Convolved Substructure: Analytically Decorrelating Jet Substructure Observables

A number of recent applications of jet substructure, in particular searches for light new particles, require substructure observables that are decorrelated with the jet mass. In this paper we introduce the Convolved SubStructure (CSS) approach, which uses a theoretical understanding of the observable to decorrelate the complete shape of its distribution. This decorrelation is performed by convolution with a shape function whose parameters and mass dependence are derived analytically. We consider in detail the case of the $D_2$ observable and perform an illustrative case study using a search for a light hadronically decaying $Z'$. We find that the CSS approach completely decorrelates the $D_2$ observable over a wide range of masses. Our approach highlights the importance of improving the theoretical understanding of jet substructure observables to exploit increasingly subtle features for performance.Comment: 20 pages, 11 figures. v2. Corrected typo in legend in Figure 5. Updated Figure 11, minor modification to conclusions on discrimination power. v3. Updated to published version. Minor typos correcte

Probing Transverse-Momentum Dependent Evolution With Groomed Jets

We propose an observable which involves measuring the properties (transverse momentum $p_{h\perp}$ and energy fraction $z_h$) of an identified hadron inside a groomed jet. The jet is identified with an anti-kT/CA algorithm and is groomed by implementing the modified mass drop procedure with an energy cut-off parameter $z_{cut}$. The transverse momentum of the hadron inside the jet is measured with respect to the groomed jet axis. We obtain a factorization theorem in the framework of Soft Collinear Effective Theory (SCET), to define a Transverse Momentum Dependent Fragmenting Jet Function (TMDFJF). The TMDFJF is factorized into collinear and collinear soft modes by matching onto SCET$_+$. We resum large logarithms in $E_J/p_{h\perp}$, where $E_J$ is the ungroomed jet energy, to NLL accuracy and apply this formalism for computing the shape of the $p_{h\perp}$ distribution of a pion produced in an $e^+ +e^-$ collision. We observe that the introduction of grooming makes this observable insensitive to non-global logarithms and particularly sensitive to non-perturbative physics of the transverse momentum dependent evolution at low values of $p_{h\perp}$, which can be probed in the variation of the cut-off parameter $z_{cut}$ of the groomer. We discuss how this observable can be used to distinguish between non-perturbative models that describe universal TMD evolution and provide a window into the three dimensional structure of hadrons.Comment: 23 pages, 4 figure

The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_\perp\ll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $\alpha_s^2$ fixed order result near $p_\perp \sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_\perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.Comment: 23 pages, 10 figure

Factorization and Resummation for Groomed Multi-Prong Jet Shapes

Observables which distinguish boosted topologies from QCD jets are playing an increasingly important role at the Large Hadron Collider (LHC). These observables are often used in conjunction with jet grooming algorithms, which reduce contamination from both theoretical and experimental sources. In this paper we derive factorization formulae for groomed multi-prong substructure observables, focusing in particular on the groomed $D_2$ observable, which is used to identify boosted hadronic decays of electroweak bosons at the LHC. Our factorization formulae allow systematically improvable calculations of the perturbative $D_2$ distribution and the resummation of logarithmically enhanced terms in all regions of phase space using renormalization group evolution. They include a novel factorization for the production of a soft subjet in the presence of a grooming algorithm, in which clustering effects enter directly into the hard matching. We use these factorization formulae to draw robust conclusions of experimental relevance regarding the universality of the $D_2$ distribution in both $e^+e^-$ and $pp$ collisions. In particular, we show that the only process dependence is carried by the relative quark vs. gluon jet fraction in the sample, no non-global logarithms from event-wide correlations are present in the distribution, hadronization corrections are controlled by the perturbative mass of the jet, and all global color correlations are completely removed by grooming, making groomed $D_2$ a theoretically clean QCD observable even in the LHC environment. We compute all ingredients to one-loop accuracy, and present numerical results at next-to-leading logarithmic accuracy for $e^+e^-$ collisions, comparing with parton shower Monte Carlo simulations. Results for $pp$ collisions, as relevant for phenomenology at the LHC, are presented in a companion paper.Comment: 66 pages, 18 figure