The Forward-Backward Asymmetry (AFB) in $Z^\prime$ physics is commonly only
perceived as the observable which possibly allows one to interpret a $Z^\prime$
signal by distinguishing different models of such (heavy) spin-1 bosons. In
this article, we examine the potential of AFB in setting bounds on or even
discovering a $Z^\prime$ at the Large Hadron Collider (LHC) and show that it
might be a powerful tool for this purpose. We analyze two different scenarios:
$Z^\prime$s with a narrow and wide width, respectively. We find that in both
cases AFB can complement the cross section in accessing $Z^\prime$ signals.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0267

Accomando, E.

Belyaev, A.

Fiaschi, J.

Mimasu, K.

Moretti, S.

Shepherd-Themistocleous, C.

English

arXiv

The Forward-Backward Asymmetry (AFB) in $Z^\prime$ physics is commonly only perceived as the observable which possibly allows one to interpret a $Z^\prime$ signal by distinguishing different models of such (heavy) spin-1 bosons. In this article, we examine the potential of AFB in setting bounds on or even discovering a $Z^\prime$ at the Large Hadron Collider (LHC) and show that it might be a powerful tool for this purpose. We analyze two different scenarios: $Z^\prime$s with a narrow and wide width, respectively. We find that in both cases AFB can complement the cross section in accessing $Z^\prime$ signals

Accomando, Elena

Belyaev, Alexander

Fiaschi, Juri

Mimasu, Ken

Moretti, Stefano

Shepherd-Themistocleous, Claire

Southampton (e-Prints Soton)

A<sub>FB</sub> as a discovery tool for Z' bosons at the LHC

The Forward-Backward Asymmetry (AFB) in Z physics is commonly only perceived as the observable which possibly allows one to interpret a

Z signal by distinguishing different models of such (heavy) spin-1 bosons. In this

article, we examine the potential of AFB in setting bounds on or even discovering

a Z at the Large Hadron Collider (LHC) and show that it might be a powerful

tool for this purpose. We analyze two different scenarios: Z

s with a narrow and

wide width, respectively. We find that in both cases AFB can complement the cross

