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1 ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS AND THEIR FIRST LHC CONSTRAINTS M. V. Chizhov a, b, V. A. Bednyakov a, I.R.Boyko a, J. A. Budagov a, M. A. Demichev a, I.V.Yeletskikh a a Joint Institute for Nuclear Research, Dubna b Centre for Space Research and Technologies, Faculty of Physics, University of Soˇa, Soˇa INTRODUCTION 611 THE CHIRAL BOSON MODEL 613 NUMERICAL SIMULATIONS OF THE CHIRAL BOSONS 615 THE FIRST EXPERIMENTAL CONSTRAINTS ON THE CHIRAL BOSONS 620 DIJET SIGNALS OF THE CHIRAL BOSONS 624 CONCLUSIONS 632 REFERENCES 634

2 ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS AND THEIR FIRST LHC CONSTRAINTS M. V. Chizhov a, b, V. A. Bednyakov a, I.R.Boyko a, J. A. Budagov a, M. A. Demichev a, I.V.Yeletskikh a a Joint Institute for Nuclear Research, Dubna b Centre for Space Research and Technologies, Faculty of Physics, University of Soˇa, Soˇa Phenomenological consequences of the Standard Model extension are summarized by means of new spin-1 chiral ˇelds with the internal quantum numbers of the electroweak Higgs doublets. The prospects for resonance production and detection of the chiral vector Z and W ± bosons at the LHC energies are considered on the basis of quantitative simulations within the CompHEP/CalcHEP package. The Z boson can be observed as a BreitÄWigner resonance peak in the invariant dilepton mass distributions in the same way as the well-known extra gauge Z bosons. However, the Z bosons have unique signatures in transverse momentum, angular and pseudorapidity distributions of the ˇnal leptons, which allow one to distinguish them from other heavy neutral resonances. In 2010, with 40 pb 1 of the LHC protonäproton data at the energy of 7 TeV, the ATLAS detector was used to search for narrow resonances in the invariant mass spectrum of e + e and μ + μ ˇnal states and high-mass charged states decaying to a charged lepton and a neutrino. No statistically signiˇcant excess above the Standard Model expectation was observed. The exclusion mass limits of 1.15 and 1.35 TeV/c 2 were obtained for the chiral neutral Z and charged W bosons, respectively. These are the ˇrst direct limits on the W and Z boson production. Based on the above, a novel strategy for the chiral boson search in the LHC dijet data is discussed. For almost all currently considered exotic models the relevant signal is expected in the central dijet rapidity region y 1,2 0 and y 1 y 2 0. On the contrary, the chiral bosons do not contribute to this region but produce an excess of dijet events far away from it. In particular, for these bosons the appropriate kinematical restrictions lead to a dip in the centrality ratio distribution over the dijet invariant mass instead of a bump expected in the most exotic models. Ê ÕÉ Ö Ë μ³ μ²μ Î ± ² É Ö Ï Ö É É μ ³μ ² μ É μ³ μ ÒÌ ± ²Ó ÒÌ μ μ μ μ μ³ 1, ±μéμ Ò μ ² ÕÉ É ± ³ ÊÉ ³ ± Éμ Ò³ Î ² ³, ± ± Ô² ±É μ ² Ò Ê ² É μ μ μ. μ μ É ²Ó μ μ ³μ ² μ Ö ³± Ì ±μ³ ÓÕÉ ÒÌ μ ³³ CompHEP/CalcHEP ³μÉ μ ³μ μ ÉÓ μ μ μ μ μ Ö μ ² ÊÕÐ μ É ±É μ Ö ± ²Ó ÒÌ ±Éμ ÒÌ Z - W ± - μ μ μ Ô ÖÌ LHC. Š ± Ï μ±μ É Ò μ μ² É ²Ó Ò ± ² μ μî Ò Z - μ μ Ò, ³ - É ³Ò Z - μ μ ³μ É ÒÉÓ ²Õ ³ μ μ μ μ³ê É- μ ±μ³ê ±Ê ² É ÒÌ ³ ÊÌ ² Éμ μ ±μ Î μ μ μ ÉμÖ Ö. ³ ³ - ² Ö μ μ Î μ³ê ³ Ê²Ó Ê, Ê ²Ê Ò² É ² Éμ μ μ Ò É μé ²Ö Z - μ μ μ μ ² ÕÉ μ Ï μ Í Ë Î ± ³ μ É ³ ( ÉÊ ³ ), ÎÉμ μ μ²ö É ² ±μ μé² Î ÉÓ Ì μé Ê Ì ÉÖ ²ÒÌ μ ÒÌ μ ÉμÖ μ² μ É ³μ É ÒÌ LHC 40 1 Ô É ²± ÕÐ Ì Ö μéμ μ 7 Ô μ³μðóõ É ±Éμ ATLAS Ò² μ μ ± Ê ± Ì É ²Ó ÒÌ μ μ ±- É É ÒÌ ³ e + e μ + μ ±μ Î ÒÌ μ ÉμÖ, É ± μ ± ÉÖ ²ÒÌ Ö ÒÌ Î É Í, ÕÐ Ì Ö Ö Ò ² Éμ É μ. Ò²μ μ Ê μ ± ±μ μ-² μ

