector effects

The final (minimal) choice includes 2 variables:

jeti

vertexi

vertextrack

track

E

EM

jetivertex

vertexi

track

track

EM

PB

“Product” variable “Boost” variable


Di-jet flavours analysisTo simplify statistical description and template construction both variables are transformed to be in [0.,1.] range. “Boost” is the only variable which has the extreme values for charm, not for beauty! The beauty here is between light and charm. Should facilitate charm separation.

“Product” variable “Boost” variable


Di-jet analysis modelVariable definitions (8 in total):

fBB – fraction of b-jet pairs in 2-jet samplefCC – fraction of c-jet pairs in 2-jet samplefBU – fraction of b-jet plus u-jet in 2-jet samplefCU – fraction of c-jet plus u-jet in 2-jet samplefBC – fraction of b-jet plus c-jet in 2-jet sample fUU=1.-fBB-fBC-fBU-fCC-fCU - not independent

vb – probability to reconstruct secondary vertex in b-jet

vc – probability to reconstruct secondary vertex in c-jetvu – probability to get fake secondary vertex in u-jet

Templates from MC (boost case):B(b) – secondary vertex boost distribution for b-jet C(b) – secondary vertex boost distribution for c-jetU(b) – secondary vertex boost distribution for u-jet

1

1

1

m

m

m

bU

bC

bB


Di-jet analysis modelCase of 2 reconstructed secondary vertices in di-jet event :

Probability:

fCUfBUfBCfUUfCCfBBNNP

total

vertices ucubcb2u

2c

2b

22 vvvvvvvvv

2)()()()(vv

2)()()()(vv

2)()()()(vv

)()(v)()(v)()(v),(

1221uc

1221ub

1221cb

212u21

2c21

2b

212

bUbCbUbCfCU

bUbBbUbBfBU

bCbBbCbBfBC

bUbUfUUbCbCfCCbBbBfBBbbD s

2-dim probability density function for the fit :

2,

212

21

),( PbbDbb

s


Di-jet analysis modelCase of single reconstructed secondary vertex in di-jet event :

Probability:

1-dim probability density function for the fit :

vvv1

1 UCBNNP

total

vertex

fCUfBUfUUU

fCUfBCfCCCfBUfBCfBBB

cubuuuv

ucbcccv

ubcbbbv

v1vv1vv1v2v1vv1vv1v2v1vv1vv1v2

)()()()( vvv1 bUUbCCbBBbD 11 )( PmDm


Di-jet analysis model 2 fitting procedures are used in analysis:1. and B are templated separately and parametrised

with b-splines (1D fit)2. Joint & B distributions are used as templates (2D

fit) 2D fit has better statistical accuracy due to explicit correlation

treatment, but they may be wrong on data so 1D fit is less biased. More important is template construction from JX Monte Carlo data

samples influence. Splitting of single process into subsamples (JX) results in highly nonuniform errors in templates. E.g. few events from J0(low p sample) with huge weights fall into several template bins. Then these bins get much higher errors and shifted(!!!) in some cases mean. It’s not known a priori how to deal correctly with such bins.

The 2 fitting methods use completely different strategies – 1D approach washes out such shifts due to b-spline smoothing, 2D fit accepts them.

1D and 2D analysis procedures are far from 100% correlated and then they are used simultaneously for data

fit


Fast simulation model Heavy flavour fractions are small fully simulated jet statistics is not enough for validation of analysis properties (bias, error estimations, etc.).

Fast simulation model is developedAll reconstructed secondary vertices in fully simulated jet events are

collected into database as a function of jet p, and flavour. Generation procedure:1. Jet pair is created according to jet p, distributions taken from data.2. Jet flavours are chosen according to the model fractions

fUU,fBB,fCC,fBC,fCU,fBU 3. From flavour content one decides whether secondary vertex is

“reconstructed” in each jet according to model efficiencies vu,vc,vb.4. If SV is “reconstructed” – its parameters are taken from database

according to jet p, (randomly chosen from nearby region).5. Finally the recorded SV parameters are smeared with detector

resolution to avoid the repetition of exactly the same numbers in generated events due to a single vertex in database chosen several times.


