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Improving Identification of Dijet Resonances at Hadron Colliders 1
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Eder Izaguirre, Brian Shuve, ’ and Itay Yavin ’ 1Perimeter Institute fo r Theoretical Physics, Waterloo, Ontario, N2L 2Y5 Canada 2Department o f Physics, McMaster University, Hamilton, Ontario, L8S 4L8 Canada (Received 1 August 2014; published 30 January 2015) The experimental detection of resonances has played a vital role in the development of subatomic physics. The overwhelming multijet backgrounds at the Large Hadron Collider (LHC) necessitate the invention of new techniques to identify resonances decaying into a pair of partons. In this Letter we introduce an observable that achieves a significant improvement in several key measurements at the LHC: the Higgs boson decay to a pair of b quarks; W±/Z ° vector-boson hadronic decay; and extensions of the standard model (SM) with a new hadronic resonance. Measuring the Higgs decay to b quarks is a central test of the fermion mass generation mechanism in the SM, whereas the W±/ Z Q production rates are important observables of the electroweak sector. Our technique is effective in large parts of phase space where the resonance is mildly boosted and is particularly well suited for experimental searches dominated by systematic uncertainties, which is true of many analyses in the high-luminosity running of the LHC. DOI: 10.1103/PhysRevLett. 114.041802
PACS numbers: 13.85.Rm, 13.87.Ce, 14.70.Pw, 14.80.Bn
Introduction.—Hadron colliders open a direct observa tional w indow on physics at the shortest distance scales. Indeed, the heaviest fundam ental particles in the standard model (SM), the top quark and the Higgs boson, were discovered at the Tevatron and LHC, respectively [1-4]. However, hadronic collisions also give rise to large rates for jet-rich processes from quantum chrom odynam ics (QCD), which can m im ic those o f a non-Q CD origin, such as jets from the decays o f electrow eak gauge and H iggs bosons. As an alternative, m any o f the properties o f the SM bosons are typically m easured in final states with one or more leptons, at the expense of sm aller signal rates resulting from the subdom inant leptonic branching ratios o f the H , W ± , and Z°. In scenarios w here there is a discrepancy between experim ental results in fully leptonic channels and the SM predictions, or w here the signal rate is very small, it is im portant to consider hadronic decays o f electroweak bosons. M oreover, some theories beyond the SM (BSM) predict the existence o f new particles that decay entirely hadronically, such as supersym m etric theories with had ronic R-parity violation [5-8]. Any im provem ent in the discrim ination o f hadronic resonances from Q CD back grounds further maxim izes a hadron collider’s ability to perform precision SM m easurem ents and its potential to discover new resonances. There are several exam ples w hich motivate an im prove ment in the identification o f hadronic resonances. The m easurem ent o f the production cross section o f W W + W Z in the semileptonic channel can help shed light on the persistent discrepancy betw een theoretical predictions of the W W production cross section and experim ental results from the fully leptonic channel [9-13]. A nother example is the precision m easurem ent o f the H iggs boson decay rate into a pair o f b quarks, w hich is an essential test o f 0031 -9 0 0 7 /1 5 /1 1 4 (4 )/0 4 1802(5)
the Higgs m echanism for generating fermion masses. Moreover, m any theoretical extensions o f the SM predict new resonances which decay into electroweak bosons and/ or directly into hadrons. An im provem ent in the ratio o f signal to background rates is im portant since searches for hadronic final states are often lim ited by systematic uncertainties, particularly with high integrated luminosity. One region o f phase space where the kinematics o f the signal differs substantially from that o f the background is the boosted resonance regime where the decay products are collimated. They can then be grouped into a single jet w hose substructure is dramatically different from that of jets originating from QCD emission. Building on earlier work [14,15], this approach was successfully applied by Butterw orth et al. [16] for the im portant case o f the Higgs boson decaying into a pair o f b quarks. Their ButterworthD avison-Rubin-Salam (BDRS) m ethod relies on the fact that the m asses o f the two leading subjets originating from the b quarks tend to be m uch sm aller than the m ass o f the entire jet, w hich reconstructs the Higgs boson. This is in contrast with jets from QCD processes, where the mass of the je t arises from a sequence o f wide-angle emissions. Therefore, the “m ass drop” between the total jet mass and the subjet m asses provides a powerful discrim inant betw een boosted Higgs bosons and QCD jets. Subsequently, variants on this m ethod have been used to identify other boosted hadronically decaying objets, such as top quarks and W ± bosons [17-26]. W hile jet substructure tools are powerful for identifying boosted resonances, these techniques typically involve paying a large penalty in signal efficiency, since many SM and BSM processes produce hadronic resonances w ithout a substantial boost. W ith sm aller boost, partons from the resonance decay are no longer collim ated to the
