Further Couplings

In this section we collect information on the two routines for
running
and
, and on other couplings
of standard and non-standard particles found in the `PYDAT1` and
`PYTCSM` common blocks. Although originally begun for applications
within the traditional particle sector, this section of `PYDAT1`
has rapidly expanded towards the non-standard aspects, and is thus more
of interest for applications to specific processes. It could therefore
equally well have been put somewhere else in this manual. Several other
couplings indeed appear in the `PARP` array in the `PYPARS`
common block, see section , and the choice between
the two has largely been dictated by availability of space. The
improved simulation of the TechniColor Strawman Model, described
in [Lan02,Lan02a], and the resulting proliferation of model
parameters, has led to the introduction of the new `PYTCSM`
common block.

**Purpose:**- to calculate the running electromagnetic coupling
constant
. Expressions used are described in
ref. [Kle89]. See
`MSTU(101)`,`PARU(101)`,`PARU(103)`and`PARU(104)`. `Q2 :`- the momentum transfer scale at which to evaluate .

**Purpose:**- to calculate the running strong coupling constant
, e.g. in matrix elements and resonance decay widths.
(The function is not used in parton showers, however, where
formulae rather are written in terms of the relevant
values.) The first- and second-order expressions are given by
eqs. () and (). See
`MSTU(111) - MSTU(118)`and`PARU(111) - PARU(118)`for options. `Q2 :`- the momentum transfer scale at which to evaluate .

**Purpose:**- to give running masses of , , , ,
and quarks according to eq. (). For all other
particles, the
`PYMASS`function is called by`PYMRUN`to give the normal mass. Such running masses appear e.g. in couplings of fermions to Higgs and technipion states. `KF :`- flavour code.
`Q2 :`- the momentum transfer scale at which to evaluate .
**Note:**- the nominal values, valid at a reference scale

,

are stored in`PARF(91) - PARF(96)`.

**Purpose:**- to give access to a number of status codes and
parameters which regulate the performance of the program as a whole.
Here only those related to couplings are described; the main
description is found in section .

`MSTU(101) :`- (D = 1) procedure for
evaluation in the
`PYALEM`function.`= 0 :`-
is taken fixed at the value
`PARU(101)`. `= 1 :`- is running with the scale, taking into account corrections from fermion loops (, , , , , , , ).
`= 2 :`-
is fixed, but with separate values at low
and high . For below (above)
`PARU(104)`the value`PARU(101)`(`PARU(103)`) is used. The former value is then intended for real photon emission, the latter for electroweak physics, e.g. of the gauge bosons.

`MSTU(111) :`- (I, D=1) order of
evaluation in the
`PYALPS`function. Is overwritten in`PYEEVT`,`PYONIA`or`PYINIT`calls with the value desired for the process under study.`= 0 :`-
is fixed at the value
`PARU(111)`. As extra safety,`PARU(117)`is set in`PYALPS`so that the first-order running agrees with the desired fixed for the value used. `= 1 :`- first-order running is used.
`= 2 :`- second-order running is used.

`MSTU(112) :`- (D = 5) the nominal number of flavours assumed in
the
expression, with respect to which is defined.
`MSTU(113) :`- (D = 3) minimum number of flavours that may be
assumed in
expression, see
`MSTU(112)`. `MSTU(114) :`- (D = 5) maximum number of flavours that may be
assumed in
expression, see
`MSTU(112)`. `MSTU(115) :`- (D = 0) treatment of
singularity for
in
`PYALPS`calls. (Relevant e.g. for QCD matrix elements in the limit, but not for showers, where`PYALPS`is not called.)`= 0 :`- allow it to diverge like .
`= 1 :`- soften the divergence to .
`= 2 :`- freeze evolution below
`PARU(114)`, i.e. the effective argument is`PARU(114)`.

`MSTU(118) :`- (I) number of flavours found and used in
latest
`PYALPS`call.

