K (transverse) jet algorithms in hadron colliders: The D0 experience Page: 3 of 9
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(a) (b) *
Beam- Beam-
(c) (d) *
Beam- Beam-
*
(e) (f)
Beam- Beam-
*
Figure 2: A simplified example of the final state of a collision between two hadrons. (a) The particles in
the event (represented by arrows) comprise a list of objects. (b-f) Solid arrows represent the final jets
reconstructed by the k1 algorithm, and open arrows represent objects not yet assigned to jets. The five
diagrams show successive iterations of the algorithm. In each diagram, a jet is either defined (when it is
well-separated from all other objects), or two objects are merged (when they have small relative k1). The
asterisk labels the relevant object(s) at each step.
interactions. All such corrections enter in the relation between the momentum of a jet measured
in the calorimeter pmeas and the "true" jet momentum ptre [ ] ]
true P tas _ P(1jet L, p.t)
mee asp0q (1)
Rjet(rgiet,pjet)
where po denotes an offset correction, and Rjet is a correction for the response of the calorimeter
to jets. A true jet is defined as being composed of only the final-state particle momenta from the
hard parton-parton scatter (i.e., before interaction in the calorimeter). Although Eq. (1) is valid for
any jet algorithm, po and the components of Rjet depend on the details of the jet algorithm. Our
calibration procedure attempts to correct calorimeter-level jets (after interactions in the calorime-
ter) to their particle-level (before the individual particles interact in the calorimeter), using the
described k1 jet algorithm, with D = 1.0. The procedure follows closely that of the calibration of
the fixed-cone jet algorithm [.']. The fixed-cone jet algorithm requires an additional scale factor
in Eq. (1), but we find no need for that kind of calorimeter-showering correction in the k1 jet
momentum calibration [ 13].
The jet momentum response, Rjet(rljet, piet), is determined as in Ref. [12], using conservation
of PT in photon-jet (y-jet) events.
The offset po corresponds to the contribution to the momentum of a reconstructed jet that is
not associated with the hard interaction. It contains two parts:
PO = Oue + Ozb,
where Oue is the offset due to the underlying event, and Ozb is an offset due to the overall detector
environment. Ozb is attributed to any additional energy in the calorimeter cells of a jet from the
combined effects of uranium noise, multiple interactions, and pile-up. The contributions of Oue
and Ozb to k1 jets are measured separately, but using similar methods. The method overlays
zero-bias (random p p crossings) or min-bias (a crossing with a hard collision) DO data and Monte
Carlo events, as described in Ref. [c].
The two terms of the offset correction Ozb and Oue for k1 jets (D = 1) are shown in Fig. 3. Using
this method for both the k1 (D = 1) and cone (R = 0.7) algorithms, the offset for the former isP504
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Elvira, V. Daniel. K (transverse) jet algorithms in hadron colliders: The D0 experience, article, December 5, 2002; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc736972/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.