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same degree and can only be grouped into a single jet if the radius parameter R of sequential jet clustering algorithms [27] is very large, since R oc mresonance/ p T. There can be several issues with this, among them the fact that con tamination from the underlying event and pileup grows with radius [28] and that defining new physics objects associated with the large-R jets requires a recalibration of detector response and other experimental effects (however, see Ref. [29]). In this Letter we propose an alternative approach to identifying hadronically decaying resonances which is not restricted to the highly boosted regime. It draws its efficacy by scaling the original mass drop with the separation between the two resolved jets, thus maintaining discrimi nating power over a wider range of dijet angular separation. Our technique involves only separately resolved jets whose properties and detector response have been well measured at the LHC, and does not require the calibration of new objects. We demonstrate the effectiveness of this new technique in identifying dijet resonances in a variety of processes, both in the SM as well as in its extensions. Earlier studies have also considered the possibility of combining resolved and boosted analyses [30]. New observable.—Consider the decay of a mildly boosted boson (V) into quarks, which are consequently well separated, and result in two resolved jets, j l and j 2. We can use the resolved jets to form the standard mass-drop variable, ( mj / m^ ) = max(m; i , mj2) / m l2, where m h is the mass of ji and m l2 is the invariant mass of the dijet system. This is a useful variable in jet substructure studies, but for well-separated jets, a major component of the background comes from a hard QCD splitting, giving rise to a mass drop that decreases as the separation increases. We there fore modify the conventional mass-drop criterion by con sidering cuts which become stricter as the separation of the jets increases, specifically imposing upper cuts on m l/ m n that scale with 1/AR12. We now give a heuristic argument for this form of cut by considering the relative typical scaling of signal and background. The mass of each individual jet arises from QCD radiation with average (m2-) = CasR2p \ / n in the small jet radius R limit through 0 ( a s), where p T is the jet’s transverse momentum and C is a color-dependent and jet-algorithm-dependent order-unity factor [31], Since R is fixed, and for mild boosts p T ~ mv/ 2, the individual jet mass for signal varies over only a limited range. On the other hand, the combined mass m12 should reconstruct the decaying V mass. By contrast, the background scaling can be very different. For example, consider W + jets proc esses, where the extra jets can arise from a hard splitting from a single parton. Since the dijets arise from a hard splitting, we expect the combined mass to scale as (m\2) — CasNR\2P j/n , where ARI2 is the separation between the individual jets and PT is the transverse momentum of the combined system. This relation will,
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of course, break down for very large AR12, but we expect it to still be useful in the intermediate region between a boosted dijet system (A R V2 < 0.4) and one where the two jets are back to back (AR12 ~ n). We thus expect the following approximate scaling for the mass-drop variable,
( 1) (2) where R is the jet radius used in defining the jets, often R «0.4. The above relations motivate the following observable,
C= — Ar u , m 12
(3)
and the following cut as a discriminant of a dijet resonance against background, C < Cc.
(4)
with Cc a parameter optimized in Monte Carlo studies. In what follows, we apply the cut, Eq. (4), to a variety of processes and find a consistent enhancement in signal over background S /B ~ 2-5. It comes at a price of a signal efficiency of 0 ( 10%-20%) and a small reduction in S/\[B . As such, it proves a powerful new tool to search for hadronic resonances in situations where the measurement is dominated by systematic uncertainties. We find that this observable significantly outperforms m ] / m ]2 and ARl2 individually (see Supplemental Material for comparison to other observables and demonstration of its robustness against MC effects and detector effects [32]). We note an alternative way of motivating the scaled mass-drop cut: if one holds m 12 fixed, the maximum virtuality 2max °f the signal partons is fixed to be (ml2/ 2)2, as can be seen in the rest frame of the resonance, while the background favors asymmetric splittings so that 2 max ~ m n- F°r fixed m12, asymmetric splittings only dominate for small AR12, while at larger AR12 the jet p T cuts make the background look signal-like with 2max~ (w 12/2 ) 2, which is why a scaled mass-drop cut is effective. While we have motivated a scaled mass-drop cut, the scaling with AR12 in Eq. (2) is only approximate. We study a generalization of the form,
i;(Rc) = — (AR12- R C),
(5)
m 12
with a similar cut as in Eq. (4). Here Rc is again some phenomenological parameter optimized in Monte Carlo simulations. This generalized cut retains a higher signal efficiency at the price of only a small reduction in S /B relative to Eq. (3).
