Tevatron Constraints on Models of the Higgs Boson with Exotic Spin and Parity Using Decays to Bottom-Antibottom Quark Pairs

Combined constraints from the CDF and D0 Collaborations on models of the Higgs boson with exotic spin $J$ and parity $P$ are presented and compared with results obtained assuming the standard model value $J^P=0^+$. Both collaborations analyzed approximately 10~fb$^{-1}$ of proton-antiproton collisions with a center-of-mass energy of 1.96 TeV collected at the Fermilab Tevatron. Two models predicting exotic Higgs bosons with $J^P=0^-$ and $J^P=2^+$ are tested. The kinematic properties of exotic Higgs boson production in association with a vector boson differ from those predicted for the standard model Higgs boson. Upper limits at the 95% credibility level on the production rates of the exotic Higgs bosons, expressed as fractions of the standard model Higgs boson production rate, are set at 0.36 for both the $J^P=0^-$ hypothesis and the $J^P=2^+$ hypothesis. If the production rate times the branching ratio to a bottom-antibottom pair is the same as that predicted for the standard model Higgs boson, then the exotic bosons are excluded with significances of 5.0 standard deviations and 4.9 standard deviations for the $J^P=0^-$ and $J^P=2^+$ hypotheses, respectively.

K. Takemasa † , 49 Y. Takeuchi † , 49 J. Tang † , 11 M. Tecchio † , 31 P.K. Teng † , 1 J. Thom †f , 15 16 G. Velev † , 15  Combined constraints from the CDF and D0 Collaborations on models of the Higgs boson with exotic spin J and parity P are presented and compared with results obtained assuming the standard model value J P = 0 + . Both collaborations analyzed approximately 10 fb −1 of proton-antiproton collisions with a center-of-mass energy of 1.96 TeV collected at the Fermilab Tevatron. Two models predicting exotic Higgs bosons with J P = 0 − and J P = 2 + are tested. The kinematic properties of exotic Higgs boson production in association with a vector boson differ from those predicted for the standard model Higgs boson. Upper limits at the 95% credibility level on the production rates of the exotic Higgs bosons, expressed as fractions of the standard model Higgs boson production rate, are set at 0.36 for both the J P = 0 − hypothesis and the J P = 2 + hypothesis. If the production rate times the branching ratio to a bottom-antibottom pair is the same as that predicted for the standard model Higgs boson, then the exotic bosons are excluded with significances of 5.0 standard deviations and 4.9 standard deviations for the J P = 0 − and J P = 2 + hypotheses, respectively. The Higgs boson discovered by the ATLAS [1] and CMS [2] Collaborations in 2012 using data produced in proton-proton collisions at the Large Hadron Collider (LHC) at CERN allows many stringent tests of the electroweak symmetry breaking in the standard model (SM) and extensions to the SM to be performed. To date, measurements of the Higgs boson's mass and width [3][4][5][6], its couplings to other particles [3,[7][8][9][10][11], and its spin and parity quantum numbers J and P [10][11][12][13][14][15][16] are consistent with the expectations for the SM Higgs boson. The CDF and D0 Collaborations at the Fermilab Tevatron observed a 3.0 standard deviation (s.d.) excess of events consistent with a Higgs boson signal, largely driven by those channels sensitive to the decay of the Higgs boson to bottom quarks (H → bb) [17,18]. The Tevatron data are also consistent with the predictions for the properties of the SM Higgs boson [18][19][20][21][22].
