200 research outputs found
Glauber Gluons and Multiple Parton Interactions
We show that for hadronic transverse energy in hadron-hadron
collisions, the classic Collins-Soper-Sterman (CSS) argument for the
cancellation of Glauber gluons breaks down at the level of two Glauber gluons
exchanged between the spectators. Through an argument that relates the diagrams
with these Glauber gluons to events containing additional soft scatterings, we
suggest that this failure of the CSS cancellation actually corresponds to a
failure of the `standard' factorisation formula with hard, soft and collinear
functions to describe at leading power. This is because the observable
receives a leading power contribution from multiple parton interaction (or
spectator-spectator Glauber) processes. We also suggest that the same argument
can be used to show that a whole class of observables, which we refer to as MPI
sensitive observables, do not obey the standard factorisation at leading power.
MPI sensitive observables are observables whose distributions in hadron-hadron
collisions are disrupted strongly by the presence of multiple parton
interactions (MPI) in the event. Examples of further MPI sensitive observables
include the beam thrust and transverse thrust.Comment: 24 pages, 8 figure
The Fully-Differential Quark Beam Function at NNLO
We present the first calculation of a fully-unintegrated parton distribution
(beam function) at next-to-next-to-leading order (NNLO). We obtain the
fully-differential beam function for quark-initiated processes by matching it
onto standard parton distribution functions (PDFs) at two loops. The
fully-differential beam function is a universal ingredient in resummed
predictions of observables probing both the virtuality as well as the
transverse momentum of the incoming quark in addition to its usual longitudinal
momentum fraction. For such double-differential observables our result provides
the part of the NNLO singular cross section related to collinear initial-state
radiation (ISR), and is important for the resummation of large logarithms
through N3LL.Comment: 17 pages, 1 figure; v2: journal versio
Double parton scattering theory overview
The dynamics of double hard scattering in proton-proton collisions is quite
involved compared with the familiar case of single hard scattering. In this
contribution, we review our theoretical understanding of double hard scattering
and of its interplay with other reaction mechanisms.Comment: 25 pages, 7 figures. Prepared for: Multiple Parton Interactions at
the LHC, Eds. P. Bartalini and J. R. Gaunt, World Scientific, Singapor
Study of scalar mesons in chiral Lagrangian frameworks
We review two approaches to studying pseudoscalar meson-meson scattering
amplitudes to beyond 1 GeV using non-linear and linear chiral Lagrangians.
These approaches use two different unitarisation techniques - a generalised
Breit Wigner prescription and K-matrix unitarization respectively. We also
report some preliminary findings on K-matrix unitarisation of the I=J=0
pion-pion scattering amplitude in the non-linear chiral Lagrangian approach and
make some remarks about the light scalar mesons.Comment: Contribution to XII Conference on Hadron Spectroscopy, Frascati 2007.
8 pages, 2 figure
Double parton scattering in the ultraviolet: addressing the double counting problem
In proton-proton collisions there is a smooth transition between the regime
of double parton scattering, initiated by two pairs of partons at a large
relative distance, and the regime where a single parton splits into a parton
pair in one or both protons. We present a scheme for computing both
contributions in a consistent and practicable way.Comment: 5 pages, 3 figures. To appear in the proeceedings of MPI@LHC 2015,
Trieste, Italy, 23-27 November 201
Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons and
The double parton distributions (dPDF), both conventional and those
corresponding to parton splitting, are calculated and compared for different
two-parton combinations. The conventional and splitting dPDFs have very similar
shape in and . We make a first quantitative evaluation of the
single-ladder-splitting contribution to double parton scattering (DPS)
production of two S- or P-wave quarkonia, two Higgs bosons and . The ratio of the single-ladder-splitting to conventional contributions is
discussed as a function of centre-of-mass energy, mass of the produced system
and other kinematical variables. Using a simple model for the dependence of the
conventional two-parton distribution on transverse parton separation (Gaussian
and independent of and scales), we find that the 2v1 contribution is as
big as the 2v2 contribution discussed in recent years in the literature. This
means that the phenomenological analyses of including only the
conventional DPS mechanism have to be revised including explicitly the
single-ladder-splitting contributions discussed here. The differential
distributions in rapidity and transverse momenta calculated for conventional
and single-ladder-splitting DPS processes are however very similar which causes
their experimental separation to be rather difficult, if not impossible. The
direct consequence of the existence of the two components (conventional and
splitting) is the energy and process dependence of the empirical parameter
. This is illustrated in our paper for the considered processes.Comment: 20 pages, 11 figures, 3 table
The Gluon Beam Function at Two Loops
The virtuality-dependent beam function is a universal ingredient in the
resummation for observables probing the virtuality of incoming partons,
including N-jettiness and beam thrust. We compute the gluon beam function at
two-loop order. Together with our previous results for the two-loop quark beam
function, this completes the full set of virtuality-dependent beam functions at
next-to-next-to-leading order (NNLO). Our results are required to account for
all collinear ISR effects to the N-jettiness event shape through N^3LL order.