section in accessing Z signals

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2015-15153-7Colloquia: LaThuile15IL NUOVO CIMENTO 38 C (2015) 153AFB as a discovery tool for Z′ bosons at the LHCE. Accomando(1), A. Belyaev(1), J. Fiaschi(1)(∗), K. Mimasu(2), S. Moretti(1)and C. Shepherd-Themistocleous(3)(1) School of Physics and Astronomy, University of SouthamptonHighfield, Southampton, SO17 1BJ, UK(2) School of Physics and Astronomy, University of Sussex, FalmerBrighton, BN1 9RH, UK(3) Particle Physics Department, STFC, Rutherford Appleton LaboratoryHarwell Science and Innovation Campus - Didcot, Oxfordshire, OX11 0QX, UKreceived 2 October 2015Summary. — The Forward-Backward Asymmetry (AFB) in Z′ physics is com-monly only perceived as the observable which possibly allows one to interpret aZ′ signal by distinguishing different models of such (heavy) spin-1 bosons. In thisarticle, we examine the potential of AFB in setting bounds on or even discoveringa Z′ at the Large Hadron Collider (LHC) and show that it might be a powerfultool for this purpose. We analyze two different scenarios: Z′s with a narrow andwide width, respectively. We find that in both cases AFB can complement the crosssection in accessing Z′ signals.PACS 12.60.Cn – Extensions of electroweak gauge sector.1. – IntroductionExtra gauge bosons are present in many Beyond Standard Model (BSM) theories.From a phenomenological point of view, the simplest case is an extra U(1) symmetrygroup in addition to the SM group. Using this approach we can study the three mainclasses of models that predict a Z ′: E6, Generalized Left-Right (GLR) symmetric andGeneralized Standard Model (GSM) [1]. All these scenarios predict rather narrow Z ′s(ΓZ′/MZ′ ∼ 0.5− 12%).Experimental searches optimized for such narrow resonances assume a very visiblepeak with a Breit-Wigner line-shape over the SM background, when looking at the invari-ant mass of the Z ′ decay products. On the basis of this assumption, the 95% ConfidenceLevel (C.L.) upper bound on the cross section is derived and limits on the mass of theresonance are extracted within the above benchmark models. Theoretical cross sectionpredictions are usually calculated in Narrow Width Approximation (NWA), or possiblythey might include Finite Width (FW) and interference effect. These can be taken into(∗) E-mail: Juri.Fiaschi@soton.ac.ukCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 E. ACCOMANDO et al.account in a model independent way, putting an appropriate cut on in the invariant massspectrum [2].However, there exist many scenarios where the NWA is not valid. Technicolor [3],Composite Higgs Models [4], scenarios where the Z ′ couples differently to the first twofermion generations with respect to the third one [5, 6] or where the new gauge sectormixes with the SM neutral one [7] are all frameworks where wide Z ′s are possible. Here,the ratio ΓZ′/MZ′ can reach the 50% value or more.Experimental searches studying these “effectively” non-resonant cases are essentiallycounting experiments: any integration over the overall invariant mass spectrum beyondthe control region seeks an excess of events spread over the SM background. The analysis,even if improved using optimized kinematical cuts, still maintains some fragile aspectsas it relies on the good understanding of the SM background. Indeed the BSM signalmight not trivially interfere with the latter, affecting the Z ′ decay product invariantmass distribution also in the low mass region. For this reason the detection of a wideresonance turns out to be quite problematic.In this article we study the effects of the inclusion of another observable into theanalysis of heavy neutral resonances: the Forward-Backward Asymmetry (AFB). Weexplore the complementary potential of AFB with respect to the “bump” or “countingexperiment” searches in both the narrow and broad Z ′ framework, respectively. Notethat, in current literature, this observable is usually adopted as a post-discovery toolto interpret the experimental evidence of a peaked signal and to possibly disentanglebetween different theoretical models that would predict it. Our purpose is to show thatAFB can be used not only for interpreting a possible discovery but also in the very samesearch process. We focus on the Z ′ discovery golden channel search at the LHC, i.e., theDrell-Yan (DY) process pp → l+l− with l = e, μ.The article is organized as follows. In sect. 2 we derive current and projected boundsfor Z ′ model benchmarks for the LHC at 7, 8 and 13TeV. In sect. 3 we discuss therole of AFB in the context of either narrow or wide resonance searches. In sect. 4 wesummarize and conclude.2. – Bounds on the Z′ massIn order to validate our analysis we reproduced current experimental limits obtainedby, e.g., the CMS collaboration after the 7 and 8TeV runs with about 20 fb−1 ofluminosity, assuming the NWA [8]. These limits are computed through the ratioRσ = σ(pp → Z ′ → l+l−)/σ(pp → Z, γ → l+l−). Rσ has been