== Alternative Left-Right Symmetric Model ==


'''Author'''


Mustafa Ashry[[BR]]

Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza, Egypt[[BR]]
Center for Fundamental Physics (CFP), Zewail City of Science and Technology, Sheikh Zayed, 12588 Giza, Egypt

'''Emails'''


mustafa[AT]sci.cu.edu.eg[[BR]]
mashry[AT]zewailcity.edu.eg

'''Model Description'''


The Alternative Left-Right Symmetric Model (ALRM) is gauged by the Left-Right symmetry group ''SU(3),,C,,×SU(2),,L,,×SU(2),,R,,×U(1),,B-L,,''. The latter ''B'' and ''L'' being the baryon and lepton numbers. An extra discrete symmetry ''S'' is imposed to distinguish between Higgs fields and their dual fields and hence their interactions; causing the absence of the tree-level flavor-changing neutral currents mediated by Higgs bosons.

As in the SM, left-handed fermions compose ''SU(2),,L,,'' doublets. Right-handed charged leptons form ''SU(2),,R,,'' doublets with corresponding extra particles (scotinos) and right-handed up-quarks form ''SU(2),,R,,'' doublets with corresponding extra down-type exotic quarks. Right-handed neutrinos and down-quarks are ''SU(2),,L,R,,'' singlets. The Higgs sector composes of an ''SU(2),,L,,''-doublet, an ''SU(2),,R,,''-doublet and a bidoublet.

The electroweak left-right symmetry ''SU(2),,L,,×SU(2),,R,,×U(1),,B-L,,'' is spontaneously broken down to the SM electroweak symmetry ''SU(2),,L,,×U(1),,Y,,'', ''Y'' being the hypercharge, by the ''SU(2),,R,,''-doublet vev, then the SM electroweak symmetry is spontaneously broken down to the ''U(1),,em,,'' through the bidoublet and the ''SU(2),,L,,''-doublet vevs. Accordingly, all fermions and gauge bosons (except of course photon) become massive via Higgs mechanism. The physical gauge sector of the model contains the electroweak gauge bosons (photon, ''W'' and ''Z'' bosons, whose masses were fixed by the experimental SM values) in addition to two extra gauge bosons (''W' '' and ''Z' '') correspond to the ''SU(2),,R,,'' group, analogous to those of the ''SU(2),,L,,'' group. Also the Weinberg angle is fixed here as an input parameter by its experimental value.

Dirac (massive) neutrinos are considered with the mixing MNS matrix implemented in the normal hierarchy. The case of Majorana neutrinos is considered in many other models' files and any type of seesaw mechanisms can be brought to be implemented here easily. Three mixed generations of quarks are considered and hence the general case of the CKM matrix is implemented. In addition, it was considered that the left-right symmetry is manifest, that is the left and right MNS and CKM mixing matrices are coincident. However, this can be generalized directly.

The model contains ten physical Higgs bosons: four neutral ''CP''-even higgs bosons, one (the lightest) of which is considered to be the SM-like one with mass fixed to have the value ''mh''=125 GeV. Four charged Higgs bosons and two ''CP''-odd pseudoscalar Higgs bosons. The mass spectra are calculated and the rotation matrices are implemented analytically.

Minimization conditions and spectrum relations are all used to express the whole model parameters and spectra in terms of only five independent (external) parameters: ''tanbeta, lambda,,2,,, lambda,,3,,, alpha,,1,,, alpha,,2,,'' and ''mu,,3,,,''. As in any two-Higgs doublet model, e.g., MSSM, ''tanbeta'' is the ratio between two vevs. The parameters ''lambda,,2,,, lambda,,3,,, alpha,,1,,, alpha,,2,,'' are dimensionless potential parameters, while ''mu,,3,,,'' is a dimension-full potential parameter.

The effective loop-induced scalar and pseudoscalar ''higgs-gluon-gluon'' and ''higgs-gamma-gamma'' vertices were implemented at leading order (LO). For the complete gg->gammagamma and pp->gammagamma analysis, '''''Madgraph''''' is used as the Monte Carlo (MC) event generator (EG), then '''''Pythia''''' is used for parton showering (PS), and for matrix element (ME) and PS merging, and also for hadronization and jet matching. Afterward, '''''Delphes''''' is used as a detector simulator, and '''''Madanalysis''''' is used for event file analysis and in recasting the LHC results. Finally, '''''Root''''' is used to produce the following histogram figures:

[[Image(https://feynrules.irmp.ucl.ac.be/attachment/wiki/ALRM/ggaa_alrm_sm_reco.png)]]
[[Image(https://feynrules.irmp.ucl.ac.be/attachment/wiki/ALRM/ppaa_alrm_sm_reco.png)]]

'''References:''' Please cite

1. M. Ashry and S. Khalil, ''Phenomenological aspects of a TeV-scale alternative left-right model'', Physical Review D 91, 015009 (2015) [[BR]][http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.015009] - [https://inspirehep.net/record/1258411] [arXiv:1310.3315]
2. Mustafa Ashry, ''TeV-scale left-right symmetric model with minimal Higgs sector'', Master Thesis, Cairo University, Cairo (2015), Egypt[[BR]][http://scholar.cu.edu.eg/?q=science_math_mashry/files/mashry_msc_thesis.pdf]

For the detailed Higgs spectrum and rotations, please cite both Refs. [1,2]


'''Acknowledgements'''


The author would like to thank his colleagues ''W. Abdallah'', the late colleague ''A. Elsayed'' and ''A. Moursy'' for their helpful hints and useful discussions. Thanks to ''B. Fuks''  for technical support and ''M. E. Peskin'' for guiding notes and fruitful discussions.