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Vector mesons from AdS/TC to the LHC

With the use of the AdS/CFT dictionary, a five-dimensional effective description of dynamical electro-weak symmetry breaking with walking behavior is constructed. The minimal model contains only two new parameters, the confinement scale and the effective coupling of the new strong sector. This parameter space is restricted by the precision electro-weak constraints and by the requirement that the five-dimensional coupling be perturbative (corresponding to the large-N regime in four-dimensional language). The lightest observable new states are a set of four nearly degenerate spin-1 states with the same quantum numbers as the standard-model electro-weak gauge bosons, and masses in the few TeV range. Their decay rate is dominated by two-fermion final states. The number of pp ->mu mu and pp ->mu nu events is studied as a function of the LHC integrated luminosity and of the two free parameters. Discovery at the LHC is possible over a significant part of the allowed parameter space up to masses of 4 TeV already with 10/fm of integrated luminosity.


INTRODUCTION
The Large Hadron Collider (LHC) will explore the physics responsible for electro-weak symmetry breaking (EWSB) in the standard model (SM), and provide information about the specific mechanism responsible for the generation of the mass of SM gauge bosons and fermions. Dynamical EWSB, often referred to as technicolor (TC), assumes that a new strongly interacting sector be responsible for the dynamical formation of a symmetry breaking condensate at the electro-weak scale [1], along the lines of chiral symmetry breaking in QCD. This idea provides a simple and elegant dynamical solution to the big hierarchy problem, i. e. the huge separation between the electro-weak scale and the Planck scale.
Model-building in the TC context faces several problems, which have over the years prevented from the formulation of a realistic and predictive model. The intrinsic difficulty of treating analytically the strong dynamics limits the extent to which a UV-complete model, based on a non-abelian SU(N T ) gauge theory, can be formulated and tested at low energies.
This fact enforces the use of an effective field theory (EFT) description when comparing to the experiments: the electro-weak chiral Lagrangian (EW-χL) [2]. This has to be completed with a mechanism for the generation of mass for the SM fermions, generically referred to as extended technicolor (ETC), which connects the SM fermions and the symmetry-breaking condensates [3] via higher-order operators arising from new interactions.
Many non-trivial properties of this EFT are known experimentally. The contribution of dimension-6 operators in the EW-χL to theŜ andT parameters [4] have to be at the most in the few × 10 −3 range [5], in contrast with much larger expectations from naif dimensional analysis (NDA). The typical scale of ETC must be in the 4 − 5 TeV range or above, which produces some tension with the requirement that ETC be efficient enough as to produce the observed large top mass. From direct and indirect searches, the low-energy spectrum should not contain any light pseudo-Nambu-Goldstone boson (pNGB), with masses in the few GeV range or below, which are a generic prediction of many TC models. Finally, the ETC sector must produce the observed pattern of masses and mixing angles for the SM fermions, while adequately suppressing new physics contributions to flavor changing neutral current (FCNC) processes.
In the context of EW-χL with generic ETC couplings, all of the above requirements can be satisfied simply by tuning to unnaturally small (or unnaturally large) values some of the coefficients in the EFT, and by assuming that the unknown UV physics (i. e. the underlying strong dynamics) be responsible for these large deviations from the natural expectations. In particular, it has long ago been suggested that a large cut-off scale might be dynamically separated from the electro-weak scale, if the underlying strong dynamics is approximately conformal over a finite energy window (walking behavior [6]). This can suppress the new physics contributions to electro-weak precision parameters [7] and FCNC currents, but not necessarily the top mass, provided the chiral condensate has a large anomalous dimension (for instance if the condensate has scaling dimension d = 2). Also, semi-realistic UV complete models of ETC have been proposed, suggesting that identifying the lightest ETC scale with this 4−5 TeV cut-off is compatible with the experimental properties of the SM mass matrices and with FCNC constraints [8].
However, in the absence of a reliable, first principle computation of the effective Lagrangian coefficients, the choice of renouncing the criterion of naturalness, and hence of allowing for large departures from their NDA estimates of the very big (potentially infinite) number of free parameters in the effective Lagrangian, leads to loss of predictive power. It is hence necessary to extend the EFT validity up to higher scales. The natural direction in which to carry this program is to extend the field content to include not only the SM gauge bosons, but also some of the lightest composite states emerging at the confinement scale from the strong dynamics. Such an approach has been followed over the years in the context of QCD, starting with the concept of vector dominance, developed with the techniques of hidden local symmetry [9] and, more recently, of deconstruction [10], and applied to the description of dynamical EWSB [11]. Though elegant, simple and very useful, this approach does not solve the problem of the proliferation of free parameters because the number of independent operators in the effective Lagrangian grows very fast with the number of new fields. A more fundamental guiding principle is necessary.