We present numerical results for both the quark and gluon beam functions up to
NNLO and N^3LL order. Numerically, the NNLO matching corrections are important.
They reduce the residual matching scale dependence in the resummed beam
function by about a factor of two.Comment: 21 pages, 6 figures; v2: journal versio
Double hard scattering without double counting
Double parton scattering in proton-proton collisions includes kinematic
regions in which two partons inside a proton originate from the perturbative
splitting of a single parton. This leads to a double counting problem between
single and double hard scattering. We present a solution to this problem, which
allows for the definition of double parton distributions as operator matrix
elements in a proton, and which can be used at higher orders in perturbation
theory. We show how the evaluation of double hard scattering in this framework
can provide a rough estimate for the size of the higher-order contributions to
single hard scattering that are affected by double counting. In a numeric
study, we identify situations in which these higher-order contributions must be
explicitly calculated and included if one wants to attain an accuracy at which
double hard scattering becomes relevant, and other situations where such
contributions may be neglected.Comment: 80 pages, 20 figures. v2: clarifications in section 4, extended
section 8, small changes elsewher
N-jettiness Subtractions for NNLO QCD Calculations
We present a subtraction method utilizing the N-jettiness observable, Tau_N,
to perform QCD calculations for arbitrary processes at next-to-next-to-leading
order (NNLO). Our method employs soft-collinear effective theory (SCET) to
determine the IR singular contributions of N-jet cross sections for Tau_N -> 0,
and uses these to construct suitable Tau_N-subtractions. The construction is
systematic and economic, due to being based on a physical observable. The
resulting NNLO calculation is fully differential and in a form directly
suitable for combining with resummation and parton showers. We explain in
detail the application to processes with an arbitrary number of massless
partons at lepton and hadron colliders together with the required external
inputs in the form of QCD amplitudes and lower-order calculations. We provide
explicit expressions for the Tau_N-subtractions at NLO and NNLO. The required
ingredients are fully known at NLO, and at NNLO for processes with two external
QCD partons. The remaining NNLO ingredient for three or more external partons
can be obtained numerically with existing NNLO techniques. As an example, we
employ our method to obtain the NNLO rapidity spectrum for Drell-Yan and
gluon-fusion Higgs production. We discuss aspects of numerical accuracy and
convergence and the practical implementation. We also discuss and comment on
possible extensions, such as more-differential subtractions, necessary steps
for going to N3LO, and the treatment of massive quarks.Comment: 51 pages, 10 figures, v2: journal versio
The Quark Beam Function at Two Loops
In differential measurements at a hadron collider, collinear initial-state
radiation is described by process-independent beam functions. They are the
field-theoretic analog of initial-state parton showers. Depending on the
measured observable they are differential in the virtuality and/or transverse
momentum of the colliding partons in addition to the usual longitudinal
momentum fraction. Perturbatively, the beam functions can be calculated by
matching them onto standard quark and gluon parton distribution functions. We
calculate the inclusive virtuality-dependent quark beam function at NNLO, which
is relevant for any observables probing the virtuality of the incoming partons,
including N-jettiness and beam thrust. For such observables, our results are an
important ingredient in the resummation of large logarithms at N3LL order, and
provide all contributions enhanced by collinear t-channel singularities at NNLO
for quark-initiated processes in analytic form. We perform the calculation in
both Feynman and axial gauge and use two different methods to evaluate the
discontinuity of the two-loop Feynman diagrams, providing nontrivial checks of
the calculation. As part of our results we reproduce the known two-loop QCD
splitting functions and confirm at two loops that the virtuality-dependent beam
and final-state jet functions have the same anomalous dimension.Comment: 27 pages, 3 figures; v2: journal versio
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