R-Parity Violating Supersymmetry and the 125 GeV Higgs signals
We study the impact of R-parity violating Supersymmetry (RPV SUSY) on the 125 GeV Higgs production and decay modes at the LHC. We assume a heavy SUSY spectrum with multi-TeV squarks and SU(2) scalar singlets as well as the decoupling limit in the SUSY Higgs sector. In this case the lightest CP-even Higgs is SM-like when R-parity is conserved. In contrast, we show that when R-parity violating interactions are added to the SUSY framework, significant deviations may occur in some production and decay channels of the 125 GeV Higgs-like state. Indeed, we assume a single-flavor (mostly third generation) Bilinear RPV (BRPV) interactions, which generate Higgs-sneutrino mixing, lepton-chargino mixing and neutrino-neutralino mixing, and find that notable deviations of may be expected in the Higgs signal strength observables in some channels, e.g., in . Moreover, we find that new and detectable signals associated with BRPV Higgs decays to gauginos, and , may also arise in this scenario. These decays yield a typical signature of () that can be much larger than in the SM, and may also be accompanied by an enhancement in the di-photon signal . We also examine potential interesting signals of Trilinear R-parity violation (TRPV) interactions in the production and decays of the Higgs-sneutrino BRPV mixed state (assuming it is the 125 GeV scalar) and show that, in this case also, large deviations up to are expected in e.g., , which are sensitive to the BRPVTRPV coupling product.
The discovery of the 125 GeV Higgs boson in 2012 HiggsDiscoveryATLAS (); HiggsDiscoveryCMS () has marked the starting point of a new era in particle physics, that of Higgs precision measurements, thus leading to a joint effort by both theorists and experimentalists, in order to unravel the true nature of the Higgs and its possible connection to New Physics (NP) beyond the SM (BSM).
The ATLAS and CMS experiments have made since then outstanding progress in the measurements of the various Higgs production and decay modes, which serve as an important testing ground of the SM. Indeed, the current status is that the measured Higgs signals are largely compatible with the SM within the errors; in some channels the combined precision is of at the level muVbbATLAS (); muVbbCMS (); muFWWATLAS (); muFWWCMS (); muFZZATLAS (); muFZZCMS (); muFgamgamATLAS (); muFgamgamCMS (); muFtautauATLAS (); muFtautauCMS (); ATLASmumu (); CMSmumu (). In particular, in the SM the main Higgs production modes include the dominant gluon-fusion channel (predominantly through the top-quark loop), , as well as the and Vector-Boson-Fusion (VBF) channels, and (the overall hard process being ), respectively. Its dominant decay mode is , which is currently measured only via the sub-dominant production mode (due to the large QCD background in the leading model ). The best sensitivity, at the level of (combining the ATLAS and CMS measurements muFWWATLAS (); muFWWCMS (); muFZZATLAS (); muFZZCMS (); muFgamgamATLAS (); muFgamgamCMS ()) is currently obtained in the Higgs decay channels to vector-bosons , when it is produced in the gluon-fusion channel.
Thus, by looking for patterns of deviations in the Higgs properties, these so-called "Higgs-signals" can, therefore, shed light on the UV theory which underlies the SM. Indeed, the Higgs plays an important role in many of the popular BSM scenarios that attempt to address the fundamental shortcomings of the SM, such as the hierarchy and flavor problems, dark matter and neutrino masses. For that reason Higgs physics has been studied within several well motivated BSM scenarios such as supersymmetry (SUSY) MartinRPC1 (); RosiekRPC2 (); Decoupling (), which addresses the hierarchy problem and Composite Higgs-models CompositeHiggs (), in which the Higgs is identified as a pseudo-Nambu-Goldstone boson associated with the breaking of an underlying global symmetry. The Higgs has also been extensively studied in a model-independent approach, using the so called SMEFT framework SMEFT (), where it is incorporated in higher dimensional operators and in Higgs-portal models HiggsPortal1 (); HiggsPortal2 (); HiggsPortal3 (); HiggsPortal4 (); HiggsPortal5 (), which address the dark matter problem.