3 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 611 É É É Î ± Î ³μ μ ÒÏ Ö ÒÌ μ Ö³ É É μ ³μ ², ÎÉμ μ μ- ² ²μ μ²êî ÉÓ μ Î Ö ³ Ò ± ²Ó ÒÌ É ²Ó ÒÌ Z - Ö ÒÌ W - μ μ μ, μμé É É μ Òe 1,15 1,35 Ô /c 2. ² Ê É μé³ É ÉÓ, ÎÉμ ÔÉμ Ò μ ³ μ Ö³Ò Ô± ³ É ²Ó Ò μ Î Ö μí Ò μ μ Ö W - Z - μ μ μ. Í ²ÓÕ ²Ó Ï μ ² μ Ö ± ²Ó ÒÌ μ μ μ ²μ μ Ö É É Ö Ì μ- ± ÊÌ É Ê ÒÌ μ ÒÉ ÖÌ LHC. ±É Î ± μ Ì μ ³ ÒÌ Ô± μé Î ± Ì ³μ ²ÖÌ μμé É É ÊÕÐ ²Ò μé ÉÖ ²ÒÌ μ μ μ ÕÉ Ö Í É ²Ó μ μ ² É Ò- É μé ÊÌ ±μ Î ÒÌ É Ê y 1,2 0 y 1 y 2 0. μ Ï μ Î ²μ μ Éμ É ²Ö ± ²Ó ÒÌ μ μ μ., μ μ μé, ÕÉ ±² ÔÉÊ μ ² ÉÓ, μ ÖÉ μ ±² ÊÌ- É Ê Ò μ ÒÉ Ö ² μé. Î É μ É, Í ²Ó Ò μ μ ± ³ É Î ± Ì μ Î ³μ É É ± ³ É μ³ê μ ²Ê ±² ± ²Ó ÒÌ μ μ μ Í É ²Ó μ μ ² É, Éμ ³Ö ± ± ±É Î ± ²Ö Ì Ô± μé Î ± Ì ³μ ² ÔÉμ μ ² É μ É Ö ³ É Ò - ÒÉμ± ²Ó ÒÌ μ ÒÉ. PACS: i; t; j INTRODUCTION Gauge interactions are the only well-established fundamental interactions in Nature. The method of the covariant derivatives leads to the unique minimal form of the gauge boson couplings to the matter fermions. Nevertheless, the Yukawa interactions of the Higgs bosons are also necessary for self-consistent construction of the Standard Model (SM). Furthermore, although the gauge symmetry allows anomalous interactions in the initial Lagrangian, all known fundamental spin-1 bosons (photon, W ±, Z boson and gluons) possess only renormalizable minimal interactions with the known fermions. The anomalous interactions are considered as effective ones and are generated at the level of the quantum loop corrections. They are usually proportional to the additional square of a small coupling constant and can be neglected in the ˇrst-order approximation. New heavy neutral gauge bosons are predicted in many extensions of the SM. They are associated with additional U(1) gauge symmetries and are generically called Z bosons. The minimal gauge interactions of these bosons with matter lead to the well-known angular distribution of outgoing leptons (the Z decay product) in the dilepton center-of-mass reference frame dσ Z d cos θ 1+A FB cos θ +cos 2 θ, (1) which at present is interpreted as a canonical signature for the intermediate vector (spin-1) bosons. The coefˇcient A FB deˇnes the backwardäforward asymmetry, depending on P -parity of Z boson couplings to matter. In addition, another type of spin-1 bosons may exist, which leads to a different signature in the angular distribution. This follows from the presence of different types of relativistic spin-1 fermion currents ψγ μ (1±γ 5 )ψ and ν [ ψσ μν (1±γ 5 )ψ], which can couple to the corresponding bosons. A clear example of such a kind of interactions is provided by the hadron physics of the quarkäantiquark mesons,

4 612 CHIZHOV M. V. ET AL. which is considered as a low-energy QCD effective theory, where gluon and quark degrees of freedom are substituted by physical hadronic states. It was pointed out [1] that three different quantum numbers J PC of existing neutral spin-1 mesons, 1, 1 ++,and1 +, cannot be assigned just to two-vector qγ μ q and axial-vector qγ μ γ 5 q quark states, which possess quantum numbers 1 and 1 ++, respectively. The additional quark states ν ( qσ μν q) and ν ( qσ μν γ 5 q) are required, which also describe vector and axial-vector mesons, but with different transformation properties with respect to the Lorentz group and with different quantum numbers 1 and 1 +, respectively. This example demonstrates that the pure tensor state, b 1 meson, exists. Furthermore, due to strong dynamics, vector ρ and ρ mesons have minimal and anomalous couplings with vector ψγ μ ψ and tensor ν ( ψσ μν ψ) interpolating currents comparable in magnitude [2Ä5]. Both the currents have the same quantum numbers J PC =1 and mix. Since the parity and charge conjugation are conserved in QCD, they deˇne the quantum numbers of the mesons. The mesons assigned to the tensor quark states are some types of excited states as far as the only orbital angular momentum with L =1contributes to the total angular momentum, while the total spin of the system is zero. This property manifests itself in their derivative couplings to matter and a different chiral structure of the anomalous interactions in comparison with the minimal gauge ones. In contrast with the minimal gauge couplings, where either only left-handed or right-handed fermions participate in the interactions, the tensor currents mix both left-handed and right-handed fermions. Therefore, like the Higgs particles, the corresponding bosons carry a nonzero chiral charge. To our knowledge, such bosons were ˇrst introduced by Kemmer [6], and they naturally appear in the extended conformal supergravity theories [7]. In fact, this QCD feature can be realized in electroweak physics as well like the technicolor models. This analogy gives us arguments in favor of existence of anomalously interacting vector bosons. Up to now no search for excited bosons has been done, but regular searches for the excited lepton and quark states f have been carried out at the modern colliders, such as LEP [8Ä10], HERA [11, 12], and Tevatron [13, 14]. These excited fermions have magnetic moment (Pauli) type couplings to ordinary matter L f excit = g Λ f σ μν f ( μ Z ν ν Z μ )+h.c., (2) where the parameter Λ is connected to the compositeness mass scale of the new physics. There are no objections to interpreting the interactions (2) from a different point of view, introducing excited boson states instead of fermionic ones ( shifting the -sign to the right from f to Z ) L Z excit = g Λ f σ μν f ( μ Z ν ν Z μ). (3)