More recently, in the context of string theory, compelling evidence has been collected confirming that some special super-Yang-Mills (SYM) strongly coupled, conformal field theories (CFT), in the regime of large number N c of fundamental colors, admit a dual description in terms of a weakly coupled, higher-dimensional gravitational theory with Anti-de Sitter (AdS) background. This is the AdS/CFT correspondence [12]. The relative simplicity and enormous power of the computational techniques provided by this correspondence suggest the idea that by perturbing and deforming in a controlled way the pure AdS background it is possible to explore a large class of weakly-coupled extra-dimension theories, that is thought to provide a dual description for a much larger class of strongly-coupled four-dimensional systems, in which both supersymmetry and conformal symmetry are (softly) broken. Simple phenomenological constructions are possible [13] along these lines. This idea has been applied with interesting results to the construction of an EFT description of QCD valid well beyond the reach of the traditional chiral Lagrangian [14].
The AdS/CFT correspondence is the guiding principle that might prove crucial in the construction of a viable and predictive EFT description of dynamical electro-weak symmetry breaking [15] [16]. I first briefly review the construction of the most minimal such EFT description of dynamical EWSB, based on the indications collected by experimental data.
The model contains only two new free parameters, and the parameter space is restricted by electro-weak precision data. In the main body of the paper I discuss the phenomenology of the spin-1 composite states (techni-ρ). Their decay rates are dominated, in the large-N T regime, by two-body decays into SM fermions. An upper bound on the strength of the relevant coupling is found, hence allowing for a controllable, perturbative study of the LHC discovery reach. A simple analysis of the production and detection at the LHC of the spin-1 states is then performed, in order to quantify the reach of the experimental project. In the pp → ℓℓ ′ + X processes, for which the SM background is very low, the uncertainties related to jet and hadronic physics are not crucial and the detector efficiency is good, a very large portion of the parameter space will be explored within the first few years.
Before beginning to construct and study the model, a comment is due, about the nature of the two aforementioned free parameters. If the underlying dynamics is that of some SU(N T ) gauge theory with some given field content, it should be possible to compute from first principles the scale of confinement, the scale of electro-weak symmetry breaking, the scaling dimension of the chiral condensate and the strength of the effective couplings of the composite states, besides proving that the theory admits an approximate IR fixed point, leading to quasi-conformal behavior near the confinement scale. Unfortunately, this cannot be done systematically and reliably with existing methods [17], and hence all of these quantities are going to be implemented in the model as free parameters.
The electro-weak symmetry breaking scale is fixed experimentally through the measured value of the Fermi constant G F . The scaling dimension d = 2 is chosen, somewhat arbitrarily, in order to reproduce the scaling arguments of walking technicolor, leading to a large enough mass for the top quark, while preserving universality of the weak couplings. The confinement scale (related to L 1 defined in the body of the paper), and the strength of the effective couplings (see ε 2 later on), cannot be decided a priori, and are treated as completely free parameters. As will be clear, a limit on the former is given by precision electro-weak physics, on the latter by the requirement that the perturbative expansion used here (and related to the large-N T expansion), be valid. Experimentally, these two parameters are related to the mass M of the excited spin-1 states, and to their relative coupling R to the SM currents, measured in units of the SM gauge coupling, both which can be extracted from pp → ℓℓ ′ + X processes. Remarkably, a very large part of the parameter space identified in this way is going to be testable at the LHC even in its early stages.

THE MODEL.
A summary of the minimal requirements for a viable model of dynamical EWSB in four dimensions allows to identify the properties of the five dimensional dual description. There must be a new strong sector possessing the global symmetry SU(2) L ×U(1) Y of the standard model. The new interaction must confine, and a symmetry breaking condensate must form.
The (weak) gauging of the global symmetry of the strong sector gives the massive SM gauge bosons and the photon. In order for higher order operators contributing to precision electroweak parameters and FCNC currents to be suppressed by a large enough scale, the strong sector has to be close to conformal over the energy range between the confinement scale and a larger ETC scale of 4 − 5 TeV. The top mass can be accommodated by assuming that the chiral condensate has scaling dimension d = 2. All the SM fermions are elementary, and do not carry quantum numbers of the new strong interactions, hence ensuring universality of the electro-weak gauge coupling.