It is widely accepted that perhaps the most appealing BSM theoretical concept is SUSY, since it essentially eliminates the gauge hierarchy problem (leaving perhaps a little hierarchy in the SUSY fundamental parameter space) and it elegantly addresses the unification of forces, as well as providing a well motivated dark matter candidate. Unfortunately, no SUSY particles have yet been observed, so that the typical SUSY scale is now pushed to the multi-TeV range, with the exception of some of the Electro-Weak (EW) interacting SUSY states, such as the lightest gauginos and SU(2) sleptons doublets. An interesting variation of SUSY, which is in fact a more general SUSY framework, includes R-parity violating (RPV) interactions RPVSUSY (). Indeed, one of the key incentives of the the RPV SUSY framework is the fact that it also addresses the generation of neutrino masses in a distinctive manner. Many studies on RPV SUSY have, therefore, focused on reconstructing the neutrino masses and oscillation data neutrinomass1 (); neutrinomass2 (); neutrinomass3 (); neutrinomass3_1 (); neutrinomass4 (); neutrinomass5 (); neutrinomass6 (); neutrinomass6_1 (); B3_neutrinomass_constraints (); neutrinomass7 (); neutrinomass8 (); neutrinomass9 (); neutrinomass10 (); neutrinomass11 (); neutrinomass12 (); neutrinomass13 (), while far less attention has been devoted to the role that RPV SUSY may play in Higgs Physics RPVHiggsValle (); RPVHiggsRosiek1 (); RPVHiggsParameterization (); 3bodyBRPVdecays1 (); Arhrib (); BRPVdiphoton (); triRPV2loopmh (); BRPVDiHiggs (); RPVBminusL (); RPVNMSSM (); UnusualRPVHiggs (); VBFRPVHiggs (). It has also been recently proposed, that an effective RPV SUSY scenario approach involving only the third generation 3rdGenSUSY () can simultaneously explain the anomaly related to B-physics and also alleviate the Hierarchy problem of the SM RPVbanomalies (). For related efforts tackling the recent B-anomalies within the RPV SUSY framework see RPVBanomaly1 (); RPVBanomaly2 (); RPVBanomaly3 ().
From the experimental side, since RPV entails the decay of the LSP, the searches for RPV signatures at the LHC are based on a different strategy than in traditional SUSY channels RPVsearchesReview (); RPVsearchatLHCdreiner (); TRPVcharginodecays (); RPVBminusLgauginodecays (); RPVPhenoLSP (); SameSignDileptonRPV (); RPVsignaturesLHC (); LongLivedSearchesRPV ().
In this paper, we propose to interpret the observed 125 GeV Higgs-like state as a Higgs-sneutrino mixed state of the RPV SUSY framework HiggsSneutrinoMixingEilamMele (); HiggsSneutrinoMixingEilamMele2 () (throughout the paper we will loosely refer to the Higgs-sneutrino mixed state as the "Higgs"). We thus study the implications and effects of RPV SUSY on the 125 GeV Higgs signals. Guided by the current non-observation of SUSY particles at the LHC, we adopt a heavy SUSY spectrum with multi-TeV squarks and SU(2) scalar singlets as well as the decoupling limit in the SUSY Higgs sector. We find that, in contrast to the R-parity conserving (RPC) heavy SUSY scenario, where the lightest CP-even Higgs is SM-like, the RPV interactions can generate appreciable deviations from the SM rates in some production and decay channels of the lightest 125 GeV Higgs-sneutrino mixed state. These are generated by either Bilinear RPV (BRPV) interactions or BRPV combined with Trilinear RPV (TRPV) interactions. In particular, we find that notable effects ranging from up to may be expected in the Higgs signal strength observables in the channels, and in the di-photon signal and that new sizable signals (see eq. (34)) associated with BRPV Higgs decays to gauginos, (), may also occur in this scenario. We study these Higgs production and decay channels under all the available constraints on the RPV SUSY parameter space.
The paper is organized as follows: in section 2 we briefly describe the RPV SUSY framework and in section 3 we layout our notation and give an overview of the measured signals of the 125 GeV Higgs-like state. In sections 4 and 5 we present our analysis and results for the BRPV and TRPV Higgs signals, respectively, and in section 6 we summarize. In Appendix A we give the relevant RPV Higgs couplings, decays and production channels, while in Appendix B we list the SUSY spectra associated with the RPV SUSY benchmark models studied in the paper.
