Flavor tagging TeV jets for physics beyond the Standard Model

We present a new scheme for tagging boosted heavy flavor jets called “μx tagging.” At the LHC, the primary method to tag b-jets relies on tracking their charged constituents. However, when highly boosted, track-based b-tags lose efficiency, and the probability to mistag light jets rises dramatically. Using muons from B hadron decay and defining a particular combination “x” of angular information and boost estimation, we find fairly flat efficiencies to tag b-jets, c-jets, light-quark jets, and light-heavy jets (containing B hadrons from gluon splitting) of b = 14%, c = 6.5%, light−light = 0.1%, and light−heavy = 0.5%, respectively. We demonstrate the usefulness of this new scheme by showing the reach for discovery of a leptophobic Z′ → bb̄ in the dijet channel.


Introduction
As searches for W and Z bosons at the CERN Large Hadron Collider (LHC) shift to TeV-scale energies, observation of their decay products becomes challenging. Observation of dijet resonances above QCD background is hampered by falling b-tagging efficiencies (28-15% around 1-2 TeV) and large light-jet fake rates of 1-2% [1]. In addition to the low purity ( fake / b ∼ 1/10), large uncertainties in the tagging efficiencies affect the mass limits; e.g., the ATLAS b-tag uncertainty is 35% for p T > 500 GeV [2]. In order to discover multi-TeV physics beyond the Standard Model (BSM), we need a better b tag with good efficiency and purity.
At this conference, we presented a new method for flavor tagging at TeV-scale energies called "μ x boosted-bottom-jet tagging" [3]. This method is derived from kinematic first principles, and provides both a well-determined 14% efficiency for b-tagging, and a factor of 10 improvement in fake rejection over existing tags ( fake / b ∼ 1/100). In Sec. 2 we summarize the algorithm and cuts for the μ x tag, show why it works, and plot its transverse momentum p T -and pseudorapidity η-dependent efficiencies. In Sec. 3 we briefly describe the application of μ x boosted-b tagging to an analysis for discovery of a leptophobic Z → bb. We summarize our results in Sec. 4. Fig. 1). In the lab frame, the boost γ B of the B hadron compresses its decay products into a narrow subjet at high energy. We define a lab frame observable where κ ≡ β B /β μ,cm . Figure 1. Nomenclature for the center-of-momentum frame and boosted lab frame.

CM
While κ is unobservable, for sufficiently boosted B hadrons (γ B γ μ,cm ≥ 3) the lab frame distribution of the muon count N vs. x is effectively independent of κ, This leads to a universal shape in x for highly boosted jets containing B hadrons. Using this shape we define the μ x boosted-b tag as a cut on two variables: We capture 90% of muons from B decay by demanding x < 3. To further isolate b decays, we note the hard fragmentation function for b quarks leads to the B hadron subjet carrying a large fraction f subjet of the total jet momentum. Hence, we demand There are two challenges in applying the μ x tag to real events: we must identify the correct decay remnant of the B hadron to reconstruct its four-vector p subjet , and we must deal with the missing muon neutrino. Most of the neutrino energy in the lab frame comes from the boost, so we use the measured four-vector of the muon as a proxy p ν = p μ > 10 GeV. In order to find the non-leptonic remnant "core" of the subjet, we need a more sophisticated algorithm.
In order to reconstruct the boosted subjet we first cluster the jet using the anti-k T algorithm with a R = 0.4. We then search for the core (generally the charm hadron remnant) by reclustering the muon and calorimeter towers with total jet energy fraction f min tower > 0.05 using a smaller R core = 0.04. We assume m core = 2 GeV (a typical charm hadron mass), and identify the "correct" core as the one which comes closest to p 2 subjet = 5.3 GeV. Since mismeasurements smear out the reconstructed energy of the subjet, if m subjet > 12 GeV we constrain the subjet mass to be 12 GeV. The parameters of the μ x tag are summarized in Table 1.  In spite of its non-trivial reconstruction, x is effectively a dynamic angular cut on the muon. Defining ξ, the lab frame angle between the muon and the core, it is possible to calculate ξ max , the maximum μ-to-core angle which produces x ≤ 3. For "soft" muons (E μ E core /18), this angular cut is relatively tight Once the muons become "hard" (E μ ≥ E core /18), the cut loosens significantly While the transition between these limits depends explicitly on the muon's p T , this dependence is small until just below the hard threshold. Thus, not only is x a smart angular cut -scaling with the energy of the core -it is a dual angular cut; tight for soft muons, looser for hard muons, and sensitive to the p T resolution of the muon system only within the narrow transition region. The separation of reconstructed b jets from light-quark-initiated jets can be seen in Fig. 2. Bottom jets (b-quarks hadronized as B hadrons) above 500 GeV produce large f subjet and x ∼ 0.8. Light jets (mostly π and K) produce either incompatible values of x > 3, or random subjet recombinations that lead to small f subjet . A small fraction of b jets is not well-reconstructed (represented by the lowf subjet tail), but it has little effect on the total efficiency. We extract the standalone μ x tagging efficiencies using PYTHIA 8.210 [4,5] fed into an ATLASlike version of DELPHES 3.2 [1], and a custom μ x tagging module MuXboostedBTagging (available on GitHub [6]). In Fig. 3 we show separate efficiencies as a function of p T and η for bottom jets, charm jets, light-light jets (where the muon came from a light-flavor hadron), and light-heavy jets (where a gluon split to bb/cc -producing heavy-flavor hadrons in the final state). The kinematic nature of the tagging variables leads to fairly flat efficiencies in pseudorapidity, and when p T > 500 GeV. The exception is the η distribution for B hadrons from gluon splitting. This leads to the intriguing possibility that the g → bb contribution to jets in the Monte Carlo could be calibrated using the rapidity dependence of these highly-boosted jets.

