Jet Reconstruction Sterman and Weinberg Phys Rev Lett

Jet Reconstruction Sterman and Weinberg: Phys. Rev. Lett. 39 (1977) 1436 Catani et al: Phys. Lett. 269 B (1991) 432 J. Huth et al: FERMILAB-Conf-90/249 -E T. Sjostrand: Pythia 5. 7 and Jetset 7. 4 Manual (in particular section 15 pag. 280 -290) Vincenzo Innocente Networks Neural

Jet Production Hadronic Jets are the result of the fragmentation and hadronization of partons (quarks or gluons). Because of color dynamics (Altarelli-Parisi evolution, coherent branching, LPHD) the emerging hadrons will be confined in a narrow cone around the direction of the parent parton 2/2/2022 Vincenzo Innocente Networks Neural 2

Jet Reconstruction l l The goal of jet reconstruction is to determine the energy and direction of the “original partons” Because of the intrinsic dynamics, jets can be defined only after a “resolution parameter” is set which essentially defines the scale at which we look at the branching phenomena. n n In pure QCD studies the “resolution parameter” will be used also to parametrized theory predictions if jets are used to reconstruct hadronic decays of heavy particles the “resolution parameter” will be tuned to obtain the best resolution and sensitivity 2/2/2022 Vincenzo Innocente Networks Neural 3

Jet Reconstruction in e+el A Jet definition for e+e- colliders should be: n n n 2/2/2022 infrared and collinear safe experimentally implementable usable in theoretical calculation subject to small hadronization correction subject to small detector correction Vincenzo Innocente Networks Neural 4

Jet Reconstruction in pp l In addition for hadron colliders we should add the requirements of minimizing the contamination from the underlying “low-pt” event n allowing a universal factorization of initial state collinear singularities A “Hard-scattering” scale should be introduced n l 2/2/2022 Vincenzo Innocente Networks Neural 5

Jet Definition l l l Two broad classes of jet algoritms exist: Cone-type Cluster-type 2/2/2022 Vincenzo Innocente Networks Neural 6

Cone Algorithm in e+el l l Define n-cones of half-angle such that all energy but a fraction is contained in the cones The algorithm should try to maximize the energy in the cones while minimizing the number of cones The major drawback of such an algorithm is the intrinsic ambiguities related to dealing with overlapping cones and the fact that is not Lorenz-invariant and therefore depends on Ecm. 2/2/2022 Vincenzo Innocente Networks Neural 7

Actual cone algorithms l A realistic cone algorithm starts with a seed (typically the most energetic track or the largest energy deposit) and clusterizes all “particles” in a -cone around it. n l The possibility to redefine the cone axis each time a new particle is added can be provided Two variant exits: n n 2/2/2022 to stop when a jet has energy less than ’Evis to reassign each particle (including not clusterized) to the closer final jet Vincenzo Innocente Networks Neural 8

Binary-joining Algorithm in e+el l l Define a “distance” yij, function of the four momentum of two particles and Lorenz-invariant set a resolution parameter ycut compute y for all pairs of particles n n 2/2/2022 if ymin < ycut combine the two particles in a single “pseudo-particle”, replace them with it and iterate otherwise stop and take the remaining pseudoparticles as the final jets Vincenzo Innocente Networks Neural 9

Invariant Mass (does not work) l l An obvious choice for yij seems to be the invariant mass: invariant mass algorithm are quite unstable because small mass clusters tend to be formed with slow particles in the center of the event. Thus, such an algorithm will clusterize fast particle around slow one, which is the opposite of what we want to achieve. 2/2/2022 Vincenzo Innocente Networks Neural 10

Jade Algorithm l l l A popular algorithm which alleviates the problem of the invariant mass is the Jade one where: The absence of masses tends to favor smaller y for faster particle The use of Evis compensates for detector resolution and acceptance effects 2/2/2022 Vincenzo Innocente Networks Neural 11

k (Durham) Algorithm l l l A new algorithm which has become very popular recently is a variant of Jade: y is the transverse momentum of the slower particle with respect the direction of the fastest one: it will naturally clusterize slow particle around fast one! This algorithm is also very attractive from a theoretical point of view as high-order corrections and logarithm resummations are “easy” to compute. 2/2/2022 Vincenzo Innocente Networks Neural 12