5 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 613 This symmetry between excited fermions and bosons further supports our interest in consideration of the anomalously interacting vector bosons. This review paper summarizes our attempts [15Ä19] to ˇll the gap in the consideration of experimental properties of heavy chiral bosons and continues discussions of possibilities of disentangling them from other particles. The material below is given in the following order. In Sec. 1 a simple chiral boson model is formulated for further consideration. Section 2 contains our numerical estimations of the boson properties in the framework of the CompHEP/CalcHEP package [20Ä22]. To this end a new model has been implemented, which includes additional new bosons and their corresponding interactions. In Sec. 3 the ˇrst experimental constraints on the masses of both chiral vector bosons are given. Section 4 briey describes new unique signatures of the bosons in dijet ˇnal states. Our conclusions are given in the last section. 1. THE CHIRAL BOSON MODEL Let us assume that the electroweak gauge sector of the SM is extended by a doublet of new spin-1 chiral bosons Wμ with the internal quantum numbers of the SM Higgs boson. There are at least three different classes of theories, all motivated by the Hierarchy problem, which predict new vector weak doublets with masses not far from the electroweak scale. In particular, they can originate from the extensions of the SM such as GaugeÄHiggs uniˇcation, larger gauge groups or technicolor models [23]. However, due to the lack of fully realistic models, the collider expectations for signals from these chiral bosons have not yet been studied in detail. Nevertheless, it is possible to point out several modelindependent and unique signatures which allow one to identify production of such bosons at the hadron colliders [15]. Since the tensor current mixes the left-handed and right-handed fermions, which in the SM are assigned to different representations, the gauge doublet should have only anomalous interactions L = g ( ) ( ) μ Wν μ W 0 ν D R σ μν UL + g ( ) ( ) UL D M D L σ μν μ Wν D + R L M μ Wν 0, (4) where M is the boson mass, g is the coupling constant of the SU(2) W weak gauge group, and U and D generically denote up-type and down-type leptons and quarks. This choice of couplings makes identical all partial fermionic decay widths of the well-known hypothetical W boson with the SM-like interactions L CC = g 2 W μ D Lγ μ U L + g 2 U L γ μ D L W + μ (5)

6 614 CHIZHOV M. V. ET AL. and the charged W ± boson with the same mass. Here we also assume universality of lepton and quark couplings with different avors. In full analogy with the above-mentioned mesons these bosons, coupled to the tensor quark currents, can be considered as excited states. This property manifests itself in their derivative couplings to fermions and in the different chiral structure of the interactions in contrast to the minimal gauge interactions. For simplicity, in (4) we have introduced only interactions with the downtype right-handed singlets, D R. In particular, in order to allow a possibility of detecting the neutral CP-even Z =(W 0 + W 0 )/ 2 bosons via their decays into charged leptons (the DrellÄYan-like process) they should couple to the down type of fermions L NC = g 2 ( lσ μν l + dσ μν d )( μ Zν 2M νzμ ). (6) Since we have introduced the complex Wμ doublet, there is an additional neutral CP-odd Z =(W 0 W 0 )/ 2 boson. However, in the case of light ˇnal states it is impossible to discriminate the multiplicative quantum numbers of the neutral bosons, namely P and C. Therefore, in the following calculations we will consider only one of them, for instance, the Z boson. For comparison we will consider topologically analogous gauge interactions of the Z boson L NC = g ( lγ μ l + 2 dγ μ d ) Z μ (7) with the same mass M. The coupling constants are chosen in such a way that all fermionic decay widths in the Born approximation of both the neutral bosons are identical. It means that their total production cross sections at the hadron colliders are nearly equal up to next-to-leading order corrections. Their total fermionic decay width M 0.034M (8) 4π is sufˇciently narrow so that they can be identiˇed as resonances at the hadron colliders in the DrellÄYan process. Furthermore, as several Higgs doublets are introduced in many of the SM extensions, the realistic model could include several gauge doublets. Using the charge-conjugated doublet Wμ c = W 0 μ (9) Γ= g2 W μ (or new ones with the hypercharges opposite to the W μ doublet) one can construct more complicated models including up-type right-handed singlets, U R, as well.

7 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS NUMERICAL SIMULATIONS OF THE CHIRAL BOSONS Up to now, any excess in the yield of the DrellÄYan process with high-energy invariant mass of the lepton pairs remains the clearest indication of possible production of a new heavy neutral boson at the hadron colliders. Therefore, we will ˇrst concentrate on consideration of the production and decay of neutral bosons, where full kinematics is experimentally reconstructible. In what follows we will use the CompHEP/CalcHEP package [20Ä22] for the numerical calculations of various distributions for the inclusive processes pp γ/z/z + X l + l + X and pp γ/z/z + X l + l + X with a CTEQ6M choice for the proton parton distribution set at s =10TeV. For both ˇnal leptons we impose angular restrictions (cuts) on the pseudorapidity range η l < 2.5 and the transverse momentum p T > 20 GeV/c, which are relevant to the general LHC detectors. Let us choose M =1TeV/c 2 as a reference mass for new heavy bosons. For the high dilepton masses, the cross sections of the new boson production with this mass at the peak is about two orders of magnitude higher (in our model) than the corresponding DrellÄYan background, being the SM γ and Z boson tails in the invariant dilepton mass distributions (Fig. 1, a). Therefore, the peak(s) should be clearly visible. Fig. 1. a) The invariant dilepton mass distributions for the Z boson (blue) and the excited chiral Z boson (red) with mass 1 TeV/c 2 together with the DrellÄYan SM background (from the photon and the Z boson) at the LHC for s =10TeV. b) The differential cross sections for the gauge Z boson (blue) and the excited chiral Z boson (red) with the DrellÄYan SM background as functions of the lepton transverse momentum at the CERN LHC The peaks in the dilepton invariant mass distributions originate from the BreitÄWigner propagator form, which is the same for both the gauge and chiral neutral bosons in the Born approximation. Concerning discovery of the charged heavy boson at the hadron colliders one believes that the cleanest method is detection of its subsequent leptonic

