We perform a phenomenological study of the invariant mass distribution of hadronic jets produced in proton-proton collisions, in conjunction with a grooming algorithm. In particular, we consider the modified MassDrop Tagger (mMDT), which corresponds to Soft Drop with angular exponent β = 0. Our calculation, which is differential in both jet mass and jet transverse momentum, resums large logarithms of the jet mass, including the full dependence on the groomer's energy threshold z cut , and it is matched to fixed-order QCD matrix elements at next-to-leading order. In order to account for non-perturbative contributions, originating from the hadronisation process and from the underlying event, we also include a phenomenological correction factor derived from Monte Carlo parton shower simulations. Furthermore, we consider two different possibilities for the jet transverse momentum: before or after grooming. We show that the former should be preferred for comparisons with upcoming experimental data essentially because the mMDT transverse momentum spectrum is not collinear safe, though the latter exhibits less sensitivity to underlying event and displays properties that may provide complementary information for probing non-perturbative effects.

We present a first-principle computation of the mass distribution of jets which have undergone the grooming procedure known as Soft Drop. This calculation includes the resummation of the large logarithms of the jet mass over its transverse momentum, up to next-to-logarithmic accuracy, matched to exact fixed-order results at next-toleading order. We also include non-perturbative corrections obtained from Monte-Carlo simulations and discuss analytic expressions for hadronisation and Underlying Event effects.Introduction The study of jets at the Large Hadron Collider (LHC) has recently taken a new turn with new substructure observables [1,2] amenable to precise theory calculations [3][4][5], including genuine theory uncertainty bands, and corresponding experimental measurements from both the CMS [6] and ATLAS [7] collaborations. The substructure techniques we concentrate on are usually referred to as grooming and they aim to reduce sensitivity to non-perturbative corrections and pileup.A first series of studies has focused on the jet mass after applying the (modified) MassDrop Tagger (mMDT) [1,8] in dijet events, as measured by the CMS collaboration [6]. On the theory side, the description of this observable requires to match a resummed calculation, important in the smallmass region, to fixed-order results, which are important for large masses. The former are obtained analytically, including to all orders terms enhanced by the large logarithms of p 2 t /m 2 with p t the jet transverse momentum and m the (groomed) jet mass. The latter is obtained from fixedorder Monte-Carlo simulations. To date, two theory calculations are available: a SCET-based next-to-leading logarithmic (NLL) resummation in the small z cut limit, matched to leading order (LO) results [4], and our previous study

Several boosted jet techniques use jet shape variables to discriminate the multi-pronged signal from Quantum Chromodynamics backgrounds. In this paper, we provide a first-principles study of an important class of jet shapes all of which put a constraint on the subjet mass: the mass-drop parameter (µ 2 ), the N -subjettiness ratio (τ ). We provide analytic results both for QCD background jets as well as for signal processes. We further study the situation where cuts on these variables are applied recursively with Cambridge-Aachen de-clustering of the original jet. We also explore the effect of the choice of axis for N -subjettiness and jet de-clustering. Our results bring substantial new insight into the nature, gain and relative performance of each of these methods, which we expect will influence their future application for boosted object searches.