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Our variable depends on the small mass of a resolved R — 0.4 jet which could be sensitive to pileup contamina tion. We have checked that pileup indeed affects the performance of our observable significantly; however, we have verified that trimming [33] with parameters optimized for small-radius jets can recover the original sensitivity to within 10%-20%. WW + WZ.—As our first example, we consider the measurement of the combined SM production cross section of WW -f WZ in the semileptonic channel, i.e., in p p -* jjdv, with the two jets reconstructing the W± or the Z°. This measurement is of particular importance given the persistent discrepancy between theory and observation in the WW cross section in the fully leptonic channel p p -*■ f v f i / [9-13], We follow the 7 TeV analysis presented by the CMS Collaboration in Ref. [34], where by far the largest back ground is W + jets. We simulated both background and signal events using madgraph 5 [35] and showering through pythia 6 [36], with matching of matrix elements to parton showers using the shower-kx scheme defined in Ref. [37]. Jets were then clustered using the anti-kT algorithm [38] with the fastjet package [39], and our simulations are in good agreement with the results of Ref. [34], At y/s = 13 TeV, we apply similar selection cuts as the CMS analysis but with the jet p T and E T cuts scaled up to 50 GeV. To quantify the gain obtained from an additional cut on £, in Fig. 1 we plot the dijet invariant mass distribution before and after the £ cut. We also show the improvement in S/ B in each dijet invariant mass bin. A gain in S/B of 3-4 is obtained with a cut of £ < 0.1 at the price of C7(10%) signal efficiency. This could improve the precision with which the WW + WZ cross section is measured at run II of the LHC at high luminosity. Higgs decay to bb.—The second example we consider is the very important SM process p p -» HW ± -> bbif u. This is a challenging rate to measure at the LHC and was the subject of the boosted analysis in Ref. [16], which inspired much subsequent work into jet substructure. We use it to demonstrate the utility of the shifted observable, Eq. (5), in maintaining a higher signal efficiency with a similar enhancement in S/B. We follow the existing analysis by ATLAS [40] done at 7 and 8 TeV and validate our simulations by applying the same event selection criteria. In what follows, we concen trate on the higher energy ran at 13 TeV and apply the same selection. Both background and signal were simulated as discussed above. For concreteness, we focus on the WH signal with two resolved ^-tagged jets and one lepton as outlined in the ATLAS analysis. We concentrate on the part of phase space where the vector-boson transverse momen tum is p j > 90 GeV, and the Higgs boson consequently has a modest boost. The dominant backgrounds after b tagging are top pair, W + jets, and diboson production. Figure 2 displays the ^-tagged dijet invariant mass
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0L................ ................. ................. .................
40
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FIG. 1 (color online). Top: Histograms of both the dominant W + jets background as well as signal before applying the cut on £, but after all of the selection criteria described in the text. Middle: The same distributions but after applying the £ cut. Bottom: Binned S/B improvement for £c = 0.08, 0.1, and 0.12. The corresponding signal efficiencies are approximately 3%, 10%, and 25%, respectively.
distributions for both background and signal at y/s = 13 TeV before and after applying the cut from Eq. (5), with £c — 0.11 and Rc = 0.2. The parameter £c is con sistent with the examples above, whereas the parameter Rc was chosen to yield an improvement in relative signal efficiency (~20%) while maintaining a similar increase in S/B of 3-4. The lower panes in Fig. 2 show the behavior of the relative signal efficiency and the efficiency ratio against the parameter Rc for various choices of £c. One generally obtains a larger efficiency with increased Rc and £c, at the price of a reduced gain in S/B. Importantly, it is possible to obtain an enhancement in S/ B without sacrificing S/s/~B. Even excluding the highly boosted region (p \ > 200 GeV), the cut on £ yields an enhancement of S/B of 2-3. In that respect, our method yields gains in regions of
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TABLE I. The ratio of signal to background efficiency gain for different values of 4 and the Z' mass. The signal efficiencies are in brackets.
1 lep., 2 jets,2 tags, p r > 9 0 GeV
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My = 600 GeV My = 800 GeV Mz, = 1000 GeV 4 = 0.09
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800 600 400 200
0
50
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150 Mbb(GeV)
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FIG. 2 (color online). In the upper two panels, we show the invariant mass of the ^-tagged jets before and after the cut, Eq. (5), for both signal and background. In the lower two panels, we show the relative signal efficiency as well as its ratio with background efficiency as a function of Rc in the mass window and the pT region indicated.
phase space complementary to that of BDRS, which targets highly boosted Higgs bosons. Searches that are limited by statistical uncertainties are difficult to improve upon with our method since S/y/B is typically not enhanced. The ATLAS H -* bb analysis [40], which combines the full 7 and 8 TeV data set, has only ~30 events in the region considered (two resolved ^-tagged jets, one lepton, and p \ > 90 GeV). However, the goal of such a search is to determine the Hbb coupling as precisely as possible, and with the accumulation of more data, statistics will be less of a concern and our method may prove useful once systematic uncertainties dominate. Z' -> WW and W' —>ZW searches.—The final example we consider is of BSM physics with a new heavy resonance decaying into two vector bosons which subsequently decay semileptonically, Z' -> WW -*• jjtfv or W' -* WZ jjfv. These two processes have similar kinematics and so we