calculated at theNext-to-Next-to-Leading Order (NNLO) in QCD using the WZPROD program [9-11](which we have adapted for Z ′ models [1] and the CTEQ6.6 package [12]).The resulting exclusion limits we compute include FW and interference effects. Thevalues we obtain are summarized in table I: they match the reported limits by CMS forthe benchmark models GSM-SSM and E6 − χ within the accuracy of 1–2% (except forthe Q model which predicts a slightly wider resonance and thus the discrepancy with theCMS results is around 5%).It is worth stressing that, in the context of narrow resonance searches, CMS adopteda dedicated cut on the invariant mass of the dilepton pairs: |Mll¯ −MZ′ | ≤ 0.05× ELHCwhere ELHC is the collider energy. This cut was designed so that the error in neglectingthe (model-dependent) FW and interference effects (between γ, Z, Z ′) are kept belowO(10%) for all models and the full range of allowed Z ′ masses under study, thus followingthe recommendations of [2].AFB AS A DISCOVERY TOOL FOR Z′ BOSONS AT THE LHC 3Table I. – Bounds on the Z′ mass derived from the latest direct searches performed by CMS atthe 7 and 8TeV LHC with integrated luminosity L = 20 fb−1.Class E6U ′(1) Models χ φ η S I NMZ′ [GeV] 2700 2560 2620 2640 2600 2570Class GLR GSMU ′(1) Models R B − L LR Y SSM T3L QMZ′ [GeV] 3040 2950 2765 3260 2900 3135 3720Table II. – Projection of discovery limits (first row) and exclusion limits (second row) on theZ′ mass from direct searches at the forthcoming Run II of the LHC at 13TeV. We assumeL = 300 fb−1.Class E6U ′(1) Models χ φ η S I NMZ′ [GeV] 4535 4270 4385 4405 4325 4290MZ′ [GeV] 5330 5150 5275 5150 5055 5125Class GLR GSMU ′(1) Models R B − L LR Y SSM T3L QMZ′ [GeV] 5175 5005 4655 5585 4950 5340 6360MZ′ [GeV] 6020 5855 5495 6435 5750 6180 8835After having verified the reliability of our code, we have been able to project futurediscovery and exclusion limits for the next run of the LHC at 13TeV and with a lumi-nosity of 300 fb−1. In both cases we have taken into account the published acceptance ×efficiency corrections and a Poisson statistic approach has been used for computing thesignificance of the signal. Requiring for the latter a significance of 2 for exclusion and 5for discovery, we obtain the results summarized in table II.3. – The role of AFB in Z′ searches: narrow and wide heavy resonancesWe define AFB as follows:(1)dσd cos θ∗l∝∑spin,col∣∣∣∣∣∑iMi∣∣∣∣∣2=sˆ23∑i,j|P ∗i Pj |[(1 + cos2 θ∗l )CijS + 2 cos θ∗l CijA ],where θ∗l is the lepton angle with respect to the quark direction in the dilepton Centre-of-Mass (CM) frame, which can be derived from the measured four-momenta of the dileptonsystem in the laboratory frame. The AFB is indeed given by the coefficient of the con-tribution to the angular distribution linear in cos θ∗l . In eq. (1),√sˆ is the invariant massof the dilepton system and Pi and Pj are the propagators of the gauge bosons involvedin the process. At the tree-level, DY production of charged lepton pairs is mediated by4 E. ACCOMANDO et al.(a) (b)(c) (d)Fig. 1. – (a) Hypothetic signal in the cross section distribution produced by a Z′ with massMZ′ = 3TeV, as predicted by the E6-I model, at the LHC at√s = 13TeV. (b) Hypotheticsignal in the A∗FB distribution produced by a Z′ with mass MZ′ = 3TeV, as predicted by theE6-I model, at the LHC at√s = 13TeV. No cut on the dilepton rapidity is imposed: |yll¯| ≥ 0.(c) Same as plot (a) within the GLR-LR model. (d) Same as plot (b) within the GLR-LR model.three gauge bosons: the SM photon and Z-boson and the hypothetical Z ′. These threevector boson exchanges all participate in the matrix element squared. The interferencesamongst these three particles have to be take into account properly. Finally, the factorsCijS and CijA in the angular distribution given in eq. (1) are the parity symmetric andanti-symmetric coefficients which are functions of the chiral quark and lepton couplings,qiL/R and eiL/R, to the i-boson with i = {γ, Z, Z ′}:CijS = (qiLqjL + qiRqjR)(eiLejL + eiRejR),(2)CijA = (qiLqjL − qiRqjR)(eiLejL − eiRejR).(3)Looking at these expressions it is clear that the analysis of AFB can give us comple-mentary informations with respect to the cross section distribution (which is proportionalto the sum of the squared chilar couplings) about the couplings between the Z ′ and thefermions. This feature has motivated several authors to study the potential of AFB ininterpreting a possible Z ′ discovery obtained in the usual cross section hunt as, e.g., inrefs. [13-16].AFB AS A DISCOVERY TOOL FOR Z′ BOSONS AT THE LHC 5The AFB is obtained by integrating the lepton angular distribution forward andbackward with respect to the quark direction. As in pp collisions the original quarkdirection is not known, one has to extract it from the kinematics of the dilepton system.In this analysis, we follow the criteria of ref. [17] and simulate the quark direction fromthe boost of the dilepton system with respect to the beam axis (z-axis). This strategy