`PARU(101) :`- (D = 0.00729735=1/137.04)
, the electromagnetic fine structure constant at
vanishing momentum transfer.
`PARU(102) :`- (D = 0.232)
, the weak mixing angle of the
standard electroweak model.
`PARU(103) :`- (D = 0.007764=1/128.8) typical
in
electroweak processes; used for
`PARU(104)`in the option`MSTU(101) = 2`of`PYALEM`. Although it can technically be used also at rather small , this value is mainly intended for high , primarily and physics. `PARU(104) :`- (D = 1 GeV) dividing line between `low' and
`high' values in the option
`MSTU(101) = 2`of`PYALEM`. `PARU(105) :`- (D = 1.16639E-5 GeV)
, the Fermi
constant of weak interactions.
`PARU(108) :`- (I) the
value obtained in the
latest call to the
`PYALEM`function. `PARU(111) :`- (D = 0.20) fix
value assumed in
`PYALPS`when`MSTU(111) = 0`(and also in parton showers when is assumed fix there). `PARU(112) :`- (I, D=0.25 GeV) used in running
expression in
`PYALPS`. Like`MSTU(111)`, this value is overwritten by the calling physics routines, and is therefore purely nominal. `PARU(113) :`- (D = 1.) the flavour thresholds, for the effective
number of flavours to use in the
expression, are
assumed to sit at
`PARU(113)`, where is the quark mass. May be overwritten from the calling physics routine. `PARU(114) :`- (D = 4 GeV) value below which the
value is assumed constant for
`MSTU(115) = 2`. `PARU(115) :`- (D = 10.) maximum
value that
`PYALPS`will ever return; is used as a last resort to avoid singularities. `PARU(117) :`- (I) value (associated with
`MSTU(118)`effective flavours) obtained in latest`PYALPS`call. `PARU(118) :`- (I)
value obtained in latest
`PYALPS`call. `PARU(121) - PARU(130) :`- couplings of a new ; for
fermion default values are given by the Standard Model values,
assuming
. Since a generation dependence is now
allowed for the couplings to fermions, the variables
`PARU(121) - PARU(128)`only refer to the first generation, with the second generation in`PARJ(180) - PARJ(187)`and the third in`PARJ(188) - PARJ(195)`following exactly the same pattern. Note that e.g. the width contains squared couplings, and thus depends quadratically on the values below.`PARU(121), PARU(122) :`- (D = , ) vector and axial couplings of down type quarks to .
`PARU(123), PARU(124) :`- (D = 0.387, 1.) vector and axial couplings of up type quarks to .
`PARU(125), PARU(126) :`- (D = , ) vector and axial couplings of leptons to .
`PARU(127), PARU(128) :`- (D = 1., 1.) vector and axial couplings of neutrinos to .
`PARU(129) :`- (D = 1.) the coupling
is
taken to be
`PARU(129)`(the Standard Model coupling) . This gives a partial width that increases proportionately to the mass. `PARU(130) :`- (D = 0.) in the decay chain
fermions, the angular distribution in
the decays is supposed to be a mixture, with fraction
`1. - PARU(130)`corresponding to the same angular distribution between the four final fermions as in (mixture of transverse and longitudinal 's), and fraction`PARU(130)`corresponding to the same way (longitudinal 's).

`PARU(131) - PARU(136) :`- couplings of a new
;
for fermions default values are given by the Standard Model
values (i.e. ). Note that e.g. the
width contains squared couplings, and
thus depends quadratically on the values below.
`PARU(131), PARU(132) :`- (D = 1., ) vector and axial couplings of a quark-antiquark pair to ; is further multiplied by the ordinary CKM factors.
`PARU(133), PARU(134) :`- (D = 1., ) vector and axial couplings of a lepton-neutrino pair to .
`PARU(135) :`- (D = 1.) the coupling
is taken to be
`PARU(135)`(the Standard Model coupling) . This gives a partial width that increases proportionately to the mass. `PARU(136) :`- (D = 0.) in the decay chain
fermions,
the angular distribution in the
decays is supposed to be a
mixture, with fraction
`1-PARU(136)`corresponding to the same angular distribution between the four final fermions as in (mixture of transverse and longitudinal 's), and fraction`PARU(136)`corresponding to the same way (longitudinal 's).

`PARU(141) :`- (D = 5.) parameter of a two Higgs
doublet scenario, i.e. the ratio of vacuum expectation values.
This affects mass relations and couplings in the Higgs sector.
If the Supersymmetry simulation is switched on,
`IMSS(1)`nonvanishing,`PARU(141)`will be overwritten by`RMSS(5)`at initialization, so it is the latter variable that should be set. `PARU(142) :`- (D = 1.) the
coupling is
taken to be
`PARU(142)`(the MSSM coupling). `PARU(143) :`- (D = 1.) the
coupling is
taken to be
`PARU(143)`(the MSSM coupling). `PARU(145) :`- (D = 1.) quadratically multiplicative factor in the
partial width in left-right-symmetric models,
expected to be unity (see [Coc91]).
`PARU(146) :`- (D = 1.) parameter, enters
quadratically as multiplicative factor in the
partial width in
left-right-symmetric models (see [Coc91]).
`PARU(151) :`- (D = 1.) multiplicative factor in the
squared Yukawa coupling, and thereby in the
partial width and the
and other
cross sections. Specifically,
`PARU(151)`, i.e. it corresponds to the factor of [Hew88]. `PARU(161) - PARU(168) :`- (D = 5*1., 3*0.) multiplicative factors
that can be used to modify the default couplings of the
particle in PYTHIA. Note that the factors enter quadratically in the
partial widths. The default values correspond to the couplings given
in the minimal one-Higgs-doublet Standard Model, and are therefore
not realistic in a two-Higgs-doublet scenario. The default values
should be changed appropriately by you. Also the last two default
values should be changed; for these the expressions of the
minimal supersymmetric Standard Model (MSSM) are given to show
parameter normalization. Alternatively, the SUSY machinery can
generate all the couplings for
`IMSS(1)`, see`MSTP(4)`.`PARU(161) :`- coupling to down type quarks.
`PARU(162) :`- coupling to up type quarks.
`PARU(163) :`- coupling to leptons.
`PARU(164) :`- coupling to .
`PARU(165) :`- coupling to .
`PARU(168) :`- coupling to in loops, in MSSM .

