scholarly journals Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms

2016 ◽  
Vol 56 (3) ◽  
pp. 149-163
Author(s):  
Vytautas Dūdėnas ◽  
Thomas Gajdosik
Keyword(s):  
Path Integral ◽  
Tree Level ◽  
Fermion Propagator ◽  
Weyl Spinor ◽  
Majorana Mass ◽  
Basic Formalism ◽  
Feynman Rules ◽  
Mass Terms ◽  
Level Analysis

We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals Synthesis of Majorana mass terms in low-energy quantum systems

2018 ◽  
Vol 20 (6) ◽  
pp. 063032
Author(s):  
L Lepori ◽  
A Celi ◽  
A Trombettoni ◽  
M Mannarelli
Keyword(s):  
Quantum Systems ◽  
Low Energy ◽  
Majorana Mass ◽  
Mass Terms ◽  
Energy Quantum

scholarly journals Bulk Majorana mass terms and Dirac neutrinos in the Randall-Sundrum model

2013 ◽  
Vol 88 (7) ◽  
Author(s):  
Abhishek M. Iyer ◽  
Sudhir K. Vempati
Keyword(s):  
Majorana Mass ◽  
Mass Terms

scholarly journals ELECTROWEAKLY INTERACTING SCALAR AND GAUGE BOSONS, AND LEPTONS, FROM FIELD EQUATIONS ON SPIN (5+1)-DIMENSIONAL SPACE

2005 ◽  
Vol 20 (01) ◽  
pp. 77-93 ◽  
Author(s):  
J. BESPROSVANY
Keyword(s):  
Dimensional Space ◽  
Spin Symmetry ◽  
Coupling Constants ◽  
Tree Level ◽  
Field Equations ◽  
Gauge Groups ◽  
Scalar Particles ◽  
Additional Information ◽  
The Standard Model ◽  
Mass Terms

Unification ideas motivate the formulation of field equations on an extended matrix-spin space. Demanding that the Poincaré symmetry be maintained, one derives scalar symmetries that are associated with flavor and gauge groups. Boson and fermion solutions are obtained with a fixed representation. A field theory can be equivalently written and interpreted in terms of elements of such a space and is similarly constrained. At 5+1 dimensions, one obtains isospin and hypercharge SU (2)L× U (1) symmetries, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. Mass terms produce breaking of the symmetry to an electromagnetic U (1), a Weinberg's angle with sin 2(θW)=0.25, and additional information on the respective coupling constants. The particles' underlying spin symmetry gives information on their masses; one reproduces the Standard Model ratio MZ/MW, and predicts possible Higgs masses of MH≈114 and MH≈161 GeV, at tree level.

scholarly journals How dark is the νR-philic dark photon?

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Garv Chauhan ◽  
Xun-Jie Xu
Keyword(s):  
Gauge Symmetry ◽  
Tree Level ◽  
Potential Importance ◽  
Dirac Mass ◽  
Dark Photon ◽  
Left Handed ◽  
Normal Matter ◽  
Belle Ii ◽  
Mass Terms ◽  
Charged Leptons

Abstract We consider a generic dark photon that arises from a hidden U(1) gauge symmetry imposed on right-handed neutrinos (νR). Such a νR-philic dark photon is naturally dark due to the absence of tree-level couplings to normal matter. However, loop-induced couplings to charged leptons and quarks are inevitable, provided that νR mix with left-handed neutrinos via Dirac mass terms. We investigate the loop-induced couplings and find that the νR-philic dark photon is not inaccessibly dark, which could be of potential importance to future dark photon searches at SHiP, FASER, Belle-II, LHC 14 TeV, etc.

NEUTRINO COUNTING WITH ONE (OR MORE) RIGHT-HANDED MAJORANA NEUTRINO

1990 ◽  
Vol 05 (24) ◽  
pp. 1933-1940 ◽  
Author(s):  
XUEQIAN LI ◽  
ZHIJIAN TAO
Keyword(s):  
Majorana Neutrino ◽  
Fourth Generation ◽  
Majorana Mass ◽  
Generation Number ◽  
Mass Terms ◽  
Normal Formula

The recent data of ALEPH and L3 collaborations seem to indicate that the generation number is likely to be three based on the normal formula. However, we show that if one or several SU(2) singlet heavy neutrinos with both the Dirac and Majorana mass terms exist, mixing with light neutrinos can cause some variations in the neutrino counting formulation and the results imply that if the extra neutrinos are very heavy, the fourth generation is not ruled out by the present data.

scholarly journals FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL

2008 ◽  
Vol 23 (02) ◽  
pp. 211-232 ◽  
Author(s):  
DANIELE BETTINELLI ◽  
RUGGERO FERRARI ◽  
ANDREA QUADRI
Keyword(s):  
Sigma Model ◽  
Dimensional Regularization ◽  
Formal Proof ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Subtraction Procedure ◽  
Feynman Rules ◽  
Local Functional ◽  
Two Parameters

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of nonchiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.

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