### Summer program 2015 : riding the W ' ave .... (LHC season 2, episode 1)

**... to reach new H**~~e~~ig(g)~~ht~~s ?

I carry on reporting some news about the hint of a signal for a new weak gauge boson W' at LHC: a potential discovery classified as "not unexpected" in a recent review by Chris Quigg. In this post I chose to follow the work from authors of a specific model reported previously in this blog just for the sake of obstinacy ;-).

The reader will encounter a detailed discussion of the scalar sector proposed to accommodate the spontaneous breaking of a left-right symmetric extension of the standard model at the TeV scale and she will get more information about the potential falsification of such a phenomenological construction expected for the end of this year thanks to the 13 TeV available now for LHC Run2!

Using LHC data at √s=8 TeV,the ATLAS and CMS Collaborations, have reported deviations from the Standard Model (SM) of statistical significance between 2 and 3σ in several final states, indicating mass peaks in the 1.8–2 TeV range [1]-[5]. The cross sections required for producing these mass peaks are consistent with the properties of aW'boson in anSU(2)_{L}×SU(2)_{R}×U(1)_{B-L}gauge theory with right-handed neutrinos that have Dirac masses at the TeV scale [6].

The spontaneous breaking of SU(2)×SU(2)×U(1) gauge groups require an extended Higgs sector. For large regions of parameter space, theW'boson have large branching fractions into heavy scalars from the Higgs sector [7][8].We show here that theW'boson hinted by the LHC data is likely to decay into H^{+}A^{0}andH^{+}H^{0}, whereH^{+},A^{0}andH^{0}are heavy spin-0 particles present in Two-Higgs-Doublet models.We compute the branching fractions for these decays and present evidence that signals for the W'→H^{+}A^{0}/H^{0}processes may already be visible in the 8 TeV LHC data.

There are numerous and diverse studies ofSU(2)_{L}×SU(2)_{R}×U(1)_{B-L}models, spanning four decades [10]. An interesting aspect of the left-right symmetric models is that they can be embedded in the minimal SO(10) grand unified theory. This scenario must be significantly modified due to the presence of Dirac masses for right-handed neutrinos required by the CMS e+e−jj events [Unless the right-handed neutrinos have TeV-scale masses with the split between two of them at the MeV scale [9]].1 The theory introduced in [6] involves at least one vectorlike fermion transforming as a doublet underSU(2)_{R}. This may be part of an additional SO(10) multiplet, but it may also be associated with completely different UV completions...

The Higgs sector of theSU(2)_{L}×SU(2)_{R}×U(1)_{B-L}gauge theory discussed in [6] consists of two complex scalar fields: anSU(2)_{R}triplet T of B−L charge +2, and anSU(2)_{L}×SU(2)_{R}bidoublet Σ of B−L charge 0.

The renormalizable Higgs potential is given by V(T)+V(T,Σ)+V(Σ)...The bidoublet-only potential V(Σ) is chosen such that by itself it does not generate a VEV for Σ...the T scalar acquires a VEV ... this breaksSU(2)_{R}×U(1)_{B-L}down to the SM hypercharge gauge group,U(1)_{Y}, leading to large masses for theW'and Z' bosons. The value of the T VEV is related to the parameters of theW'boson. In the next section we will show that the parameters indicated by the LHC mass peaks near 2 TeV implyu_{T}≈ 3−4 TeV.

The triplet field includes 6 degrees of freedom, and can be written as T = (T1, T2, T3), with Ti (i = 1, 2, 3) complex scalars... The fields of definite electric charge, which are combinations of the Ti components, include three Nambu-Goldstone bosons (G_{R}^{±}, G_{R}^{-}). These become the longitudinal degrees of freedom of theW'^{±}and Z' bosons. The three remaining fields are a real scalar T^{0}, a doubly-charged scalarT^{++}and its charge conjugate state T^{--}... For quartic couplings in the 0.1–1 range and in the absence of fine tuning, theT^{0}andT^{++}particles have masses comparable to, or heavier thanW'

The mixed terms, which involve both the T and Σ scalars, will induce a nonzero VEV {proportional tov_{H}} wherev_{H}=174 GeV is the electroweak scale. We are interested in the case where v_{H}/u_{T}∼1/20. The effect of the Σ VEV on the T^{0}andT^{++}masses and couplings is thus negligible. At energy scales below theT^{0}andT^{++}masses, the scalar sector consists only of Σ, which is the same as two Higgs doublets.

....Besidesh^{0}and the longitudinal W^{±}and Z, the bidoublet field Σ includes the heavy scalarsH^{±},H^{0},A^{0}. The range of allowed masses for these particles spans more than an order of magnitude, from the weak scale to theSU(2)_{R}breaking scale. If they are lighter than the W' boson, then W' decays may provide the main mechanisms for production of these scalar particles at hadron colliders.

...ForM_{W'}_{,}≈1.9 TeV and g_{R}≈0.45–0.6 (as determined in [6], by comparing theW'^{ }production cross section to the CMS dijet excess [4]), we find theSU(2)_{R }breaking scale u_{T}≈ 3–4 TeV.

...The main decay modes for the heavy Higgs bosons areA^{0},H^{0}→tt̅and H^{+}→tb̅. If their masses are below M_{W'}/2, then the cascade decayW'→H^{±}A^{0}/H^{0}→3t+b→3W+4b has a branching fraction of up to 3% and provides a promising way for discovering all these particles. An excess of events, with a statistical significance of about 3σ, has been reported by the ATLAS Collaboration [17] in the final state with two leptons of same charge and two or more b jets. We have shown that this can be explained by the cascade decay ofW'if the heavy Higgs bosons have masses in the 400–700 GeV range.

TheSU(2)_{L}×SU(2)_{R}×U(1)_{B-L}gauge theory presented here depends on only a few parameters, whose ranges are already determined by accounting for the deviations from the SM mentioned above. The various phenomena predicted by this gauge theory can thus be confirmed or ruled out in the near future.

In Run 2 of the LHC, the W' production cross section is large, in the 1–2 pb range at √s=13 TeV. Besides resonant production of WZ, Wh^{0}, jj and tb, there are severalW'discovery modes:W^{'}→ τN^{τ}→ ττjj, ττtb, eτjj, eτtb andW^{'}→eN^{τ}→eejj, eetb would test the existence of the heavy right-handed neutrinoN^{τ }{with benchmark mass of 1 TeV}, while W'→H^{±}A^{0}/H^{0}→3t+b, W'→WA^{0}/H^{0}→Wtt̅, W'→H^{±}h^{0}→tbh^{0}and others would test the existence of the heavy Higgs bosons.

Another promising search channel for the heavy neutral Higgs bosons, independent of theW', follows from production in association with a tt̅pair, which has a cross section of the order of 10 fb at √s=13 TeV.With more data, the Z' boson analyzed in [6] will also be accessible in a variety of channels.

(Submitted on 7 Jul 2015)

Summertime is a good opportunity to build wonderful sandcastles but few withstand waves ...

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