We consider a class of minimal extensions of the Standard Model with an extra
massive neutral gauge boson Z'. They include both family-universal models,
where the extra U(1) is associated with (B-L), and non-universal models where
the Z' is coupled to a non-trivial linear combination of B and the lepton
flavours. After giving an estimate of the range of parameters compatible with a
Grand Unified Theory, we present the current experimental bounds, discussing
the interplay between electroweak precision tests and direct searches at the
Tevatron. Finally, we assess the discovery potential of the early LHC.Comment: 6 pages, 2 figures. Talk given at the 2nd Young Researchers Workshop
  "Physics Challenges in the LHC Era", Frascati, May 10 and 13, 201

Salvioni, Ennio

English

arXiv

We consider a class of minimal extensions of the Standard Model with an extra massive neutral gauge boson Z'. They include both family-universal models, where the extra U(1) is associated with (B −L), and non-universal models where the Z' is coupled to a non-trivial linear combination of B and the lepton flavours. We discuss the interplay between electroweak precision tests and direct searches at the Tevatron, to assess the discovery potential of the early LHC

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DOI 10.1393/ncc/i2011-10777-1Colloquia: IFAE 2010IL NUOVO CIMENTO Vol. 33 C, N. 6 Novembre-Dicembre 2010Minimal Z ′ models and the early LHCE. Salvioni(∗)Dipartimento di Fisica, Universita` di Padova and INFN, Sezione di PadovaVia Marzolo 8, I-35131 Padova, Italy(ricevuto l’ 8 Ottobre 2010; pubblicato online l’8 Febbraio 2011)Summary. — We consider a class of minimal extensions of the Standard Modelwith an extra massive neutral gauge boson Z′. They include both family-universalmodels, where the extra U(1) is associated with (B −L), and non-universal modelswhere the Z′ is coupled to a non-trivial linear combination of B and the leptonflavours. We discuss the interplay between electroweak precision tests and directsearches at the Tevatron, to assess the discovery potential of the early LHC.PACS 14.70.Pw – Other gauge bosons.1. – IntroductionExtra neutral gauge bosons, known in the literature as Z ′, appear in many proposalsfor Beyond-the-Standard Model (BSM) physics; for a review, see for instance [1]. Here wefocus on minimal Z ′, previously studied in [2], which stand out both for their simplicity,and because they could arise in several BSM scenarios, such as, e.g., Grand UnifiedTheories (GUTs) and string compactifications.2. – TheoryFollowing [3], we consider a minimal extension of the SM gauge group that includesan additional Abelian factor, labeled U(1)X , commuting with SU(3)c×SU(2)L×U(1)Y .The fermion content of the SM is augmented by one right-handed neutrino per family. Werequire anomaly cancellation, as this allows us to write the Lagrangian of the model onlyin terms of renormalizable operators. If family-universality is imposed, then the anomalycancellation conditions (ACC) yield a unique solution: X = (B − L), where B and Lare baryon and lepton number, respectively(1). However, if the requirement of family-(∗) E-mail: ennio.salvioni@pd.infn.it(1) The most general solution to the ACC is X = a Y +b (B−L), with a, b arbitrary coefficients.However, the hypercharge component can be absorbed in the kinetic mixing in the class of modelswe consider.c© Societa` Italiana di Fisica 157158 E. SALVIONIuniversality is relaxed, it can be shown that the following set of family-dependent chargessatisfy the ACC: X =∑a=e, μ, τ (λa/3)(B − 3La), where La are the lepton flavours. Wewill consider a specific example of such non-universal Z ′ in the following.In the basis of mass eigenstates for vectors, and with canonical kinetic terms, theneutral-current Lagrangian reads LNC = eJμemAμ + gZ(ZμJμZ + Z ′μJμZ′), where Aμ isthe photon coupled to the em current, while (Zμ, Z ′μ) are the massive states, whichcouple to the currents (JμZ , JμZ′), respectively, obtained from JμZ0 =∑f [T3L(f) −sin2 θW Q(f)] fγμf and JμZ′ 0 = (1/gZ)∑f [gY Y (f) + gX X(f)] fγμf via a rotation ofthe Z−Z ′ mixing angle θ′. The latter is given by tan θ′ = −(gY /gZ)M2Z0/(M2Z′ −M2Z0).Thus, under our minimal assumptions, only three parameters beyond the SM ones aresufficient to describe the Z ′ phenomenology: the physical mass of the extra vector, MZ′ ,and the two coupling constants (gY , gX) which appear in the definition of JμZ′ 0 . Inthe following discussion, we normalize these couplings to the SM Z0 coupling, namelyg˜Y,X = gY,X/gZ .3. – Bounds from present dataThe measurements providing constraints on minimal Z ′ can be divided into twoclasses: electroweak precision tests (EWPT) and direct searches at the Tevatron.3.1. Electroweak precision tests. – Measurements performed at LEP1 and at low energymainly constrain Z-Z ′ mixing, whereas