8 616 CHIZHOV M. V. ET AL. decay into an isolated high transverse-momentum charged lepton (better without a prominent associated jet activity). In this case the heavy new boson can be observed through the Jacobian peak in the transverse p T or m T distribution. It has become proverbial (see, for example, the textbook [24]) that the Jacobian peak is an inevitable characteristic of any two-body decay. However, it is not the case for decays of the new chiral bosons [25]. It has been found in [26] that tensor interactions lead to a new angular distribution of the outgoing fermions dσ(q q Z /W f f) cos 2 θ, (10) d cos θ in comparison with the well-known vector interaction result dσ(q q Z /W f f) d cos θ 1+cos 2 θ. (11) It was realized later [25] that this property ensures a distinctive signature for the detection of the new interactions at the hadron colliders. At ˇrst sight, the small difference between the distributions (10) and (11) seems unimportant. However, the absence of the constant term in the ˇrst case results in very new experimental signatures. The angular distribution for vector interactions (11) includes a nonzero constant term, which leads to the kinematical singularity in the p T distribution of the ˇnal fermion 1 cos θ 1 (12) (M/2)2 p 2 T in the narrow width approximation Γ M 1 (s M 2 ) 2 + M 2 Γ 2 π MΓ δ(s M 2 ). (13) This singularity is transformed into a well-known Jacobian peak due to a ˇnite width of the resonance. In contrast, the pole in the decay distribution of the Z /W bosons is canceled out and the fermion transverse momentum p T distribution even reaches zero at the kinematical endpoint p T = M/2, rather than the Jacobian peak (at the kinematical endpoint M/2) for the gauge bosons (Fig. 1, b). Therefore, even the lepton transverse momentum distribution demonstrates a difference between the gauge and chiral bosons. According to (10), there exists a characteristic plane, perpendicular to the beam axis in the parton rest frame, where emission of ˇnal-state pairs is forbidden. The nonzero probability in the perpendicular direction in the laboratory frame is due to the longitudinal boosts of colliding partons. So, at the Fermilab Tevatron the production of such heavy bosons occurs almost at the threshold with

9 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 617 Fig. 2. The differential cross sections for the gauge Z boson (blue) and the excited chiral Z boson (red) decaying to a lepton pair with the invariant mass 800 <M ll < 1200 GeV/c 2 as functions of the lepton pseudorapidity at the Fermilab Tevatron s = 1.96 TeV (a) and at the CERN LHC s =14TeV (b) approximately zero longitudinal momenta. Hence, the lepton pseudorapidity distribution for the chiral bosons has a minimum at η l =0(Fig. 2, a). On the other hand, the CERN LHC is sufˇciently powerful to produce heavy bosons with the mass M =1TeV/c 2 with high longitudinal boosts. Therefore, the pseudorapidity distributions for the gauge and chiral bosons at the LHC look similar (Fig. 2, b). In order to make more substantial and experiment-looking conclusions, let us investigate signal distributions selecting only on-peak events with the invariant dilepton masses in the range 800 <M ll < 200 GeV/c 2. To this end (as a test example) in [17] for these dilepton masses and kinematical restrictions η l < 2.5 and the transverse lepton momentum p T > 20 GeV/c we have simulated production of dilepton events via pp γ/z/z + X l + l + X and pp γ/z/z + X l + l + X for the LHC integrated luminosity of 100 pb 1 and s =10TeV. As far as the center-of-mass energy for the 2010Ä2011 runs was 7 TeV, at which the cross sections are roughly half as large, 200 pb 1 of data will be equivalent to the case with s =10TeV. For the Z and Z bosons (with mass 1 TeV/c 2 ) production cross sections σ Z =0.45 pb and σ Z =0.41 pb were obtained. The values respectively transform into 44.9 and 41.2 dilepton events in the mass window of 800 <M ll < 1200 GeV/c 2 (see Fig. 3). Under the same kinematical conditions the SM gives 0.6 events with the production cross section 5.75 fb. As already mentioned, the peaks in the invariant mass distributions originate from the BreitÄWigner propagator form, which is the same for both Z and Z bosons in the leading Born approximation. Therefore, in order to discriminate them we need to investigate additional distributions selecting only on-peak

10 618 CHIZHOV M. V. ET AL. Fig. 3. The invariant mass dilepton distributions for the gauge Z boson (a) and the excited chiral Z boson (b) simulated with the common mass 1 TeV/c 2. They consist of 44.9 and 41.2 dilepton events in the mass window of 800 <M ll < 1200 GeV/c 2 for Z and Z bosons events with the invariant dilepton masses in the optimal window size [M 2Γ, M +2Γ]. According to [15], a crucial difference between the neutral chiral bosons and other resonances should come from the analysis of the angular distribution of the ˇnal-state leptons with respect to the boost direction of the heavy boson in the rest frame of the latter (the CollinsÄSoper frame [27]) (Fig. 4). Instead of a smoother angular distribution for the gauge interactions (a), a peculiar swallowtail shape of the chiral boson distribution (b) occurs with a dip at cos θcs =0. It will indicate the presence of the new interactions. Neither scalars nor other particles possess such a type of angular behavior. Indeed, the angular distribution of outgoing leptons for the Z Fig. 4. The differential lepton angular distributions of the gauge Z boson (a) andthe excited chiral Z boson (b) as functions of cos θcs for M =1TeV/c 2

11 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 619 bosons will lead to the large negative value of the so-called centre-edge asymmetry A CE : σ A CE = +1/2 1/2 dσ d cos θcs d cos θcs +1 +1/2 + dσ d cos θcs d cos θcs + 1/2 1 dσ d cos θcs d cos θcs, (14) while the distributions of other known resonances (even with different spins) possess positive or near-zero asymmetries. Using this asymmetry, one can strongly reduce the systematic uncertainties from the hadron structure [28]. Another unexpected consequence of the new form of angular distribution (10) is a very different shape of the event distribution over pseudorapidity difference (η 1 η 2 ) between both outgoing charged leptons. It is shown in Fig. 5. Combining these distributions one will have a possibility of differentiating these bosons for higher resonance masses. Fig. 5. The differential distributions for the gauge Z boson (a) and the excited chiral Z boson (b) as functions of the difference of the lepton pseudorapidities for M =1TeV/c 2 We would like again to consider the distributions of the lepton transverse momentum p T. As mentioned before and demonstrated for our simulated sample in Fig. 6, the relevant Z and W boson decay distributions have a broad smooth hump with the maximum below the kinematical endpoint, instead of an expected sharp Jacobian peak. Therefore, in contrast to the usual procedure of the direct and precise determination of the W resonance mass, the new distribution does not allow doing it for W bosons. Moreover, even a relatively small decay width