Fast simulation model Fast simulation demonstrated that 2010 statistics is not enough for reliable simultaneous estimation of all 8 model parameters. Then it was chosen to fix 2 SV reconstruction efficiencies on MC values. Beauty and charm vertex reconstruction efficiencies are chosen to be fixed because they are most precisely predicted by Monte Carlo.

In our analysis of 2010 data we fit simultaneously 6 model parameters (vc,vb are fixed):

light jet fake vertex probability (vu). five flavour fractions (fBB,fBC,fCC,fCU,fBU)

Both 1D and 2D models with 6 parameters demonstrate correct behavior with fast simulation (next slides…)


Fast simulation model 2D fitting model performance with fast simulation (200 tries)


Fast simulation model 2D fitting model pulls with fast simulation (200 tries)


Data selection• Jets are selected in ID volume ||<2.1 to guarantee

the performance of vertex reconstruction.• Usual jet cleaning cuts are applied on data.• Anti-kt R=0.4 jets are used.• Analysis is done in leading jet p bins . They are

chosen to match ATLAS single jet trigger thresholds.

oThe A-D 2010 periods are used for [40,60] and [60,80] bins with L1 jet trigger. For other bins E-I 2010 periods with EF triggers are used.

oSubleading jet p is also restricted in analysis to decrease systematic due to p dependence of templates.


Vertex reconstruction efficiencies

The efficiencies are obtained as weighted average over all JX PYTHIA samples.


Vertex asymmetry The amount of reconstructed secondary vertices in

leading and subleading jets is DIFFERENT in di-jet event.

One of the reasons is the semileptonic decays of heavy flavours. Jet energy disappears with neutrino, what automatically makes the

heavy flavour jet subleading.

Qualitatively described by MC

BUT DISAGREE(!!!) with data quantitatively


Vertex asymmetry The SV asymmetry is coming from mixed heavy+light jet

pairs.

Reason of data-MC discrepancy here could be either bad description of semileptonic decays in PYTHIA or bad

description of gluon splitting (also causes jet energy loss)

Asymmetry is added to the fitting model. The exact reason is unclear (doesn’t seem PYTHIA problem, but…) then for

baseline result the asymmetry is fixed on MC values.

Changes due to free asymmetry parameter in the are taken as systematics.


Data fit quality Example: data description in [80,120] GeV bin with 2D fit


Fit results Data in each p bin are fitted with 1D and 2D methods.Fit results are combined with error dependent weights.

Statistical error in bin is calculated from 1D and 2D errors assuming 100% correlation between them.

First – probability to get fake vertex in light jet :

�� data fit�� Monte Carlo (PYTHIA)

Leading jet p GeV


Fit results Fitted di-jet flavour fractions compared with PYTHIA

predictions

�� data fit�� Monte Carlo (PYTHIA)

Leading jet p GeV

Leading jet p GeV

fUU fraction is estimated from others fUU=1-fBB-fBC-fCC-fBU-fCU


Fit results Fitted di-jet flavour fractions compared with other generators. MC boxes

represent statistical errors. At particle jet level MC band should be much more narrow.


Unfolding to particle jet level

Exists, but requires some final polishing. That’s why not presented here.

However changes in flavour fractions are very small just because they are ratios !


Systematics Systematic due to SV asymmetry discrepancy between

data and MC.Is checked by leaving free the b-jet asymmetry in the

fit.


Systematics Systematic due to template shape description.

Done by using templates made from inclusive jets.No di-jet selection, much bigger statistics, different

production mechanisms.

Different MC statistics produces additional statistical fluctuations, so the average shift for all p bins is taken as

systematic of give model parameter.

To be completed with another MC generators…


Systematics Systematic due to charm and beauty vertex reconstruction

efficiencies. Can be estimated from data using the tight link between these

efficiencies and fake vertex probability in light jet. Due to vertex reconstruction algorithm they are controlled by single

parameter. Then data-MC difference in fake vertex probability can be translated to vc/vb uncertainties.

They are estimated to be 1.1% for charm and 2% for beauty

To be completed with another MC generators…

Changes in results due to simultaneous change of vc by 1.1% and vb by 2%


Status

1. The measurements are done and now they are under final polishing.

2. Systematic needs to be completed with different MC generators. Corresponding MC samples are being processed right now.

3. Backup note should be finished soon.

Documents

14/06/11 Jet physics 1 Flavour fractions in di-jet system V.Kostyukhin C.Lapoire M.Lehmacher Bonn