4.5 (0.12) 2.9 (0.29) 2.0 (0.48)
4.9 (0.27) 3.1 (0.40) 2.0 (0.54)
3.4 (0.16) 2.2 (0.29) 1.6 (0.42)
focus on the former for concreteness. This example allows us to investigate the performance of the cut as the boost of the hadronic W varies with the Z' mass (the boost is ~ M y / 2 M w). We follow the 7 TeV ATLAS analysis of Ref. [41] and simulate both background and signal events as described above, concentrating on the dominant ft and W + jets backgrounds. We apply all cuts from the ATLAS diboson analysis. In Table I we show the ratio of signal to background efficiency gain for various values of 4 and the Z' mass. The efficiency is calculated in a window of within 10% of My . The improvement in sensitivity is significant because, for example, a mass point ( My — 800 GeV), which was only marginally excluded due to large (~30%) systematic uncertainties, can be thoroughly ruled out. Conclusions.—In this Letter, we introduced a new observable that improves the identification of resonances that decay to two resolved jets. It is the product of the massdrop variable known from jet substructure studies and the dijet separation AR12. Importantly, it uses only small-radius jets as employed by ATLAS and CMS, and a cut on this observable can be applied in a straightforward way to existing analyses without additional calibrations needed for large-radius clustering. We illustrated the efficacy of this observable and its generalization in enhancing S /B in important SM as well as BSM processes. The cut easily lends itself to optimization associated with the interplay between S /B enhancement and signal efficiency. Thus, it can be used in searches with different ratios of systematic to statistical uncertainties. Many more processes can benefit from this observable, and we leave to future study the elucidation of its utility. We thank David Miller, Max Swiatlowski, and Scott Thomas for helpful discussions. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET) and Compute/Calcul Canada. B. S. is supported in part by the Canadian Institute of Particle Physics. I. Y. is grateful to the Mainz Institute for Theoretical Physics (MITP) for its hospitality and support during the completion of this work. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
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[1] S. Abachi et al. (DO Collaboration), Phys. Rev. Lett. 74, 2632 (1995). [2] F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 74. 2626 (1995). [3] G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 716, 1 (2012). [4] S. Chatrchyan et a l (CMS Collaboration), Phys. Lett. B 716, 30 (2012). [5] S. Weinberg, Phys. Rev. D 26, 287 (1982). [6] N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982). [7] L. J. Hall and M. Suzuki, Nucl. Phys. B231, 419 (1984). [8] R. Barbier, C. Berat, M. Besancon, M. Chemtob, A. Deandrea et al., Phys. Rep. 420, 1 (2005). [9] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 87, 112001 (2013). [10] S. Chatrchyan et al. (CMS Collaboration), Eur. Phys. J. C 73, 2610 (2013). [11] D. Curtin, P. Jaiswal, P. Meade, and P.-J. Tien, J. High Energy Phys. 08 (2013) 068. [12] P. Meade, H. Ramani, and M. Zeng, Phys. Rev. D 90, 114006 (2014). [13] P. Jaiswal and T. Okui, Phys. Rev. D 90, 073009 (2014). [14] M .H . Seymour, Z. Phys. C 62, 127 (1994). [15] J. M. Butterworth, B. E. Cox, and J. R. Forshaw, Phys. Rev. D 65, 096014 (2002). [16] J.M . Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008). [17] D .E . Kaplan, K. Rehermann, M. D. Schwartz, and B. Tweedie, Phys. Rev. Lett. 101, 142001 (2008). [18] T. Plehn, G. P. Salam, and M. Spannowsky, Phys. Rev. Lett. 104, 111801 (2010). [19] S. D. Ellis, C. K. Vermilion, and J. R. Walsh, Phys. Rev. D 81, 094023 (2010). [20] J. Thaler and L.-T. Wang, J. High Energy Phys. 07 (2008) 092. [21] J. Thaler and K. Van Tilburg, J. High Energy Phys. 03 (2011) 015. [22] D. E. Soper and M. Spannowsky, Phys. Rev. D 84, 074002 ( 2011 ).
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[23] A. Hook, M. Jankowiak, and J. G. Wacker, J. High Energy Phys. 04 (2012) 007. [24] A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, J. High Energy Phys. 05 (2014) 146. [25] A. J. Larkoski, G. P. Salam, and J. Thaler, J. High Energy Phys. 06 (2013) 108. [26] M. Jankowiak and A. J. Larkoski, J. High Energy Phys. 06 (2011) 057. [27] G. P. Salam, Eur. Phys. J. C 67, 637 (2010). [28] G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 05 (2012) 128. [29] B. Nachman, P. Nef, A. Schwartzman, and M. Swiatlowski, arXiv: 1407.2922. [30] M. Gouzevitch, A. Oliveira, J. Rojo, R. Rosenfeld, G. P. Salam, and V. Sanz, J. High Energy Phys. 07 (2013) 148. [31] S. Ellis, J. Huston, K. Hatakeyama, P. Loch, and M. Tonnesmann, Prog. Part. Nucl. Phys. 60, 484 (2008). [32] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett. 114.041802 for more evidence in favour of the robustness of the observable C and its validation in Monte Carlo simulations. [33] D. Krohn, J. Thaler, and L.-T. Wang, J. High Energy Phys. 02 (2010) 084. [34] S. Chatrchyan et al. (CMS Collaboration), Eur. Phys. J. C 73, 2283 (2013). [35] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, J. High Energy Phys. 06 (2011) 128. [36] T. Sjostrand, S. Mrenna, and P. Z. Skands, J. High Energy Phys. 05 (2006) 026. [37] J. Alwall, S. de Visscher, and F. Maltoni, J. High Energy Phys. 02 (2009) 017. [38] M. Cacciari, G. P. Salam, and G. Soyez, J. High Energy Phys. 04 (2008) 063. [39] M. Cacciari, G. P. Salam, and G. Soyez, Eur. Phys. J. C 72, 1896 (2012). [40] G. Aad et al. (ATLAS Collaboration), Report No. ATLASCOM -CONF-2013-080, 2013. [41] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 87, 112006 (2013).