2 The RPV SUSY framework
where are the up(down)-type Higgs supermultiplet and are the leptonic SU(2) doublet(charged singlet) supermultiplets. The are quark SU(2) doublet supermultiplets and are SU(2) up(down)-type quark singlet supermultiplets. Also, are generation labels and SU(2) contractions are not explicitly shown.
If R-parity is violated, then both lepton and baryon numbers may no longer be conserved in the theory. In particular, when lepton number is violated then the and superfields, which have the same gauge quantum numbers, lose their identity since there is no additional quantum number that distinguishes between them. One can then construct additional renormalizable RPV interactions simply by replacing in (1). Thus, the SUSY superpotential can violate lepton number (or more generally R-parity) via Yukawa-like trilinear term (TRPV) and/or a mass-like bilinear RPV term (BRPV) as follows (see e.g., RPVSUSY (); Roy:1992ps (); Bhattacharyya:1996nj (); Dreiner:1997uz (); Roy:1997ca (); MohapatraRPV (); SarahTRPVlink ()):
where is anti-symmetric in the first two indices due to SU(2) gauge invariance (here also SU(2) labels are not shown).
Moreover, if R-parity is not conserved then, in addition to the usual RPC soft SUSY breaking terms, one must also add new trilinear and bilinear soft terms corresponding to the RPV terms of the superpotential, e.g., to the ones in (2). For our purpose, the relevant ones to be added to the SUSY scalar potential are the following soft breaking mass-like terms neutrinomass6 (); neutrinomass4 (); neutrinomass1 (); Roy:1996bua (); Diaz:1997xc (); Chang:1999ih (); Mukhopadhyaya:1999gy (); Davidson:1999mc ():
where and are the scalar components of and , respectively.
In what follows, we will consider a single generation BRPV scenario, i.e., that in eq. (3) R-Parity is violated only among the interactions of a single slepton. In particular, we will be focusing mainly on the 3rd generation bilinear soft breaking mixing term, , which mixes the 3rd generation (tau-flavored) left-handed slepton neutral and charged fields with the neutral and charged up-type Higgs fields, respectively. The bilinear soft term leads in general to a non-vanishing VEV of the tau-sneutrino, . However, since lepton number is not a conserved quantum number in this scenario,the and superfields lose their identity and can be rotated to a particular basis in which either or are set to zero neutrinomass1 (); Davidson:1999mc (); Ferrandis:1998ii (); Davidson:2000ne (); Grossman:2000ex (). In what follows, we choose for convenience to work in the “no VEV” basis, , which simplifies our analysis below. In this basis the minima conditions in the scalar potential read (we follow below the notation of the package SARAH Sarah (); Sarah1 (); Sarah2 () and use some of the expressions given in Sarahlink ()):
where is the soft breaking bilinear term (i.e., corresponding to the -term in the superpotential) and are the VEV’s of the up and down Higgs fields, .
Without loss of generality, in what follows, we parameterize in terms of the physical pseudo-scalar mass using the RPC MSSM relation (see e.g., RPVHiggsParameterization ()), thus defining the soft BRPV "measure" as (from now on and throughout the rest of the paper we drop the generation index of the BRPV terms):
so that will be given in terms of a new BRPV parameter :
We also define, in a similar way, the measure of BRPV in the superpotential, , via:
2.1 The RPV SUSY scalar sector and Higgs-Sneutrino mixing
Using eqs. (4)–(8), the induced CP-odd and CP-even scalar mass matrices squared reads (see e.g., Sarahlink ()):111The CP-odd scalar mass matrix, , has a massless state which corresponds to the Goldstone boson.222We note that too large values of may drive (depending on the other free-parameters in the Higgs sector) the lightest mass-squared eigenstates of both the CP-even and CP-odd mass matrices to non-physical negative values. We will thus demand non-negative mass-squared physical eigenvalues for the CP-even and CP-odd physical states by bounding accordingly.
with , and . The -sneutrino mass term, , is given in the RPV SUSY framework by:
where is the soft left-handed slepton mass term, . We have denoted in eq. (12) the -sneutrino mass term in the RPC limit by (note that the correction to in the BRPV framework is ). Note also that we have added in the CP-even sector the dominant top-stop loop corrections, , which are required in order to lift the lightest Higgs mass to its currently measured value FeynHiggs (); see also discussion on the Higgs mass filter in section 4.