12 620 CHIZHOV M. V. ET AL. Fig. 6. The differential distributions for the Z boson (a) and the chiral excited Z boson (b) as functions of the lepton transverse momentum p T for M =1TeV/c 2,theLHC integrated luminosity of 100 pb 1 and s =10TeV of the chiral bosons has a wide p T as resonances at hadron colliders. distribution that obscures their identiˇcation 3. THE FIRST EXPERIMENTAL CONSTRAINTS ON THE CHIRAL BOSONS The ˇrst direct experimental search for the excited chiral vector bosons was performed by the ATLAS Collaboration [29Ä31] in At the LHC energy of 7 TeV with the integral luminosity around 40 pb 1, the ATLAS detector was used for searching for narrow resonances in the invariant mass spectrum above 110 GeV/c 2 of e + e and μ + μ ˇnal states. The main physical results of the relevant paper Search for High-Mass Dilepton Resonances in pp Collisions at s =7TeV with the ATLAS Experiment [32] are presented in Fig. 7 together with main backgrounds and expected Z decay signals for three masses around 1TeV/c 2. Expected signals from the Z boson decays considered in this paper (are shown in Fig. 8) have similar shapes and approximately 40% larger cross sections. Three interesting events in the vicinity of m ee = 600 GeV/c 2 and a single event at m μμ = 768 GeV/c 2 are observed. All details of the data selection and the physical data analysis can be found in [32]. It is seen that both the dielectron and dimuon invariant mass distributions are well described by the prediction from SM processes. From these ˇgures one can conclude that no statistically signiˇcant excess above the SM expectation is observed with these data samples. Nevertheless, these distributions were for the ˇrst time used to obtain a lower direct mass limit (1.152 TeV/c 2, see below) for the neutral chiral Z boson described in this paper. To this end, 95% CL exclusion limits on

13 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 621 Fig. 7. Dielectron (a) and dimuon (b) invariant mass distributions measured by the ATLAS Collaboration in 2010 [32]. They are compared with all expected backgrounds and three examples of Z signals Z production and its dilepton decay, σb, for the combination of the electron and muon Z boson decay channels were used. The combination was performed by deˇning the likelihood function in terms of the total number of Z events produced in both channels. In the three cases (dielectron, dimuon, and combined channels), the 95% CL σb limit was used to set mass limits for each of the considered models. The observed combined mass limit for the Sequential Standard Model Z SSM is TeV/c 2. The limits on the E6-motivated Z bosons are in the range 0.738Ä TeV/c 2. Although the angular lepton decay distributions are not the same for Z and Z bosons, it was found that the difference in geometrical acceptance is negligible for the boson pole masses above 750 GeV/c 2. Therefore, the same

14 622 CHIZHOV M. V. ET AL. Fig. 8. Dielectron (a) and dimuon (b) invariant mass distributions after ˇnal selection, compared to the stacked sum of all expected backgrounds, with three examples of Z signals overlaid procedure as for the Z bosons is used to calculate the limit on σb(z l + l ) and on the Z boson mass in each channel and for their combination. Finally the observed combined lower mass limit for the Z boson is TeV/c 2.Thisis the ˇrst direct mass limit on this particle. The Z limits are about 100Ä200 GeV/c 2 more stringent than the corresponding limits on all considered Z bosons. Furthermore, in 2010 the ATLAS Collaboration searched for high-mass states, such as heavy charged gauge bosons (W, W ), decaying to a charged lepton and a neutrino (see Fig. 9). The relevant paper Search for High-Mass States with One Lepton Plus Missing Transverse Momentum in ProtonÄProton Collisions at s =7TeV with the ATLAS Detector contains all details of event selection and physical data analysis [33].

15 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 623 Fig. 9. a) Spectra of p T (top), missing E T (center), and m T (bottom) for the muon channel obtained in [33]. The points represent the ATLAS data and the ˇlled histograms show the stacked backgrounds. Open histograms are W signals. The QCD background is estimated from the data. b) Limits at 95% CL for W production in the decay channels W /W eν (top), W /W μν (center), and their combination (bottom). The solid lines show the observed limits with all uncertainties. The expected limit is indicated with dashed lines surrounded by shaded 1σ and 2σ bands. Dashed lines show the theory predictions with their uncertainties indicated by solid lines The search for heavy charged resonances inclusively produced at the LHC looks more complicated than the search for neutral states due to the absence of the second decay particle Å the undetectable neutrino. In this case the kinematic

16 624 CHIZHOV M. V. ET AL. variable used to identify the W /W is the transverse mass m T = 2p T ET miss (1 cos φ lν ) which displays a Jacobian peak that, for W lν, falls sharply above the resonance mass. Here p T is the lepton transverse momentum, ET miss is the magnitude of the missing transverse momentum (missing E T ), and φ lν is the angle between the p T and missing E T vectors. In the analysis [33], transverse refers to the plane perpendicular to the colliding beams, longitudinal means parallel to the beams, θ and φ are the polar and azimuthal angles with respect to the longitudinal direction, and pseudorapidity is deˇned as η = ln (tan (θ/2)). The main physical results obtained in [33] and relevant to our consideration are given in Fig. 9. The left panel of Fig. 9 shows the p T, missing E T, and m T spectra measured in the muon decay channel for the data, for the expected background, and for three examples of W signals at different masses as open histograms. The W boson signals are not shown. The QCD background is estimated from the data. The signal and other background samples are normalized using the integrated luminosity of the data and the NNLO (near-nnlo for t-tbar) cross sections. Furthermore, the σb uncertainties for the W boson are obtained by varying renormalization and factorization scales and by varying PDFs. Only the latter are employed for the W boson search. One can see from the ˇgures that the agreement between the data and the expected background is rather good. No excess beyond the Standard Model expectations is observed. The lower mass limits expected and obtained from these measurements are depicted in Fig. 9, b. The ˇgure also shows the expected limits and the theoretical W /W σb as a function of m T for both channels and their combination. The intersection between the central theoretical prediction and the observed limits provides the 95% CL lower limit on the mass. It was found that the charged chiral W boson considered in the paper was excluded for masses below TeV/c 2. These are the ˇrst direct limits on the W boson production. 4. DIJET SIGNALS OF THE CHIRAL BOSONS In what follows we will extend the set of possible experimental observables of the chiral bosons to the rich ˇeld of hadron ˇnal states, in particular, we consider peculiarity of the decay of these bosons into two hadronic jets. In fact, we will draw extra attention to a novel signal of new physics in the dijet data at the hadron colliders. It is usually accepted that all exotic models predict that these two jets populate the central (pseudo)rapidity region where y 1,2 0. Contrariwise, the excited bosons do not contribute into this region, but produce an excess of dijet