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Improving Identification of Dijet Resonances at Hadron Colliders 1
12
12
Eder Izaguirre, Brian Shuve, ’ and Itay Yavin ’ 1Perimeter Institute fo r Theoretical Physics, Waterloo, Ontario, N2L 2Y5 Canada 2Department o f Physics, McMaster University, Hamilton, Ontario, L8S 4L8 Canada (Received 1 August 2014; published 30 January 2015) The experimental detection of resonances has played a vital role in the development of subatomic physics. The overwhelming multijet backgrounds at the Large Hadron Collider (LHC) necessitate the invention of new techniques to identify resonances decaying into a pair of partons. In this Letter we introduce an observable that achieves a significant improvement in several key measurements at the LHC: the Higgs boson decay to a pair of b quarks; W±/Z ° vector-boson hadronic decay; and extensions of the standard model (SM) with a new hadronic resonance. Measuring the Higgs decay to b quarks is a central test of the fermion mass generation mechanism in the SM, whereas the W±/ Z Q production rates are important observables of the electroweak sector. Our technique is effective in large parts of phase space where the resonance is mildly boosted and is particularly well suited for experimental searches dominated by systematic uncertainties, which is true of many analyses in the high-luminosity running of the LHC. DOI: 10.1103/PhysRevLett. 114.041802
PACS numbers: 13.85.Rm, 13.87.Ce, 14.70.Pw, 14.80.Bn
Introduction.—Hadron colliders open a direct observa tional w indow on physics at the shortest distance scales. Indeed, the heaviest fundam ental particles in the standard model (SM), the top quark and the Higgs boson, were discovered at the Tevatron and LHC, respectively [1-4]. However, hadronic collisions also give rise to large rates for jet-rich processes from quantum chrom odynam ics (QCD), which can m im ic those o f a non-Q CD origin, such as jets from the decays o f electrow eak gauge and H iggs bosons. As an alternative, m any o f the properties o f the SM bosons are typically m easured in final states with one or more leptons, at the expense of sm aller signal rates resulting from the subdom inant leptonic branching ratios o f the H , W ± , and Z°. In scenarios w here there is a discrepancy between experim ental results in fully leptonic channels and the SM predictions, or w here the signal rate is very small, it is im portant to consider hadronic decays o f electroweak bosons. M oreover, some theories beyond the SM (BSM) predict the existence o f new particles that decay entirely hadronically, such as supersym m etric theories with had ronic R-parity violation [5-8]. Any im provem ent in the discrim ination o f hadronic resonances from Q CD back grounds further maxim izes a hadron collider’s ability to perform precision SM m easurem ents and its potential to discover new resonances. There are several exam ples w hich motivate an im prove ment in the identification o f hadronic resonances. The m easurem ent o f the production cross section o f W W + W Z in the semileptonic channel can help shed light on the persistent discrepancy betw een theoretical predictions of the W W production cross section and experim ental results from the fully leptonic channel [9-13]. A nother example is the precision m easurem ent o f the H iggs boson decay rate into a pair o f b quarks, w hich is an essential test o f 0031 -9 0 0 7 /1 5 /1 1 4 (4 )/0 4 1802(5)
the Higgs m echanism for generating fermion masses. Moreover, m any theoretical extensions o f the SM predict new resonances which decay into electroweak bosons and/ or directly into hadrons. An im provem ent in the ratio o f signal to background rates is im portant since searches for hadronic final states are often lim ited by systematic uncertainties, particularly with high integrated luminosity. One region o f phase space where the kinematics o f the signal differs substantially from that o f the background is the boosted resonance regime where the decay products are collimated. They can then be grouped into a single jet w hose substructure is dramatically different from that of jets originating from QCD emission. Building on earlier work [14,15], this approach was successfully applied by Butterw orth et al. [16] for the im portant case o f the Higgs boson decaying into a pair o f b quarks. Their ButterworthD avison-Rubin-Salam (BDRS) m ethod relies on the fact that the m asses o f the two leading subjets originating from the b quarks tend to be m uch sm aller than the m ass o f the entire jet, w hich reconstructs the Higgs boson. This is in contrast with jets from QCD processes, where the mass of the je t arises from a sequence o f wide-angle emissions. Therefore, the “m ass drop” between the total jet mass and the subjet m asses provides a powerful discrim inant betw een boosted Higgs bosons and QCD jets. Subsequently, variants on this m ethod have been used to identify other boosted hadronically decaying objets, such as top quarks and W ± bosons [17-26]. W hile jet substructure tools are powerful for identifying boosted resonances, these techniques typically involve paying a large penalty in signal efficiency, since many SM and BSM processes produce hadronic resonances w ithout a substantial boost. W ith sm aller boost, partons from the resonance decay are no longer collim ated to the
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same degree and can only be grouped into a single jet if the radius parameter R of sequential jet clustering algorithms [27] is very large, since R oc mresonance/ p T. There can be several issues with this, among them the fact that con tamination from the underlying event and pileup grows with radius [28] and that defining new physics objects associated with the large-R jets requires a recalibration of detector response and other experimental effects (however, see Ref. [29]). In this Letter we propose an alternative approach to identifying hadronically decaying resonances which is not restricted to the highly boosted regime. It draws its efficacy by scaling the original mass drop with the separation between the two resolved jets, thus maintaining discrimi nating power over a wider range of dijet angular separation. Our technique involves only separately resolved jets whose properties and detector response have been well measured at the LHC, and does not require the calibration of new objects. We demonstrate the effectiveness of this new technique in identifying dijet resonances in a variety of processes, both in the SM as well as in its extensions. Earlier studies have also considered the possibility of combining resolved and boosted analyses [30]. New observable.