A
bstract
Discriminating quark jets from gluon jets is an important but challenging problem in jet substructure. In this paper, we use the concept of mutual information to illuminate the physics of ...quark/gluon tagging. Ideal quark/gluon separation requires only one bit of truth information, so even if two discriminant variables are largely uncorrelated, they can still share the same “truth overlap”. Mutual information can be used to diagnose such situations, and thus determine which discriminant variables are redundant and which can be combined to improve performance. Using both parton showers and analytic resummation, we study a two-parameter family of generalized angularities, which includes familiar infrared and collinear (IRC) safe observables like thrust and broadening, as well as IRC unsafe variants like
p
T
D
and hadron multiplicity. At leading-logarithmic (LL) order, the bulk of these variables exhibit Casimir scaling, such that their truth overlap is a universal function of the color factor ratio
C
A
/C
F
. Only at next-to-leading-logarithmic (NLL) order can one see a difference in quark/gluon performance. For the IRC safe angularities, we show that the quark/gluon performance can be improved by combining angularities with complementary angular exponents. Interestingly, LL order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations between observables, but there are significant differences in the predicted quark/gluon discrimination power. For the IRC unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative “weighted-energy function”, providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination.
A
bstract
The extraction of transverse momentum dependent distributions (TMDs) in semi-inclusive deep inelastic scattering (SIDIS) is complicated by the presence of both initial- and final-state ...nonperturbative physics. We recently proposed measuring jets (in- stead of hadrons) as a solution, showing that for the Winner-Take-All jet axis the same factorization formulae valid for hadrons applied to jets of arbitrary size. This amounts to simply replacing TMD fragmentation functions by our TMD jet functions. In this paper we present the calculation of these jet functions at one loop. We obtain phenomenological results for
e
+
e
−
→
dijet (Belle II, LEP) and SIDIS (HERA, EIC) with a jet, building on the arTeMiDe code. Surprisingly, we find that the limit of large jet radius describes the full
R
results extremely well, and we extract the two-loop jet function in this limit using Event2, allowing us to achieve N
3
LL accuracy. We demonstrate the perturbative convergence of our predictions and explore the kinematic dependence of the cross section. Finally, we investigate the sensitivity to nonperturbative physics, demonstrating that jets are a promising probe of proton structure.
A
bstract
We study the transverse momentum spectrum of hadrons in jets. By measuring the transverse momentum with respect to a judiciously chosen axis, we find that this observable is insensitive to ...(the recoil of) soft radiation. Furthermore, for small transverse momenta we show that the effects 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 modification effects in heavy-ion collisions and identifying boosted heavy resonances.
A
bstract
LHC measurements involve cuts on several observables, but resummed calculations are mostly restricted to single variables. We show how the resummation of a class of double-differential ...measurements can be achieved through an extension of Soft-Collinear Effective Theory (SCET). A prototypical application is
pp
→
Z
+ 0 jets, where the jet veto is imposed through the beam thrust event shape
T
, and the transverse momentum
p
T
of the
Z
boson is measured. A standard SCET analysis suffices for
p
T
∼
m
Z
1
/
2
T
1
/
2
and
p
T
∼
T
, but additional collinear-soft modes are needed in the intermediate regime. We show how to match the factorization theorems that describe these three different regions of phase space, and discuss the corresponding relations between fully-unintegrated parton distribution functions, soft functions and the newly defined collinear-soft functions. The missing ingredients needed at NNLL/NLO accuracy are calculated, providing a check of our formalism. We also revisit the calculation of the measurement of two angularities on a single jet in JHEP 1409 (2014) 046, finding a correction to their conjecture for the NLL cross section at
O
α
s
2
.
A
bstract
Multivariate analyses are emerging as important tools to understand properties of hadronic jets, which play a key role in the LHC experimental program. We take a first step towards precise
...and
differential theory predictions, by calculating the cross section for
e
+
e
−
→ 2 jets differential in the angularities
e
α
and
e
β
. The logarithms of
e
α
and
e
β
in the cross section are jointly resummed to next-to-next-to-leading logarithmic accuracy, using the SCET
+
framework we developed, and are matched to the next-to-leading order cross section. We perform analytic one-loop calculations that serve as input for our numerical analysis, provide controlled theory uncertainties, and compare our results to P
ythia
. We also obtain predictions for the cross section differential in the ratio
e
α
/e
β
, which cannot be determined from a fixed-order calculation. The effect of nonperturbative corrections is also investigated. Using E
vent
2, we validate the logarithmic structure of the single angularity cross section predicted by factorization theorems at
O
α
s
2
, highlighting the importance of recoil for specific angularities when using the thrust axis as compared to the winner-take-all axis.