Ref. [23] proposed to use the Tevatron data to test models for the Higgs boson with exotic spin and parity, using events in which the exotic Higgs boson X is produced in association with a W or a Z boson and decays to a bottom-antibottom quark pair, X → bb. This proposal used two of the spin and parity models in Ref. [24], one with a pseudoscalar J P = 0 − state and the other with a graviton-like J P = 2 + state. For the SM Higgs boson, which has J P = 0 + , the differential production rate near threshold is linear in β, where β = 2p/ √ŝ , p is the momentum of the X boson in the VX (V = W or Z) reference frame, and √ŝ is the total energy of the VX system in its rest frame. For the pseudoscalar model, the dependence is proportional to β 3 . For the graviton-like model, the dependence is proportional to β 5 ; however, not all J P = 2 + models share this β 5 factor [23]. These powers of β alter the kinematic distributions of the observable decay products of the vector boson and the Higgs-like boson X, most notably the invariant mass of the VX system, which has a higher average value in the J P = 0 − hypothesis than in the SM 0 + case, and higher still in the J P = 2 + hypothesis. These models predict neither the production rates nor the decay branching fractions of the X particles.
The ATLAS and CMS Collaborations recently reported strong evidence for Higgs boson decays to fermions [25][26][27][28][29][30], with sensitivity dominated by the H → τ + τ − decay mode, though they have not yet performed spin and parity tests using fermionic decays. The particle decaying fermionically for which the Tevatron also found evidence might not be the same as the particle discovered through its bosonic decays at the LHC. Tests of the spin and parity [23] with Tevatron data therefore provide unique information on the identity and properties of the new particle or particles. The CDF and D0 Collaborations have re-optimized their SM Higgs boson searches to test the exotic Higgs boson models in the WH → ℓνbb [31,32], ZH → ℓ + ℓ − bb [33,34], and WH + ZH → E / T bb [35,36] channels, where ℓ = e or µ and E / T is the missing transverse energy [37]. In this letter we report a combination of the CDF [21] and D0 [22] studies of the J P assignments of the state X, with mass m X = 125 GeV/c 2 , in the X → bb decay.
The CDF and D0 detectors are multipurpose solenoidal spectrometers surrounded by hermetic calorimeters and muon detectors designed to study the products of 1.96 TeV proton-antiproton (pp) collisions [38,39]. All searches combined here use the complete Tevatron data sample, which, after data quality requirements, corresponds to 9.45 -9.7 fb −1 of integrated luminosity, depending on the experiment and the search channel.
Standard model Higgs boson signal events are simulated using the leading-order (LO) calculation from pythia [40], with CTEQ5L (CDF) and CTEQ6L1 (D0) [41] parton distribution functions (PDFs). The J P = 0 − and J P = 2 + signal samples are generated using madgraph 5 version 1.4.8.4 [42], with modifications provided by the authors of Ref. [23]. Subsequent particle showering is modeled by pythia. We normalize the SM Higgs boson rate predictions to the highest-order calculations available. The WH and ZH cross sections are calculated at next-to-next-to-leading-order (NNLO) precision in the strong interaction, and next-to-leading-order (NLO) precision in the electroweak corrections [43][44][45][46]. We use the branching fractions for Higgs boson decay from Ref. [47]. These rely on calculations using hdecay [48] and prophecy4f [49].
The predictions of the dominant background rates and kinematic distributions are treated in the following way. Diboson (WW, WZ, and ZZ) Monte Carlo (MC) samples are normalized using the NLO calculations from mcfm [50]. For tt, we use a production cross section of 7.04 ± 0.70 pb [51], which is based on a top quark mass of 173 GeV/c 2 [52] and MSTW 2008 NNLO PDFs [53]. The single top quark production cross section is assumed to be 3.15 ± 0.31 pb [54]. For details of the generators used, see Ref. [55]. Data-driven methods are used to normalize the V plus light-flavor and heavy-flavor jet backgrounds [60] using V data events containing no b-tagged jets [61], which have negligible signal content [62,63]. The MC modeling of the kinematic distributions of the background predictions is described in Refs. [31][32][33][34][35][36].