17 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 625 events over the almost at QCD background in χ =exp y 1 y 2 away from this region. At the hadron colliders, inclusive dijet production has one of the largest cross sections and allows data-driven background estimation at the early stage of the collider operation. The feature can be used to search for a signal of new physics in the very early data. In particular, a possible bump in the dijet invariant mass spectrum would indicate the presence of a resonance decaying into two energetic partons. Nevertheless, we could say nothing about its nature, because this bump stems from the BreitÄWigner propagator form, which is characteristic of any type of resonance regardless of its other properties, like spin, internal quantum number, etc. Therefore, other observables are necessary in order to conˇrm the bump and to reveal the resonance properties. As in the lepton case (discussed above), this kind of observable could be the dijet distribution over the polar angle θ, which is an angle between the axis of the jet pair and the beam direction in the dijet rest frame. This distribution is directly sensitive to the resonance spin and the dynamics of the underlying process [27]. While the QCD processes are dominated by t-channel gluon exchanges, which lead to the Rutherford-like dijet distribution 1/(1 cos θ) 2, exotic physics processes proceed mainly through the s channel, where the spin of the resonance uniquely deˇnes the angular distribution. For high-mass resonances and practically massless partons it is convenient to use the helicity formalism since the helicity is a good quantum number for massless particles. In fact, in the center-of-momentum frame of a particle with spin s and helicity λ ( s λ s) decaying into two massless particles with helicities λ 1 and λ 2, the angular distribution of the outgoing particle can be written as [34] dγ s d cos θdφ = 1 64π 2 M 2s π ei(λ δ)φ d s λδ (θ) Ms λ 1λ 2, (15) where δ λ 1 λ 2 with s δ s. The reduced decay amplitude M s λ 1λ 2 is only a function of s and the helicities of the outgoing particles. It does not dependent on the azimuthal φ and polar θ angles. The θ dependence is concentrated only in the well-known d functions d s λδ (θ). Furthermore, the absolute value of the dijet rapidity difference is related to the polar scattering angle θ with respect to the beam axis by the formula Δy y 1 y 2 =ln[(1+ cos θ )/(1 cos θ )] 0 and is invariant under boosts along the beam direction. The choice of the other variable χ exp (Δy) =(1+ cos θ )/(1 cos θ ) 1 is motivated by the fact that the distribution of the Rutherford scattering is at in this variable. These variables allow systematic consideration of angular decay distributions of resonances with different spins and different interactions with partons. The simplest case of the resonance production of a (pseudo)scalar particle h with spin 0 in the s channel leads to a uniform decay distribution in the

18 626 CHIZHOV M. V. ET AL. scattering angle dγ 0 (h q q) d 0 d cos θ (16) The spin-1/2 fermion resonance, like an excited quark q, leads to asymmetric decay distributions for the given spin parton conˇgurations dγ 1/2 (q qg) 1/2 d 2 d cos θ 1/2,±1/2 1 ± cos θ. (17) However, the choice of the variables which depend on the absolute value of cos θ cancels out the apparent dependence on cos θ. In other words, both distributions (17) for dijet events look like uniform distributions in Δy and χ. According to the simple formula dγ d(δy/χ) = d cos θ d(δy/χ) dγ d cos θ, (18) the uniform distribution leads to kinematical peaks at the small values Δy =0 (the dotted curve in Fig. 10, a) andχ =1(the dotted curve in Fig. 10, b) dγ 0 dδy e Δy (e Δy +1) 2 and dγ 0 dχ 1 (χ +1) 2. (19) There are two different possibilities for spin-1 resonances. The gauge bosons, which are associated with additional U(1) gauge symmetry (or transform under the adjoint representation of the extra gauge group), are generally called Z (W ) particles. They have minimal gauge interactions with the known light fermions (see Eqs. (7) and (5)), which preserve the fermion chiralities and possess maximal Fig. 10. The normalized angular dijet distributions as functions of the absolute value of the rapidity difference (a) and the χ variable (b) for the scalar (or/and spin-1/2) bosons, the gauge bosons with the minimal coupling, and the excited bosons are shown by the dotted, dash-dotted, and solid curves, respectively. From [18]

19 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 627 helicities λ = ±1. At a symmetric pp collider, like the LHC, such interactions lead to the symmetric angular distribution (11) of the decay products over the polar angle θ: dγ 1 (Z q q) d 1 11 d cos θ 2 + d cos 2 θ. (20) Similar to the uniform distribution (16), this one also leads to kinematical peaks at small values of Δy =0(the dash-dotted curve in Fig. 10, a) andχ =1(the dash-dotted curve in Fig. 10, b) dγ 1 dδy eδy (e 2Δy +1) dγ 1 (e Δy +1) 4 and dχ χ2 +1 (χ +1) 4. (21) Another possibility is the resonance production and decay of new longitudinal spin-1 bosons with helicity λ =0. These bosons arise in many extensions [23] of SM which solve the hierarchy problem. They are transformed as doublets (Z W ) under the fundamental representation of the SM SU(2) W group like the SM Higgs boson. They are above-mentioned extra chiral bosons (see (4)). While the Z bosons with helicities λ = ±1 are produced in left(right)-handed quark and right(left)-handed antiquark fusion, the longitudinal Z bosons can be produced through the anomalous chiral couplings with the ordinary light fermions in left-handed or right-handed quarkäantiquark fusion [15]. As already noted before, these anomalous couplings lead to a different angular distribution of the resonance decay dγ 1(Z q q) d 1 d cos θ 00 2 cos 2 θ. (22) As has already been noted for the dilepton case, the absence of the constant term in (22) results in novel experimental signatures. First of all, the uniform distribution (16) for scalar and spin-1/2 particles and the distribution (20) for gauge vector bosons with minimal coupling include a nonzero constant term, which leads to a kinematic singularity in the transverse momentum distribution of the ˇnal parton (as for charged leptons, see (12) and (13)). After smearing of the resonance ˇnite width, the singularity is transformed into the well-known Jacobian peak (the dash-dotted curve in Fig. 11, a). The analytic expression of the p T distribution describing the Jacobian peak with ˇnite width can be found in [35]. Using the same method one can derive an analogous distribution for the excited bosons (the solid curve in Fig. 11, a). dγ 1 dp T p T (4p 2 T M 2 ) 2 +Γ 2 M 2 4p 2 T + M 2. (23) In contrast to the previous case, the pole in the decay distribution of the excited bosons is canceled out and the ˇnal parton p T distribution has a broad smooth

