VOLUME 79, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 29 DECEMBER 1997 il t, 5 Limits on Anomalous Couplings from Higgs Boson Production at the Fermilab Tevatron Collider F. de Campos,1 M. C. Gonzalez-Garcia,1,2 and S. F. Novaes1 1Instituto de Fı´sica Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, Braz 2Instituto de Fı´sica Corpuscular-IFIC/CSIC, Departament de Fı´sica Teòrica, Universitat de València, 46100 Burjasso València, Spain (Received 18 July 1997) We estimate the attainable limits on the coefficients of dimension-6 operators from the analysis of Higgs boson phenomenology, in the framework of a SULs2d 3 UY s1d gauge-invariant effective Lagrangian. Our results, based on the data sample already collected by the collaborations at Fermilab Tevatron, show that the coefficients of Higgs-vector boson couplings can be determined with unprecedented accuracy. Assuming that the coefficients of all “blind” operators are of the same magnitude, we are also able to impose more restrictive bounds on the anomalous vector-boson triple couplings than the present limit from double gauge boson production at the Tevatron collider. [S0031-9007(97)04882-5] PACS numbers: 14.70.Fm, 13.40.Em, 13.85.Qk, 14.80.Cp - eir irs - ct - e a- n- d, e f- nt d f d Despite the impressive agreement of the standard mo (SM) predictions for the fermion-vector boson coupling with the experimental results, the couplings among th gauge bosons are not determined with the same accura The gauge structure of the model completely determin these self-couplings, and any deviation can indicate t existence of new physics. Effective Lagrangians are useful to describe and e plore the consequences of new physics in the boso sector of the SM [1–4]. After integrating out the heav degrees of freedom, anomalous effective operators c represent the residual interactions between the light sta Searches for deviations on the couplingsWWV sV ­ g, Zd have been carried out at different colliders and re cent results [5] include the ones by CDF [6], and D0 Co laborations [7,8]. Forthcoming perspectives on this sear at LEP II CERN Collider [9,10], and at upgraded Fermi lab Tevatron Collider [11] were also reported. In the framework of effective Lagrangians respectin the local SULs2d 3 UY s1d symmetry linearly realized, the modifications of the couplings of the Higgs fieldsHd to the vector gauge bosonssV d are related to the anomalous triple vector boson vertex [2–4,12]. In this Letter, we show that the analysis of an anomalously coupled Hig boson production at the Fermilab Tevatron is able furnish tighter bounds on the coefficients of the effectiv Lagrangians than the present available limits. We stu the associatedHV process 210 0031-9007y97y79(26)y5210(4)$10.00 del s e cy. es he x- nic y an tes. - l- ch - g gs to e dy pp̄ ! qq̄ ! WyZs! ff̄ 0d 1 Hs! ggd , (1) and the vector boson fusion process pp̄ ! qq̄0WWsZZd ! j 1 j 1 Hs! ggd , (2) taking into account the100 pb21 of integrated luminos- ity already collected by the Fermilab Tevatron Collabora tions. Recently, the D0 Collaboration has presented th results for the search of high invariant–mass photon pa in pp̄ ! ggjj events [13]. We show, based on their re sults, that it may be possible to obtain a significant indire limit on anomalousWWVcoupling under the assumption that the coefficients of the “blind” effective operators con tributing to the Higgs-vector boson couplings are of th same magnitude. It is also possible to restrict the oper tors that involve just Higgs boson couplingsHVV, and therefore cannot be bounded by theW1W2 production at LEP II. Let us start by considering a general set of dimensio 6 operators involving gauge bosons and the Higgs fiel respecting local SULs2d 3 UY s1d symmetry, andC andP conserving which contains eleven operators [2,3]. Som of these operators either affect only the Higgs sel interactions or contribute to the gauge boson two-poi functions at tree level and can be strongly constraine from low energy physics below the present sensitivity o high energy experiments [3,4]. The remaining five blin operators can be written as [2–4] Leff ­ X i fi L2 Oi ­ 1 L2 h fWWW TrfŴmnŴnrŴm r g 1 fW sDmFdyŴmnsDnFd 1 fBsDmFdyB̂mnsDnFd 1 fWW FyŴmnŴmnF 1 fBBFyB̂mnB̂mnFj , (3) whereF is the Higgs field doublet, and B̂mn ­ isg0y2dBmn , Ŵmn ­ isgy2dsaWa mn , © 1997 The American Physical Society VOLUME 79, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 29 DECEMBER 1997 e n ) r is 1). g ar with Bmn andWa mn being the field strength tensors of th U(1) and SU(2) gauge fields, respectively. In the unitary gauge, the operatorsOW and OB give rise to both anomalous Higgs-gauge boson couplings a to new triple and quartic self-couplings among the gau bosons, while the operatorOWWW solely modifies the gauge boson self-interactions [12]. The operatorsOWW andOBB affect onlyHVVcouplings, like HWW, HZZ, Hgg, and HZg, since their contribu- tion to theWWg and WWZ tree-point couplings can be completely absorbed in the redefinition of the SM field and gauge couplings. Therefore, one cannot obtain a constraint on these couplings from the study of anomalo trilinear gauge boson couplings. These anomalous