<chapter name="Flavour Selection"> <h2>Flavour Selection</h2> The <code>StringFlav</code> class handles the choice of a new flavour in the fragmentation process, and the production of a new hadron from a set of input flavours. It is mainly used by the string fragmentation machinery (including ministrings), but also e.g. in some particle decays and for some beam-remnant cases. The basic concepts are in agreement with <ref>And83</ref>. The baryon-sector implementation is based on the <code>MSTJ(12)=3</code> option of PYTHIA 6, i.e. new SU(6) weights scheme with at most one popcorn meson. <p/> The relative production rates of different particle species is influenced by the parameters below. Some have only an impact on one specific quantity, but most directly or indirectly have consequences for many observables. Therefore the values to use have to be viewed in the context of a complete <aloc href="Tunes">tune</aloc>. <h3>New flavours</h3> The main parameters of the selection of a new flavour are <parm name="StringFlav:probStoUD" default="0.19" min="0.0" max="1.0"> the suppression of <ei>s</ei> quark production relative to ordinary <ei>u</ei> or <ei>d</ei> one. </parm> <parm name="StringFlav:probQQtoQ" default="0.09" min="0.0" max="1.0"> the suppression of diquark production relative to quark production, i.e. of baryon relative to meson production. </parm> <parm name="StringFlav:probSQtoQQ" default="1.00" min="0.0" max="1.0"> the suppression of strange diquark production relative to light diquark production, over and above the one already given by <code>probStoU</code>. </parm> <parm name="StringFlav:probQQ1toQQ0" default="0.027" min="0.0" max="1.0"> the suppression of spin 1 diquark production relative to spin 0 one, apart from the factor of 3 enhancement of spin 1 from counting the number of states. </parm> <pvec name="StringFlav:probQQ1toQQ0join" default="0.5,0.7,0.9,1.0" min="0.0" max="1.0"> when two already produced quarks are to be combined to a diquark, e.g. in the junction framework, these numbers give the suppression of spin 1 diquark production relative to spin 0 one, apart from the factor of 3 enhancement of spin 1 from counting the number of states. The four components give the suppression when the heaviest quark is <ei>u/d</ei>, <ei>s</ei>, <ei>c</ei> or <ei>b</ei>, respectively. These parameters are seldom used and currently not constrained by any data, so very much a guesswork. </pvec> <h3>Standard-meson production</h3> The bulk of the particle production corresponds to the lowest-lying pseudoscalar and vector multiplets. Their production rates are determined by the parameters in this section. <p/> For a given set of flavours, produced according to the probabilities outlined above, the ratio of vector-to-pseudocalar meson production is described by the parameters below. The maximum allowed rate for each case has been set according to spin-counting rules, but we expect the real rates to be lower, especially for lighter mesons, owing to the vector-pseudoscalar mass splitting. <parm name="StringFlav:mesonUDvector" default="0.62" min="0." max="3."> the relative production ratio vector/pseudoscalar for light (<ei>u</ei>, <ei>d</ei>) mesons. </parm> <parm name="StringFlav:mesonSvector" default="0.725" min="0." max="3."> the relative production ratio vector/pseudoscalar for strange mesons. </parm> <parm name="StringFlav:mesonCvector" default="1.06" min="0." max="3."> the relative production ratio vector/pseudoscalar for charm mesons. </parm> <parm name="StringFlav:mesonBvector" default="3.0" min="0." max="3."> the relative production ratio vector/pseudoscalar for bottom mesons. </parm> <p/> Inside each light-quark meson nonet, an octet-singlet mixing angle describes the mixing of the two flavour-diagonal isoscalar = 0 states. (For terminology and details see <ref>Yao06</ref>, chapter 14 on the quark model.) This angle is needed to specify the probability for such a <ei>q qbar</ei> state to project onto a specific meson. More transparent formulae are obtained by introducing the angle <ei>alpha = theta + 54.7</ei> degrees: <eq> f = (uubar + ddbar)/sqrt(2) * sin(alpha) + ssbar * cos(alpha)<br/> f' = (uubar + ddbar)/sqrt(2) * cos(alpha) - ssbar * sin(alpha) </eq> <parm name="StringFlav:thetaPS" default="-15." min="-90." max="90."> gives the mixing angle <ei>theta_PS</ei> in the pseudoscalar meson sector (which is rather poorly determined), expressed in degrees. Here <ei>f</ei> is associated with <ei>eta'</ei> and <ei>f'</ei> with <ei>eta</ei>. (This standard but counterintuitive choice is fixed up in the code by replacing <ei>alpha → 90^0 - alpha</ei> so that <ei>eta ↔ eta'</ei>; relative signs do not matter since we are interested in probabilities only.) </parm> <parm name="StringFlav:thetaV" default="36." min="-90." max="90."> gives the mixing angle <ei>theta_V</ei> in the vector meson sector (which is somewhat better determined), expressed in degrees. Here <ei>f</ei> is associated with <ei>omega</ei> and <ei>f'</ei> with <ei>phi</ei>. </parm> <p/> Further, the simple model overestimates the production of <ei>eta</ei> and, in particular, <ei>eta'</ei> mesons, which can be rectified by <parm name="StringFlav:etaSup" default="0.63" min="0." max="1."> the additional suppression of <ei>eta</ei> production, multiplying the normal production probability. Thus 0 means no <ei>eta</ei> at all are produced, while 1 means full rate. </parm> <parm name="StringFlav:etaPrimeSup" default="0.12" min="0." max="1."> the additional suppression of <ei>eta'</ei> production, multiplying the normal production probability. Thus 0 means no <ei>eta'</ei> at all are produced, while 1 means full rate. </parm> <h3>Excited-meson production</h3> