/usr/share/pythia8-data/xmldoc/StandardModelParameters.xml is in pythia8-data 8.1.65-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 | <chapter name="Standard-Model Parameters">
<h2>Standard-Model Parameters</h2>
<h3>The strong coupling</h3>
The <code>AlphaStrong</code> class is used to provide a first- or
second-order running <ei>alpha_strong</ei> (or, trivially, a
zeroth-order fixed one). Formulae are the standard ones found in
<ref>Yao06</ref>. The second-order expression used, eq. (9.5),
may be somewhat different in other approaches (with differences
formally of higher order), so do not necessarily expect perfect
agreement, especially not at small <ei>Q^2</ei> scales. The starting
<ei>alpha_strong</ei> value is defined at the <ei>M_Z</ei> mass scale.
The <ei>Lambda</ei> values are matched at the <ei>b</ei> and <ei>c</ei>
flavour thresholds, such that <ei>alpha_strong</ei> is continuous.
For second-order matching an approximate iterative method is used.
<p/>
Since we allow <ei>alpha_strong</ei> to vary separately for
hard processes, timelike showers, spacelike showers and multiparton
interactions, the relevant values can be set in each of these classes.
The default behaviour is everywhere first-order running.
<p/>
The <ei>alpha_strong</ei> calculation is initialized by
<code>init( value, order)</code>, where <code>value</code>
is the <ei>alpha_strong</ei> value at <ei>M_Z</ei> and <code>order</code>
is the order of the running, 0, 1 or 2. Thereafter the value can be
calculated by <code>alphaS(scale2)</code>, where
<code>scale2</code> is the <ei>Q^2</ei> scale in GeV^2.
<p/>
For applications inside shower programs, a second-order <code>alpha_s</code>
value can be obtained as the product of the two functions
<code>alphaS1Ord(scale2)</code> and <code>alphaS2OrdCorr(scale2)</code>,
where the first gives a simple first-order running (but with the
second-order <ei>Lambda</ei>) and the second the correction factor,
below unity, for the second-order terms. This allows a compact handling
of evolution equations.
<h3>The electromagnetic coupling</h3>
The <code>AlphaEM</code> class is used to generate a running
<ei>alpha_em</ei>. The input <code>StandardModel:alphaEMmZ</code>
value at the <ei>M_Z</ei> mass is matched to a low-energy behaviour
with running starting at the electron mass threshold. The matching
is done by fitting an effective running coefficient in the region
betweeen the light-quark treshold and the charm/tau threshold. This
procedure is approximate, but good enough for our purposes.
<p/>
Since we allow <ei>alpha_em</ei> to vary separately for
hard processes, timelike showers, spacelike showers and multiparton
interactions, the choice between using a fixed or a running
<ei>alpha_em</ei> can be made in each of these classes.
The default behaviour is everywhere first-order running.
The actual values assumed at zero momentum transfer and
at <ei>M_Z</ei> are only set here, however.
<parm name="StandardModel:alphaEM0" default="0.00729735"
min="0.0072973" max="0.0072974">
The <ei>alpha_em</ei> value at vanishing momentum transfer
(and also below <ei>m_e</ei>).
</parm>
<parm name="StandardModel:alphaEMmZ" default="0.00781751"
min="0.00780" max="0.00783">
The <ei>alpha_em</ei> value at the <ei>M_Z</ei> mass scale.
Default is taken from <ref>Yao06</ref>.
</parm>
<p/>
The <ei>alpha_em</ei> calculation is initialized by
<code>init(order)</code>, where <code>order</code> is the order of
the running, 0 or 1, with -1 a special option to use the fix value
provided at <ei>M_Z</ei>. Thereafter the value can be
calculated by <code>alphaEM(scale2)</code>, where
<code>scale2</code> is the <ei>Q^2</ei> scale in GeV^2.
<h3>The electroweak couplings</h3>
There are two degrees of freedom that can be set, related to the
electroweak mixing angle:
<parm name="StandardModel:sin2thetaW" default="0.2312"
min="0.225" max="0.240">
The sine-squared of the weak mixing angle, as used in all <ei>Z^0</ei>
and <ei>W^+-</ei> masses and couplings, except for the vector couplings
of fermions to the <ei>Z^0</ei>, see below. Default is the MSbar value
from <ref>Yao06</ref>.