The (quasi-conformal) energy window just above the electro-weak scale is described by a slice of AdS 5 , i.e. by a five-dimensional space-time containing a warped gravity background given by the metric: where x µ are four-dimensional coordinates, η µν the Minkoski metric with signature (+, −, −, −), and z is the extra (warped) dimension. The dimensionful parameter L is the AdS 5 curvature, and sets the overall scale of the model. Conformal symmetry is broken by the boundaries with L 0 > L, where L 0 and L 1 correspond to the UV and IR cut-offs of the conformal theory, i. e. to the ETC scale and to the confinement scale respectively.
The field content in the bulk of the five-dimensional model consists of a complex scalar Φ transforming as a (2, 1/2) of the gauged SU (2) The bulk action for Φ and the gauge bosons and the boundary terms are where the covariant derivative is given by and where the Yang-Mills action is written in terms of the antisymmetric field-strength tensors W µν and B µν . In the action, M 2 is a bulk mass term for the scalar, and g and g ′ are the (dimensionful) gauge couplings in five-dimensions.
Without loss of generality: The localized potentials produce the z-dependent vacuum expectation value (VEV) of the scalar field that induces electro-weak symmetry breaking. For M 2 = −4/L 2 , in the λ i → +∞ limit, (in which the transverse degrees of freedom become infinitely massive and decouple from the spectrum) the bulk equation of the motion admits the solution by appropriately choosing v 0 /v 1 , so as to describe a chiral condensate of dimension d = 2.
The localized kinetic terms for the gauge bosons are required by holographic renormalization [18] in order to retain a finite SM gauge coupling in the L 0 → 0 limit, and renormalizing the otherwise divergent kinetic terms of the SM gauge bosons. This procedure ensures that the SM gauge couplings be independent of the strength of the bulk coupling, and that all physical quantities be independent of any UV-sensitive details, such as the precise value of L 0 and the UV-brane dynamics.
The SM fermions, and hence the SM currents, are localized at the UV boundary. They do not feel the strong interactions, and their mass is induced by localized, Yukawa-like dimension-5 couplings to the symmetry-breaking background. An alternative way, not explored here, of enhancing the top mass consists of assuming that the top (or possibly the whole third family) takes part directly in the strong dynamics, as in topcolor models [19].
In this case the top would be composite, and hence would propagate in the fifth dimension, as happens in the higgsless context [20] and in several recent composite Higgs models [21].
While admissible, these models violate tree-level universality of the gauge interactions, hence adding to the difficulties connected with precision electro-weak and FCNC constraints, and lead to the introduction of a much larger set of free parameters in the SM fermion sector.
Several other examples of viable, but non-minimal, choices, not discussed in the following, might be the addition of localized kinetic terms for the scalar, or the choice of inducing non trivial mixing in the localized kinetic terms for the gauge bosons, or delocalizing the first two family fermions, all of which would affect the parametersŜ, or the choice of gauging the whole SU(2) R in the bulk, so as to have a custodial symmetry forT .

ELECTRO-WEAK PHENOMENOLOGY.
I discuss only the spin-1 sector of the model, in unitary gauge. The spin-0 sector consists of the transverse degrees of freedom of Φ, integrated out in the λ i → ∞ limit, and the pseudo-scalar sector, which does not contain a zero mode, and is neglected in this paper for the sake of simplicity.
I define, as usual: so that the massless mode of V µ is the photon, and the lightest mode of A µ is the Z boson.
After Fourier transformation in the four-dimensional Minkoski coordinates: and analogous for W 1,2 and V , where q = √ q 2 is the four-dimensional momentum. In the limit in which one neglects the gauge coupling, and hence cubic and quartic self-interactions, the bulk equations are: where This approximation, and the approximation of restricting all the analysis at the tree-level, are valid provided the effective coupling g/ √ L < ∼ O (1), which corresponds to the large-N T limit.
The bulk equations can be solved exactly. Substituting the solutions in the action, the bulk part of the action vanishes identically. Choosing Neumann boundary conditions in the IR leaves a non-vanishing UV-localized action, that can be written as where P µν ≡ η µν − q µ q ν /q 2 , and where i = B, W a . The matrix of the polarizations π i,j (q 2 ) of the SM gauge bosons can be written in terms of the action evaluated at the UV boundary: where N is chosen to produce canonical kinetic terms in the limit in which the heavy resonances decouple. The precision electro-weak parameters are defined aŝ where g 4 are the (dimensionless) gauge couplings of the SM in four-dimensions, and where π ′ ≡ dπ/dq 2 .