The physical CP-even mass eigenstates in the RPV framework, which we denote below by , are obtained upon diagonalizing the CP-even scalar mass-squared matrix:
where are the corresponding weak states of in the CP-even Higgs sector and is the unitary matrix which diagonlizes , defined here as:
We would like to emphasize a few aspects and features of the BRPV SUSY framework which are manifest in the CP-even Higgs mass matrix and spectrum and are of considerable importance for our study in this paper:
We will be interested in the properties (i.e., production and decay modes) of , which is the lightest CP-even Higgs state in the BRPV framework. This state has a Sneutrino component due to the Higgs-sneutrino mixing terms (i.e., ) in the CP-even Higgs mass matrix HiggsSneutrinoMixingEilamMele (); HiggsSneutrinoMixingEilamMele2 (). The element is the one which corresponds to the Sneutrino component in and is, therefore, responsible for the mixing phenomena. It depends on and thus shifts some of the RPC light-Higgs couplings, as will be discussed below. In particular, we interpret the observed 125 GeV Higgs-like state as the lightest Higgs-sneutrino mixed state and, in our numerical simulations below, we demand GeV, in accordance with the LHC data where we allow some room for other SUSY contributions to the Higgs mass, i.e., beyond the simplified RPV framework discussed in this work.
The elements and correspond to the and components in . They are independent of the soft BRPV parameter at , so that, at leading order in , they are the same as the corresponding RPC elements.
Guided by the current non-observation of new sub-TeV heavy Higgs states at the LHC, we will assume the decoupling limit in the SUSY Higgs sector DecouplingHaber (); DecouplingCarena (); Decoupling (), in which case the RPC Higgs couplings are SM-like. We will demonstrate below that the BRPV effects may be better disentangled in this case.
2.2 The Gaugino sector
With the BRPV term in the superpotential ( in eq. (2)) and assuming only 3rd generation BRPV, i.e., only , the neutralinos and charginos mass matrices read:
where , , and (dropping the generation index, see eq. (9)). Also, is the bare mass of the -lepton and in we have added the loop-induced BRPV contributions and to the tau-neutrino mass B3_neutrinomass_constraints () (which is used in section 4 in order to constrain the BRPV parameters and ). Finally, and are the neutralino mass matrix and the chargino mass matrix in the RPC limit, respectively, which depend on the U(1) and SU(2) gaugino mass terms and , on the bilinear RPC term, on and on the Z-boson mass and the Weinberg angle (see e.g., Sarahlink ()).
The physical neutralino and chargino states, and , respectively, are obtained by diagonalizing their mass matrices in (15) and (16). For the neutralinos we have (i.e., with only 3rd generation neutrino-neutralino mixing):
where are the neutralino weak states and is the unitary matrix which diagonlizes in (15). In particular, we identify the lightest neutralino state in the RPV setup, , as the -neutrino . Note that the entries enter in the Higgs couplings to a pair of neutralinos and, in particular, generates the coupling (), where is the 2nd lightest neutralino state corresponding to the lightest neutralino in the RPC case (see Appendix A.4). As will be discussed in section 4, this new RPV coupling opens a new Higgs decay channel , if and also enters in the the loop-induced contribution to .
In the chargino’s case, since the matrix is not symmetric, it is diagnolized with the singular value decomposition procedure, which ensures a positive mass spectrum:
The chargino physical states are then obtained from the weak states and by:
where, here also, the lightest chargino is identified as the -lepton, i.e., and the elements of the chargino rotation matrices enter in the Higgs couplings to a pair of charginos. Thus, the decay corresponds in the RPV framework to . In addition, if , then the decay (i.e., the decay ) is also kinematically open (see Appendix A.4).
3 The 125 GeV Higgs signals
The measured signals of the 125 GeV Higgs-like particle are sensitive to a variety of new physics scenarios, which may alter the Higgs couplings to the known SM particles that are involved in its production and decay channels.
We will use below the Higgs “signal strength" parameters, which are defined as the ratio between the Higgs production and decay rates and their SM expectations:
where and are the normalized production and decays factors which, in the narrow Higgs width approximation, read:
and is the total width of the 125 GeV Higgs (SM Higgs). Also, represents the parton content in the proton which is involved in the production mechanism and is the Higgs decay final state.
