== Alternative Left-Right Symmetric Model ==


'''Author'''


Mustafa Ashry[[BR]]

1. Center for Fundamental Physics, Zewail City of Science and Technology, Sheikh Zayed, 12588 Giza, Egypt
2. Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza, Egypt

'''Emails'''


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

'''Model Description'''



As any other left-right symmetric model, ALRM is a QFT gauged by ''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.

As in the SM, left fermions compose ''SU(2)_L'' doublets. Right charged leptons are accommodated in ''SU(2)_R'' doublets with corresponding extra particles (scotinos) and right up-quarks in ''SU(2)_R'' doublets with corresponding extra down-type exotic quarks. Right 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 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 electroweak symmetry is broken down to the ''U(1)_em'' through the bidoublet and the ''SU(2)_L''-doublet vevs. Accordingly, all ferminos 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) in addition to two extra gauge bosons (''W' '' and ''Z' '') correspond to the ''SU(2)_R'' group.

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 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 spectrum is 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''. 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. The charged Higgs masses are implemented as external parameters.

The effective loop-induced h->gg and h->gammagamma, Zgamma, ZZ decays were added. For the complete pp->gammagamma is illustrated in the following figure: [https://feynrules.irmp.ucl.ac.be/attachment/wiki/ALRM/pp-%3Egammagamma.png]. Madgraph, Pythi and Madanalysis were used to produce this figure.

'''References'''


1. M. Ashry and S. Khalil, ''Phenomenological aspects of a TeV-scale alternative left-right model'', Physical Review D 91, 015009 (2015) (arXiv:1310.3315) ([https://inspirehep.net/record/1258411]).
1. Mustafa Ashry, ''TeV-scale left-right symmetric model with minimal Higgs sector'', Master Thesis, Cairo University, Cairo (2015), Egypt ([http://scholar.cu.edu.eg/sites/default/files/science_math_mashry/files/mashry_msc.thesis.pdf]).

'''Warnings'''


For the CalcHEP files, it's advised to use those uploaded to the page ([https://feynrules.irmp.ucl.ac.be/attachment/wiki/ALRM/ALRM_CalcHEP.rar]) and not to reproduce them again from the model files. In the latter case, you will be faced by a conflict between the string size produced by FeynRules and this allowed by CalcHEP. In fact, those CalcHEP files uploaded to the page are general and there is no need to produce them again, unless you have modified the model itself and want to generate the new ones.

'''Acknowledgements'''


Special thanks to ''W. Abdallah''; being revised the CalcHEP files and fixed the string size errors manually. The author would like to thank ''W. Abdallah'', the late colleague ''A. Elsayed'' and ''A. Moursy'' for their helpful hints and useful discussions. Thanks to Prof. ''M. E. Peskin'' and Dr. ''B. Fucks'' for replying the questions and for their guiding notes.[[BR]]