c plings were extensively studied in electron-positron col sions [12,14,15]. We consider in this Letter Higgs production at th Fermilab Tevatron collider with its subsequent decay in two photons [16]. This channel in the SM occurs a the one-loop level and it is quite small, but due to th new interactions (3), it can be enhanced and even beco dominant. We focus on the signatures,ngg, s, ­ e, md, and jjgg, coming from the reactions (1) and (2). Ou results show that the cross section for the,,gg final state is too small to give any reasonable constraints. We have included in our calculations all SM (QCD plus electroweak), and anomalous contributions that le to these final states. The SM one-loop contributions the Hgg and HZg vertices were introduced through the use of the effective operators with the correspondi form factors in the coupling [17]. Neither the narrow width approximation for the Higgs boson contributions nor the effectiveW boson approximation were employed We consistently included the effect of all interference between the anomalous signature and the SM backgrou A total of 42 (32) SM (anomalous) Feynman diagram are involved in the subprocesses of,ngg [18] for each leptonic flavor, while 1928 (236) participate injjgg signature [19]. The SM Feynman diagrams were genera by Madgraph [20] in the framework of Helas [21]. The anomalous contributions arising from the Lagrangian ( were implemented in Fortran routines and were includ accordingly. We have used the MRS (G) [22] set of proto structure functions with the scaleQ2 ­ ŝ. The cuts applied on the final state particles are simi to those used by the experimental collaborations [6– In particular, when studying theggjj final state we have closely followed the results recently presented by the D Collaboration [13], i.e., for the photons jhg1j , 1.1 or 1.5 , jhg1j , 2, p g1 T . 20 GeV, jhg2j , 1.1 or 1.5 , jhg2j , 2.25, p g2 T . 25 GeV,X $p g T . 10 GeV. e nd ge s ny us ou- li- e to t e me r ad to ng - , . s nd. s ted 3) ed n lar 8]. 0 For thelngg final state jhej , 1.1 or 1.5 , jhej , 2, jhmj , 1 , p e,m T . 20 GeV, pyT . 20 GeV. For thejjgg final state jhj1j , 2 , p j1 T . 20 GeV, jhj2j , 2.25 , p j2 T . 15 GeV,X $p j T . 10 GeV, Rgj . 0.7 , 40 # Mjj # 150 GeV. We also assumed an invariant-mass resolution for th two photons ofDMggyMgg ­ 0.15y p Mgg © 0.007 [16]. Both signal and background were integrated over a invariant-mass bin of62DMgg centered aroundMH . The signature of thejjgg process receives contribu- tions from both associated production andWWyZZ fu- sion. For the sake of illustration, we show in Fig. 1(a the invariant mass distribution of the two photons fo MH ­ 70 GeV andfBByL2 ­ 100 TeV22, without any cut on Mgg or Mjj. We can clearly see from Fig. 1(b) that after imposing the Higgs mass reconstruction, there a significant excess of events in the regionMjj , MW ,Z corresponding to the process of associate production ( It is also possible to distinguish the tail correspondin to the Higgs production fromWWyZZ fusion (2), for FIG. 1. (a) Two photon invariant mass distribution for the background (shaded histogram) and for the signal (cle histogram) before applying any cut, forMH ­ 70 GeV and fBByL2 ­ 100 TeV22. (b) Two jet invariant mass distribution, after the cut on the two photon invariant mass. 5211 VOLUME 79, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 29 DECEMBER 1997 d e r e s of . t t n n e t in e n, Z Mjj . 100 GeV. We isolate the majority of events due to associated production, and the corresponding backgrou by integrating over a bin centered on theW or Z mass, which is equivalent to the invariant mass cut listed abov After imposing all the cuts, we get a reduction o the signal event rate which depends on the Higgs ma For thejjgg final state the geometrical acceptance an background rejection cuts account for a reduction fact of 15% for MH ­ 60 GeV rising to 25% for MH ­ 160 GeV. We also include in our analysis the particl identification and trigger efficiencies which vary from 40% to 70% per particle lepton or photon [7,8]. For th jjgg s,nggd final state we estimate the total effect o these efficiencies to be 35% (30%). We therefore obta an overall efficiency for thejjgg final state of 5.5% to 9% for MH ­ 60–160 GeV in agreement with the results of Ref. [13]. For thelngg signature, the main physics backgroun comes fromWgg. After imposing all cuts and efficien- cies the background is reduced far below the experimen sensitivity. For thejjgg final state the dominant physics background is a mixed QCD-QED process. Again, whe cuts and efficiencies are included, it is reduced to less th 0.2 events for the present luminosity [13]. Dominant backgrounds, however, are due to miside tification when a jet fakes a photon that has been es mated to occur with a probability of a few times1024 [7]. Although this probability is small, it becomes the mai source of background for thejjgg final state because of the very large multijet cross section. In Ref. [13] thi background is estimated to lead to3.5 6 1.3 events with invariant massMgg . 