A
bstract
The azimuthal angular decorrelation of a vector boson and jet is sensitive to QCD radiation, and can be used to probe the quark-gluon plasma in heavy-ion collisions. By using a recoil-free ...jet definition, the sensitivity to contamination from soft radiation on the measurement is reduced, and the complication of non-global logarithms is eliminated from our theoretical calculation. Specifically we will consider the
p
T
n
recombination scheme, as well as the
n
→ ∞ limit, known as the winner-take-all scheme. These jet definitions also significantly simplify the calculation for a track-based measurement, which is preferred due to its superior angular resolution. We present a detailed discussion of the factorization in Soft-Collinear Effective Theory, revealing why the transverse momentum
q
→
T
is more complicated than the azimuthal angle. We show that potential glauber contributions do not spoil our factorization formalism, at least up to and including order
α
s
3
. The resummation is carried out using the renormalization group, and all necessary ingredients are collected or calculated. We conclude with a detailed phenomenological study, finding an enhanced matching correction for high jet
p
T
due to the electroweak collinear enhancement of a boson emission off di-jets. We also compare with the P
ythia
event generator, finding that our observable is very robust to hadronization and the underlying event.
We investigate the use of jets to measure transverse-momentum-dependent distributions (TMDs). The example we use to present our framework is the dijet momentum decorrelation at lepton colliders. ...Translating this momentum decorrelation into an angle θ≪1, we analyze the factorization of the cross section for the cases θ≫R, θ∼R, and θ≪R, where R is the jet radius. Critically, for the winner-take-all axis, the jet TMD has the same double-scale renormalization group evolution as TMD fragmentation functions for all radii R. TMD fragmentation functions in factorization theorems may then simply be replaced by the jet TMDs we calculate, and all ingredients to perform the resummation to next-to-next-to-leading logarithmic accuracy are available. Our approach also applies to semi-inclusive deep inelastic scattering, where a jet instead of a hadron is measured in the final state, and we find a clean method to probe the intrinsic transverse momentum of quarks and gluons in the proton that is less sensitive to final-state nonperturbative effects.
A
bstract
We develop the framework to perform all-orders resummation of electroweak logarithms of
Q/M
for inclusive scattering processes at energies
Q
much above the electroweak scale
M
. We ...calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 → 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov double logarithms, is computed. If only the invariant mass of the final state is measured, all electroweak logarithms can be resummed by the PDF evolution, at least to LL. However, simply identifying a lepton in the final state requires the corresponding fragmentation function and introduces angular dependence through the exchange of soft gauge bosons. Furthermore, we show the importance of polarization effects for gauge bosons, due to the chiral nature of SU(2) — even the gluon distribution in an unpolarized proton becomes polarized at high scales due to electroweak effects. We justify our approach with a factorization analysis, finding that the objects entering the factorization theorem do not need to be SU(2) × U(1) gauge singlets, even though we perform the factorization and resummation in the symmetric phase. We also discuss a range of extensions, including jets and how to calculate the EW logarithms when you are fully exclusive in the central (detector) region and fully inclusive in the forward (beam) regions.
A
bstract
We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in
e
+
e
−
collisions. This will enable a precise ...extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effective Theory, and present all ingredients needed for the joint resummation of the transverse momentum and thrust spectrum at NNLL accuracy. One kinematic region can give rise to non-global logarithms (NGLs), and we describe how to include the leading NGLs. We also discuss alternative measurements in
e
+
e
−
collisions that can be used to access the TMD fragmentation function. Finally, by using crossing symmetry, we obtain a new way to constrain TMD parton distributions, by measuring the displacement of the thrust axis in
ep
collisions.
A
bstract
In double parton scattering (DPS), two partonic collisions take place between one pair of colliding hadrons. The effect of DPS can be significant for precision measurements due to the ...additional radiation from secondary partonic collisions, and especially for specific processes such as same-sign
WW
production. Its effect is usually included through Monte Carlo parton showers. In a factorization approach to DPS, the initial state is described by double parton distributions (DPDs). These are currently poorly constrained by experiment, but provide a view on interesting correlations between partons in the hadron. Here we show that the Large Momentum Effective Theory approach can be applied to DPDs. Specifically, we present a general matching relation between DPDs and lattice-calculable quasi-DPDs for general flavor, spin and color structures. We furthermore calculate the one-loop matching coefficients for the quark-quark DPDs, verifying that the infrared logarithms and divergences cancel in the matching. While we restrict to the flavor-non-singlet case, we do take color and spin correlations into account. Interestingly, quasi-DPDs combines nontrivial features from both the collinear and transverse momentum dependent quasi-parton distribution functions. This represents a first step in extending the quasi-PDF approach to DPDs, opening up a new way to constrain these distributions using lattice QCD.
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