Jet axes and universal transverse-momentum-dependent fragmentation
Received: December
Jet axes and universal transverse-momentum- dependent fragmentation
Open Access 0 1 3 6 7
c The Authors. 0 1 3 6 7
0 University of Amsterdam
1 Ciudad Universitaria , 28040 Madrid , Spain
2 Nikhef, Theory Group
3 Los Alamos , NM 87545 , U.S.A
4 Departamento de F sica Teorica II, Universidad Complutense de Madrid
5 Theoretical Division , MS B283 , Los Alamos National Laboratory
6 Science Park 105 , 1098 XG, Amsterdam , The Netherlands
7 Science Park 904 , 1098 XH Amsterdam , The Netherlands
We study the transverse momentum spectrum of hadrons in jets. By measuring the transverse momentum with respect to a judiciously chosen axis, we this observable is insensitive to (the recoil of) soft radiation. Furthermore, for small transverse momenta we show that the e ects of the jet boundary factorize, leading to a new transverse-momentum-dependent (TMD) fragmentation function. In contrast to the usual TMD fragmentation functions, it does not involve rapidity divergences and is universal in the sense that it is independent of the type of process and number of jets. These results directly apply to sub-jets instead of hadrons. We discuss potential applications, which include studying nuclear modi cation e ects in heavy-ion collisions and identifying boosted heavy resonances.
dependent; fragmentation; Jets; QCD Phenomenology
1 Introduction 2 Framework 2.1
NLO maching coe
Fragmenting jet function
TMD fragmentation function
Boundary function
Results for moments
A De ning recoil-free jet functions
A.1 One-loop example
B Clustering algorithms
C Results on anomalous dimensions
Standard transverse momentum dependent fragmentation functions
De nitions for TMD fragmentation inside a jet
3 Jet factorization and TMD fragmentation Factorization of fragmentation from perturbative radiation Factorization of TMD fragmentation from jet de nition Factorization for large radius jets
All-orders anomalous dimension of JTMDFF
C.2 One-loop anomalous dimensions in moment space
Introduction
In the analysis of events from hadron colliders it is common to use jets to organize the
nal states of hard interactions, making it natural to ask how the QCD con nement of
hadrons is realized in this context. The picture that arises from QCD factorization is that
we have the hard scattering, whose calculation is given in terms of partonic degrees of
freedom, initiating the jet. At the short-distance scale of the hard-scattering, we have a
quark or gluon of a much lower \o -shellness" exiting the hard interaction in a more or
less de nite direction. The subsequent branching does not change this direction much,
but does gives rise to a host of additional partons loosely grouped into a jet. These are
the perturbative remains of the slightly o -shell parton. Lastly, these additional partons
the observed hadrons.
Ultimately, to understand the dynamics of con nement within
jets, we would like to have a means of comparing the partonically generated momentum
distribution inside the jet to the observed hadronic momentum distribution. In addition
to momentum, one would also like to understand how quantum numbers, like spin, avor,
or charge, are transported from the hard scattering into the hadronic nal state.
; : : : produced by a parton
The fragmentation function di!h(zh; ) describes the distribution of the
longitudinale.g. ref. [4])
X Z dz
where Q is the scale of the hard scattering. A crucial feature of fragmentation is that it is
universal, i.e. insensitive to the underlying hard scattering or the soft background radiation.
In eld-theoretic terms this means that the same QCD matrix element for di!h captures the
fragmentation dynamics, and can be factorized from the hard scattering. Thus
fragmentation measurements at hadron-hadron, hadron-electron, and electron-positron colliders can
all be compared. However, when combining hadron analysis with modern jet algorithms
one begins to worry that the de nition of the jet itself could potentially spoil this
universality, since any given jet de nition will have more or less sensitivity to the underlying event
or hard scattering process. As we will see in this paper this can take a rather subtle form.
Fragmentation of hadrons inside jets has also been studied extensively, but without
accounting for the transverse momentum dependence of the hadrons.
When the jet is
su ciently narrow, its dynamics can be factorized from the hard scattering process. For
fragmentation in exclusive processes (i.e. with a speci c number of jets) this was studied
using event shapes (hemisphere jets) in refs. [5{10] and with a jet algorithm in refs. [11{
14]. Inclusive jet production with a jet algorithm was investigated in refs. [15{18]. The
applications that were considered range from comparisons to LHC measurements of charged
hadron spectra [12] to unravelling quarkonium production channels [13].
fragmentation in jets has also been considered [19{22], to e.g. describe jet charge [19].
The observables that w (...truncated)