[u/mrichter/AliRoot.git] / PYTHIA8 / pythia8175 / phpdoc / StandardModelParameters.php

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<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 <i>alpha_strong</i> (or, trivially, a 
zeroth-order fixed one). Formulae are the standard ones found in 
[<a href="Bibliography.php" target="page">Yao06</a>]. 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 <i>Q^2</i> scales. The starting 
<i>alpha_strong</i> value is defined at the <i>M_Z</i> mass scale.
The <i>Lambda</i> values are matched at the <i>b</i> and <i>c</i> 
flavour thresholds, such that <i>alpha_strong</i> is continuous.
For second-order matching an approximate iterative method is used.
 
<p/>
Since we allow <i>alpha_strong</i> 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 <i>alpha_strong</i> calculation is initialized by 
<code>init( value, order)</code>, where <code>value</code> 
is the <i>alpha_strong</i> value at <i>M_Z</i> 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 <i>Q^2</i> 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 <i>Lambda</i>) 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
<i>alpha_em</i>. The input <code>StandardModel:alphaEMmZ</code>
value at the <i>M_Z</i> 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
between the light-quark threshold and the charm/tau threshold. This
procedure is approximate, but good enough for our purposes. 

<p/>
Since we allow <i>alpha_em</i> to vary separately for 
hard processes, timelike showers, spacelike showers and  multiparton 
interactions, the choice between using a fixed or a running 
<i>alpha_em</i> 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 <i>M_Z</i> are only set here, however. 

<br/><br/><table><tr><td><strong>StandardModel:alphaEM0 </td><td></td><td> <input type="text" name="1" value="0.00729735" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.00729735</strong></code>; <code>minimum = 0.0072973</code>; <code>maximum = 0.0072974</code>)</td></tr></table>
The <i>alpha_em</i> value at vanishing momentum transfer
(and also below <i>m_e</i>). 
  

<br/><br/><table><tr><td><strong>StandardModel:alphaEMmZ </td><td></td><td> <input type="text" name="2" value="0.00781751" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.00781751</strong></code>; <code>minimum = 0.00780</code>; <code>maximum = 0.00783</code>)</td></tr></table>
The <i>alpha_em</i> value at the <i>M_Z</i> mass scale. 
Default is taken from [<a href="Bibliography.php" target="page">Yao06</a>].
  

<p/>
The <i>alpha_em</i> 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 <i>M_Z</i>.   Thereafter the value can be 
calculated by <code>alphaEM(scale2)</code>, where 
<code>scale2</code> is the <i>Q^2</i> 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:

<br/><br/><table><tr><td><strong>StandardModel:sin2thetaW </td><td></td><td> <input type="text" name="3" value="0.2312" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.2312</strong></code>; <code>minimum = 0.225</code>; <code>maximum = 0.240</code>)</td></tr></table>
The sine-squared of the weak mixing angle, as used in all <i>Z^0</i> 
and <i>W^+-</i> masses and couplings, except for the vector couplings 
of fermions to the <i>Z^0</i>, see below. Default is the MSbar value 
from [<a href="Bibliography.php" target="page">Yao06</a>].
  

<br/><br/><table><tr><td><strong>StandardModel:sin2thetaWbar </td><td></td><td> <input type="text" name="4" value="0.2315" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.2315</strong></code>; <code>minimum = 0.225</code>; <code>maximum = 0.240</code>)</td></tr></table>
The sine-squared of the weak mixing angle, as used to derive the vector 
couplings of fermions to the <i>Z^0</i>, in the relation 
<i>v_f = a_f - 4 e_f sin^2(theta_W)bar</i>. Default is the
effective-angle value from [<a href="Bibliography.php" target="page">Yao06</a>].
  

<p/>
The Fermi constant is not much used in the currently coded matrix elements,
since it is redundant, but it is available:

<br/><br/><table><tr><td><strong>StandardModel:GF </td><td></td><td> <input type="text" name="5" value="1.16637e-5" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.16637e-5</strong></code>; <code>minimum = 1.0e-5</code>; <code>maximum = 1.3e-5</code>)</td></tr></table>
The Fermi coupling constant, in units of GeV<i>^-2</i>. 
  

