On searches for anomalous WWW interaction at the LHC
PPrepared for submission to JHEP
On searches for anomalous WWW interaction atthe LHC
B.A. Arbuzov I.V. Zaitsev
M.V. Lomonosov Moscow State University,119991 Moscow, Russia
E-mail: [email protected] , [email protected] Abstract:
The process p + p → W ± W + W − with lepton decays of W -bosons is shown tobe promising for improving conditions for studies of parameter λ , which is the anomaloustriple W -bosons interaction coupling constant. a r X i v : . [ h e p - ph ] M a y ontents W + W + W − and W − W − W + production in pp reactions at the LHC 23 Conclusion 7 The totality of data acquired by LHC confirms predictions of the Standard Model. Mean-while the numerous attempts for obtaining even indications for deviations from the SMwere not successful. Mostly these efforts were aimed at a quest for effects of the so-calledNew Physics, that is of wouldbe effects of the Supersymmetry, Extra Dimensions, DarkMatter and some other radical hypotheses. However, there may be also quite interestingwouldbe effects, which are connected just with more conventional physics of the StandardModel, but with those, which are of a non-perturbative origin.Indeed, the Standard Model has two main constituents: QCD and the electroweaktheory (EWT in what follows). Both theories are the renormalizable ones. Hence theperturbation theory is duly defined and give quite definite predictions.Nevertheless, in QCD the existence of the non-perturbative contributions is inevitable.They define e.g. non-zero vacuum averages: gluon condensate and quark condensate < G µν G µν >, < ¯ q q > ; (1.1)the behaviour of running coupling α s ( Q ) and some other actual effects. For the moment theexistence of non-perturbative effects in EWT is not evident to the same extent as in QCD.However, the arguments were expressed for such effects being present in the electroweakinteractions as well.We would discuss in the present note an example of the would be non-perturbativeefffect, connected with anomalous triple electro-weak bosons interaction, first proposed inworks [1, 2]. − G F (cid:15) abc W aµν W bνρ W cρµ ; (1.2) W aµν = ∂ µ W aν − ∂ ν W aµ + g (cid:15) abc W bµ W cν . with form-factor F ( p i ) , which guarantees effective interaction (1.2) acting in a limitedregion of the momentum space. A possibility of the spontaneous generation of effectiveinteraction (1.2) was first considered in work [3] and was studied in more details in work [4].Interaction constant G is connected with conventional definitions in the following way G = − g λM W ; (1.3)– 1 –here g ( M Z ) (cid:39) . is the electroweak coupling. Interaction (1.2) contains both anomalousthree-boson vertex and four-boson vertex, which are proportional to constant G (1.3) (five-boson and six-boson terms will not enter to the present calculations). The best experimentallimitations obtained in experiments at LHC for parameter λ read − . < λ < .
011 ; (1.4) − . < λ < . (1.5) − . < λ < . . (1.6)Result (1.4) corresponds to LHC energy √ s = 8 T eV and integral luminosity L = 18 f b − [5],while recent result (1.5) corresponds to LHC energy √ s = 13 T eV and integral luminosity L = 36 . f b − [6]. We see, that the progress in an accuracy from (1.4) up to (1.5) is notvery substantial. The process, which was studied in [5, 6] p + p → jet + jet + W ± . (1.7)Result (1.6) is extracted from recent work [7] in which process p p → W Z was studied at √ s = 13 T eV . The measurements of the anomalous triple gauge couplings at LHC usingthis process, as well as process p p → W γ , were discussed in detail in recent work [8].In the present paper we would discuss another effective channel for a study of thewouldbe interaction (1.2). W + W + W − and W − W − W + production in pp reactions at the LHC Let us consider no jets processes p + p → W + W + W − + no jet ; (2.1) p + p → W − W − W + + no jet . (2.2)In these processes we have to study the following decays of final state W -bosons W + W + W − → µ + µ + e − + neutrinos ; W + W + W − → e + e + µ − + neutrinos ; (2.3) W − W − W + → µ − µ − e + + neutrinos ; W − W − W + → e − e − µ + + neutrinos. (2.4)So, we have in processes (2.1,2.2) no jets, three charged leptons in the final state anda missing energy, which is carried by neutrinos. Decays (2.3,2.4) contain leptons of thesame flavour bearing same electric charges, and different flavour leptons with oppositecharges. This signature is, practically, free from background of processes, different frombasic reactions (2.1,2.2). On the contrary, provided we have pairs l + l − , there are significantcontributions from photons, Z-bosons etc , and cross-sections become more than an order ofmagnitude larger than those for reactions (2.1,2.2), while the effect under the study remainspractically the same. – 2 – igure 1 . Diagrams for subprocess u + D → W + W + W − . Figure 2 . Diagrams for subprocess U + d → W + W − W − . Leading order diagrams for processes (2.1,2.2) for the main channels with initial states uD and dU are shown at Figures 1,2. Analogous sets of diagrams are also taken into accountfor initial states uS, cD, cS, sU, dC, sC . Calculations are performed in the framework ofCompHEP package for evaluation of Feynmann diagrams, integration over multi-particlephase space and event generation [9].Results of calculations with the use of CompHEP package of diagrams for processes (2.1,2.2) are shown in Table 1, where we estimate also event numbers of processes (2.3, 2.4) for– 3 –wo values of the integral luminosity. The first one is already achieved L = 36 . f b − andthe second one is L = 130 f b − , which presumably is expected for the overall Run II result-ing value. We present results in dependence on the module of parameter λ . Calculationsshow that the results in the Table as well as in the subsequent ones in fact do not dependon the sign of λ . Table 1.LO cross sections of three-boson production W + W − W ± and event numbers with signature(2.3, 2.4) for two values of the integral luminosity for √ s = 13 T eV at the LHC for sixvalues of | λ | . | λ | σ f b N . ±
18 203 ±
14 115 ±
11 74 ± ± ± ± N . ±
18 177 ±
14 88 ±
11 47 ± ± ± N ±
34 726 ±
27 412 ±
20 263 ±
16 175 ±
13 130 ±
11 95 ± N ±
34 631 ±
27 317 ±
20 168 ±
16 80 ±
13 35 ± W production at √ s = 13 T eV are presented. For the process under the discussion(2.1,2.2) the following result was obtained σ W W W = 0 . +0 . − . pb. (2.5)Comparing this result with calculations of cross-sections presented at Table 1, we estimatethe possible value of | λ | , which corresponds to result (2.5) | λ | = 0 . +0 . − . . (2.6)The result is safely inside limitations (1.4, 1.5).Let us consider also another process of the three-boson production p + p → W + W − Z + no jet ; (2.7)We have also to take into account characteristic leptonic decays of the bosons, which leadto the following combinations under the condition, that an invariant mass of the two lastoppositely charged leptons corresponds to the Z boson: W + W − Z → µ + e − e + e − + neutrinos ; W + W − Z → µ − e + e + e − + neutrinos ; (2.8) W + W − Z → µ + e − µ + µ − + neutrinos ; W + W − Z → µ − e + µ + µ − + neutrinos. Calculations lead to results shown in Table 2.– 4 –able 2.Cross sections of process W + W − Z in the leading order and event numbers with signa-ture (2.8) for two values L at LHC, √ s = 13 T eV at the LHC for six values of | λ | . | λ | σ f b N . ± ± ± ± ± ± ± N . ± ± ± ± ± ± N ±
13 104 ±
10 61 ± ± ± ± ± N ±
13 86 ±
10 43 ± ± ± ± p + p → W + W − Zσ W W Z = 0 . +0 . − . pb ; (2.9)we have with calculations, presented in Table 2 | λ | = 0 . +0 . − . . (2.10)Let us quote also the estimate for possible value of parameter | λ | , which was obtained inwork [11] from data for process p + p → ¯ ttH + X ; (2.11) | λ | = 0 . +0 . − . . (2.12)All these estimates do not contradict restrictions (1.4, 1.5, 1.6). Results (2.6, 2.10, 2.12) aremutually consistent, and each one do not contradict to the zero value for λ . In our approacheffects in these three processes have the same origin and are connected with anomalousinteraction (1.2) with effective coupling constant (1.3), which is defined