The event selections are similar (CDF), or identical (D0), to those used in their SM counterparts [31][32][33][34][35][36]. For the WH → ℓνbb analyses, events are selected with one identified lepton (e or µ), jets, and large E / T . For the CDF WH → ℓνbb analysis, only events with two jets are used. Events are classified into separate categories based on the quality of the identified lepton. Separate categories are used for events with a high-quality muon or central electron candidate, an isolated track, or a forward electron candidate. Within the lepton categories, five exclusive b-tag categories, comprising two single-tag and three double-tag categories, are formed. The multivariate b-tagger used by CDF [64] was trained on SM Higgs boson signal MC events. Few of these events contained jets with with transverse energy E T > 200 GeV and thus the tagger does not perform well for such jets. Hence, only jets with E T < 200 GeV are considered. For the D0 WH → ℓνbb analysis, events are selected with two or three jets. The data are split by lepton flavor and jet multiplicity (two or three jet subchannels), and by the output of the b-tagging algorithm applied to all selected jets in the event. This channel, along with the other two D0 channels, uses a multivariate b-tagging algorithm [65,66]. Four exclusive b-tag categories, one single-tag and three double-tag, are formed. In the SM Higgs boson search, boosted decision trees are used as the final discriminating variables; here they are used to further subdivide the selected data sample into high-and low-purity categories.
The ZH → ℓ + ℓ − bb analyses require two isolated leptons and at least two jets. The CDF analysis separates events into one single-and three double-b-tag samples and uses neural networks to select loose dielectron and dimuon candidates. The jet energies are corrected for E / T using a neural network [67]. The CDF analysis uses a multistep discriminant based on neural networks, where two discriminant functions are used to define three sep-arate regions of the final discriminant function. The D0 ZH → ℓ + ℓ − bb analysis separates events into nonoverlapping samples of events with either a single or double b-tag. To increase the signal acceptance, the selection criteria for one of the leptons are loosened to include isolated tracks not reconstructed in the muon detector and electron candidates from the intercryostat region of the D0 detector. Combined with the dielectron and dimuon categories, these provide four independent lepton subchannels. A kinematic fit is used to optimize reconstruction. Random forests (RF) of decision trees [68,69] are used to provide the final variables in the SM Higgs boson search. The first RF is designed to discriminate against tt events and divides events into tt-enriched and tt-depleted single-tag and double-tag regions. Only events in the tt-depleted regions are considered in this study. These regions contain approximately 94% of the SM signal.
For the ZH → ννbb analyses, the selections used by CDF and D0 are similar to the WH selections, except that all events with isolated leptons are rejected and more stringent techniques are applied to reject the multijet background. In a sizable fraction of WH → ℓνbb signal events, the lepton is undetected. Such events often are selected in the ZH → ννbb samples, so these analyses are also referred to as V H → E / T bb. The CDF analysis uses three non-overlapping b-tag categories (two doubleand one single-tag) and two jet categories (two-or threejet events), giving a total of six subchannels. In the D0 analysis, exactly two jets are required and two exclusive double-tag categories are defined using the sum of the b-tagging outputs for each of the two selected jets.
Both CDF and D0 have a 50% larger acceptance for the J P = 0 − and J P = 2 + signals in the ZH → ννbb analyses compared with the SM Higgs boson signal, largely due to the fact that the exotic signal events are more likely to pass the trigger thresholds for E / T , a consequence of the larger average V X invariant masses. The other two channels, WH → ℓνbb and ZH → ℓ + ℓ − bb, do not benefit as much from the additional E / T in these events, as they rely on the lepton triggers, which are more efficient than the E / T triggers in the relevant kinematic regions.
Unlike their SM counterparts, these analyses are optimized to distinguish the J P = 0 − and the J P = 2 + hypotheses from the SM 0 + hypothesis. The exotic particles are considered either in addition to, or replacing, the SM Higgs boson. A mixture of all three states is not considered.
The CDF multivariate analysis (MVA) discriminants were newly trained to separate the exotic Higgs boson signals from the SM backgrounds [21]. In the WH → ℓνbb and V H → E / T bb channels, events classified as background-like by the new discriminants are then classified according to the SM-optimized MVA discriminants in order to improve the performance of tests between the SM and exotic hypotheses.