<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 [<a href="Bibliography.php" target="page">Yao06</a>] - 
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.  

<br/><br/><table><tr><td><strong>StandardModel:Vud </td><td></td><td> <input type="text" name="6" value="0.97383" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.97383</strong></code>; <code>minimum = 0.973</code>; <code>maximum = 0.975</code>)</td></tr></table>
The <i>V_ud</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vus </td><td></td><td> <input type="text" name="7" value="0.2272" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.2272</strong></code>; <code>minimum = 0.224</code>; <code>maximum = 0.230</code>)</td></tr></table>
The <i>V_us</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vub </td><td></td><td> <input type="text" name="8" value="0.00396" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.00396</strong></code>; <code>minimum = 0.0037</code>; <code>maximum = 0.0042</code>)</td></tr></table>
The <i>V_ub</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vcd </td><td></td><td> <input type="text" name="9" value="0.2271" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.2271</strong></code>; <code>minimum = 0.224</code>; <code>maximum = 0.230</code>)</td></tr></table>
The <i>V_cd</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vcs </td><td></td><td> <input type="text" name="10" value="0.97296" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.97296</strong></code>; <code>minimum = 0.972</code>; <code>maximum = 0.974</code>)</td></tr></table>
The <i>V_cs</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vcb </td><td></td><td> <input type="text" name="11" value="0.04221" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.04221</strong></code>; <code>minimum = 0.0418</code>; <code>maximum = 0.0426</code>)</td></tr></table>
The <i>V_cb</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vtd </td><td></td><td> <input type="text" name="12" value="0.00814" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.00814</strong></code>; <code>minimum = 0.006</code>; <code>maximum = 0.010</code>)</td></tr></table>
The <i>V_td</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vts </td><td></td><td> <input type="text" name="13" value="0.04161" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.04161</strong></code>; <code>minimum = 0.039</code>; <code>maximum = 0.043</code>)</td></tr></table>
The <i>V_ts</i> CKM matrix element.
  

<br/><br/><table><tr><td><strong>StandardModel:Vtb </td><td></td><td> <input type="text" name="14" value="0.9991" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.9991</strong></code>; <code>minimum = 0.99907</code>; <code>maximum = 0.9992</code>)</td></tr></table>
The <i>V_tb</i> CKM matrix element.
  

<h3>The CoupSM class</h3> 

The <code><?php $filepath = $_GET["filepath"];
echo "<a href='ProgramFlow.php?filepath=".$filepath."' target='page'>";?>Pythia</a></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.

<a name="method1"></a>
<p/><strong>CoupSM::CoupSM() &nbsp;</strong> <br/>
the constructor does nothing. Internal.
  

<a name="method2"></a>
<p/><strong>void CoupSM::init(Settings& settings, Rndm* rndmPtr) &nbsp;</strong> <br/>
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 <?php $filepath = $_GET["filepath"];
echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>Couplings and Scales</a>. 
Internal.
  

<a name="method3"></a>
<p/><strong>double CoupSM::alphaS(double scale2) &nbsp;</strong> <br/>
the <i>alpha_strong</i> value at the quadratic scale <code>scale2</code>.
  

<a name="method4"></a>
<p/><strong>double CoupSM::alphaS1Ord(double scale2) &nbsp;</strong> <br/>
a first-order overestimate of the full second-order <i>alpha_strong</i> 
value at the quadratic scale <code>scale2</code>.
  

<a name="method5"></a>
<p/><strong>double CoupSM::alphaS2OrdCorr(double scale2) &nbsp;</strong> <br/>
a multiplicative correction factor, below unity, that brings the 
first-order overestimate above into agreement with the full second-order
<i>alpha_strong</i> value at the quadratic scale <code>scale2</code>.
  

<a name="method6"></a>
<p/><strong>double CoupSM::Lambda3() &nbsp;</strong> <br/>
  
<strong>double CoupSM::Lambda4() &nbsp;</strong> <br/>
  
<strong>double CoupSM::Lambda5() &nbsp;</strong> <br/>
the three-, four-, and five-flavour <i>Lambda</i> scale.
  