ismotivated by the fact that at the LHC the dilepton events at high invariant mass comefrom the annihilation of either valence quarks with sea antiquarks or sea quarks with seaantiquarks. As the valence quarks carry away, on average, a much larger fraction of theproton momentum than the sea antiquarks, the boost direction of the dilepton systemshould give a good approximation of the quark direction. A leptonic forward-backwardasymmetry can thus be expected with respect to the boost direction. In contrast, thesubleading number of dilepton events which originate from the annihilation of quark-antiquark pairs from the sea must be symmetric.As a measure of the boost, we define the dilepton rapidity yll¯ =12 ln[E+PzE−Pz], whereE and Pz are the energy and the longitudinal momentum of the dilepton system. Weidentify the quark direction through the sign of yll¯. In this way, one can define the“reconstructed” AFB, from now on called A∗FB . Namely, we have defined A∗FB usingthe θ∗l reconstructed angle, which is the angle between the final state lepton and theincoming quark direction in the CM of the dilepton system.In the following we are going to show the impact of AFB on the significance of thesignal. For this purpose we give the general definition of significance α for a genericobservable:(4) α =|O1 −O2|√δO21 + δO22.where the Ois (i = 1, 2) are the value of the observable in two hypothesis scenarios withuncertainty δOi. In the case of AFB we will use the statistical uncertainty:(5) δAFB =√4LσFσB(σF + σB)3=√(1−A2FB)σL =√(1−A2FB)N,where L is the integrated luminosity and N the total number of events. One can thussee that the significance is proportional to the root of the total number of events. Thismean that the imposition of a stringent cut on the boost variable, yll¯, in spite of guid-ing the AFB spectrum towards its true line shape, will decrease the statistics and, byconsequence, the resulting significance of the signal.With this background in mind we are going to show how AFB can be used also as apowerful tool to search for new physics.3.1. Narrow heavy resonances. – We start comparing the shape of the AFB distribu-tion as a function of the dilepton invariant mass√sˆ with the differential cross sectiondistribution. We are showing here two interesting cases: the E6-I (figs. 1(a) and (b)) andGLR-LR (figs. 1(c) and (d)) models.As one can see, the role played by the interference is extremely important (also whenreconstructed). In the E6-I case the AFB peak is heavily accentuated, while in theGLR-LR case the peak is shifted to a lower value in the invariant mass distribution. Incontrast, the cross section distribution is almost interference free if the |Mll¯ −MZ′ | ≤6 E. ACCOMANDO et al.(a) (b)Fig. 2. – (a) Binned significance of an hypothetic signal produced by a Z′ with massMZ′ = 3TeV, as predicted by the E6-I model, at the LHC at√s = 13TeV and L = 100 fb−1,in the three observables: cross section, AFB and A∗FB . (b) Same as (a) for the GLR-LR model.0.05 × ELHC cut is imposed. In interpreting the experimental data coming from AFBmeasurements instead it is mandatory to include the interference independently on anykinematical cut.In terms of significance of the AFB signal (fig. 2), we obtain that for the E6-I casethe peak leads to a significance which is comparable with what we get from the bumpin the cross section, even after reconstruction. Thus, it can be used as a very validalternative as the AFB observable is very reliable in terms of systematic uncertainties:since it comes from the ratio of scross sections, strong cancellations happen between theuncertainties on the forward and backward cross sections, upon taking into account theirmutual correlations. In the GLR-LR case instead the interference effects shift the AFBpeak to a lower invariant mass region, as mentioned above, which might lead to an earlyhint of the presence of new physics, i.e., even before the Z ′ pole is reached.3.2. Wide heavy resonances. – Here, we discuss the role of A∗FB in searches for a newZ ′ characterized by a large width. Such a heavy and wide particle is predicted by variousmodels. A benchmark scenario for experimental analyses is the wide version of the SSMdescribed in ref. [7]. The proposal is to have a heavy copy of the SM neutral gaugeboson Z, with same couplings to ordinary matter and SM gauge bosons. Owing to theZ ′ decay into SM charged gauge bosons, whose rate grows with the third power of theZ ′ mass, the total width of the new heavy particle can be quite large: ΓZ′/MZ′  50%and above.In this case, the invariant mass distribution of the two final state leptons does notshow in the cross section a resonant (or peaking) structure around the physical mass ofthe Z ′ standing sharply over a smooth background, but just a broad shoulder spreadover the SM background. This result is plotted in fig. 3(a), where we consider a Z ′ withmass MZ′ = 1.5TeV and width ΓZ′/MZ′ = 80%. The line shape of the resonance is notwell defined