We will consider below the signal strength signals which are associated with the leading hard production mechanisms: gluon-fusion, , production, , and VBF, .333We neglect Higgs production via , which, although included in the ATLAS and CMS fits, is 2-3 orders of magnitudes smaller than the gluon-fusion channel. Note that additional sources of Higgs production via heavy SUSY scalar decays may be present as well SoniHeavyScalarpaper (). The -fusion production channel, which is negligible in the SM due to the vanishingly small SM Yukawa couplings of the light-quarks, will be considered for the TRPV scenario in the next section. We will use the usual convention, denoting by the gluon-fusion channel and by the and VBF channels; for clarity and consistency with the above definitions, we will also explicitly denote the underlying hard production mechanism by a bracketed superscript. The decay channels that will be considered below are and .
In particular, in the BRPV SUSY scenario we have:
for the production factors and
for the decay factors, where and the RPC and couplings, and , as well as the decay widths for are given in Appendix A. In particular, the and VBF production channels as well as the Higgs decays to a pair of and bosons are not changed in our BRPV setup (i.e., in the no-VEV basis ) with respect to the RPC SUSY framework. For the total Higgs width in the RPV SUSY scenario we add the new decay channels and when they are kinematically open (see next section).
Finally, in the numerical simulations presented below we use the combined ATLAS and CMS signal strength measurements (at 13 TeV) which are listed in Table 1.
4 Bilinear RPV - Numerical results
To quantify the impact of BRPV on the 125 GeV Higgs physics we performed a numerical simulation, evaluating all relevant Higgs production and decays modes under the following numerical and parametric setup (for recent work in this spirit see BRPVdiphoton (); triRPV2loopmh ()):
Our relevant input parameters are , where is used as a common left-handed (soft) squark mass (i.e., ) for both the stop and sbottom states (see Appendix A.3) and .
In the stop sector we have assumed a degeneracy between the right and left-handed soft masses, i.e., ; this is also used in the calculation of the stop-top loop corrections to the CP-even scalar mass matrix, see FeynHiggs (). On the other hand, in the sbottom and stau sectors we keep the right-handed soft mass terms, , as free-parameters.
We adopt the Minimal Flavor Violation (MFV) setup for the squarks and sleptons soft trilinear terms, assuming that they are proportional to the corresponding Yukawa couplings: , for .444For the fermion Yukawa couplings we have for the down-type quarks and leptons and for up-type quarks. We thus vary the common trilinear soft term for all the squarks and sleptons states.
We randomly vary the model input parameters within fixed ranges which are listed in Table 2. In some instances and depending on the RPV scenario analyzed below, these ranges are refined for the purpose of optimizing the BRPV effect, thereby focusing on more specified regions of the RPV SUSY parameter space.
In cases where the Higgs decays to gauginos, we consider light gaugino states with a mass GeV (see e.g. Gambit ()), which requires a higgsino mass parameter and/or gaugino mass parameters of .
We impose the following set of "filters" and constraints to ensure viable model configurations:
Higgs mass: We fix the lightest Higgs mass to its observed value in the computation of the Higgs production and decay rates. Nonetheless, we allow for a theoretical uncertainty of GeV in the calculated Higgs mass (leaving some room for other possible SUSY contributions that are not accounted for in our minimal RPV SUSY framework), thus requiring that GeV. In particular, we include in the leading top-stop corrections (see Eq. (11)) and the sbottom and stau 1-loop contributions (which are not explicitly added in Eq. (11) but can be relevant for large MSSMCornered ()):
where here , , , and and it is understood that and are the masses of the two lightest slepton states ( being the massless Goldstone boson).
Neutrino masses: The RPV parameters are subject to constraints from various processes TRPVbounds (), such as flavor violating -decays btosg1 (); btosg2 (); btosg3 (); btosg4 () and Higgs decays 3bodyBRPVdecays1 (), as well as radiative leptonic decays, e.g., mutoeg1 (); mutoeg2 (). Other notable quantities that are sensitive to the RPV parameter-space constraints are, e.g., Electric Dipole Moments (EDM’s) EDM1 (); EDM2 (); EDM3 () and neutrino masses neutrinomass1 (); neutrinomass2 (); neutrinomass3 (); neutrinomass4 (); neutrinomass5 (); neutrinomass6 (); B3_neutrinomass_constraints (). A recent paper reviewing the various constraints on the RPV parameter-space is given in Arhrib () and bounds on the TRPV couplings can be found in RPVsearchatLHCdreiner (); lambdaprimeconstraints2 ().