<a name="method7"></a>
<p/><strong>double CoupSM::alphaEM(double scale2) &nbsp;</strong> <br/>
the <i>alpha_em</i> value at the quadratic scale <code>scale2</code>.
  

<a name="method8"></a>
<p/><strong>double CoupSM::sin2thetaW() &nbsp;</strong> <br/>
  
<strong>double CoupSM::cos2thetaW() &nbsp;</strong> <br/>
the sine-squared and cosine-squared of the weak mixing angle, as used in 
the gauge-boson sector.
  

<a name="method9"></a>
<p/><strong>double CoupSM::sin2thetaWbar() &nbsp;</strong> <br/>
the sine-squared of the weak mixing angle, as used to derive the vector 
couplings of fermions to the <i>Z^0</i>.
  

<a name="method10"></a>
<p/><strong>double CoupSM::GF() &nbsp;</strong> <br/>
the Fermi constant of weak decays, in GeV<i>^-2</i>.
  

<a name="method11"></a>
<p/><strong>double CoupSM::ef(int idAbs) &nbsp;</strong> <br/>
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.
  

<a name="method12"></a>
<p/><strong>double CoupSM::vf(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::af(int idAbs) &nbsp;</strong> <br/>
the vector and axial charges of a fermion, by the absolute sign of the PDF 
code (<i>a_f = +-1, v_f = a_f - 4. * sin2thetaWbar * e_f</i>).
  

<a name="method13"></a>
<p/><strong>double CoupSM::t3f(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::lf(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::rf(int idAbs) &nbsp;</strong> <br/>
the weak isospin, left- and righthanded charges of a fermion, by the 
absolute sign of the PDF code (<i>t^3_f = a_f/2, l_f = (v_f + a_f)/2,
r_f = (v_f - a_f)/2</i>; you may find other conventions in the literature
that differ by a factor of 2).
  

<a name="method14"></a>
<p/><strong>double CoupSM::ef2(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::vf2(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::af2(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::efvf(int idAbs) &nbsp;</strong> <br/>
  
<strong>double CoupSM::vf2af2(int idAbs) &nbsp;</strong> <br/>
common quadratic combinations of the above couplings:
<i>e_f^2, v_f^2, a_f^2, e_f * v_f, v_f^2 + a_f^2</i>.
  

<a name="method15"></a>
<p/><strong>double CoupSM::VCKMgen(int genU, int genD) &nbsp;</strong> <br/>
  
<strong>double CoupSM::V2CKMgen(int genU, int genD) &nbsp;</strong> <br/>
the CKM mixing element,or the square of it, for
up-type generation index <code>genU</code> 
(<i>1 = u, 2 = c, 3 = t, 4 = t'</i>) and
down-type generation index <code>genD</code>
(<i>1 = d, 2 = s, 3 = b, 4 = b'</i>).
  

<a name="method16"></a>
<p/><strong>double CoupSM::VCKMid(int id1, int id2) &nbsp;</strong> <br/>
  
<strong>double CoupSM::V2CKMid(int id1, int id2) &nbsp;</strong> <br/>
the CKM mixing element,or the square of it, for
flavours <code>id1</code> and <code>id2</code>, both in the 
range from <i>-18</i> to <i>+18</i>. The sign is here not 
checked (so it can be used both for <i>u + dbar -> W+</i>
and <i>u -> d + W+</i>, 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. 
  

<a name="method17"></a>
<p/><strong>double CoupSM::V2CKMsum(int id) &nbsp;</strong> <br/>
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. 
  

<a name="method18"></a>
<p/><strong>int CoupSM::V2CKMpick(int id) &nbsp;</strong> <br/>
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. 
  