Taking for simplicity L 0 → L, and expanding for small L 0 → 0, from [16]: where, having imposed Neumann boundary conditions in the IR, and The localized counterterm cancels the logarithmic divergences, and for N 2 = ε 2 /L 0 all the dependence on L 0 disappears (at leading order in L 0 ), the limit L 0 → 0 can be taken, and the model is renormalized, with finite (dimensionless) SM couplings g (′) 2 4 = ε 2 g (′) 2 /L.
The mass of the W gauge boson is approximately given by while M 2 Z ≃ (g 2 + g ′ 2 )/g 2 M 2 W . Substituting in the precision parameters yields: I take as indicative of the experimentally allowed ranges (at the 3σ level): from [5]. These bounds are extrapolated to the case of a Higgs boson with mass of 800 GeV.
The comparison has to be done with some caution, since the one-loop level SM analysis used in the extraction of the bounds is not reliable for a heavy, strongly coupled Higgs, the mass of which is not controllable in this model.
For reasonable values of ε > 1/2, such that the five-dimensional tree-level analysis performed here holds, the bounds onT have no significant effect in restricting the parameter space of the model. The implementation of a custodial symmetry is unnecessary. Form the approximate expression forŜ comes the limit on the confinement scale L 1 of the model: where i = v, a, +, c i are normalization constants, determined, at finite L 0 , by with while c ′ 1,2 ≡ c 1,2 (µ Z → µ W ). The masses of the techni-ρ are obtained by solving: The mode corresponding to the excited photon has a mass where k 0 < k < 4.7 is a monotonically growing function of ε, with k 0 ≃ 2.4 being the first zero of J 0 (z). The (exact) relation between ε and k = M γ ′ L 1 is given by As a result, the mass is a growing function of ε, but the growth saturates at large ε toward a constant. This somewhat peculiar behavior has to do with the way the limits are taken in the present context: the SM gauge couplings (known experimentally) are kept fixed while going to large-N T , so that the gauging of the global symmetry, although always weak and controllable, becomes stronger than the effective coupling of the strong sector itself, and hence its effect is not just a perturbation of the expectations deduced by analyzing the large-N T limit of a generic strongly coupled model with a global symmetry.
The couplings to the electro-magnetic, neutral and charged weak currents of the techni-ρ's are related to the SM gauge boson couplings by the L 0 → 0 limit of: For the electro-magnetic case, it is possible to explicitly write (making use of the relation between k and ε) the dependence on k of the ratio of couplings to the SM fermions as illustrated by Figure 2: Again, this quantity is only marginally sensitive to electro-weak symmetry breaking, and hence g ′ c.c. /g c.c. ≃ g ′ n.c. /g n.c. ≃ e ′ 4 /e 4 . Some comments are in order. First of all, notice the absolute upper bound on R < ∼ 0.65.
This model is not compatible with the scenario, often discussed in the literature, in which the new heavy gauge bosons have the same coupling to the SM currents as the SM gauge bosons. At small ε (small k), where the large-N T approximations should not be trusted, the coupling grows linearly with k ∝ ε 2 ∝ N T . This is consistent with the expectation from QCD-like models that, holding the techni-ρ mass fixed, the decay constants grow with N T .
Going to large ε 2 ∝ N T , this behavior changes smoothly, and the couplings decrease with N T , consistently with the large-N T picture itself, and the narrow-width approximation.
The cubic coupling between gauge bosons can be read off the Yang-Mills action with the replacement W 3 = (g ′ V + gA)/ √ g 2 + g ′ 2 . The relevant cubic couplings g a ′ bc for the computation of the techni-ρ decay rates Γ[a ′ → bc] into longitudinally polarized SM gauge bosons are: with the expressions defined above for the wave functions.
More comments are in order, about the different behavior of the cubic couplings. All of them vanish in the limit in which there is no electro-weak symmetry breaking, and vanish asymptotically at larg-N T (large ε 2 ). On one hand, this implies that g γ ′ W W < M 2 W /M 2 W ′ . On the other hand, it implies that it is not possible to approximate the bulk profiles with the expression valid for the unbroken case, and it is hence necessary to perform the integrations numerically. A precise computation of these couplings is somewhat problematic also from a more rigorous point of view: they arise at the next-to-leading order in the large-N T expansion, and are hence sensitive to higher-order effects that have not been included in the action under study here. The (numerical) estimate produced here should not be taken too literally, because affected by large intrinsic uncertainties. For the purposes of the present analysis it is enough to show that, in the interesting region of the parameter-space, these interactions are subleading and can be neglected, as will be shown in the next section.