by parameter λ .In the framework of this hypothesis we may average out three results (2.6, 2.10, 2.12), andcome to preliminary rough estimate | λ | = 0 . ± . . (2.13)This estimate is also consistent with the zero effect. However with increasing integralluminosity we may hope to achieve decisive results on a possibility of λ being of the orderof magnitude of the mean value of estimate (2.13).It would be instructive to compare results being shown in Table 1 with those, whichcould be obtained in a course of studying of the same process at √ s = 8 T eV . In doingthis we would present estimates for integral luminosity L = 19 f b − , which was achieved inexperiment [5] leading to limitations (1.4). Results are shown in Table 2. By comparingTable 1 and Table 2 we see, that the effect in reaction under the discussion for conditions,which correspond to √ s = 8 T eV with the actual luminosity, is practically absent, whilefor √ s = 13 T eV one may hope for essential improving of data (1.4, 1.5) even for integralluminosity L = 36 f b − . The integral luminosity L = 130 f b − , which presumably mightbe achieved in RUN II, provides a quite effective tool for dealing with effects of small | λ | even as small as | λ | (cid:39) . . – 5 –able 3.LO cross sections of three-boson production W + W − W ± for √ s = 8 T eV at the LHC forsix values of | λ | and predicted number of events for L = 19 f b − . | λ | σ f b N ± ± ± ± ± ± ± . N ± ± ± ± ± ± p + p → W ± Z γ + no jet ; (2.14)which also could be used to define parameter λ more exactly. Again with application of theCompHEP [9], we calculate corresponding cross sections of the reaction (2.14) in dependenceon a minimal γ transverse momentum for | λ | in the same region. In estimating of eventnumber we take into account the following leptonic signatures provided an invariant massof the two last oppositely charged leptons corresponds to the Z boson: W ± Z γ → µ ± e + e − γ + neutrino ; W ± Z γ → e ± µ + µ − γ + neutrino ; (2.15) W ± Z γ → µ ± µ + µ − γ + neutrino ; W ± Z γ → e ± e + e − γ + neutrino. Table 4.Leading order cross-section of W ± Zγ production for √ s = 13 T eV at the LHC with p γT > GeV and estimates for event numbers for two values of an integral luminosityin dependence of value | λ | . | λ | σ f b N . ±
11 81 ± ± ± ± ± ± N . ±
11 67 ± ± ± ± ± N ±
21 290 ±
17 170 ±
13 118 ±
11 82 ± ± ± N ±
21 238 ±
17 118 ±
13 66 ±
11 30 ± ± W ± Zγ production for √ s = 13 T eV at the LHC with p γT > GeV and estimates for event numbers for two values of an integral luminosityin dependence of value | λ | . | λ | σ f b N . ±
11 71 ± ± ± ± ± ± N . ±
11 66 ± ± ± ± ± N ±
20 254 ±
16 134 ±
12 84 ± ± ± ± N ±
20 236 ±
16 116 ±
12 66 ± ± ± – 6 –ith account of leptonic branching ratios of W, Z we see from Table 4 and Table 5, thatwhile processes (2.1, 2.2) with decays (2.3, 2.4) are much more promising for looking forsmall λ effects than process (2.14) with decays (2.15), the last one (2.14) nevertheless couldgive additional information on the problem of non-perturbative contributions, especiallywith cut-off p γT = 100 GeV . The study of processes, which was discussed above would provide essential improvement ofrestrictions for value of λ , in particular, give decisive answer for a possibility (2.13) | λ | (cid:39) . . (3.1)Especially we would draw attention to processes p p → W + W + W − ; p p → W − W − W + ; (3.2)and look for the low background experimental signature p p → µ + µ + e − + invisible ; p p → µ − µ − e + + invisible ; (3.3) p p → e + e + µ − + invisible ; p p → e − e − µ + + invisible. in which according to Table 1 the effect essentially exceeds the SM predictions.We would draw attention to an importance of searches for non-perturbative effectsin the electro-weak interaction. Just anomalous interaction of W -bosons (1.2) in case ofconfirmation of its existence would open a new region of investigations in the field of thenon-perturbative electro-weak physics. References [1] K. Hagiwara, R. D. Peccei, D. Zeppenfeld and K. Hikasa,
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