I review the current experimental bounds and theoretical predictions for
different kinds of heavy neutral vector bosons.Comment: Talk given at: V Workshop Italiano sulla fisica p-p ad LHC, Perugia,
  Italy, 30 Jan. - 2 Feb. 200

Contino, Roberto

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I review the current experimental bounds and theoretical predictions for different kinds of heavy neutral vecto

Contino Roberto

Archivio istituzionale della Ricerca - Scuola Normale Superiore

Z', Z(KK), Z* and all that: Current bounds and theoretical prejudices on heavy neutral vector bosons

CONTINO, ROBERTO

Archivio della ricerca- Università di Roma La Sapienza

Z', Z_KK, Z* and all that: current bounds and theoretical
 prejudices on heavy neutral vector bosons

I review the current experimental bounds and theoretical predictions for different kinds of heavy neutral vector bosons.I review the current experimental bounds and theoretical predictions for different kinds of heavy neutral vector bosons

CERN Document Server

Z ′, ZKK, Z∗ and all that: current bounds and theoretical prejudices onheavy neutral vector bosons.R.ContinoCERN Physics Department, Theory Division, CH-1211 Geneva 23, SwitzerlandAbstract. – I review the current experimental bounds and theoretical predictionsfor different kinds of heavy neutral vector bosons.1. – The case of a “standard” Z ′Heavy neutral vector bosons appear in the particle content of many extensions ofthe Standard Model (SM), and their detection in dilepton channels is often mentionedas one example of early discovery mode at the Large Hadron Collider (LHC). I thistalk I will briefly review the theoretical lore and the present experimental bounds onthese heavy particles.The interaction of a heavy Z ′ with the Standard Model fermions and Higgs bosoncan be parametrized in terms of the overall coupling strengths g[Ψ]Z′ , g[H]Z′ , and of(quantized) charges za, zH :LZ′ = −14Z ′µνZ′µν + g[Ψ]Z′∑aZ ′µ Ψ¯azaγµΨa + g[H]Z′ H†zHZ ′µiDµH + h.c. , (1)where a = Q, d, u, L, e runs over all SU(2)L SM representations. The last term, inparticular, leads to Z ′ − Z mixing after electroweak symmetry breaking (EWSB).A natural possibility is that the Z ′ is the gauge field of a new local symmetrybroken at high energies, so that g[Ψ]Z′ = g[H]Z′ = gZ′ . To avoid large flavor-changingneutral currents, it is also commonly assumed in the literature that the couplingsof the Z ′ to the SM fermions are flavor universal. I will refer to this case as thatof a “standard” Z ′ [1]. Examples are: a heavy B − L gauge boson; a Zψ fromE6 Grand Unified Theories, where E6 → SO(10)× U(1)ψ at the unification scale(gZ′ = g2 tan θW and charge equal to√5/72 (−√5/72) for all left-handed (right-handed) SM fermions); a heavy replica of the SM Z, (gZ′ = g2/ cos θW and chargesgiven by (T3L −Q sin2 θW )); a heavy replica of the hypercharge.The main indirect bounds on the Z ′ mass and couplings come from LEP experi-ments. A tree-level exchange of a heavy Z ′ affects both the off-pole LEP2 observables,through the generation of four-fermion contact interactions ∝ g[Ψ] 2Z′ , and the Z-pole1arXiv:0804.3195v1  [hep-ph]  20 Apr 2008∝ g[Ψ] 2Z′M2Z′(a)∝ g[H]Z′ g[Ψ]Z′M2Z′∝ g[H] 2Z′M2Z′(b) (c)Figure 1: Corrections to LEP observables from the tree-level exchange of a heavy Z ′:contact interactions (a); vertex corrections (b); corrections to the ρ parameter (c).LEP1 observables via the Z ′ − Z mixing, see figure 1. In the case of the latter, itis useful to distinguish between vertex corrections ∝ g[H]Z′ g[Ψ]Z′ , and corrections to theρ parameter ∝ g[H] 2Z′ . These corrections are said to be oblique, or universal, if theycan be recast as pure modifications of the SM gauge boson self energies by making asuitable redefinition of fields. In this case it has been shown that all LEP observablescan be expressed in terms of only four parameters, or form factors: Sˆ, Tˆ , W , Y [2].For example, a heavy hypercharge leads to oblique corrections, while a heavy B −L,a Zψ or a heavy Z are not oblique. Notice that the oblique basis does not usuallycoincide with the mass-eigenstates basis. Besides LEP indirect constraints, directexclusion limits on the Drell-Yan production qq¯ → Z ′ → l+l−, l = e, µ come fromD6O and CDF experiments [3].The left plot of figure 2 shows the bounds on a heavy B − L with mass MZ′ andarbitrary coupling strength gZ′ . The (darker) blue region is excluded by the CDFRunII results of [3], which were derived collecting 1.3 fb−1 of data. The exclusionregion in (lighter) gray is instead obtained using the fit to the LEP electroweak dataof reference [4]. 