but the A∗FB observable could help to interpret a possible excess of eventsand it is shown in fig. 3(b). From the significance plots below one can see that the A∗FBshape could be visible at the 2σ level in a region where the significance from the crosssection is decreasing.AFB AS A DISCOVERY TOOL FOR Z′ BOSONS AT THE LHC 7(a) (b)Fig. 3. – (a) Binned differential cross section as a function of the dilepton invariant mass aspredicted by the GSM-SM model for a Z′ with mass MZ′ = 1.5TeV and ΓZ′/MZ′ = 80%.Error bars are included. The results are for the LHC at√s = 13TeV and L = 300 fb−1.Acceptance cuts are included (pT > 25GeV and yl < 2.5). (b) Same as plot (a) for the A∗FBdistribution.The experimental method based on the counting experiment is based on the assump-tion that the control region is new physics free. But, this is not the case for wide Z ′s. Inthese scenarios, the interference between the extra Z ′ and the SM γ, Z is so sizable that itcan invade the control region. If not correctly interpreted, these interference effects couldinduce one to underestimate the SM background with the consequence of overestimatingthe extracted mass bounds. Having all these uncertainties to deal with, the support of asecond observable like AFB is thus crucial for wide Z ′ searches.4. – ConclusionsIn this paper we have considered the scope of using AFB in Z ′ searches at the LHCin the neutral DY channel. Such a variable has traditionally been used for diagnosticpurposes in presence of a potential signal previously established through a standardresonance search via the cross section. However, based on the observation that it isaffected by systematics less than cross sections (being a ratio of the latter), we havestudied the possibility of using AFB as a search tool for a variety of Z ′ models, E6,GLR, GSM, embedding either a narrow or wide resonance. The focus was on determiningwhether such a resonance could be sufficiently wide and/or weakly coupled such that anormal resonance search may not fully identify it and, further, whether the AFB couldthen provide a signal of comparable or higher significance to complement or even surpassthe scope of more traditional analyses.We have found promising results. In the case of narrow width Z ′s, we have proventhat the significance of AFB based searches can be comparable with the usual bumpsearch. Further, we have emphasized the fact that the AFB distribution mapped indilepton invariant mass can present features amenable to experimental investigation notonly in the peak region but also significantly away from the latter. In the case of wideZ ′, the AFB search could have a better sensitivity than the cross section studies thanksto a more peculiar line-shape. In essence, here, AFB in specific regions of the invariantmass of the reconstructed Z ′ could be sensitive to broad resonances much more thanthe cross section, wherein the broad distribution of the signal seemingly merges with thebackground.8 E. ACCOMANDO et al.∗ ∗ ∗We are grateful to Patrik Svantesson for stimulating discussions. This work is sup-ported by the Science and Technology Facilities Council, grant number ST/L000296/1.All authors acknowledge partial financial support through the NExT Institute.REFERENCES[1] Accomando E., Belyaev A., Fedeli L., King Stephen F. and Shepherd-Themistocleous C., Phys. Rev. D, 83 (2011) 075012.[2] Accomando E., Becciolini D., Belyaev A., Moretti S. and Shepherd-Themistocleous C., JHEP, 1310 (2013) 153.[3] Belyaev A., Foadi R., Frandsen M. T., Jarvinen M., Sannino F. et al., Phys. Rev.D, 79 (2009) 035006.[4] Barducci D., Belyaev A., De Curtis S., Moretti S. and Pruna G. M., JHEP, 1304(2013) 152.[5] Kim Y. G. and Lee K. Y., Phys. Rev. D, 90 (2014) 117702.[6] Malkawi E. and Yuan C. P., Phys. Rev. D, 61 (2000) 015007.[7] Altarelli G., Mele B. and Ruiz-Altaba M., Z. Phys. C, 45 (1989) 109.[8] CMS Collaboration, arXiv:1412.6302 (2014).[9] Hamberg R., van Neerven W. L. and Matsuura T., Nucl. Phys. B, 359 (1991) 343–405.[10] van Neerven W. L. and Zijlstra E. B., Nucl. Phys. B, 382 (1992) 11–62.[11] Hamberg R., Matsuura T. and van Neerven W. L., ZWPROD program (1989–2002)http://www.lorentz.leidenuniv.nl/research/neerven/DECEASED/Welcome.html.[12] Kretzer S., Lai H. L., Olness F. I. and Tung W. K., Phys. Rev. D, 69 (2004) 114005.[13] Langacker P., Robinett R. W. and Rosner J. L., Phys. Rev. D, 30 (1984) 1470.[14] Carena M. S., Daleo A., Dobrescu B. A. and Tait T. M. P., Phys. Rev. D, 70 (2004)093009.[15] Petriello F. and Quackenbush S., Phys. Rev. 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AFB as a discovery tool for Z′ bosons at the LHC

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$A_{FB}$ as a discovery tool for $Z^\prime$ bosons at the LHC

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AFBA_{FB}AFB​ as a discovery tool for Z′Z^\primeZ′ bosons at the LHC

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$A_{FB}$ as a discovery tool for $Z^\prime$ bosons at the LHC