102
4 Standard Model Measurements
tion z of a parton initiating the jet. Jet fragmentation functions can be probed by
measurements of the relative momentum of charged particle tracks inside jets [583],
providing valuable input for the modelling of fragmentation in event generators. A
recent measurement by ATLAS [580] uses ζ = p
particle
T
/ p
jet
T instead of z, which is a
better proxy for the starting scale of the parton shower evolution at hadron colliders.
Measurements of partial fractions of the fragmentation functions probe how much of
the jet energy is carried by particles of a given p T fraction. The fraction of particles
carrying 10% or less of the jet p T changes very little across a jet p T of 300–2500 GeV
and asymptotically approaches 96%. A strong p T dependence is introduced when ζ
is lowered. The fraction of jet particles with ζ < 1% increases logarithmically with
jet p T , while the fraction of particles with ζ < 0.1% increases more rapidly [580].
Additional information is carried by the moments of the ζ distribution, which are
well described by Pythia and Herwig, while Sherpa displays some discrepancies
with the data. A less-well probed aspect of jet fragmentation is the fragmentation of
g → bb, important for H tagging and analyses probing final states with b quarks.
While studies on well separated b quark pairs exist, data with
√
s = 13 TeV allow for
the first time a measurement of jet fragmentation in collimated g → bb production at
high p T [584]. In this analysis, quark and gluon flavour fractions have been fit to the
data to remove contributions from processes other than g → bb. The fitted fractions
significantly disagree with the Pythia predictions, suggesting that further studies
can lead to an improvement in the modelling of heavy flavour production at high p T .
Comparisons of unfolded distributions at the particle level with simulations suggest
that these data have the power to constrain the modelling of gluon polarisation.
Another variable related to n ch is the jet charge, defined as the p T -weighted sum
of the electric charges of the jet constituents. Jet charge is sensitive to the charge
of the parton initiating the jet. At the LHC, the mean of the jet charge distribution
increases with increasing p T for the more forward of the leading p T jets, due to the
increasing fraction of jets from valence up-type quarks. The jet charge is sensitive
to non-perturbative effects and can be used to test and improve the modelling of
final state radiation. Unfolded measurements of jet charge distributions have been
reported by ATLAS [585] and CMS [586] using 8 TeV data.
Observables less sensitive to non-perturbative effects are k T splitting scales.
These probe the energy scale of the last combination step in the clustering process. An unfolded measurement in W +jets production with 7 TeV data [587] reveals
that higher order perturbative corrections are important to model the hard region
with
√
d k > 20 GeV, while resummation and non-perturbative effects are important in softer regions. Another observable characterising the parton splitting is
z g = p T,2 /( p T,1 + p T,2 ) [213], calculated on the branch of a jet fulfilling the soft
drop condition in Eq. (2.41). This variable is closely related to the QCD splitting
function, which is singular in the collinear limit and thus not experimentally accessible. However, the cross section as a function of z g approximates the QCD splitting
function in the high-energy limit and can thus be used to probe this universal function.
The distribution in z g can be predicted from first principles because of its Sudakov
safety, making z g a potent probe of the underlying 1 → 2 splittings in QCD. The
4 Standard Model Measurements
tion z of a parton initiating the jet. Jet fragmentation functions can be probed by
measurements of the relative momentum of charged particle tracks inside jets [583],
providing valuable input for the modelling of fragmentation in event generators. A
recent measurement by ATLAS [580] uses ζ = p
particle
T
/ p
jet
T instead of z, which is a
better proxy for the starting scale of the parton shower evolution at hadron colliders.
Measurements of partial fractions of the fragmentation functions probe how much of
the jet energy is carried by particles of a given p T fraction. The fraction of particles
carrying 10% or less of the jet p T changes very little across a jet p T of 300–2500 GeV
and asymptotically approaches 96%. A strong p T dependence is introduced when ζ
is lowered. The fraction of jet particles with ζ < 1% increases logarithmically with
jet p T , while the fraction of particles with ζ < 0.1% increases more rapidly [580].
Additional information is carried by the moments of the ζ distribution, which are
well described by Pythia and Herwig, while Sherpa displays some discrepancies
with the data. A less-well probed aspect of jet fragmentation is the fragmentation of
g → bb, important for H tagging and analyses probing final states with b quarks.
While studies on well separated b quark pairs exist, data with
√
s = 13 TeV allow for
the first time a measurement of jet fragmentation in collimated g → bb production at
high p T [584]. In this analysis, quark and gluon flavour fractions have been fit to the
data to remove contributions from processes other than g → bb. The fitted fractions
significantly disagree with the Pythia predictions, suggesting that further studies
can lead to an improvement in the modelling of heavy flavour production at high p T .
Comparisons of unfolded distributions at the particle level with simulations suggest
that these data have the power to constrain the modelling of gluon polarisation.
Another variable related to n ch is the jet charge, defined as the p T -weighted sum
of the electric charges of the jet constituents. Jet charge is sensitive to the charge
of the parton initiating the jet. At the LHC, the mean of the jet charge distribution
increases with increasing p T for the more forward of the leading p T jets, due to the
increasing fraction of jets from valence up-type quarks. The jet charge is sensitive
to non-perturbative effects and can be used to test and improve the modelling of
final state radiation. Unfolded measurements of jet charge distributions have been
reported by ATLAS [585] and CMS [586] using 8 TeV data.
Observables less sensitive to non-perturbative effects are k T splitting scales.
These probe the energy scale of the last combination step in the clustering process. An unfolded measurement in W +jets production with 7 TeV data [587] reveals
that higher order perturbative corrections are important to model the hard region
with
√
d k > 20 GeV, while resummation and non-perturbative effects are important in softer regions. Another observable characterising the parton splitting is
z g = p T,2 /( p T,1 + p T,2 ) [213], calculated on the branch of a jet fulfilling the soft
drop condition in Eq. (2.41). This variable is closely related to the QCD splitting
function, which is singular in the collinear limit and thus not experimentally accessible. However, the cross section as a function of z g approximates the QCD splitting
function in the high-energy limit and can thus be used to probe this universal function.
The distribution in z g can be predicted from first principles because of its Sudakov
safety, making z g a potent probe of the underlying 1 → 2 splittings in QCD. The