6 Calorimetry
261
safe, but results in irregular jet boundaries and complicates the underlying event
corrections. Recent work [119] has given rise to an improved version, the anti-k T
algorithm, which is safe against infrared and collinear divergences of QCD, and
has regular boundaries. This algorithm is now the “default” of most LHC analyses
using jets. Remarkably, despite the complexity and magnitude of the experimental
corrections, modern analyses (and Monte Carlos) achieve experimental jet resolutions comparable to (sometimes even better than) the resolution measured for single
hadrons: σ (E jet )/E) ≈ α/
√
E particles (GeV) ⊕ c, where
E particles represent the
energy of the particles associated with the jet and where α is close to the stochastic
and c close to the constant term measured for single hadrons [120, 121].
Within a jet, the electromagnetic part—coming mostly from π 0 decays—is
better reconstructed than the charged hadrons—mostly π ± and K ± or long-lived
neutral hadrons (K 0 L , n, , . . . ). While the latter are only detected in the hadronic
calorimeter, modern algorithms aim to “replace” charged hadrons reconstructed in
the hadronic calorimeter by the associated charged track, whose momentum is better
reconstructed than the calorimeter energy. While this individual replacement of
particles requires complex algorithms, the procedure has been constantly improved,
giving rise to “particle flow” algorithms (see Sect. 6.2.9) which are alternatives to
jet reconstruction from calorimeters alone. CMS [122] in general prefers the more
performant “particle flow” rather than calorimeter reconstruction. Particle flow is
well suited for algorithms analyzing a substructure within jets in view, for example,
of distinguishing between jets originating from a high p T W or Z from quark or
gluon jets [113].
The jet energy scale can be experimentally validated studying specific final states
in which the jet is balanced by a well measured object, such as γ + jet(s) or
Z + jet(s). Another powerful constraint is provided by W’s decaying into two jets.
A convenient source for identified Ws is the ttbar final state, abundantly produced
at the LHC. In the p T range from 30 GeV to 300 GeV, the linearity of the jet energy
scale over the whole angular range is better than 2% in both experiments [123, 124].
The measurement of MET’ is the only way to infer the production of neutrinos or weakly interacting SUSY-type particles. It is defined as the negative
vector sum of the momentum of all reconstructed objects (leptons, photons, jets)
in an event, projected onto the plane transverse to the collision direction. In
general, a “soft term” is added corresponding to tracks or energy deposits not
associated to the reconstructed objects. At high luminosity, in order to avoid
unwanted contributions from pile-up, only tracks are considered, because of their
unambiguous association with the corresponding collision vertex. Empirically, a
MET resolution of σ (E missing )/E ≈ 0.7α/
√ E Tparticles (GeV) is observed (at low
luminosity) for soft collisions with α expressing the stochastic term for single
hadron resolution. Calorimetric systems with an acceptance of at least |η| ~5 and
very good ‘hermeticity’ are required to achieve this performance.
For events with high p T jets, at high luminosity and after adequate corrections
for the contribution of the underlying event, and of residual pile-up, the resolution
is only weakly increasing with the number of collisions during the relevant bunch
261
safe, but results in irregular jet boundaries and complicates the underlying event
corrections. Recent work [119] has given rise to an improved version, the anti-k T
algorithm, which is safe against infrared and collinear divergences of QCD, and
has regular boundaries. This algorithm is now the “default” of most LHC analyses
using jets. Remarkably, despite the complexity and magnitude of the experimental
corrections, modern analyses (and Monte Carlos) achieve experimental jet resolutions comparable to (sometimes even better than) the resolution measured for single
hadrons: σ (E jet )/E) ≈ α/
√
E particles (GeV) ⊕ c, where
E particles represent the
energy of the particles associated with the jet and where α is close to the stochastic
and c close to the constant term measured for single hadrons [120, 121].
Within a jet, the electromagnetic part—coming mostly from π 0 decays—is
better reconstructed than the charged hadrons—mostly π ± and K ± or long-lived
neutral hadrons (K 0 L , n, , . . . ). While the latter are only detected in the hadronic
calorimeter, modern algorithms aim to “replace” charged hadrons reconstructed in
the hadronic calorimeter by the associated charged track, whose momentum is better
reconstructed than the calorimeter energy. While this individual replacement of
particles requires complex algorithms, the procedure has been constantly improved,
giving rise to “particle flow” algorithms (see Sect. 6.2.9) which are alternatives to
jet reconstruction from calorimeters alone. CMS [122] in general prefers the more
performant “particle flow” rather than calorimeter reconstruction. Particle flow is
well suited for algorithms analyzing a substructure within jets in view, for example,
of distinguishing between jets originating from a high p T W or Z from quark or
gluon jets [113].
The jet energy scale can be experimentally validated studying specific final states
in which the jet is balanced by a well measured object, such as γ + jet(s) or
Z + jet(s). Another powerful constraint is provided by W’s decaying into two jets.
A convenient source for identified Ws is the ttbar final state, abundantly produced
at the LHC. In the p T range from 30 GeV to 300 GeV, the linearity of the jet energy
scale over the whole angular range is better than 2% in both experiments [123, 124].
The measurement of MET’ is the only way to infer the production of neutrinos or weakly interacting SUSY-type particles. It is defined as the negative
vector sum of the momentum of all reconstructed objects (leptons, photons, jets)
in an event, projected onto the plane transverse to the collision direction. In
general, a “soft term” is added corresponding to tracks or energy deposits not
associated to the reconstructed objects. At high luminosity, in order to avoid
unwanted contributions from pile-up, only tracks are considered, because of their
unambiguous association with the corresponding collision vertex. Empirically, a
MET resolution of σ (E missing )/E ≈ 0.7α/
√ E Tparticles (GeV) is observed (at low
luminosity) for soft collisions with α expressing the stochastic term for single
hadron resolution. Calorimetric systems with an acceptance of at least |η| ~5 and
very good ‘hermeticity’ are required to achieve this performance.
For events with high p T jets, at high luminosity and after adequate corrections
for the contribution of the underlying event, and of residual pile-up, the resolution
is only weakly increasing with the number of collisions during the relevant bunch