</parm>
<parm name="StandardModel:sin2thetaWbar" default="0.2315"
min="0.225" max="0.240">
The sine-squared of the weak mixing angle, as used to derive the vector
couplings of fermions to the <ei>Z^0</ei>, in the relation
<ei>v_f = a_f - 4 e_f sin^2(theta_W)bar</ei>. Default is the
effective-angle value from <ref>Yao06</ref>.
</parm>
<p/>
The Fermi constant is not much used in the currently coded matrix elements,
since it is redundant, but it is available:
<parm name="StandardModel:GF" default="1.16637e-5"
min="1.0e-5" max="1.3e-5">
The Fermi coupling constant, in units of GeV<ei>^-2</ei>.
</parm>
<h3>The quark weak-mixing matrix</h3>
The absolute values of the Cabibbo-Kobayashi-Maskawa matrix elements are
set by the following nine real values taken from <ref>Yao06</ref> -
currently the CP-violating phase is not taken into account in this
parametrization. It is up to the user to pick a consistent unitary
set of new values whenever changes are made.
<parm name="StandardModel:Vud" default="0.97383" min="0.973" max="0.975">
The <ei>V_ud</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vus" default="0.2272" min="0.224" max="0.230">
The <ei>V_us</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vub" default="0.00396" min="0.0037" max="0.0042">
The <ei>V_ub</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vcd" default="0.2271" min="0.224" max="0.230">
The <ei>V_cd</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vcs" default="0.97296" min="0.972" max="0.974">
The <ei>V_cs</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vcb" default="0.04221" min="0.0418" max="0.0426">
The <ei>V_cb</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vtd" default="0.00814" min="0.006" max="0.010">
The <ei>V_td</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vts" default="0.04161" min="0.039" max="0.043">
The <ei>V_ts</ei> CKM matrix element.
</parm>
<parm name="StandardModel:Vtb" default="0.9991" min="0.99907" max="0.9992">
The <ei>V_tb</ei> CKM matrix element.
</parm>
<h3>The CoupSM class</h3>
The <code><aloc href="ProgramFlow">Pythia</aloc></code> class contains a
public instance <code>coupSM</code> of the <code>CoupSM</code> class.
This class contains one instance each of the <code>AlphaStrong</code>
and <code>AlphaEM</code> classes, and additionally stores the weak couplings
and the quark mixing matrix mentioned above. This class is used especially
in the calculation of cross sections and resonance widths, but could also
be used elsewhere. Specifically, as already mentioned, there are separate
<code>AlphaStrong</code> and <code>AlphaEM</code> instances for timelike
and spacelike showers and for multiparton interactions, while weak couplings
and the quark mixing matrix are only stored here. With the exception of the
first two methods below, which are for internal use, the subsequent ones
could also be used externally.
<method name="CoupSM::CoupSM()">
the constructor does nothing. Internal.
</method>
<method name="void CoupSM::init(Settings& settings, Rndm* rndmPtr)">
this is where the <code>AlphaStrong</code> and <code>AlphaEM</code>
instances are initialized, and weak couplings and the quark mixing matrix
are read in and set. This is based on the values stored on this page and
among the <aloc href="CouplingsAndScales">Couplings and Scales</aloc>.
Internal.
</method>
<method name="double CoupSM::alphaS(double scale2)">
the <ei>alpha_strong</ei> value at the quadratic scale <code>scale2</code>.
</method>
<method name="double CoupSM::alphaS1Ord(double scale2)">
a first-order overestimate of the full second-order <ei>alpha_strong</ei>
value at the quadratic scale <code>scale2</code>.
</method>
<method name="double CoupSM::alphaS2OrdCorr(double scale2)">
a multiplicative correction factor, below unity, that brings the
first-order overestimate above into agreement with the full second-order
<ei>alpha_strong</ei> value at the quadratic scale <code>scale2</code>.