TECHNI-ρ DECAY RATES.
The techni-ρ resonances decay both via new strong interactions (to longitudinally polarized SM gauge bosons) and via weak-interactions (due to the direct coupling to SM fermions).
In all of this analysis, the basic assumption is that there are no other new states lighter than the techni-ρ's.
Explicitly, the decay rates of the heavy gauge bosons into a final state of two light gauge bosons read up to corrections of O(M 2 W,Z /M 2 W ′ ), where the effective couplings have been computed in the previous section. This expression can be directly compared, via the Goldstone boson equivalence theorem, to the result in a QCD-like theory Γ[ρ → ππ] = Mρ 48π g 2 ρππ . The decay rates to SM fermions can be read from the leading order expressions for the decay rates of the SM gauge bosons, appropriately modified to include the decay to top, the heavier mass and the new effective coupling. For the massive W ′ one can compare to the result in the SM in the limit of vanishing top mass: which differs from the experimental value of 2.1 GeV by the top-bottom final state. Rescaling: For the Z boson, at the tree level, for vanishing masses of the final-state fermions, summing over the three families (top included) would yield: which is bigger than the measured width Γ Z ≃ 2.5 GeV , roughly by the top contribution.
Hence, the partial width of the Z ′ to SM fermions: Finally, for the massive photon The decay either to SM gauge bosons or to SM fermions dominates the total width of the heavy states, depending on the value of ε (or of k, see Fig. 3). At small k (i. e. small ε 2 ∝ N T ), the dominant decay channel is the one with longitudinal gauge bosons in the final state (as would be the case in a QCD-like theory). This decay rate is a monotonically decreasing function of ε 2 , it scales as Γ ∝ 1/N T and hence the partial width decreases fastly going toward the large-N T regime, while it is asymptotically large at small-N T .
The decay rate to SM fermions is not a monotonic function of ε, as clear from the effective coupling R (see figure 2). Starting at intermediate values of ε > ∼ 1/2, the decay rate of the spin-1 resonances is dominated by two-fermion final states. At large values of ε, both decay rates fall down as 1/ε 2 , but still the two-fermion final state dominates. Validity of the perturbative approach followed here requires that ε > 1/2. In this range, decay into fermions is always the dominant channel. The experimental signature of this model reduces to that of a model with a complete set of quasi-degenerate heavy copies of the SM gauge bosons, which decay to the same channels as the SM gauge bosons.
This is the most intriguing and important result of this analysis. It means that, experimentally, the signature to look at is a relatively clean one, with a two-body final state that can be explored even in early stages of the LHC program. In this case, the theoretical control over the estimates is good, since the one-point functions relevant here are better controlled that the three-point functions relevant for decays into SM gauge bosons, and since at large ε all the resonances become narrow.

TWO-LEPTON PROCESSES AT THE LHC.
For the discovery of Z ′ and γ ′ at the LHC I focus on pp → µ + µ − + X. Identical considerations apply also to final states with two electrons, which experimentally is a more favorable channel [22]. Decay to τ and to hadrons, conceptually very similar at the parton level, would require a more refined analysis of the hadronization process. At the parton level, this process is described by qq → µ + µ − . It has only s-channel contribution, and can be written by generalizing the SM tree-level results [23] σ where In this expression Q (f ) is the electric charge, and the couplings of the SM elementary fermion f are defined by while the propagators for the V gauge boson by In order to compute the physical cross-sections, define, for a, b = u, d, s, c, b, where at the LHC √ s = 14 TeV,ŝ is the c.m. energy of the parton-parton (or equivalently muon-muon) system and the φ a are parton distribution fuctions as defined by the CTEQ collaboration [25], evaluated at the relevant partonic scale. The cross-section is where the factor of 3 comes from the average over initial color states.
The analog process involving a charged vector state is described by: The pp cross-section is hence: Unfortunately, the longitudinal energy of the neutrino is not a measurable quantity. In terms of the transverse mass m T of the lepton/neutrino pair: and the observable is the integral overŝ of the differential cross-section

APPROXIMATE ANALYSIS AND DISCUSSION
Requiring that N(pp → µ + µ − + X) > 10, it is possible to study the range of parameter space explored by the LHC as a function of its integrated luminosity. Fig. 4 shows a preliminary study, with no background included and assuming perfect detector efficiency. No QCD correction (K-factor) is added.