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	29
	30	<h2>Standard-Model Parameters</h2>
	31
	32	<h3>The strong coupling</h3>
	33
	34	The <code>AlphaStrong</code> class is used to provide a first- or
	35	second-order running <i>alpha_strong</i> (or, trivially, a
	36	zeroth-order fixed one). Formulae are the standard ones found in
	37	[<a href="Bibliography.php" target="page">Yao06</a>]. The second-order expression used, eq. (9.5),
	38	may be somewhat different in other approaches (with differences
	39	formally of higher order), so do not necessarily expect perfect
	40	agreement, especially not at small <i>Q^2</i> scales. The starting
	41	<i>alpha_strong</i> value is defined at the <i>M_Z</i> mass scale.
	42	The <i>Lambda</i> values are matched at the <i>b</i> and <i>c</i>
	43	flavour thresholds, such that <i>alpha_strong</i> is continuous.
	44	For second-order matching an approximate iterative method is used.
	45
	46	<p/>
	47	Since we allow <i>alpha_strong</i> to vary separately for
	48	hard processes, timelike showers, spacelike showers and multiparton
	49	interactions, the relevant values can be set in each of these classes.
	50	The default behaviour is everywhere first-order running.
	51
	52	<p/>
	53	The <i>alpha_strong</i> calculation is initialized by
	54	<code>init( value, order)</code>, where <code>value</code>
	55	is the <i>alpha_strong</i> value at <i>M_Z</i> and <code>order</code>
	56	is the order of the running, 0, 1 or 2. Thereafter the value can be
	57	calculated by <code>alphaS(scale2)</code>, where
	58	<code>scale2</code> is the <i>Q^2</i> scale in GeV^2.
	59
	60	<p/>
	61	For applications inside shower programs, a second-order <code>alpha_s</code>
	62	value can be obtained as the product of the two functions
	63	<code>alphaS1Ord(scale2)</code> and <code>alphaS2OrdCorr(scale2)</code>,
	64	where the first gives a simple first-order running (but with the
65	second-order <i>Lambda</i>) and the second the correction factor,
66	below unity, for the second-order terms. This allows a compact handling
67	of evolution equations.
68
69	<h3>The electromagnetic coupling</h3>
70
71	The <code>AlphaEM</code> class is used to generate a running
72	<i>alpha_em</i>. The input <code>StandardModel:alphaEMmZ</code>
73	value at the <i>M_Z</i> mass is matched to a low-energy behaviour
74	with running starting at the electron mass threshold. The matching
75	is done by fitting an effective running coefficient in the region
76	between the light-quark threshold and the charm/tau threshold. This
77	procedure is approximate, but good enough for our purposes.
78
79	<p/>
80	Since we allow <i>alpha_em</i> to vary separately for
81	hard processes, timelike showers, spacelike showers and multiparton
82	interactions, the choice between using a fixed or a running
83	<i>alpha_em</i> can be made in each of these classes.
84	The default behaviour is everywhere first-order running.
85	The actual values assumed at zero momentum transfer and
86	at <i>M_Z</i> are only set here, however.
87
88	<br/><br/><table><tr><td><strong>StandardModel:alphaEM0 </td><td></td><td> <input type="text" name="1" value="0.00729735" size="20"/>   (<code>default = <strong>0.00729735</strong></code>; <code>minimum = 0.0072973</code>; <code>maximum = 0.0072974</code>)</td></tr></table>
89	The <i>alpha_em</i> value at vanishing momentum transfer
90	(and also below <i>m_e</i>).
91
92
93	<br/><br/><table><tr><td><strong>StandardModel:alphaEMmZ </td><td></td><td> <input type="text" name="2" value="0.00781751" size="20"/>   (<code>default = <strong>0.00781751</strong></code>; <code>minimum = 0.00780</code>; <code>maximum = 0.00783</code>)</td></tr></table>