20 628 CHIZHOV M. V. ET AL. Fig. 11. The ˇnal parton transverse momentum (a) and the angular (b) distributions from the decay of the gauge (dash-dotted curves) and excited (solid curves) bosons. From [18] hump [25] with a maximum at p T = (M 2 +Γ 2 )/8 M/ 8 below the kinematic endpoint p T = M/2 instead of a sharp Jacobian peak, which obscures their experimental identiˇcation as resonances. Therefore, the transverse jet momentum is not the appropriate variable for the excited boson search. Another striking feature of the distribution (22) is the forbidden decay direction perpendicular to the boost of the excited boson in the rest frame of the latter (the CollinsÄSoper frame [27]). It leads to a profound dip at cos θ =0 in the CollinsÄSoper frame [15] in comparison with the gauge boson distribution (Fig. 11, b). Similar dips also occur at the small values Δy =0[17] (the solid curve in Fig. 10, a) andχ =1(the solid curve in Fig. 10, b) dγ 1 dδy eδy (e Δy 1) 2 (e Δy +1) 4 and dγ 1 dχ (χ 1)2 (χ +1) 4. (24) It can be seen from Fig. 10 that the excited bosons have a unique signature in the angular distributions. They manifest themselves through the absolute minima at the small values Δy =0and χ =1and absolute maxima right away from the origin. So, the rapidity difference distribution reaches the absolute maximum at Δy =ln(3+ 8) 1.76 and at χ =3for the angular distribution in the dijet variable χ. These features will be considered below in more detail. In order to have more practical analysis, it is convenient to use equidistant binning in log χ [36], which corresponds to periodic cell granularity of the calorimeter in η. In this case the smooth χ-spectra (see Eqs. (21) and (24)) are transformed into histograms with the maximum in the lowest bin for the gauge bosons with the minimal coupling and with the maximum in the bin containing the value χ = for the excited bosons (Fig. 12).

21 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 629 Fig. 12. The normalized histograms of χ spectra for the gauge bosons with the minimal coupling (a) and for the excited bosons (b). From [18] Using distributions in (pseudo)rapidity and χ one can construct two useful ratios of numbers of events N measured under speciˇed experimental constraints schematically given below in brackets. The ˇrst is the wide-angle to small-angle ratio N(1 <χ<a) R χ (a, b) = N(a <χ<b), (25) and the second is centrality or the η ratio of both jets R η (a, b) = N( η 1,2 <a) N(a < η 1,2 <b). (26) The ratios are less affected by the systematic uncertainties and can be used for searching for new physics in dijet data. To understand how they work, let us suppose that one has found some bump in the experimental dijet invariant mass distribution. Then we can compare the angular distributions for on-peak events (or events comprising the bump) and off-peak events (or events far away from the bump), using the aforementioned ratios. At the moment we ignore the complications of experimental separation of on-peak events from the offpeak ones. Since the QCD background is dominated by the Rutherford-like distribution, we can consider, as an approximation, a simple case where the QCD dijet χ distribution is at. It means that for the selected equal kinematical regions b a = a 1 (b =2a 1), the ratio R χ for the off-peak events should be approximately one and does not depend on the dijet mass. When the on-peak events originate from the new physics and have the angular distribution different from the one predicted in QCD, the ratio R χ should deviate from one. Due to an excess at small χ values irrespective of the maximal χ value (in our case equals to a) one has R χ > 1 for all known exotic models, except the excited bosons, when one expects R χ < 1.

22 630 CHIZHOV M. V. ET AL. In order to emphasize the effect of the excited bosons (to increase sensitivity to these bosons), we need to choose a value of a, which makes the ratio as small as possible R χ (a, 2a 1) = N QCD + N new (<a) N QCD + N new (>a) 1+ N new(< a) N new (>a) < 1. (27) N QCD Here N new (<a) and N new (>a) denote the number of events generated by the new physics in the regions 1 <χ<aand a<χ<2a 1, respectively. Simple integration gives the QCD contribution N QCD (1 <χ<a) a dχ = N QCD (a< χ<2a 1) 2a 1 a dχ =(a 1). Simialr integrations of the χ distribution (24) in 1 <χ<aand a<χ<2a 1 give N new (<a) (a 1) 3 /(a +1) 3 and N new (>a) (a 1) 3 /a 3 N new (<a), respectively. Therefore, due to the monotonic increase of the distribution (24) to the maximum at χ =3it is possible to reach the minimal value for (27) with the parameters a 1.87 and b In our ideal case these parameters are optimal for the search for excited bosons with the ratio (25). The larger value a 1/( 3 2 1) 3.85 will lead to a compensation of the contributions from the low and high χ parts (N new (<a) N new (>a)), and R χ 1 again. For the QCD generated dijets the centrality ratio R η (26) is also almost constant and should not depend on the dijet invariant mass when the parameters a and b are ˇxed. When a dijet new-physics signal takes place, this ratio could deviate from its constant value. Signal events for almost all exotic models are expected in the central (pseudo)rapidity region. Therefore, one could see a bump in the R η distribution as a function of the dijet mass. Contrariwise, the signal from the excited bosons could lead to a novel signature: instead of the bump one will have a dip in the distribution at the resonance mass. To investigate quantitatively this possibility we have again used the CompHEP package [20, 21], which was extended with the excited bosons model of [37]. In particular, two-dimensional pseudorapidity distributions were generated for 2 2 processes proceeding through the gauge W and excited W boson resonances with the same mass 550 GeV/c 2 at s =7TeV pp collider (Fig. 13). The CTEQ6L parton distribution functions were used. For both ˇnal jets we impose cuts on the pseudorapidity η < 2.5 and the transverse momentum p T > 30 GeV/c. To minimize the potential differences in jet response and efˇciency of jet registration between the inner and outer dijet events one can choose the central region of the calorimeter η < 1. Using calculations given in the scatter plots (Fig. 13) one can estimate the centrality ratios (26) for the gauge 1