`PARU(171) - PARU(178) :`- (D = 7*1., 0.) multiplicative factors
that can be used to modify the default couplings of the
particle in PYTHIA. Note that the factors enter quadratically in
partial widths. The default values for
`PARU(171) - PARU(175)`correspond to the couplings given to in the minimal one-Higgs-doublet Standard Model, and are therefore not realistic in a two-Higgs-doublet scenario. The default values should be changed appropriately by you. Also the last two default values should be changed; for these the expressions of the minimal supersymmetric Standard Model (MSSM) are given to show parameter normalization. Alternatively, the SUSY machinery can generate all the couplings for`IMSS(1)`, see`MSTP(4)`.`PARU(171) :`- coupling to down type quarks.
`PARU(172) :`- coupling to up type quarks.
`PARU(173) :`- coupling to leptons.
`PARU(174) :`- coupling to .
`PARU(175) :`- coupling to .
`PARU(176) :`- coupling to , in MSSM .
`PARU(177) :`- coupling to , in MSSM .
`PARU(178) :`- coupling to in loops, in MSSM .

`PARU(181) - PARU(190) :`- (D = 3*1., 2*0., 2*1., 3*0.)
multiplicative factors that can be used to modify the default
couplings of the particle in PYTHIA. Note that the factors
enter quadratically in partial widths. The default values for
`PARU(181) - PARU(183)`correspond to the couplings given to in the minimal one-Higgs-doublet Standard Model, and are therefore not realistic in a two-Higgs-doublet scenario. The default values should be changed appropriately by you.`PARU(184)`and`PARU(185)`should be vanishing at the tree level, in the absence of CP-violating phases in the Higgs sector, and are so set; normalization of these couplings agrees with what is used for and . Also the other default values should be changed; for these the expressions of the Minimal Supersymmetric Standard Model (MSSM) are given to show parameter normalization. Alternatively, the SUSY machinery can generate all the couplings for`IMSS(1)`, see`MSTP(4)`.`PARU(181) :`- coupling to down type quarks.
`PARU(182) :`- coupling to up type quarks.
`PARU(183) :`- coupling to leptons.
`PARU(184) :`- coupling to .
`PARU(185) :`- coupling to .
`PARU(186) :`- coupling to (or to ), in MSSM .
`PARU(187) :`- coupling to (or to ), in MSSM .
`PARU(188) :`- As
`PARU(186)`, but coupling to rather than . `PARU(189) :`- As
`PARU(187)`, but coupling to rather than . `PARU(190) :`- coupling to in loops, 0 in MSSM.

`PARU(191) - PARU(195) :`- (D = 4*0., 1.) multiplicative factors
that can be used to modify the couplings of the particle
in PYTHIA. Currently only
`PARU(195)`is in use. See above for related comments.`PARU(195) :`- coupling to (or to ), in MSSM .

`PARU(197):`- (D = 0.) coupling to
within a two-Higgs-doublet model.
`PARU(198):`- (D = 0.) coupling to
within a two-Higgs-doublet model.

`PARJ(180) - PARJ(187) :`- couplings of the
second generation fermions to the , following the same pattern
and with the same default values as the first one in
`PARU(121) - PARU(128)`. `PARJ(188) - PARJ(195) :`- couplings of the
third generation fermions to the , following the same pattern
and with the same default values as the first one in
`PARU(121) - PARU(128)`.

**Purpose:**- to give access to a number of switches and parameters
which regulate the simulation of the TechniColor Strawman Model
[Lan02,Lan02a], plus a few further parameters related to
the simulation of compositeness, mainly in earlier incarnations of
TechniColor.

`ITCM(1) :`- (D = 4) , number of technicolors;
fixes the relative values of
and
.
`ITCM(2) :`- (D = 0) Topcolor model.
`= 0 :`- Standard Topcolor. Third generation quark couplings to
the coloron are proportional to , see
`RTCM(21)`below; first two generations are proportional to . `= 1 :`- Flavor Universal Topcolor. All quarks couple with strength proportional to .

