The following is the input files for Standard Model.
\% ----------------------- File: mode_input -------------------- \\
\% The standard model in unitary gauge \\
algebraic$
%------------------------- Gauge fields -------------------------------
% The first is the gauge field. So in the mode, you must input
% how many gauge fields and for each gauge field, declare SU(n) ( we
% have just realize SU(n) gauge field in the system), notation for the
% field, goupling constant, gauge fix term and gauge parameter ( different
% gauge can be chosen by differnet gauge fix term and different gauge
% parameter), and you should indicate if the gauge symeetry is breaking
% or not.
gaugefields:=
% No. Name SU(n) notation coupling gaugefixterm gauge_pa breaking
'((1 u 1 b g1 gfix1 infinite yes )
(2 su 2 a g gfix2 infinite yes )
(3 su 3 gs g3 gfix3 1 no )
)$
gfix1:=pd(b(v),v)$
gfix2:=pd(a(i1,v),v)$
gfix3:=pd(gs(i1,v),v)$
% where b is the u(1) field, a is the su(2) field and gs is the su(3) field.
%----------------------------------------------------------------------
%------------------------ Matter fields --------------------------------
% The second is the matter field. for each matter field, you must input
% the name, 2 times spin, chiral ( r --- right, l --- left or r-l
% together) and then the gauge group parameter for each gauge group
% ( for u(1), it is u(1) charge and for su(n), it is mutiplet number)
%
matterinput:={{name, 2*spin, chiral, "|g", 1, 2, 3},
{ hig, 0 , rl , 1, 2, 0},
{ el , 1, l , -1, 2, 0},
{ er , 1, r , -2, 0, 0},
{ q1l , 1, l , 1/3, 2, 3},
{ q1dr, 1, r , -2/3, 0, 3},
{ q1ur, 1, r , 4/3, 0, 3}
}$
% where:
% hig is the Higgs boson doublet with u(1) charge 1 and su(3) singelet.
% el is the electron left-hand doublet with u(1) charge -1 and su(3) singelet.
% er is the electron right-hand singelet with u(1) charge -2 and su(3)
% singelet.
% q1l is the first generation quark left-hand doublet with u(1) charge
% 1/3 and su(3) triplet.
% q1dr is the first generation down quark right-hand singelet with u(1)
% charge -2/3 and su(3) triplet.
% q1ur is the first generation up quark right-hand singelet with u(1)
% charge 4/3 and su(3) triplet.
%----------------------------------------------------------------------
%------------------------ Charge list of particles ------------------------
% In fact, The charge of particles can be calculated out by using the
% definition of charge and the definition of all the fields.
pchalist:={{hig,h0(0)}, %hig field's componet h0 is of charge 0.
{el,nue(0),ee(-1)}, %el field's componets nue -- 0, ee -- -1.
{er,ee(-1)}, %er field's componet ee is of charge -1.
{q1l,qu(2/3),qd(-1/3)}, %q1l's componets qu -- 2/3, qd -- -1/3.
{q1ur, qu(2/3)}, %q1ur's componet qu -- 2/3.
{q1dr, qd(-1/3)}, %q1dr's componet qd -- -1/3.
{a,w(1),w(-1),z(0),p(0)},%a's componets w -- 1, z -- 0, p --0.
{b,p(0),z(0)}, %a's componets z -- 0, p --0.
{gs,gs(0)} %gs's componet gs -- 0.
};
%----------------------------------------------------------------------
%------------------- Definition of mutiplet -------------------------
%
% To definition the mutiplet is not a trivial thing in general case,
% the definition of vector mutiplets can be done in the following way.
% the definition of tensor mutiplet are realized in SU(5) gauge theory
% case.
%
% name n_group 1_componet 2_componet ...
mdefl:={{hig, {2, 0 , (v0+h0)/2**0.5}},
{el , {2, nue , ee}},
{er , {2, ee }},
{q1l , {2, qu , qd}},
{q1dr, {2, qd }},
{q1ur, {2, qu }},
{qu, {3, qu(1), qu(2) , qu(3)}},
{qd, {3, qd(1) , qd(2) , qd(3)}}
}$
vancumexpectation:='((hig v0));
% where hig is the Higgs doublet for the second gauge group su(2)
% and the definition of it's componets are given in unitary gauge.
% the vancume expextation of hig is v0 so that in the 2_componet
% expression of hig there is only one higgs field h0.
% el, q1l are electron and first generation quark left-hand double for
% the second gauge field su(2).
% er, q1dr and q1ur are electron, first generation down quark and up quark
% right-hand singelet for the second gauge field su(2).
% the qu, qd which appeared in q1l,q1dr,q1ur componets are triplet for
% the third guage field su(3).
%-------------------------------------------------------------------------
%------------------- Fermion mix -------------------------
%
% Definition of Fermion Generation:
% Generation is a very useful concept in physical model. We can construct
% the lagrangian for only one generation, then add almost the same terms
% for the other generation and make some rotations which are caused by
% Yukawa coupling or Higgs self-interaction terms. In the following, we
% just introduce the definition for fermion generations.
% There are three generation quark and lepton in the SM as shown in the
% following
realfamily:='((q1l q2l q3l) (q1dr q2dr q3dr) (q1ur q2ur q3ur)
(qu qc qt) (qd qs qb)
(el mul taul) (er mur taur)
(ee mu tau) (nue numu nut)
);
% where (q1l q2l q3l) is the three generations of left-hand double quark,
% (q1dr q2dr q3dr) is the three generations of right-hand singlet down quark,
% (q1ur q2ur q3ur) is the three generations of right-hand singlet up quark.
% (qu qc qt) and (qd qs qb) are the coressponding componets for the three
% generation quarks.