</method>
<method name="double CoupSM::Lambda3()">
</method>
<methodmore name="double CoupSM::Lambda4()">
</methodmore>
<methodmore name="double CoupSM::Lambda5()">
the three-, four-, and five-flavour <ei>Lambda</ei> scale.
</methodmore>
<method name="double CoupSM::alphaEM(double scale2)">
the <ei>alpha_em</ei> value at the quadratic scale <code>scale2</code>.
</method>
<method name="double CoupSM::sin2thetaW()">
</method>
<methodmore name="double CoupSM::cos2thetaW()">
the sine-squared and cosine-squared of the weak mixing angle, as used in
the gauge-boson sector.
</methodmore>
<method name="double CoupSM::sin2thetaWbar()">
the sine-squared of the weak mixing angle, as used to derive the vector
couplings of fermions to the <ei>Z^0</ei>.
</method>
<method name="double CoupSM::GF()">
the Fermi constant of weak decays, in GeV<ei>^-2</ei>.
</method>
<method name="double CoupSM::ef(int idAbs)">
the electrical charge of a fermion, by the absolute sign of the PDF code,
i.e. <code>idAbs</code> must be in the range between 1 and 18.
</method>
<method name="double CoupSM::vf(int idAbs)">
</method>
<methodmore name="double CoupSM::af(int idAbs)">
the vector and axial charges of a fermion, by the absolute sign of the PDF
code (<ei>a_f = +-1, v_f = a_f - 4. * sin2thetaWbar * e_f</ei>).
</methodmore>
<method name="double CoupSM::t3f(int idAbs)">
</method>
<methodmore name="double CoupSM::lf(int idAbs)">
</methodmore>
<methodmore name="double CoupSM::rf(int idAbs)">
the weak isospin, left- and righthanded charges of a fermion, by the
absolute sign of the PDF code (<ei>t^3_f = a_f/2, l_f = (v_f + a_f)/2,
r_f = (v_f - a_f)/2</ei>; you may find other conventions in the literature
that differ by a factor of 2).
</methodmore>
<method name="double CoupSM::ef2(int idAbs)">
</method>
<methodmore name="double CoupSM::vf2(int idAbs)">
</methodmore>
<methodmore name="double CoupSM::af2(int idAbs)">
</methodmore>
<methodmore name="double CoupSM::efvf(int idAbs)">
</methodmore>
<methodmore name="double CoupSM::vf2af2(int idAbs)">
common quadratic combinations of the above couplings:
<ei>e_f^2, v_f^2, a_f^2, e_f * v_f, v_f^2 + a_f^2</ei>.
</methodmore>
<method name="double CoupSM::VCKMgen(int genU, int genD)">
</method>
<methodmore name="double CoupSM::V2CKMgen(int genU, int genD)">
the CKM mixing element,or the square of it, for
up-type generation index <code>genU</code>
(<ei>1 = u, 2 = c, 3 = t, 4 = t'</ei>) and
down-type generation index <code>genD</code>
(<ei>1 = d, 2 = s, 3 = b, 4 = b'</ei>).
</methodmore>
<method name="double CoupSM::VCKMid(int id1, int id2)">
</method>
<methodmore name="double CoupSM::V2CKMid(int id1, int id2)">
the CKM mixing element,or the square of it, for
flavours <code>id1</code> and <code>id2</code>, both in the
range from <ei>-18</ei> to <ei>+18</ei>. The sign is here not
checked (so it can be used both for <ei>u + dbar -> W+</ei>
and <ei>u -> d + W+</ei>, say), but impossible flavour combinations
evaluate to zero. The neutrino sector is numbered by flavor
eigenstates, so there is no mixing in the lepton-neutrino system.
</methodmore>
<method name="double CoupSM::V2CKMsum(int id)">
the sum of squared CKM mixing element that a given flavour can couple to,
excluding the top quark and fourth generation. Is close to unity
for the first two generations. Returns unity for the lepton-neutrino
sector.
</method>
<method name="int CoupSM::V2CKMpick(int id)">
picks a random CKM partner quark or lepton (with the same sign as
<code>id</code>) according to the respective squared elements, again
excluding the top quark and fourth generation from the list of
possibilities. Unambiguous choice for the lepton-neutrino sector.
</method>
</chapter>
<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
|