Depending on the channel, D0 uses either the recon-structed dijet mass or the MVA used in the SM Higgs boson search to separate events into high-and low-purity samples. The mass of the VX system is then used to discriminate between the exotic and SM hypotheses [22]. For the ZH → ℓℓbb analysis the invariant mass of the two leptons and the two highest p T jets is used. For the ℓνbb and ννbb final states the transverse mass M T is used, 2 and the transverse momenta of the Z and W bosons are taken to be p Z T = E T and p W T = E T + p ℓ T , respectively. The number of contributing channels is large, and their sensitivities vary from one to another. To visualize the data in a way that emphasizes the sensitivity to the exotic signals, we follow Ref. [18]. Bins of the final discriminant for all channels are ordered by increasing signalto-background ratio (s/b) and are shown in comparison with predicted yields from signal and background processes for the J P = 0 − and J P = 2 + searches in Fig. 1 separately. The backgrounds are fit to the data in each case, allowing the systematic uncertainties to vary within their a priori constraints. The exotic signals are normalized to the SM cross section times branching ratio multiplied by an exotic-signal scaling factor, µ exotic . They are shown in Fig. 1 with µ exotic = 1. The scaling factor for the SM Higgs boson signal is denoted by µ SM . A value of one for either µ SM or µ exotic corresponds to a cross section times branching ratio as predicted for the SM Higgs boson. Both figures show agreement between the background predictions and the observed data over five orders of magnitude with no evidence for an excess of exotic signal-like candidates.
We follow Ref. [18] and perform both Bayesian and modified frequentist calculations of the upper limits on exotic X boson production with and without SM Higgs production, best-fit cross sections allowing for the simultaneous presence of a SM Higgs boson and an exotic X boson, and hypothesis tests for signals assuming various production rate times branching ratio values for the exotic bosons. Both methods use likelihood calculations based on Poisson probabilities that include SM background processes and signal predictions for the SM Higgs and exotic bosons multiplied by their respective scaling factors, µ SM and µ exotic . Systematic uncertainties on the predicted rates and on the shapes of the distributions and their correlations are treated as described in Ref. [18]. Theoretical uncertainties in cross sections and branching ratios are considered fully correlated between CDF and D0, and between analysis samples. The uncertainties on the measurements of the integrated luminosities, which are used to normalize the expected signal yields and the MC-based background rates, are 6.0% (CDF) and 6.1% (D0). Of these values, 4% arises from the inelastic pp cross section [70], which is fully correlated between CDF and D0. The dominant uncertainties on the backgrounds are constrained by the data in low s/b regions of the discriminant distributions. Different methods were used by CDF and D0 to estimate V +jets and multijet backgrounds and so their uncertainties are considered uncorrelated. Similarly, the uncertainties on the data-driven estimates of the b-tag efficiencies are considered uncorrelated between CDF and D0, as are the uncertainties on the jet energy scales, the trigger efficiencies, and lepton identification efficiencies. We quote Bayesian upper limits and best-fit cross sections assuming uniform priors for non-negative signal cross sections, and we use the modified frequentist method to perform the hypothesis tests. Systematic uncertainties are parameterized by nuisance parameters with Gaussian priors, truncated so that no predicted yield for any process in any search channel is negative. For both the J P = 0 − and J P = 2 + models, we compute two 95% credibility upper limits on µ exotic , one assuming µ SM = 1 and the other assuming µ SM = 0. The expected limits are the median expectations assuming no exotic boson is present. The results are listed in Table I. Two-dimensional credibility regions, which are the smallest regions containing 68% and 95% of the posterior probabilities, are shown in Fig. 2. The points in the (µ SM , µ exotic ) planes that maximize the posterior probability densities are shown as the best-fit values. These best-fit values are (µ SM =1.0, µ 0 − = 0) for the search for the J P = 0 − state, and (µ SM =1.1, µ 2 + = 0) for the search for the J P = 2 + state. We also derive upper limits on the fraction f JP = µ exotic /(µ exotic +µ SM ), as functions of the total µ = µ exotic + µ SM , assuming a uniform prior probability density in non-negative f JP , extended to include fractions larger than 1.0 in order not to saturate the limits at f JP = 0.95 for µ < 0.6, where the test is weak. The results are shown in Fig. 3.