94	The <i>alpha_em</i> value at the <i>M_Z</i> mass scale.
95	Default is taken from [<a href="Bibliography.php" target="page">Yao06</a>].
96
97
98	<p/>
99	The <i>alpha_em</i> calculation is initialized by
100	<code>init(order)</code>, where <code>order</code> is the order of
101	the running, 0 or 1, with -1 a special option to use the fix value
102	provided at <i>M_Z</i>. Thereafter the value can be
103	calculated by <code>alphaEM(scale2)</code>, where
104	<code>scale2</code> is the <i>Q^2</i> scale in GeV^2.
105
106	<h3>The electroweak couplings</h3>
107
108	There are two degrees of freedom that can be set, related to the
109	electroweak mixing angle:
110
111	<br/><br/><table><tr><td><strong>StandardModel:sin2thetaW </td><td></td><td> <input type="text" name="3" value="0.2312" size="20"/>   (<code>default = <strong>0.2312</strong></code>; <code>minimum = 0.225</code>; <code>maximum = 0.240</code>)</td></tr></table>
112	The sine-squared of the weak mixing angle, as used in all <i>Z^0</i>
113	and <i>W^+-</i> masses and couplings, except for the vector couplings
114	of fermions to the <i>Z^0</i>, see below. Default is the MSbar value
115	from [<a href="Bibliography.php" target="page">Yao06</a>].
116
117
118	<br/><br/><table><tr><td><strong>StandardModel:sin2thetaWbar </td><td></td><td> <input type="text" name="4" value="0.2315" size="20"/>   (<code>default = <strong>0.2315</strong></code>; <code>minimum = 0.225</code>; <code>maximum = 0.240</code>)</td></tr></table>
119	The sine-squared of the weak mixing angle, as used to derive the vector
120	couplings of fermions to the <i>Z^0</i>, in the relation
121	<i>v_f = a_f - 4 e_f sin^2(theta_W)bar</i>. Default is the
122	effective-angle value from [<a href="Bibliography.php" target="page">Yao06</a>].
123
124
125	<p/>
126	The Fermi constant is not much used in the currently coded matrix elements,
127	since it is redundant, but it is available:
128
129	<br/><br/><table><tr><td><strong>StandardModel:GF </td><td></td><td> <input type="text" name="5" value="1.16637e-5" size="20"/>   (<code>default = <strong>1.16637e-5</strong></code>; <code>minimum = 1.0e-5</code>; <code>maximum = 1.3e-5</code>)</td></tr></table>
130	The Fermi coupling constant, in units of GeV<i>^-2</i>.
131
132
133	<h3>The quark weak-mixing matrix</h3>
134
135	The absolute values of the Cabibbo-Kobayashi-Maskawa matrix elements are
136	set by the following nine real values taken from [<a href="Bibliography.php" target="page">Yao06</a>] -
137	currently the CP-violating phase is not taken into account in this
138	parametrization. It is up to the user to pick a consistent unitary
139	set of new values whenever changes are made.
140
141	<br/><br/><table><tr><td><strong>StandardModel:Vud </td><td></td><td> <input type="text" name="6" value="0.97383" size="20"/>   (<code>default = <strong>0.97383</strong></code>; <code>minimum = 0.973</code>; <code>maximum = 0.975</code>)</td></tr></table>
142	The <i>V_ud</i> CKM matrix element.
143
144
145	<br/><br/><table><tr><td><strong>StandardModel:Vus </td><td></td><td> <input type="text" name="7" value="0.2272" size="20"/>   (<code>default = <strong>0.2272</strong></code>; <code>minimum = 0.224</code>; <code>maximum = 0.230</code>)</td></tr></table>
146	The <i>V_us</i> CKM matrix element.
147
148
149	<br/><br/><table><tr><td><strong>StandardModel:Vub </td><td></td><td> <input type="text" name="8" value="0.00396" size="20"/>   (<code>default = <strong>0.00396</strong></code>; <code>minimum = 0.0037</code>; <code>maximum = 0.0042</code>)</td></tr></table>