60 GeV, and it has been consis- tently included in our derivation of the attainable limits. In the lngg channel the dominant fake backgroun is the Wgj channel, when the jet mimics a photon We estimated the contribution of this channel to yiel Nback , 0.01 events [7] at 95% C.L. We have also estimated the various QCD fake backgrounds such jjj, jjg, andjgg, with the jet faking a photon and/or electron plus fake missing, which are to be negligible. The coupling Hgg derived from (3) involvesfWW and fBB [12]. In consequence, the anomalous signatu ff̄gg is possible only when those couplings are no vanishing. The couplingsfB andfW , on the other hand, affect the production mechanisms for the Higgs boson. what follows, we present our results for three differen TABLE I. Allowed range offyL2 in TeV22 at 95% C.L., assuming the scenario (i)s fBB ­ fWW ¿ fB, fW d for the different final states, and for different Higgs boson masses for an integrated luminosity of100 pb21. MH sGeVd 100 150 200 250 ,ngg Run I s241 74d s283 113d s,2200 .200d s,2200 .200d Run II s213 36d s222 46d s257 135d s2195 .200d TeV33 s23.8 8d s24.8 20d s228 60d s245 83d jjgg Run I s220 49d s226 64d s296 .100d s,2100 .100d Run II s28.4 26d s211 31d s236 81d s264 .100d TeV33 s24.2 6.5d s24.5 12d s219 40d s228 51d 5212 nd, e. n ss. d or e e f in d tal n an n- ti- n s d . d as re t In t scenarios of the anomalous coefficients: (i) Suppresse VVV couplings compared to theHgg vertex: fBB,WW ­ f ¿ fB,W (ii) All coupling with the same magnitude and sign: fBB,WW ,B,W ­ f. (iii) All coupling with the same magnitude but different relative sign:fBB,WW ­ f ­ 2fB,W . In order to establish the attainable bounds on th coefficients, we imposed an upper limit on the numbe of signal events based on Poisson statistics [23]. For th jjgg final state we use the results from Ref. [13], where no event has been reported in the100 pb21 sample. For the other cases, the limit on the number of signal event was conservatively obtained assuming that the number observed events coincides with the expected background Table I shows the range offyL2 that can be excluded at 95% C.L. with the present Tevatron luminosity in the scenario (i). We should remind the reader tha this scenario will not be restricted by LEP II data on W1W2 production since there are no trilinear vector boson couplings involved. As seen in the table, the bes limits are obtained for thejjgg final state, and they are more restrictive than the ones coming frome1e2 ! ggg or bb̄g at LEP II [15]. For the scenarios (ii) and (iii), the limits derived from our study lead to constraints on the triple gauge boso coupling parameters. The most general parametrizatio for the WWV vertex can be found in Ref. [1]. When only the operators (3) are considered, it contains thre independent parameters. If it is further assumed tha fB ­ fW , only two free parameters remain, which are usually chosen asDkg and lg. This is usually quoted in the literature as the HISZ scenario [4]. Since we are assumingfB ­ fW our results can be compared to the derived limits from triple gauge boson studies in the HISZ scenario. In Fig. 2, we show the region in theDkg 3 MH that can be excluded through the analysis of the present Tevatron data, accumulated Run I, with an integrated luminosity of100 pb21 [13], for scenarios (ii) and (iii). For the sake of comparison, we also show in Fig. 2 th best available experimental limit onDkg [5,8] and the expected bounds, from double gauge boson productio from an updated Tevatron Run II, with1 fb21, and TeV33 with 10 fb21 [11], and from LEP II operating at 190 GeV with an integrated luminosity of500 fb21 [10]. In all cases the results were obtained assuming the HIS scenario. We can see that, forMH & 200f170g GeV, the VOLUME 79, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 29 DECEMBER 1997 . , , . , t. - C . D , . D s. FIG. 2. Excluded region in theDkg 3 MH plane for an integrated luminosity of100 pb21, and for scenarios (ii) (clear shadow) and (iii) (dark shadow). The present and futur bounds onDkg are also shown (see text for details). limit that can be established at 95% C.L. from the Higg production analysis for scenario (ii) [(iii)], based on the present Tevatron luminosity is tighter than the prese limit coming from gauge boson production. When the same analysis is performed for the upgrad Tevatron, a more severe restriction on the coefficient the anomalous operators is obtained. For instance, fro pp̄ ! jjgg, in scenario (ii) we get, forMH ­ 150 GeV: For RunII with 1 fb21, 29 , f , 25 s20.06 , Dkg , 0.16d; for TeV33 with 10 fb21, 24 , f , 15 s20.03 , Dkg , 0.1d. In conclusion, we have shown that the Fermilab Teva tron analysis of an anomalous Higgs boson productio may be used to impose strong limits on new effectiv interactions. Under the assumption that the coefficien of the four “blind” effective operators contributing to Higgs-vector boson couplings are of the same magnitud the study can give rise to a significant indirect limit on anomalousWWg couplings. Furthermore, the Tevatron is able to set constraints on those operators contributing new Higgs interactions for Higgs masses far beyond th kinematical reach of LEP II. We want to thank R. 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