`ITCM(5) :`- (D = 0) presence of anomalous couplings in Standard Model
processes, see section for further details.
`= 0 :`- absent.
`= 1 :`- left-left isoscalar model, with only and quarks composite (at the probed scale).
`= 2 :`- left-left isoscalar model, with all quarks composite.
`= 3 :`- helicity-non-conserving model, with only and quarks composite (at the probed scale).
`= 4 :`- helicity-non-conserving model, with all quarks composite.
`= 5 :`- coloured technihadrons, affecting the standard QCD cross sections by the exchange of Coloron or Colored Technirho, see section .

`RTCM(1) :`- (D = 82 GeV) , the Technicolor decay
constant.
`RTCM(2) :`- (D = 4/3) , charge of up-type technifermion;
the down-type technifermion has a charge .
`RTCM(3) :`- (D = 1/3) , where is the
mixing angle between isotriplet technipion interaction and mass
eigenstates.
`RTCM(4) :`- (D = ) , where is the
mixing angle between the isosinglet
interaction
and mass eigenstates.
`RTCM(5) :`- (D = 1) Clebsch for technipi decays to charm. Appears
squared in decay rates.
`RTCM(6) :`- (D = 1) Clebsch for technipi decays to bottom. Appears
squared in decay rates.
`RTCM(7) :`- (D = 0.0182) Clebsch for technipi decays to top,
estimated to be
. Appears squared in decay rates.
`RTCM(8) :`- (D = 1) Clebsch for technipi decays to .
Appears squared in decay rates.
`RTCM(9) :`- (D = 0) squared Clebsch for isotriplet technipi decays
to gluons.
`RTCM(10) :`- (D = 4/3) squared Clebsch for isosinglet technipi
decays to gluons.
`RTCM(11) :`- (D = 0.05) technirho-techniomega mixing parameters.
Allows for isospin-violating decays of the techniomega.
`RTCM(12) :`- (D = 200 GeV) vector technimeson decay parameter.
Affects the decay rates of vector technimesons into technipi plus
transverse gauge boson.
`RTCM(13) :`- (D = 200 GeV) axial mass parameter for
technivector decays to transverse gauge bosons and technipions.
`RTCM(21) :`- (D = ) tangent of Topcolor mixing angle,
in the scenario with coloured technihadrons described in section
and switched on with
`ITCM(5) = 5`. For`ITCM(2) = 0`, the coupling of the to light quarks is suppressed by`RTCM(21)`whereas the coupling to heavy ( and ) quarks is enhanced by 1/`RTCM(21)`. For`ITCM(21) = 1`, the coupling to quarks is universal, and given by 1/`RTCM(21)`. `RTCM(22) :`- (D = ) sine of isosinglet technipi mixing
with Topcolor currents.
`RTCM(23) :`- (D = 0) squared Clebsch for colour-octet technipi decays
to charm.
`RTCM(24) :`- (D = 0) squared Clebsch for colour-octet technipi decays
to bottom.
`RTCM(25) :`- (D = 0) squared Clebsch for colour-octet technipi decays
to top.
`RTCM(26) :`- (D = 5/3) squared Clebsch for colour-octet technipi
decays to gluons.
`RTCM(27) :`- (D = 250 GeV) colour-octet technirho decay parameter for
decays to technipi plus gluon.
`RTCM(28) :`- (D = 250 GeV) hard mixing parameter between
colour-octet technirhos.
`RTCM(29) :`- (D = ) magnitude of element of the
**U(2)**matrices that diagonalize U-type technifermion condensates. `RTCM(30) :`- (D = 0 Radians) phase for the element described above,
`RTCM(29)`. `RTCM(31) :`- (D = ) Magnitude of element of the
**U(2)**matrices that diagonalize D-type technifermion condensates. `RTCM(32) :`- (D = 0 Radians) phase for the element described above,
`RTCM(31)`. `RTCM(33) :`- (D = 1) if
, then
is redefined to be
.
It thus prevents the coloron from becoming wider than its mass.
`RTCM(41) :`- (D = 1000 GeV) compositeness scale , used in
processes involving excited fermions, and for Standard Model processes
when
`ITCM(5)`is between 1 and 4. `RTCM(42) :`- (D = 1.) sign of the interference term between the
standard cross section and the compositeness term ( parameter);
should be ; used for Standard Model processes when
`ITCM(5)`is between 1 and 4. `RTCM(43) - RTCM(45) :`- (D = 3*1.) strength of the
**SU(2)**,**U(1)**and**SU(3)**couplings, respectively, in an excited fermion scenario; cf. , and of [Bau90]. `RTCM(46) :`- (D = 0.) anomalous magnetic moment of the
in process 20;
, where ()
is the Standard Model value.