150	The <i>V_ub</i> CKM matrix element.
151
152
153	<br/><br/><table><tr><td><strong>StandardModel:Vcd </td><td></td><td> <input type="text" name="9" value="0.2271" size="20"/>   (<code>default = <strong>0.2271</strong></code>; <code>minimum = 0.224</code>; <code>maximum = 0.230</code>)</td></tr></table>
154	The <i>V_cd</i> CKM matrix element.
155
156
157	<br/><br/><table><tr><td><strong>StandardModel:Vcs </td><td></td><td> <input type="text" name="10" value="0.97296" size="20"/>   (<code>default = <strong>0.97296</strong></code>; <code>minimum = 0.972</code>; <code>maximum = 0.974</code>)</td></tr></table>
158	The <i>V_cs</i> CKM matrix element.
159
160
161	<br/><br/><table><tr><td><strong>StandardModel:Vcb </td><td></td><td> <input type="text" name="11" value="0.04221" size="20"/>   (<code>default = <strong>0.04221</strong></code>; <code>minimum = 0.0418</code>; <code>maximum = 0.0426</code>)</td></tr></table>
162	The <i>V_cb</i> CKM matrix element.
163
164
165	<br/><br/><table><tr><td><strong>StandardModel:Vtd </td><td></td><td> <input type="text" name="12" value="0.00814" size="20"/>   (<code>default = <strong>0.00814</strong></code>; <code>minimum = 0.006</code>; <code>maximum = 0.010</code>)</td></tr></table>
166	The <i>V_td</i> CKM matrix element.
167
168
169	<br/><br/><table><tr><td><strong>StandardModel:Vts </td><td></td><td> <input type="text" name="13" value="0.04161" size="20"/>   (<code>default = <strong>0.04161</strong></code>; <code>minimum = 0.039</code>; <code>maximum = 0.043</code>)</td></tr></table>
170	The <i>V_ts</i> CKM matrix element.
171
172
173	<br/><br/><table><tr><td><strong>StandardModel:Vtb </td><td></td><td> <input type="text" name="14" value="0.9991" size="20"/>   (<code>default = <strong>0.9991</strong></code>; <code>minimum = 0.99907</code>; <code>maximum = 0.9992</code>)</td></tr></table>
174	The <i>V_tb</i> CKM matrix element.
175
176
177	<h3>The CoupSM class</h3>
178
179	The <code><?php $filepath = $_GET["filepath"];
180	echo "<a href='ProgramFlow.php?filepath=".$filepath."' target='page'>";?>Pythia</a></code> class contains a
181	public instance <code>coupSM</code> of the <code>CoupSM</code> class.
182	This class contains one instance each of the <code>AlphaStrong</code>
183	and <code>AlphaEM</code> classes, and additionally stores the weak couplings
184	and the quark mixing matrix mentioned above. This class is used especially
185	in the calculation of cross sections and resonance widths, but could also
186	be used elsewhere. Specifically, as already mentioned, there are separate
187	<code>AlphaStrong</code> and <code>AlphaEM</code> instances for timelike
188	and spacelike showers and for multiparton interactions, while weak couplings
189	and the quark mixing matrix are only stored here. With the exception of the
190	first two methods below, which are for internal use, the subsequent ones
191	could also be used externally.
192
193	<a name="method1"></a>
194	<p/><strong>CoupSM::CoupSM()  </strong> <br/>
195	the constructor does nothing. Internal.
196
197
198	<a name="method2"></a>
199	<p/><strong>void CoupSM::init(Settings& settings, Rndm* rndmPtr)  </strong> <br/>
200	this is where the <code>AlphaStrong</code> and <code>AlphaEM</code>
201	instances are initialized, and weak couplings and the quark mixing matrix
202	are read in and set. This is based on the values stored on this page and
203	among the <?php $filepath = $_GET["filepath"];
204	echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>Couplings and Scales</a>.
205	Internal.
206
207
208	<a name="method3"></a>
209	<p/><strong>double CoupSM::alphaS(double scale2)  </strong> <br/>