—Consider the decay of a mildly boosted boson (V) into quarks, which are consequently well separated, and result in two resolved jets, j l and j 2. We can use the resolved jets to form the standard mass-drop variable, ( mj / m^ ) = max(m; i , mj2) / m l2, where m h is the mass of ji and m l2 is the invariant mass of the dijet system. This is a useful variable in jet substructure studies, but for well-separated jets, a major component of the background comes from a hard QCD splitting, giving rise to a mass drop that decreases as the separation increases. We there fore modify the conventional mass-drop criterion by con sidering cuts which become stricter as the separation of the jets increases, specifically imposing upper cuts on m l/ m n that scale with 1/AR12. We now give a heuristic argument for this form of cut by considering the relative typical scaling of signal and background. The mass of each individual jet arises from QCD radiation with average (m2-) = CasR2p \ / n in the small jet radius R limit through 0 ( a s), where p T is the jet’s transverse momentum and C is a color-dependent and jet-algorithm-dependent order-unity factor [31], Since R is fixed, and for mild boosts p T ~ mv/ 2, the individual jet mass for signal varies over only a limited range. On the other hand, the combined mass m12 should reconstruct the decaying V mass. By contrast, the background scaling can be very different. For example, consider W + jets proc esses, where the extra jets can arise from a hard splitting from a single parton. Since the dijets arise from a hard splitting, we expect the combined mass to scale as (m\2) — CasNR\2P j/n , where ARI2 is the separation between the individual jets and PT is the transverse momentum of the combined system. This relation will,
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of course, break down for very large AR12, but we expect it to still be useful in the intermediate region between a boosted dijet system (A R V2 < 0.4) and one where the two jets are back to back (AR12 ~ n). We thus expect the following approximate scaling for the mass-drop variable,
( 1) (2) where R is the jet radius used in defining the jets, often R «0.4. The above relations motivate the following observable,
C= — Ar u , m 12
(3)
and the following cut as a discriminant of a dijet resonance against background, C < Cc.
(4)
with Cc a parameter optimized in Monte Carlo studies. In what follows, we apply the cut, Eq. (4), to a variety of processes and find a consistent enhancement in signal over background S /B ~ 2-5. It comes at a price of a signal efficiency of 0 ( 10%-20%) and a small reduction in S/\[B . As such, it proves a powerful new tool to search for hadronic resonances in situations where the measurement is dominated by systematic uncertainties. We find that this observable significantly outperforms m ] / m ]2 and ARl2 individually (see Supplemental Material for comparison to other observables and demonstration of its robustness against MC effects and detector effects [32]). We note an alternative way of motivating the scaled mass-drop cut: if one holds m 12 fixed, the maximum virtuality 2max °f the signal partons is fixed to be (ml2/ 2)2, as can be seen in the rest frame of the resonance, while the background favors asymmetric splittings so that 2 max ~ m n- F°r fixed m12, asymmetric splittings only dominate for small AR12, while at larger AR12 the jet p T cuts make the background look signal-like with 2max~ (w 12/2 ) 2, which is why a scaled mass-drop cut is effective. While we have motivated a scaled mass-drop cut, the scaling with AR12 in Eq. (2) is only approximate. We study a generalization of the form,
i;(Rc) = — (AR12- R C),
(5)
m 12
with a similar cut as in Eq. (4). Here Rc is again some phenomenological parameter optimized in Monte Carlo simulations. This generalized cut retains a higher signal efficiency at the price of only a small reduction in S /B relative to Eq. (3).
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Our variable depends on the small mass of a resolved R — 0.4 jet which could be sensitive to pileup contamina tion. We have checked that pileup indeed affects the performance of our observable significantly; however, we have verified that trimming [33] with parameters optimized for small-radius jets can recover the original sensitivity to within 10%-20%. WW + WZ.—As our first example, we consider the measurement of the combined SM production cross section of WW -f WZ in the semileptonic channel, i.e., in p p -* jjdv, with the two jets reconstructing the W± or the Z°. This measurement is of particular importance given the persistent discrepancy between theory and observation in the WW cross section in the fully leptonic channel p p -*■ f v f i / [9-13], We follow the 7 TeV analysis presented by the CMS Collaboration in Ref. [34], where by far the largest back ground is W + jets. We simulated both background and signal events using madgraph 5 [35] and showering through pythia 6 [36], with matching of matrix elements to parton showers using the shower-kx scheme defined in Ref. [37]. Jets were then clustered using the anti-kT algorithm [38] with the fastjet package [39], and our simulations are in good agreement with the results of Ref. [34], At y/s = 13 TeV, we apply similar selection cuts as the CMS analysis but with the jet p T and E T cuts scaled up to 50 GeV. To quantify the gain obtained from an additional cut on £, in Fig. 1 we plot the dijet invariant mass distribution before and after the £ cut. We also show the improvement in S/ B in each dijet invariant mass bin. A gain in S/B of 3-4 is obtained with a cut of £ < 0.1 at the price of C7(10%) signal efficiency. This could improve the precision with which the WW + WZ cross section is measured at run II of the LHC at high luminosity. Higgs decay to bb.—The second example we consider is the very important SM process p p -» HW ± -> bbif u. This is a challenging rate to measure at the LHC and was the subject of the boosted analysis in Ref. [16], which inspired much subsequent work into jet substructure. We use it to demonstrate the utility of the shifted observable, Eq. (5), in maintaining a higher signal efficiency with a similar enhancement in S/B. We follow the existing analysis by ATLAS [40] done at 7 and 8 TeV and validate our simulations by applying the same event selection criteria. In what follows, we concen trate on the higher energy ran at 13 TeV and apply the same selection. Both background and signal were simulated as discussed above. For concreteness, we focus on the WH signal with two resolved ^-tagged jets and one lepton as outlined in the ATLAS analysis. We concentrate on the part of phase space where the vector-boson transverse momen tum is p j > 90 GeV, and the Higgs boson consequently has a modest boost. The dominant backgrounds after b tagging are top pair, W + jets, and diboson production. Figure 2 displays the ^-tagged dijet invariant mass
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0L................ ................. ................. .................
