# Multi-boson production Page: 4 of 8

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CDF Run II Preliminary

[ L=3.6fb

120 Fitted Templates EZW+jets

y 100 WZ

- m zz

lL 0 tt

E ww

60 -4- Data

--- Nominal MC

40 -

20 -

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Matrix Element Likelihood Ratio (LRWW)

Fig. 6. Likelihood ratio distribution for data compared with fit-

ted signal and backgrounds templates and with the nominal

MC prediction.

where "TSpeC is defined as:

Nrspec { T if AQ(L7T,lj) > z

sin(0( T,1, Tj)) if AQ(LTl,j) <

This definition is a requirement that VT transverse to

each lepton or jet in the event is greater than the min-

imum threshold if VT points along that object, so that

losing energy from just one such object in an event would

not allow it to enter the sample. Furthermore, in or-

der to suppress the heavy flavor contribution, the invari-

ant mass of the two selected leptons is required to be

M1+- > 16 GeV/c2.

To measure the WW production cross section, a ma-

trix element probability for each event to be a WW event

has been calculated. This probability is used to build a

likelihood ratio discriminant, and the normalization of

WW process is extracted by a fit, using MC templates.

The event-by-event matrix element probability density

Pm (Robs) is defined for the four processes (m) WW, ZZ,

W- and W+jets, as:

Pm(robs) <rn(y)G(Xs, y)dy (1)

wherexobs

y

Urn

c(y)are the observed "leptons" andV T,

are the true lepton four-vectors (include

neutrinos),

is leading-order theoretical calculation of

the cross-section for the process m,

is total event efficiency x acceptance,G(xobs, y) is an analytic model of resolution effects,

1

is the normalization.

Since the neutrinos are not reconstructed, the unob-

served degrees of freedom (DOF) are integrated out in

equation (1), reducing the number of the DOF to eight,

measured in the selected events.The event probability densities are used to construct

a likelihood ratio discriminant:LRWW(xobs)

Pww (xobs)

Pww(xobs) + E k1P1(xobs)where k, is the expected fraction for each background,

with EZ k, 1.

A binned maximum likelihood method is used to ex-

tract the WW cross section using the shape of the

LRww distributions for signal and backgrounds along

with their estimated normalizations and systematic un-

certainties. The likelihood function is formed from a

product of Poisson probabilities for each bin in LRww

distribution (Fig. 6.). Additionally Gaussian constraints

are applied for each systematic indetermination Sc *.

The likelihood function is defined as:\ " ( > . s2

(2)

where n, is the number of data events in the i-th bin and

, is the total expectation for the i-th bin, given by:Y, = C (I + ffjSc)] (NfrP)2

A La j(3)

This formulation includes the proper correlation of

the different systematic uncertainties. In equation (3)

(NXP), and ffk are the expected number of events in

the i-th bin and the fractional uncertainty associated

with the systematic Sc for the process k. The param-

eter ak is the ratio between the measured cross section

and the predicted one: it is freely floating for the WW

process and is fixed to 1 for all other processes.

The measured cross section for the production of WW

events is:

o(pp -> WW) 12.1 0.9 (stat.) +i.4 (syst.) pb

This is in good agreement with the theoretical predic-

tion o(pp -> WW) 11.66 0.70 pb and is the best

measurement to date of the production cross section of

the pp -> WW process.

The PT distribution of the leading lepton for each se-

lected event is used to extract 95% C.L. limits on the

ZWW and -WW aTGC parameters. The measured

limits are reported in Table 4.

The DO collaboration analysed the WW production

[9] in a data sample corresponding to 1 fb-1, utilizing the

final states described above, with competitive results for

both the production cross section measurement and the

aTGC limits evaluation. The measured cross section:

oj(pp - WW) 11.5 2.1 (stat.+syst.) 0.7 (lumi.) pb

is consistent with the SM expectation of 12.0 0.7 pb.

To enhance the sensitivity to anomalous couplings se-

lected events are sorted according to both leading and

trailing lepton PT into a two-dimensional histogram.

For each bin the selected number of WW events pro-

duced is parametrized by a quadratic function in three-

dimensional (Ar2 , A2 , Agf) space or two-dimensional

(Ar, A) space, as appropriate for the TGC relationship

scenario under study. In the three-dimensional case,

*Details about the systematic uncertainties can be found in [8]4

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### Reference the current page of this Article.

Mastrandrea, Paolo. Multi-boson production, article, September 1, 2010; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc1012956/m1/4/: accessed December 9, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.