We find that the strongest constraints on the BRPV parameters and are from neutrino masses. In particular, neutrino masses can be generated at tree-level when only and at the 1-loop level if also . In the former case , while at 1-loop , see B3_neutrinomass_constraints (). For example, the 1-loop contribution to the neutrino masses, which enters in eq. (15) is B3_neutrinomass_constraints () (for the expression of which is rather lengthy we refer the reader to B3_neutrinomass_constraints ()):
where is the neutralino mixing matrix in the RPC limit (i.e., corresponding to which is the 4X4 RPC block in (15)), are the neutralino masses in the RPC case, i.e., , and is defined in B3_neutrinomass_constraints (). Also, we have used our definition for the BRPV parameter in eq. (8) and . Furthermore, is the mass of the heavy CP-even Higgs state and is the sneutrino mass.
We use below the current Laboratory bounds on the muon and -neutrino masses: MeV and MeV PDG2017 (). In particular, in our numerical simulations, we evaluate the contribution of and to the relevant neutrino mass for each run, i.e., calculating and and requiring the lightest physical neutralino state ( or depending on the RPV scenario considered, see eq. (15)) to have a mass below these bounds.
Higgs signals: For each point/model in our RPV SUSY parameter-space we calculate all the Higgs signal strengths in Table 1 and require them to agree with the measured ones at the level.
4.1 Higgs decays to Gauginos
We study here the pure BRPV Higgs decays and , see also RPVHiggsValle (); RPVHiggsRosiek1 () (for another interesting variation of RPV Higgs decays to gauginos see UnusualRPVHiggs ()). Depending on the scenario under consideration, we require GeV and/or GeV, in which case the BRPV decays and/or are kinematically open, respectively (also adding them to the total Higgs width ).
We consider four BRPV scenarios for the parameter space associated with the gaugino sector:
S1A: A gaugino-like scenario with NearlyDegChargNeut (), and nearly degenerate lightest neutralino and chargino with a mass lighter than the Higgs mass: GeV. In this case, both decays and are kinematically allowed.
S1B: A higgsino-like scenario with NearlyDegChargNeut (), and nearly degenerate lightest neutralino and chargino with a mass lighter than the Higgs mass: GeV. In this case also, both decays and are kinematically open.
S2: No degeneracy in the gaugino sector with GeV and GeV, so that only the decay channel is kinematically open.
S3: No degeneracy in the gaugino sector with both GeV and a significant branching fraction in the neutralino channel : and a kinematically open decay with much smaller rate.
We give in Fig. 1 a scatter plot of the surviving model configurations in the – plane for the above four BRPV scenarios, where and . We can see that within the two S1 scenarios, S1A yields larger decay rates in both channels and , in particular, reaching a width MeV. In the S2 scenario we expect a BRPV signal only in the channel ( is kinematically closed, see above), which can also reach a width of MeV. Finally, we see that the S3 scenario is expected to give the largest BRPV decay rate in the neutralino channel , reaching MeV, which is more than 10% of the total SM Higgs width; in this case, the BRPV Higgs decay channel to a chargino, is effectively closed due to a limited phase-space. We thus see that the different Si SUSY scenarios that we have outlined above, probe different regions in the – BRPV Higgs decays plane, where the cases without the mass degeneracy (scenarios S2 and S3) we obtain a better sensitivity to the neutralino channel .
In Table 3 we list four representative benchmark models BMi (i.e., sets of input parameters) which correspond to the four Si scenarios considered above. These sample benchmark models maximize the BRPV effect (i.e., decay rates) associated with the Si scenarios; the corresponding BRPV Higgs decay width into a single neutralino and a single chargino are given in Table 4. As can be seen from Table 3, all four BM models require low . Note also that BM3, for which we obtain a width of MeV (see Table 4) is characterized by the hierarchy in the gaugino sector.