In order to study the properties of these resonances, large statistics is required. Fig. 5 shows the expected distribution of the number of events for two examples of allowed points in the parameter space, both at the boundary of the exclusion region from precision electroweak data L 1 = 1/0.89 TeV −1 and for integrated luminosity of 100 fm −1 . The background shown here is the contribution to the same parton-level process of the SM photon, W and Z.
Accidental backgrounds from higher order processes are not included, perfect efficiency and purity of the signal, and energy resolutions, have been used (even for the missing energy), and no kinematical cuts applied.
The simple numerical study performed here and shown in Fig. 4 and Fig. 5  Establishing (or excluding) this model, requires to distinguish in the µ + µ − peak the contribution of γ ′ and Z ′ , and a precise measurement of the couplings to up and down quarks, which are going to be quite difficult, because of the large mass of the vector states.
For the discovery of the W ′ , and the measurement of the helicity of its couplings [24], the smearing of the m T distribution represents a serious limitation. To some extent, this can be improved with higher luminosity, and adding together the µ, e and possibly τ final states. and of m T for µ + ν µ (right diagrams). Upper diagrams for ε = 0.6 (or equivalently for M γ ′ = 2.78 TeV and R = 0.55). Lower diagrams for for ε = 1.1 (or equivalently for M γ ′ = 3.80 TeV and R = 0.25).

CONCLUSIONS
I constructed a viable model for dynamical electro-weak symmetry breaking by using the five-dimensional language of the AdS/CFT correspondence. I confronted the model with the indirect constraints from precision electro-weak measurements, and identified a large section of the two-dimensional parameter space that is still allowed and will be directly tested at the LHC even with relatively low luminosity.
The model is constructed so as to shares some of the basic properties of more traditional walking technicolor models, but differs from them in two fundamental ways. First of all, the validity of the perturbative expansion used in the five-dimensional construction requires to assume that the underlying dynamics be well approximated by the large-N T regime of some fundamental SU(N T ) theory, and only in that regime the results are reliable. The parameter controlling this expansion is ε, and the analysis is performed assuming that ε > ∼ 1/2. Second, the EFT construction used here treats as separate, independent parameters the scales of confinement of the underlying strong dynamics and the scale of symmetry breaking. Electroweak precision constraints are avoided by assuming a (very moderate) hierarchy between the two, the confinement scale being related to the IR cut-off of the conformal sector L 1 < ∼ 1/0.89 TeV −1 . This is enough to suppressŜ, whileT does not play an important role.
The spectrum contains no light Higgs, but a tower of spin-1 states with quantum numbers identical to the SM gauge bosons are the signature to be looked for at the LHC. The states in the first excited level, denoted by γ ′ , W ′ and Z ′ , are going to have degenerate masses in the few TeV range. The decay to longitudinally polarized SM gauge bosons, which is experimentally challenging, is important (or dominant) only at small values of ε, i. e. in the small-N T regime, which cannot be described reliably within the approach followed here.
Most important, in the regime in which the control over the EFT is good, at large values of ε (large-N T limit), the spin-1 states decay mostly into SM fermions via direct coupling to the SM currents. An absolute upper bound for this coupling is found, insuring that the the width is always small, and that perturbative treatment of the relevant production and decay rates is accurate.
The search for these new states can be done with traditional analysis methods used for the search of new heavy gauge bosons with SM-like couplings. The neutral states can be discovered already with 10 fm −1 integrated luminosity in the 2.5 − 4 TeV mass range, provided the parameter R, controlling the coupling to the SM currents compared to that of the SM gauge bosons, is not too small. Measurement of R and M γ ′ are enough to determine the two free parameters ε and L 1 of the EFT. In order to distinguish this model from a generic Z ′ scenario, larger luminosity must be cumulated, so as to discover also the charged W ′ , distinguish Z ′ and γ ′ , and show that the masses and the ratios of couplings R are approximately the same for all the new states. Distinguishing the γ ′ from the Z ′ and establishing the nature of the W ′ can be challenging, in view both of the largish masses and of the upper limit R < ∼ 0.65, but should be possible over a significant part of the parameter space, once the design luminosity for the LHC is reached.
I would like to thank Stephen Ellis, Matthew Strassler and Wu-Ki Tung for useful discussions. This work is partially supported by the Department of Energy grant DE-FG02-96ER40956.