1For a Z ′ coupling strength equal to the SM value, gZ′ = g′ = g2 tan θW , CDFexcludes masses up to ∼ 950 GeV, while the bound from LEP is MZ′ & 1.65 TeV.Even for such latter values of the mass, the Drell-Yan production rate pp→ Z ′ → l+l−(l = e, µ) at the LHC is still large, σ × BR ' 200 fb, corresponding to a discoveryluminosity of ∼ 100 pb−1, see figure 2 and [6]. Similar results hold for a Zψ, a heavy1The plots in figure 2 and 3 have been obtained computing the Z ′ production cross section withthe approximate formula in eq.(3.16) of reference [5]. This gives a reasonably accurate result exceptfor low masses, where it slightly underestimates the cross section.2ΣHpp®Z'L´BRHZ'®llL103 fb102 fb10 fb1 fbExcluded by LEPExcludedbyTevatron0.5 1.0 1.5 2.0 2.5 3.0 3.50.51.01.52.0MZ' @TeVDgZ'g 'Z' = Heavy HB-LLΣHpp®Z'L´BRHZ'®llL102 fb10 fb1 fb0.1 fbExcluded by LEPExcludedbyTevatron0.5 1.0 1.5 2.0 2.5 3.0 3.50.51.01.52.0MZ' @TeVDgZ'g 'ZΨ from E6SOH10LFigure 2: Constraints on the mass and the coupling strength of a heavy B − L (left plot)and a Zψ from E6/SO(10) (right plot). The coupling strengths are expressed in units of theSM value g′ = g2 tan θW . The red curves report the production rate σ(pp → Z ′ → l+l−),with l = e, µ.hypercharge and a heavy Z. The case of the Zψ is shown in the right plot of figure 2.Larger values of gZ′ are more constrained by LEP, requiring larger integratedluminosities for a discovery. In particular, a strongly coupled Z ′ (1  gZ′ < 4pi) isexcluded by LEP unless it has a very large mass. The most robust constraint comesfrom the contact interactions of fig.1(a), which are proportional to g[Ψ] 2Z′ : for genericcharges za ∼ O(1) the ratio (g[Ψ]Z′ /MZ′) cannot be too large. On the other hand, thetree-level correction to the ρ parameter will vanish if the Z ′ originates from a newsector that preserves a custodial symmetry after EWSB [7]. In this case, the onlyother constraint comes from the vertex correction of fig.1(c), leaving the possibilityof a large value of g[H]Z′ provided g[Ψ]Z′ is small. In fact, different coupling strengths g[H]Z′and g[Ψ]Z′ can naturally emerge in theories where both the heavy vector and the Higgsfield are bound states of a new strongly-interacting dynamics.2. – Strongly coupled Z∗Particularly attractive and theoretically motivated is the possibility that the SMgauge fields themselves have some degree of compositeness: they could arise as ad-mixtures of an elementary field Aµ with a tower of resonances of the strong sector,ρˆµ. In complete analogy with the photon-ρ mixing occurring in QCD, the Aµ − ρˆµ3mixing can proceed via a mass termLmix = M2∗2(gelg∗Aµ − ρˆµ)2, (2)where gel and g∗ denote respectively the gauge coupling of Aµ and the couplingstrength among three composite states. It is natural to assume 1  g∗ < 4pi, andgel . 1. Due to Lmix, the combination (gelAµ − g∗ρˆµ) acquires a mass M∗, while theorthogonal one – to be identified with the SM gauge field – remains massless. Afterrotating from the elementary/composite basis to the mass-eigenstates basis, one has:|SM〉 = cos θ |Aµ〉+ sin θ |ρˆµ〉|heavy〉 =− sin θ |Aµ〉+ cos θ |ρˆµ〉tan θ =gelg∗, gSM =gelg∗√g2el + g2∗' gel . (3)Here θ parametrizes the degree of compositeness of the SM field. While the Higgsin such a scheme is a full composite (solving in this way the SM hierarchy problemvia dimensional transmutation), the SM fermions can also be partial composites as aconsequence of their mixing with a tower of fermionic resonances of the strong sector.Theories with a warped extra dimension, with their 4-dimensional dual description,are explicit realizations of this scenario (see, for example, [8]). In particular, the towerof heavy resonances in the mass eigenstate basis is interpreted as the Kaluza-Klein(KK) modes of the higher-dimensional theory.The phenomenology of a heavy neutral vector Z∗ that is the result of the ele-mentary/composite mixing of eq.