% where (el mul taul) is the three generations of left-hand double lepton,
% (er mur taur) is the three generations of right-hand singlet lepton,
% (ee mu tau) and (nue numu nut) are the coressponding componets for the
% three generation leptons.
% Mix Matrices:
mixlist:='(
(l (s1 (qd qs qb)) (s2 (qu qc qt))
(se1 (ee mu tau)) (se1 (nue numu nut))
)
(r (t1 (qd qs qb)) (t2 (qu qc qt))
(te1 (ee mu tau))
)
);
% Definition of CKM Matrix: ]
mixlistcondition:={s2(-1)*s1(1)=>v_ckm(1)};
% where the mix matrix for the three left-hand generations are:
% mix matrix s1 for (qd qs qb), mix matrix s2 for (qu qc qt),
% mix matrix se1 for (ee mu tau) and (nue numu nut).
% The reason that the mix matrix of (nue numu nut) can be chosen as
% the smae mix matrix of ( ee mu tau) is due to that nue, numu, nut
% have the same mass so they can be mixed in any way. The choice of
% the same mix matrix se1 for (ee mu tau) and (nue numu nut) make
% representation in the simplist way. For eaxmple, If you have a model
% with the neutrons (nue numu nut) are of different masses, you must
% choose different mix matrices for leptons and neutrons and as a result
% that you need to definition CKM matrix for leptons in the above
% mixlistcondition.
% The mix matrix for the three right-hand generations are:
% mix matrix t1 for (qd qs qb), t2 for (qu qc qt)
% and te1 for (ee mu tau).
%------------------------------------------------------------------------
%-------------------------- Globel Symmetry ------------------------------
%
% The third is the globel symmetry of the model, there are lepton number
% conservation as globel symmetry in Standrad Model and the lepton numbers
% are set to each particles in the model. gbsymmetrylist is the globel
% symmetry list.
gbsymmetrylist:={len,lmuon,ltau};
gbsymmetrydata:={{len, {el,1}, {er,1}},
{lmuon,{mul,1}, {mur,1}},
{ltau, {taul,1}, {taur,1}}}$
% where globel symmetry number len are 1 for el and 1 for er,
% globel symmetry number lmuon are 1 for mul and 1 for mur,
% globel symmetry number ltau are 1 for taul and 1 for taur.
% In the system, it is supposed that the lepton number of particles
% which do not appeared in each lepton number table in the gbsymmetrydata
% are set to zero and all the globel symmetry numbers for anti-particles
% are set to the minus times that of the particles.
%----------------------------------------------------------------------
%-------------------- Masses and Other Paramters ------------------------
% The names of masses of all the particles are given in the following
% table phymass and all the zero mass particles are also set it's mass
% to zero in the table.
phymass:={{w, wm}, {z, zm}, {p, 0}, {h0, hm},
{ee, fme},{nue, 0},
{mu, fmmu},{numu, 0},
{tau, fmtau},{nut, 0},
{qd, fmd}, {qu, fmu},
{qs, fms}, {qc, fmc},
{qb, fmb}, {qt, fmt}
}$
% The parameter set are chosen in table phyinput and this set is used
% as physical input of the model, or it can be called as the choice of scheme.
% To change scheme, your can choose different physical input in the table.
% For eaxmple, to use Z boson's mass zm instead of the w boson's mass wm,
% to use electronic coupling g1 instead of sin(thta), for this propose,
% the relation of g1,g and thta in the paramters relation table construles
% should be changed.
phyinput:={wm, hm, g, sin(thta),
fme,
fmmu,
fmtau,
fmd, fmu,
fms, fmc,
fmb, fmt
}$
% ----------------- Mix of vector boson -----------------------
%
mixrules:={ a(1,~v) => (w(1,v)+w(-1,v))/2**0.5,
a(2,~v) => (w(-1,v)-w(1,v))/2**0.5/i,
a(3,~v) => z(0,v),
b(~v) => p(0,v) };
bosonmix:='((sxpz p z));
%-----------------------------------------------------------------
% ----------------- Mix of Higgs boson -----------------------
% The mix of Higgs boson will appeared in the model with more than
% one Higgs mutiplet. For eaxmple, in the two Higgs doublet model.
%-----------------------------------------------------------------
% ------------ Mix of Higgs boson and vector boson -------------
% The mix of Higgs boson and vector boson is required to be cancelled
% by some terms appeared in the gauge fix terms and the system will
% automatically add these terms to the gauge fix term given in above
% gauge fields section.
%-----------------------------------------------------------------
% --------- Mix Matrices of Higgs boson and vector boson---------
matrixlist:={ {sxpz,{cos(thta),sin(thta)},{-sin(thta),cos(thta)}}
};
%where matrixlist is the list of all the boson mix matrices. the
%mix angle thta of photon and Z boson is introduce the it's mix
%matrix expression.
%-----------------------------------------------------------------
% --------- To solve parameter relations---------
% it is obvious that not all the parameters appeared in the model are
% indepandent and some of them should be expressed by others. In the
% following, there are two way to choose which parameters should be
% expressed by others. One is to put the expressions of the parameters
% into the list construles and another is to put the parameters in the
% list mixfix, then the system will give the expression when it deal the
% mix of particles.
mixfix:={};
construles:={ g1=>g*sin(thta)/cos(thta)
};
% The following is the another way.
%mixfix:={g1};
%construles:={ };
%
%----------------------------------------------------------------------
%---------------------- The charge definition --------------------------
charge:=tp(2,3)+tp(1,1)/2;
%where tp(n,m) represent the m-th generator of the n-th gauge group
;end$
%%----------------------------------------------------------------------