210	the <i>alpha_strong</i> value at the quadratic scale <code>scale2</code>.
211
212
213	<a name="method4"></a>
214	<p/><strong>double CoupSM::alphaS1Ord(double scale2)  </strong> <br/>
215	a first-order overestimate of the full second-order <i>alpha_strong</i>
216	value at the quadratic scale <code>scale2</code>.
217
218
219	<a name="method5"></a>
220	<p/><strong>double CoupSM::alphaS2OrdCorr(double scale2)  </strong> <br/>
221	a multiplicative correction factor, below unity, that brings the
222	first-order overestimate above into agreement with the full second-order
223	<i>alpha_strong</i> value at the quadratic scale <code>scale2</code>.
224
225
226	<a name="method6"></a>
227	<p/><strong>double CoupSM::Lambda3()  </strong> <br/>
228
229	<strong>double CoupSM::Lambda4()  </strong> <br/>
230
231	<strong>double CoupSM::Lambda5()  </strong> <br/>
232	the three-, four-, and five-flavour <i>Lambda</i> scale.
233
234
235	<a name="method7"></a>
236	<p/><strong>double CoupSM::alphaEM(double scale2)  </strong> <br/>
237	the <i>alpha_em</i> value at the quadratic scale <code>scale2</code>.
238
239
240	<a name="method8"></a>
241	<p/><strong>double CoupSM::sin2thetaW()  </strong> <br/>
242
243	<strong>double CoupSM::cos2thetaW()  </strong> <br/>
244	the sine-squared and cosine-squared of the weak mixing angle, as used in
245	the gauge-boson sector.
246
247
248	<a name="method9"></a>
249	<p/><strong>double CoupSM::sin2thetaWbar()  </strong> <br/>
250	the sine-squared of the weak mixing angle, as used to derive the vector
251	couplings of fermions to the <i>Z^0</i>.
252
253
254	<a name="method10"></a>
255	<p/><strong>double CoupSM::GF()  </strong> <br/>
256	the Fermi constant of weak decays, in GeV<i>^-2</i>.
257
258
259	<a name="method11"></a>
260	<p/><strong>double CoupSM::ef(int idAbs)  </strong> <br/>
261	the electrical charge of a fermion, by the absolute sign of the PDF code,
262	i.e. <code>idAbs</code> must be in the range between 1 and 18.
263
264
265	<a name="method12"></a>
266	<p/><strong>double CoupSM::vf(int idAbs)  </strong> <br/>
267
268	<strong>double CoupSM::af(int idAbs)  </strong> <br/>
269	the vector and axial charges of a fermion, by the absolute sign of the PDF
270	code (<i>a_f = +-1, v_f = a_f - 4. * sin2thetaWbar * e_f</i>).
271
272
273	<a name="method13"></a>
274	<p/><strong>double CoupSM::t3f(int idAbs)  </strong> <br/>
275
276	<strong>double CoupSM::lf(int idAbs)  </strong> <br/>
277
278	<strong>double CoupSM::rf(int idAbs)  </strong> <br/>
279	the weak isospin, left- and righthanded charges of a fermion, by the
280	absolute sign of the PDF code (<i>t^3_f = a_f/2, l_f = (v_f + a_f)/2,
281	r_f = (v_f - a_f)/2</i>; you may find other conventions in the literature
282	that differ by a factor of 2).
283
284
285	<a name="method14"></a>
286	<p/><strong>double CoupSM::ef2(int idAbs)  </strong> <br/>
287
288	<strong>double CoupSM::vf2(int idAbs)  </strong> <br/>
289
290	<strong>double CoupSM::af2(int idAbs)  </strong> <br/>
291
292	<strong>double CoupSM::efvf(int idAbs)  </strong> <br/>
293
294	<strong>double CoupSM::vf2af2(int idAbs)  </strong> <br/>
295	common quadratic combinations of the above couplings:
296	<i>e_f^2, v_f^2, a_f^2, e_f * v_f, v_f^2 + a_f^2</i>.
297
298
299	<a name="method15"></a>
300	<p/><strong>double CoupSM::VCKMgen(int genU, int genD)  </strong> <br/>
301
302	<strong>double CoupSM::V2CKMgen(int genU, int genD)  </strong> <br/>
303	the CKM mixing element,or the square of it, for
304	up-type generation index <code>genU</code>
305	(<i>1 = u, 2 = c, 3 = t, 4 = t'</i>) and
306	down-type generation index <code>genD</code>