A search for leptophobic Z → bb
Very massive Z bosons are expected to exist in many BSM models. We test the μ x boosted-bottom tag by examining the reach at a 13 TeV LHC for a leptophobic Z decaying to bb or cc. For this study we choose a U(1) B Lagrange density with a flavor-independent coupling to quarks [7,8].
We simulate the signal and backgrounds using a MLM-matched MadEvent sample [9] and CT14llo PDFs [10] fed through PYTHIA into DELPHES. In addition to demanding one or two μ x tags (as defined in Sec. 2), we require |η j | < 2.7, and Δη j j < 1.5. We reconstruct a dijet mass out of the two leading-p T jets, and look for a resonance in the mass window [0.85, 1.25] × M Z B .
The results for 5σ discovery of this leptophobic Z are shown in Fig. 4 for a two-tag, and onetag inclusive sample, compared to current exclusion limits from Ref. [7]. In 100 fb −1 of integrated luminosity at 13 TeV, a two b-tag analysis could discover a Z of 3 TeV if the universal coupling g B ∼ 2.5. For this particular model, the single-tag inclusive search would be more effectiveallowing for discovery up to nearly 1 TeV above current mass limits. Should a discovery not be made, the two-tag search (not shown) would set a 95% C.L. exclusion comparable to the one-tag discovery reach; while the one-tag search would set a 95% C.L. exclusion that can access g B couplings a factor of 2 smaller than current limits, and masses up to 2 TeV higher.

Conclusions
In this paper we discuss the new μ x boosted-bottom-jet tag. Combining angular information x from B hadron decay with jet substructure f subjet in TeV-scale jets allows for tagging efficiencies of b = 14%, c = 6.5%, light−light = 0.1%, and light−heavy = 0.5%, respectively. The results here focused on ATLAS because their standalone non-isolated muon tagging efficiency is publicly available. We expect that if CMS has similar non-isolated muon tagging capability this tag will be just as effective, since it is kinematically driven and not sensitive to fine details of the detector.
When applying the μ x tag to a search for leptophobic Z bosons, we find that the reach for discovery at a 13 TeV LHC is about 1 TeV higher than current limits. If a Z is not found, 95% C.L.  . 5σ discovery reach for a leptophobic Z with universal coupling in the with one or two boosted-b tags at a 13 TeV LHC compared to exclusion limits from Ref. [7]. Also shown is the 95% C.L. exclusion reach of the one-tag analysis.
exclusion limits can be set up to 2 TeV higher, or for g B couplings a factor of 2 smaller, than the current limits. In addition to Z → bb, the μ x tag should be of immediate use in the search for W → tb in the boosted-top and boosted-bottom channel [11] conducted by the ATLAS Collaboration [2].