data collected at LEP2 constrain effective four-fermion operators. To compute the bounds from EWPT on minimal Z ′, we integrate outthe heavy vector and use the effective Lagrangian thus obtained to perform a global fitto the data. The results are shown in fig. 1, for the universal “χ model”, correspondingto a particular direction in the (g˜Y , g˜BL) plane often considered in the literature.3.2. Tevatron direct searches. – The CDF and D0 Collaborations have derived,from the non-observation of discrepancies with the SM expectations, upper limits onσ(pp → Z ′) × Br(Z ′ → +−) ( = e, μ) [4]. To extract bounds on minimal Z ′, wecompute the same quantity at NLO in QCD, and compare it with the limits publishedby the experimental collaborations. The summary of bounds from EWPT and from theTevatron is shown in fig. 1 for the χ model. We see that bounds from EWPT have a linearbehaviour in coupling vs. mass, because all the effects due to the Z ′ in the low-energyeffective Lagrangian depend on the ratio gZ′/MZ′ , whereas bounds from the Tevatronbecome negligible above a certain kinematic limit, which is of the order of 1TeV. Thusfor low masses the Tevatron data give the strongest limits, while above a certain value ofMZ′ (which is of the order of 500GeV for the χ model) bounds from EWPT are stronger.4. – Early LHC reachIn 2010/2011 the LHC will run at a centre-of-mass energy of 7TeV, collecting up to1 fb−1 of integrated luminosity L [5]. Therefore, it is interesting to ask whether thereare any minimal Z ′ which are both allowed by the present constraints and accessible fordiscovery in such early phase. To answer this question, we have performed a NLO analysisanalogously to the Tevatron case, requiring the Z ′ signal to be at least a 5σ fluctuationover the SM-Drell Yan background. The results are compared with present bounds infig. 1, for the χ model. We see that for L ∼ 100 pb−1 (the luminosity approximatelyMINIMAL Z′ MODELS AND THE EARLY LHC 159Fig. 1. – (Colour on-line) Left: comparison of bounds from EWPT (red), Tevatron (blue),and discovery reach of the early LHC (green curves, from left to right: 50, 100, 200, 400 and1000 pb−1 at 7TeV, and 400 pb−1 at 10TeV) for the χ model. See [3] for the normalization ofgZ′ . Right: present bounds and discovery prospects of the LHC at 7TeV and 50 pb−1 for themuonphilic model with g˜Y = 0. The yellow bands correspond to the GUT-favoured regions,see [3] for details.foreseen for 2010), no discovery is possible. On the other hand, for L ∼ 1 fb−1 someunexplored regions become accessible; however, Z ′s compatible with GUTs are still outof reach, and more energy and luminosity will be needed to test them.4.1. The muonphilic model . – We have seen that universal models are strongly con-strained by the present data. On the other hand, when we consider non-universal cou-plings to leptons, the bounds can be significantly altered. In particular, we can considerthe case where X = B − 3Lμ, which we called “muonphilic Z ′”. If kinetic mixing isnegligible, i.e. g˜Y ≈ 0, then the Z ′ has vanishing coupling to the electron. As a conse-quence, bounds from EWPT are strongly relaxed, the only surviving constraints comingfrom (g − 2)μ and ν-N scattering (NuTeV). On the other hand, the Tevatron reach islimited to MZ′ ≤ 1TeV: therefore the LHC has access to a wide region of unexploredparameter space already with a very low luminosity at 7TeV, as shown in fig. 1.5. – ConclusionsWe have discussed the present bounds and the early LHC reach on minimal Z ′ models,showing that the former cannot be neglected when assessing the latter. We have foundthat exploration of universal models, coupled to (B − L), may need more energy andluminosity than those foreseen for 2010/2011. On the other hand, we have presenteda non-universal model, the muonphilic Z ′, which is weakly constrained by present dataand could be discovered at the LHC with very limited integrated luminosity.REFERENCES[1] Langacker P., Rev. Mod. Phys., 81 (2008) 1199, arXiv:0801.1345 [hep-ph].[2] Appelquist A., Dobrescu B. A. and Hopper A. R., Phys. Rev. D, 68 (2003) 035012,arXiv:hep-ph/0212073.[3] Salvioni E., Villadoro G. and Zwirner F., JHEP, 11 (2009) 068, arXiv:0909.1320 [hep-ph]; Salvioni E., Strumia A., Villadoro G. and Zwirner F., JHEP, 03 (2010) 010,arXiv:0911.1450 [hep-ph].160 E. SALVIONI[4] Aaltonen T. et al. (CDF Collaboration), Phys. Rev. Lett., 102 (2009) 031801,arXiv:0810.2059 [hep-ex]; Phys. Rev. Lett., 102 (2009) 091805, arXiv:0811.0053 [hep-ex]; D0 Collaboration, D0 note 5923-CONF (July 2009), http://www-d0.fnal.gov/Run2Physics/WWW/results/prelim/NP/N66/.[5] Bertolucci S., these proceedings.

Minimal Z' models and the early LHC

SALVIONI, ENNIO

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Minimal Z' models and the early LHC

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