40
60
80 Mjj(GeV)
100
120
FIG. 1 (color online). Top: Histograms of both the dominant W + jets background as well as signal before applying the cut on £, but after all of the selection criteria described in the text. Middle: The same distributions but after applying the £ cut. Bottom: Binned S/B improvement for £c = 0.08, 0.1, and 0.12. The corresponding signal efficiencies are approximately 3%, 10%, and 25%, respectively.
distributions for both background and signal at y/s = 13 TeV before and after applying the cut from Eq. (5), with £c — 0.11 and Rc = 0.2. The parameter £c is con sistent with the examples above, whereas the parameter Rc was chosen to yield an improvement in relative signal efficiency (~20%) while maintaining a similar increase in S/B of 3-4. The lower panes in Fig. 2 show the behavior of the relative signal efficiency and the efficiency ratio against the parameter Rc for various choices of £c. One generally obtains a larger efficiency with increased Rc and £c, at the price of a reduced gain in S/B. Importantly, it is possible to obtain an enhancement in S/ B without sacrificing S/s/~B. Even excluding the highly boosted region (p \ > 200 GeV), the cut on £ yields an enhancement of S/B of 2-3. In that respect, our method yields gains in regions of
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a u
V 7= 13T eV /L dt= 300fb-i
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TABLE I. The ratio of signal to background efficiency gain for different values of 4 and the Z' mass. The signal efficiencies are in brackets.
1 lep., 2 jets,2 tags, p r > 9 0 GeV
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WH(bb)
My = 600 GeV My = 800 GeV Mz, = 1000 GeV 4 = 0.09
2000
4 = o.n
1000
4 = 0.13
1 lep., 2 jets,2 tags, p Tv >90 GeV 4=0.11, Rc=0.2
800 600 400 200
0
50
100
150 Mbb(GeV)
200
250
FIG. 2 (color online). In the upper two panels, we show the invariant mass of the ^-tagged jets before and after the cut, Eq. (5), for both signal and background. In the lower two panels, we show the relative signal efficiency as well as its ratio with background efficiency as a function of Rc in the mass window and the pT region indicated.
phase space complementary to that of BDRS, which targets highly boosted Higgs bosons. Searches that are limited by statistical uncertainties are difficult to improve upon with our method since S/y/B is typically not enhanced. The ATLAS H -* bb analysis [40], which combines the full 7 and 8 TeV data set, has only ~30 events in the region considered (two resolved ^-tagged jets, one lepton, and p \ > 90 GeV). However, the goal of such a search is to determine the Hbb coupling as precisely as possible, and with the accumulation of more data, statistics will be less of a concern and our method may prove useful once systematic uncertainties dominate. Z' -> WW and W' —>ZW searches.—The final example we consider is of BSM physics with a new heavy resonance decaying into two vector bosons which subsequently decay semileptonically, Z' -> WW -*• jjtfv or W' -* WZ jjfv. These two processes have similar kinematics and so we
4.5 (0.12) 2.9 (0.29) 2.0 (0.48)
4.9 (0.27) 3.1 (0.40) 2.0 (0.54)
3.4 (0.16) 2.2 (0.29) 1.6 (0.42)
focus on the former for concreteness. This example allows us to investigate the performance of the cut as the boost of the hadronic W varies with the Z' mass (the boost is ~ M y / 2 M w). We follow the 7 TeV ATLAS analysis of Ref. [41] and simulate both background and signal events as described above, concentrating on the dominant ft and W + jets backgrounds. We apply all cuts from the ATLAS diboson analysis. In Table I we show the ratio of signal to background efficiency gain for various values of 4 and the Z' mass. The efficiency is calculated in a window of within 10% of My . The improvement in sensitivity is significant because, for example, a mass point ( My — 800 GeV), which was only marginally excluded due to large (~30%) systematic uncertainties, can be thoroughly ruled out. Conclusions.