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LanHEP ­ a package for automatic generation of Feynman
rules from the Lagrangian. Updated version 2.3.
A. Semenov
November 16, 2007
Abstract
This short note describes new features of the version 2.3 of the LanHEP software package;
in particular, high spin particles and setting up the output tables format.
1 High spin particles
The particles with the spin 3/2 and 2 can be declared by means of spinor3 and tensor statements.
The syntax is the same as for old scalar, spinor and vector statements:
spinor3 g:(gravitino, mass Mgno=0.23).
tensor G:(graviton, mass MG=600).
2 Particle table format
New option allows to modify the format of the output particle table and to add new proprties (new
columns in the table). The new format is set by means of prtcformat statement, for example, the
default CompHEP table format can be set by:
prtcformat fullname:' Full Name ',
name:' p ',
aname:' ap',
spin2,color,mass,width, aux,
texname:' latex P name ',
atexname:' latex aP name ' .
Each column of the table is described by the entry prop:title=value, where prop is the name of
particle property, title is shown in the title line, and value is default value used if the property of
specific particle is not set. Important: the width of title fixes the width of the table column, so it
should be wide enough to contain records for this property for any particle. If not specified, property
name is used as title, and blank space for default value.
There is a set of predefined properties (table columns) which exist in CompHEP by now plus the
electric charge of a particle:
. fullname 'Long' particle name.
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. name Particle name used in vertices table.
. aname Antiparticle.
. spin2 Twice spin, integer 0---4.
. mass Particle mass.
. width Particle width.
. echarge Particle electric charge, integer or ratio N/3. The value is generated automatically if
the CheckEM(photon, coupling) statement is used in the model file.
. echarge3 Three times electric charge, integer.
. color Dimension of the color SU(3) group representation (one of 1,3,8).
. aux Specify the particle as left or right fermion, boson in Feynman gauge (see CompHEP
manual).
. texname LaTeX notation to be used for this particle.
. atexname Same for antiparticle. If not set, bar{texname} is used.
Besides these predefined properties, the user can introduce new ones. One can add, say, PDG
particle number to the table:
prtcformat fullname:' Full Name ',
name:' p ',
aname:' ap',
spin2,color,mass,width, aux,
pdg:'PDG ID',
texname:' latex P name ',
atexname:' latex aP name ' .
Then the pair prop value can be written in the particle declaration statement:
scalar h:(higgs, mass Mh, pdg 123, width wh).
Another statement prtcprop can solve two problems. First, it can declare a property (or a few of
them) which are not included in the particle table, but they still can be used in particle declarations
for further use in the future. For example, one can declare pdg property:
prtcprop pdg.
and use it in the particle declarations even though CompHEP does not support this property now
for future extensions. In this case, particle table format is not changed. Several properties can be
listed, separated by comma.
Another problem is to set a new property for all particles in the model. There is no need to
modify all particles declarations in the model, one can use statement like this:
prtcprop pdg:(h=123, g=124, f=125).
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In this example h,g,f are some particles and the numbers are values of a property. Only new properties
can be assigned to particles in this way, but not the predefined ones. If one wants to set, for example,
the particle masses by this statement, new property (say mymass) should be declared and included
into table format.
If some property is set to a number, a ratio, some particle or parameter name, then it can be
used in the Lagrangian expressions as (prop particle), e.g. electric charge can be used to describe
quark­photon interaction:
lterm (echarge q)*EE*Q*gamma*q*A.
3 Lagrangian table setup
The format and content of the Lagrangian (vertices) table can be tuned by several options set by
option statement:
option opname=value.
and by some command line options.
. chepCFWidth Width of Common Factor field, default is 50.
. chepLPWidth Width of Lorentz Part field, default is 600.
. RemDotWithFerm options (default value 1) tells LanHEP to replace g µ# by (# µ # # + # # # µ )/2 in
the vertices with fermions (CompHEP requirement). If this replacement is not neccessary put
this option to 0.
. ReduceGamma5 (default value 1) removes (1 ± # 5 )/2 operators in the vertices with lefthand or
righthand fermions (e.g. neutrinos) replacing them by 0 or 1. Put this option to 0 to keep
projector operators in such vertices.
. MultByI (default value 0 for CompHEP output, 1 for LaTeX) In CompHEP tables, common i
in the vertices is not shown, so imaginary unit appears only in the vertices with pseudoscalars.
Setting this option to 1 allows to restore it, making ComHEP vertices the same as in textbooks.
. WriteAll (default 0) Setting this option to 1 makes LanHEP write into CompHEP table all
vertices: 2­legs vertices, 1­legs ones (they can appear from incorrectly written Higgs potential)
and also the vertices with more than 4 legs. The command line option ­allvrt has the same
e#ect.
. MaxiLegs allows to limit the number of legs in the vertices produced when WriteAll is active.
. WriteColors (default 0) Set this option to 1 to write color structure of vertices explicitely.
Also the command line options ­colors can be used.
When the WriteColors option is set to 1, color matrices and dot products are written in the
Lorentz Part, e.g. QCD plus quark­photon interactions produces the following vertices file:
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QCD
Lagrangian
P1 |P2 |P3 |P4 |> Factor <|> dLagrangian/ dA(p1) dA(p2) dA(p3)
G |G |G | |gg |m2.p3*m1.m3*F(c1,c2,c3)
| | | | ­m1.p3*m2.m3*F(c1,c2,c3)
| | | | +m3.p1*m1.m2*F(c1,c2,c3)
| | | | ­m2.p1*m1.m3*F(c1,c2,c3)
| | | | ­m3.p2*m1.m2*F(c1,c2,c3)
| | | | +m1.p2*m2.m3*F(c1,c2,c3)
G.C |G.c |G | |­gg |m3.p2*F(c1,c2,c3)
Q |q |G | |gg |L(c1,c2,c3)*G(m3)
Q |q |A | |ee/3 |c1.c2*G(m3)
G |G |G |G |gg^2 |m1.m3*m2.m4*F(c1,c2,c0)*F(c3,c4,c0)
| | | | ­m1.m4*m2.m3*F(c1,c2,c0)*F(c3,c4,c0)
| | | | +m1.m2*m3.m4*F(c1,c3,c0)*F(c2,c4,c0)
| | | | ­m1.m4*m2.m3*F(c1,c3,c0)*F(c2,c4,c0)
| | | | +m1.m2*m3.m4*F(c1,c4,c0)*F(c2,c3,c0)
| | | | ­m1.m3*m2.m4*F(c1,c4,c0)*F(c2,c3,c0)
Here q/Q is a quark, G -- gluon , G.c -- gloun ghost field, and A -- photon. F stand for antisym­
metric structure constants (D for symmetric ones), L -- Gell­Mann matrices. The Lorentz part is
shown one monomial per line just to make the expression fit into the page, usually there is one line
per vertex (option chepBreakLines set to 1 to made this e#ect).
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