(3) – or, equivalently, that of a KK in a warpedextra-dimensional theory – is rather different from the phenomenology of a “stan-dard” Z ′. The LEP2 precision tests imply that the degree of compositeness of thelight fermions has to be very small. On the other hand, the large top quark masscan find a natural explanation if the top is mainly composite. This means that theDrell-Yan production of Z∗ will mostly proceed via the interaction of its elementarycomponent with the light partons of the proton. The coupling strength for this scat-tering is ∼ gel sin θ = gSM tan θ, implying a suppression factor tan θ = gel/g∗  1compared to the SM value. Moreover, the same factor will also suppress the decayrate to light quarks and leptons. The Z∗ will instead couple strongly, via its com-posite component, to all the SM particles with a sizable degree of compositeness: theHiggs, the longitudinally polarized W and Z’s, the top and bottom quarks. In otherwords, the Z∗ will mainly decay to hZL, W+LW−L , tt¯ or bb¯, while the branching ratioto a pair of electrons or muons will be quite small. For example, the decay rates of a4ΣHpp®W3*L´BRHW3*®llL102 fb10 fb1 fb0.1 fb10-2 fbExcludedbyLEPExcluded by Tevatron0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01.01.52.02.53.03.54.0M*@TeVDg*Figure 3: Constraints on the mass and the coupling strength of vectorial resonances inthe adjoint of SU(2)L×SU(2)R×U(1)B−L (see text). The red curves report the productionrate of the neutral W ∗3 to two charged leptons: σ(pp→W ∗3 → l+l−), with l = e, µ.heavy W ∗3 (the neutral component of a heavy SU(2)L triplet) are [8]Γ (W ∗3 → qq¯) = 3 Γ(W ∗3 → ll¯) ' g22 tan2θ32piM∗Γ (W ∗3 → tLt¯L) = Γ(W ∗3 → bLb¯L)=(sin2ϕL cot θ − cos2ϕL tan θ) g2232piM∗Γ (W ∗3 → ZLh) = Γ(W ∗3 → W+LW−L)=g22 cot2θ192piM∗ ,(4)where sinϕL is the degree of compositeness of tL and bL. For M∗ = 3 TeV, tan θ = 1/6,sinϕL = 0.4, one has a total decay rate Γtot(W∗3 ) = 170 GeV and BR(ee, µµ) = 0.1%,BR(tt, bb) = 5%.The plot of figure 3 shows the experimental constraints on a strong sector with anSU(2)L×SU(2)R×U(1)B−L global invariance and vectorial resonances (two chargedand three neutral states) in the adjoint representation.The larger symmetry is required to have an unbroken custodial invariance afterEWSB and protect the ρ parameter from large tree-level corrections. At the sametime, however, it leads to several massive vectors, which makes the constraint fromthe vertex corrections in fig.1(c) stronger. The (lighter) gray region represents theportion of the (M∗, g∗) plane excluded by the LEP precision measurements. The LEP2constraint on contact interactions becomes negligible for g∗ & 1, since the coupling ofthe heavy vectors to the light SM fermions scales as g[Ψ]Z∗ = gSM tan θ ' gSM(gSM/g∗).In that limit the dominant constraint comes from the Sˆ parameter, which does not5depend on g∗ since g[H]Z∗ = gSM cot θ ' gSM(g∗/gSM), hence g[Ψ]Z∗ g[H]Z∗ = g2SM = constant.The dashed curve shows how much the LEP bound is relaxed by adding a correction∆ρ = ∆Tˆ = 1× 10−3, which might come, for example, from the 1-loop contributionof new heavy fermions. The blue area is the region excluded by the CDF data ofreference [3].Superimposed in red are the curves reporting the production rate of the neutralW ∗3 in the dilepton channel. One can see that in most of the region allowed byLEP the rate is quite small, so that the observation of this channel will probablyrequire very large integrated luminosities. On the other hand, a discovery can comeearlier from the other final states. According to the analysis of reference [9], a Z∗with mass M∗ = 2 TeV (3 TeV) and g∗ ' 3.9 can be discovered in the Zh channelwith ∼ 100 fb−1 (1 ab−1). Observing the W+W− channel will instead require moreintegrated luminosity.* * *I would like to thank Slava Rychkov and Alessandro Strumia for interesting discus-sions and useful comments.References[1] For a recent review see: P. Langacker, arXiv:0801.1345 [hep-ph].[2] R. Barbieri, A. Pomarol, R. Rattazzi and A. Strumia, Nucl. Phys. B 703 (2004)127.[3] T. Aaltonen et al. [CDF Collaboration] Phys. Rev. Lett. 99 (2007) 171802;R. J. Hooper [D0 Collaboration] Int. J. Mod. Phys. A 20 (2005) 3277.[4] G. Cacciapaglia, C. Csaki, G. Marandella and A. Strumia Phys. Rev. D 74 (2006)033011.[5] A. Leike, Phys. Rept. 317 (1999) 143.[6] Talk by D. del Re and A. Ventura, these proceedings.[7] P. Sikivie, L. Susskind, M. B. Voloshin and V. I. Zakharov, Nucl. Phys. B 173(1980) 189.[8] R. Contino, T. Kramer, M. Son and R. Sundrum, JHEP 0705 (2007) 074.[9] K. Agashe et al., Phys. Rev. D 76 (2007) 115015.6

Z', Z_KK, Z* and all that: current bounds and theoretical prejudices on heavy neutral vector bosons

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