—In this Letter, we introduced a new observable that improves the identification of resonances that decay to two resolved jets. It is the product of the massdrop variable known from jet substructure studies and the dijet separation AR12. Importantly, it uses only small-radius jets as employed by ATLAS and CMS, and a cut on this observable can be applied in a straightforward way to existing analyses without additional calibrations needed for large-radius clustering. We illustrated the efficacy of this observable and its generalization in enhancing S /B in important SM as well as BSM processes. The cut easily lends itself to optimization associated with the interplay between S /B enhancement and signal efficiency. Thus, it can be used in searches with different ratios of systematic to statistical uncertainties. Many more processes can benefit from this observable, and we leave to future study the elucidation of its utility. We thank David Miller, Max Swiatlowski, and Scott Thomas for helpful discussions. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET) and Compute/Calcul Canada. B. S. is supported in part by the Canadian Institute of Particle Physics. I. Y. is grateful to the Mainz Institute for Theoretical Physics (MITP) for its hospitality and support during the completion of this work. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
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[1] S. Abachi et al. (DO Collaboration), Phys. Rev. Lett. 74, 2632 (1995). [2] F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 74. 2626 (1995). [3] G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 716, 1 (2012). [4] S. Chatrchyan et a l (CMS Collaboration), Phys. Lett. B 716, 30 (2012). [5] S. Weinberg, Phys. Rev. D 26, 287 (1982). [6] N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982). [7] L. J. Hall and M. Suzuki, Nucl. Phys. B231, 419 (1984). [8] R. Barbier, C. Berat, M. Besancon, M. Chemtob, A. Deandrea et al., Phys. Rep. 420, 1 (2005). [9] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 87, 112001 (2013). [10] S. Chatrchyan et al. (CMS Collaboration), Eur. Phys. J. C 73, 2610 (2013). [11] D. Curtin, P. Jaiswal, P. Meade, and P.-J. Tien, J. High Energy Phys. 08 (2013) 068. [12] P. Meade, H. Ramani, and M. Zeng, Phys. Rev. D 90, 114006 (2014). [13] P. Jaiswal and T. Okui, Phys. Rev. D 90, 073009 (2014). [14] M .H . Seymour, Z. Phys. C 62, 127 (1994). [15] J. M. Butterworth, B. E. Cox, and J. R. Forshaw, Phys. Rev. D 65, 096014 (2002). [16] J.M . Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008). [17] D .E . Kaplan, K. Rehermann, M. D. Schwartz, and B. Tweedie, Phys. Rev. Lett. 101, 142001 (2008). [18] T. Plehn, G. P. Salam, and M. Spannowsky, Phys. Rev. Lett. 104, 111801 (2010). [19] S. D. Ellis, C. K. Vermilion, and J. R. Walsh, Phys. Rev. D 81, 094023 (2010). [20] J. Thaler and L.-T. Wang, J. High Energy Phys. 07 (2008) 092. [21] J. Thaler and K. Van Tilburg, J. High Energy Phys. 03 (2011) 015. [22] D. E. Soper and M. Spannowsky, Phys. Rev. D 84, 074002 ( 2011 ).
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week ending 30 JANUARY 2015
[23] A. Hook, M. Jankowiak, and J. G. Wacker, J. High Energy Phys. 04 (2012) 007. [24] A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, J. High Energy Phys. 05 (2014) 146. [25] A. J. Larkoski, G. P. Salam, and J. Thaler, J. High Energy Phys. 06 (2013) 108. [26] M. Jankowiak and A. J. Larkoski, J. High Energy Phys. 06 (2011) 057. [27] G. P. Salam, Eur. Phys. J. C 67, 637 (2010). [28] G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 05 (2012) 128. [29] B. Nachman, P. Nef, A. Schwartzman, and M. Swiatlowski, arXiv: 1407.2922. [30] M. Gouzevitch, A. Oliveira, J. Rojo, R. Rosenfeld, G. P. Salam, and V. Sanz, J. High Energy Phys. 07 (2013) 148. [31] S. Ellis, J. Huston, K. Hatakeyama, P. Loch, and M. Tonnesmann, Prog. Part. Nucl. Phys. 60, 484 (2008). [32] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett. 114.041802 for more evidence in favour of the robustness of the observable C and its validation in Monte Carlo simulations. [33] D. Krohn, J. Thaler, and L.-T. Wang, J. High Energy Phys. 02 (2010) 084. [34] S. Chatrchyan et al. (CMS Collaboration), Eur. Phys. J. C 73, 2283 (2013). [35] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, J. High Energy Phys. 06 (2011) 128. [36] T. Sjostrand, S. Mrenna, and P. Z. Skands, J. High Energy Phys. 05 (2006) 026. [37] J. Alwall, S. de Visscher, and F. Maltoni, J. High Energy Phys. 02 (2009) 017. [38] M. Cacciari, G. P. Salam, and G. Soyez, J. High Energy Phys. 04 (2008) 063. [39] M. Cacciari, G. P. Salam, and G. Soyez, Eur. Phys. J. C 72, 1896 (2012). [40] G. Aad et al. (ATLAS Collaboration), Report No. ATLASCOM -CONF-2013-080, 2013. [41] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 87, 112006 (2013).
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