Fixed number of jets l l Binary-joining Algorithms are also very effective to clusterize the particles of an event in a fixed number of jets. This turns to be very useful when discriminating QCD events from heavy particle decays. It is enough to stop when n jets are left. The ymin of the event (called yn->n-1 as it is the ycut above which the event will become a (n-1)-jet event) gives an indication of how much the event is a “real” n-jet event. 2/2/2022 Vincenzo Innocente Networks Neural 13

Recombination scheme l l l The most obvious way of creating a new “pseudoparticle” recombining the two with smaller distance seems to be adding the 4 -momentums (E-scheme) For the Jade algorithm this produces instability in particular for the hadronization corrections. So other schemes, which essentially force the mass of the pseudo -particles to zero and then try to preserve somehow momentum and energy conservation, has been adopted. The k algorithm seems not to suffer of these problems and the more natural E-scheme can be adopted 2/2/2022 Vincenzo Innocente Networks Neural 14

Re-association l l l Another problem of Binary-joining Algorithms (again more for Jade) is the fact that particles could be closer (in any metric) to a jet different from the one which they belong Re-associaton of particles to the “closer” final jet is a normal practice which however could produce an event with a different ymin Jetset “luclus” algorithm implements a reassociation after each recombination step, which makes it more rigorous although slow 2/2/2022 Vincenzo Innocente Networks Neural 15

Resolution considerations l l The choice of recombination and re-association schemes affects mainly hadronization and detector corrections which, besides jet counting, turn into angular and energy resolution of the jets (how far the reconstructed jet lays from the original parton) Therefore the details of the jet algorithm can depend strongly on the detector and the physics analysis 2/2/2022 Vincenzo Innocente Networks Neural 16

Jets in pp collisions l Hadron collisions differs from e+e- collisions in many respect: n n 2/2/2022 hard-scattering partons account only form a small (unknown) fraction of the available Ecm the center of mass of the hard-scattering is moving the particle belonging to the underlying “low-pt event” will inevitably overlap with those emerging from the hard-scattering “initial state radiation” jets exist and should be explicitly accounted for in non QCD studies (searches for heavy particles in the final state) Vincenzo Innocente Networks Neural 17

Cone algorithms in pp collisions l To fulfill Lorenz-invariance n n 2/2/2022 cones are defined in a pseudo-rapidity ( -ln(tan /2)) azimuth ( ) metric energy is measured in the transverse plane with respect to the beam-axis (Et). Vincenzo Innocente Networks Neural 18

Cones in pp l l In the “cylindrical” - -Et space, - algorithms can then be applied in an almost straightforward way and should be optimized to minimize the effect of hadronization and the influence of the underlying events. n n 2/2/2022 Studies using UA 1/2 CDF and D 0 data have shown that a value of R 0=0. 7 compensate these effects set the hard-scattering scale Vincenzo Innocente Networks Neural 19

k algorithm in hadron collisions l l Recently the k algorithm has been proposed also for hadron collisions: It required a pre-clustering of hadrons to distinguish between hard-scattered and beamjets 2/2/2022 Vincenzo Innocente Networks Neural 20

k algorithm in hadron collisions l Define a hard-scattering scale Et Use as distance the transverse momentum normalized to this scale l Compute also the distance from the beams l 2/2/2022 Vincenzo Innocente Networks Neural 21

Pre-cluster l Take the smaller among yij and yip n n n l If it is >1 do nothing If yij is the smaller, combine i&j in a new “pseudo-particle” as usual If one of the yip is the smaller, assign the iparticle to the beam-jets and remove it from the process Iterate until all remaining pseudo-particles have yij and yip >1 2/2/2022 Vincenzo Innocente Networks Neural 22

Jet resolution l l At this stage we have separated the hard scattered hadrons from the underlying event at a scale Et At this point we can clusterized these hadrons using a ycut=Q 02/Et 2<1 forming jets at a smaller scale Q 0<Et using the usual algorithm. 2/2/2022 Vincenzo Innocente Networks Neural 23