307	(<i>1 = d, 2 = s, 3 = b, 4 = b'</i>).
308
309
310	<a name="method16"></a>
311	<p/><strong>double CoupSM::VCKMid(int id1, int id2)  </strong> <br/>
312
313	<strong>double CoupSM::V2CKMid(int id1, int id2)  </strong> <br/>
314	the CKM mixing element,or the square of it, for
315	flavours <code>id1</code> and <code>id2</code>, both in the
316	range from <i>-18</i> to <i>+18</i>. The sign is here not
317	checked (so it can be used both for <i>u + dbar -> W+</i>
318	and <i>u -> d + W+</i>, say), but impossible flavour combinations
319	evaluate to zero. The neutrino sector is numbered by flavor
320	eigenstates, so there is no mixing in the lepton-neutrino system.
321
322
323	<a name="method17"></a>
324	<p/><strong>double CoupSM::V2CKMsum(int id)  </strong> <br/>
325	the sum of squared CKM mixing element that a given flavour can couple to,
326	excluding the top quark and fourth generation. Is close to unity
327	for the first two generations. Returns unity for the lepton-neutrino
328	sector.
329
330
331	<a name="method18"></a>
332	<p/><strong>int CoupSM::V2CKMpick(int id)  </strong> <br/>
333	picks a random CKM partner quark or lepton (with the same sign as
334	<code>id</code>) according to the respective squared elements, again
335	excluding the top quark and fourth generation from the list of
336	possibilities. Unambiguous choice for the lepton-neutrino sector.
337
338
339	<input type="hidden" name="saved" value="1"/>
340
341	<?php
342	echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
343
344	<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
345	</form>
346
347	<?php
348
349	if($_POST["saved"] == 1)
350	{
351	$filepath = $_POST["filepath"];
352	$handle = fopen($filepath, 'a');
353
354	if($_POST["1"] != "0.00729735")
355	{
356	$data = "StandardModel:alphaEM0 = ".$_POST["1"]."\n";
357	fwrite($handle,$data);
358	}
359	if($_POST["2"] != "0.00781751")
360	{
361	$data = "StandardModel:alphaEMmZ = ".$_POST["2"]."\n";
362	fwrite($handle,$data);
363	}
364	if($_POST["3"] != "0.2312")
365	{
366	$data = "StandardModel:sin2thetaW = ".$_POST["3"]."\n";
367	fwrite($handle,$data);
368	}
369	if($_POST["4"] != "0.2315")
370	{
371	$data = "StandardModel:sin2thetaWbar = ".$_POST["4"]."\n";
372	fwrite($handle,$data);
373	}
374	if($_POST["5"] != "1.16637e-5")
375	{
376	$data = "StandardModel:GF = ".$_POST["5"]."\n";
377	fwrite($handle,$data);
378	}
379	if($_POST["6"] != "0.97383")
380	{
381	$data = "StandardModel:Vud = ".$_POST["6"]."\n";
382	fwrite($handle,$data);
383	}
384	if($_POST["7"] != "0.2272")
385	{
386	$data = "StandardModel:Vus = ".$_POST["7"]."\n";
387	fwrite($handle,$data);
388	}
389	if($_POST["8"] != "0.00396")
390	{
391	$data = "StandardModel:Vub = ".$_POST["8"]."\n";
392	fwrite($handle,$data);
393	}
394	if($_POST["9"] != "0.2271")
395	{
396	$data = "StandardModel:Vcd = ".$_POST["9"]."\n";
397	fwrite($handle,$data);
398	}
399	if($_POST["10"] != "0.97296")
400	{
401	$data = "StandardModel:Vcs = ".$_POST["10"]."\n";
402	fwrite($handle,$data);
403	}
404	if($_POST["11"] != "0.04221")
405	{
406	$data = "StandardModel:Vcb = ".$_POST["11"]."\n";
407	fwrite($handle,$data);
408	}
409	if($_POST["12"] != "0.00814")
410	{
411	$data = "StandardModel:Vtd = ".$_POST["12"]."\n";
412	fwrite($handle,$data);
413	}
414	if($_POST["13"] != "0.04161")
415	{
416	$data = "StandardModel:Vts = ".$_POST["13"]."\n";
417	fwrite($handle,$data);
418	}
419	if($_POST["14"] != "0.9991")
420	{
421	$data = "StandardModel:Vtb = ".$_POST["14"]."\n";
422	fwrite($handle,$data);
423	}
424	fclose($handle);
425	}
426
427	?>
428	</body>
429	</html>
430
431	<!-- Copyright (C) 2013 Torbjorn Sjostrand -->