23 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 631 Fig. 13. The two-dimensional pseudorapidity distributions (scatter plots) of dijet events for the gauge bosons with the minimal coupling (a) and for the excited bosons (b). The central region η1,2 < 0.5 and outer regions 0.5 < η1,2 < 1.0 are depicted. The hatched squared regions correspond to selected events with opposite pseudorapidity signs. From [18] and excited bosons Rη (0.5, 1.0) 1.08 and Rη (0.5, 1.0) (28) The dramatic difference between these two numbers is clearly seen, it should lead to the corresponding experimental signature. Since the QCD ratio RηQCD (0.5, 1.0) 0.6 is located right between the numbers, the gauge bosons with the minimal coupling will lead to an increase in the QCD ratio at the resonance mass, while the excited bosons should decrease the ratio. It is interesting to notice that a hint of this type of the novel signature can be seen in the lowstatistics distribution of the η-ratio versus the dijet invariant mass in the ATLAS data in approximately the same mass range, 450 < Mjj < 600 GeV, as for the resonance bump in the dijet events [38]. Unfortunately, one should stress that the extensions of the signal region up to η < 1.3 and the central region up to η < 0.7 do not change drastically the QCD ratio RηQCD (0.7, 1.3) 0.55, but dilute the signal from the excited bosons since Rη (0.7, 1.3) In order to increase the sensitivity to the excited bosons one can consider the centrality ratio only for the dijet events with the opposite pseudorapidities Rη (η1 η2 ) 0 = Rη (the hatched regions in Fig. 13). In this case the difference between R and R increases R η (0.5, 1.0) 1.12 and R η (0.5, 1.0) 0.25, (29)

24 632 CHIZHOV M. V. ET AL. Fig. 14. The normalized histograms of the Δη-spectra for the gauge bosons with the minimal coupling (a) and for the excited bosons (b). The solid curves correspond to the theoretical formulas (21) and (24). From [18] but we lose half of the statistics. Therefore, it is convenient to consider the distribution in Δη η 1 η 2 0 for the events in the rectangle region Δη <b and η B η 1 + η 2 <c.thecutη B <cis necessary to reduce the effect of the parton distribution functions on different Δη bins. The corresponding centrality ratio R Δη is deˇned as N(Δη <a) R Δη (a, b, c) =. (30) N(a <Δη <b) ηb <c The normalized histograms of the Δη-spectra and the theoretical curves are shown in Fig. 14 for the following parameters values: b =3.5 and c =1.5. It can be seen from the ˇgure that the theoretical distributions describe very well the above-mentioned simulation data. In the same way as it was done for the χ distribution of the excited bosons, one can maximize the deviation of R Δη (a, b, c) from the QCD ratio R QCD Δη = N (a) (b a) QCD /N QCD. One ˇnds the desired minimum of R Δη (a, b, c), which corresponds to the maximal deviation from QCD, for c =1.5, b =1and a =0.67 [18]. CONCLUSION In this review, phenomenological consequences of the Standard Model extension are summarized by means of new spin-1 chiral ˇelds with the internal quantum numbers of the electroweak Higgs doublets. It is worth stressing that the new type of spin-1 chiral bosons can exist. They are well motivated from the point of view of the Hierarchy problem and are predicted by at least three different classes of theories that represent different approaches to explanation of

25 ANOMALOUSLY INTERACTING NEW EXTRA VECTOR BOSONS 633 the relative lightness of the Higgs doublets. The decay distributions of the chiral bosons differ drastically from the distributions of the known gauge bosons and can be distinguished from others. The discovery of this type of distributions will point to existence of compositeness, new symmetry and even extra dimensions. The prospects for resonance production and detection of the chiral vector Z and W ± bosons at the LHC energies are considered on the basis of quantitative simulations within the CompHEP/CalcHEP package. The experimental signatures of the excited chiral heavy Z bosons are considered and compared with those of the gauge Z bosons. The Z boson can be observed as a BreitÄWigner resonance peak in the invariant dilepton mass distributions in the same way as the well-known extra gauge Z bosons. This naturally puts the chiral bosons on the list of very interesting objects for early searches with the ˇrst LHC data. Moreover, Z bosons have unique signatures in transverse momentum, angular, and pseudorapidity distributions of the ˇnal decay products, which allow one to distinguish them from other heavy neutral resonances. In particular, there is no Jacobian peak in the transverse momentum distribution of the decay products, and the angular distribution (in the CollinsÄSoper frame for high on-peak invariant masses) has a peculiar swallowtail shape. In 2010, with 40 pb 1 of the LHC protonäproton data at energy 7 TeV, the ATLAS detector was used to search for narrow resonances in the invariant mass spectrum of e + e and μ + μ ˇnal states and high-mass charged states decaying to a charged lepton and a neutrino. No statistically signiˇcant excess above the Standard Model expectation was observed. Therefore, low mass limits of 1.15 and 1.35 TeV/c 2 were obtained for the neutral chiral Z and charged W bosons, respectively. These are the ˇrst direct limits on the W and Z boson production. Finally, a novel strategy for the neutral chiral boson search in the LHC dijet data is discussed. For almost all currently considered exotic models the relevant signal is expected in the central dijet rapidity region y 1,2 0 and y 1 y 2 0. Contrariwise, the excited bosons do not contribute to this region but produce an excess of dijet events far away from it. In particular, for these bosons the appropriate kinematic restrictions can lead to a dip in the centrality ratio distribution over the dijet invariant mass instead of a bump expected in the most exotic models. We expect that the experimental results, presented here and based on low statistics of 2010 will be very soon improved with much higher statistics of Furthermore, we plan to extend our search for excited bosons by means of thorough investigation of the dijet data from the ATLAS detector at the LHC. Acknowledgements. We are very grateful to O. Fedin and his colleagues for fruitful cooperation, V. G. Kadyshevsky and N. A. Russakovich for support