In the modified frequentist approach [71,72] we compute p values for the discrete two-hypothesis tests, the SM Higgs boson hypothesis (the "null" hypothesis) (µ SM =1, µ exotic =0) and the exotic ("test") hypothesis (µ SM =0, µ exotic =1), both assuming that SM background processes are present. The choice of setting µ exotic = 1 in the test hypothesis is arbitrary; the sensitivity of the test is reduced if a smaller value is assumed. We use the log-likelihood ratio, LLR, defined to be −2 ln(p(data|test)/p(data|null), where the numerator and denominator are maximized over systematic uncertainty variations [18]. The LLR distributions are shown in the supplemental material [73]. We define the p values p null = P (LLR ≤ LLR obs |SM) and p test = P (LLR ≥ LLR obs |exotic). The median expected p values p exotic null,med in the test hypothesis and p SM test,med in the SM hypothesis quantify the sensitivities of the two-hypothesis tests for exclusion and discovery, respectively. Table II lists these p values for both exotic models, as well as CL s = p test /(1 − p null ) [71] for the Tevatron combination. To compute p test and the expected values of p null and p test , Wilks's theorem is used [74].
The similarity of the limits and p values obtained for the J P = 0 − and the J P = 2 + searches is expected since the exotic models predict excesses in similar portions of kinematic space.
In summary, we combine CDF's and D0's tests for the presence of a pseudoscalar Higgs boson with J P = 0 − and a graviton-like boson with J P = 2 + in the WX → ℓνbb, the ZX → ℓ + ℓ − bb, and the VX → E / T bb search channels using models described in Ref. [23]. The masses of the exotic bosons are assumed to be 125 GeV/c 2 . No evidence is seen for either exotic particle, either in place of the SM Higgs boson or produced in a mixture with a J P = 0 + Higgs boson. In both searches, the best-fit cross section times the decay branching ratio into a bottom- I: Observed and median expected Bayesian upper limits at the 95% credibility level on µexotic for the pseudoscalar (J P = 0 − ) and graviton-like (J P = 2 + ) boson models, assuming either that the SM Higgs boson is also present (µSM = 1) or absent (µSM = 0).

Channel
Observed Upper limits at 95% credibility on the rate of the production of an exotic Higgs boson in the absence of a SM J P = 0 + signal are set at 0.36 times the SM Higgs production rate for both the J P = 0 − and the J P = 2 + hypotheses. If the production rate of the hypothetical exotic particle times its branching ratio to a bottomantibottom quark pair is the same as that predicted for the SM Higgs boson, then the exotic models are excluded with significances of 5.0 s.d. and 4.9 s.d. for the J P = 0 − and J P = 2 + hypotheses, respectively.

Acknowledgments
We thank the Fermilab staff and technical staffs of the participating institutions for their vital contributions. We acknowledge support from the Department of Energy   The posterior probability density as a function of µ 0 − assuming µSM = 1 and a uniform prior density for non-negative µ 0 − , (b) the posterior probability density as a function of µ 0 − assuming µSM = 0 and a uniform density for non-negative µ 0 − , and (c) the posterior probability density as a function of the fraction of exotic boson production, µ 0 − /(µ 0 − + µSM), assuming µ 0 − + µSM = 1, and a uniform prior density for non-negative values of the fraction. The dashed vertical lines indicate the observed limits. Figures (d), (e), and (f) show the corresponding results for the J P = 2 + boson searches.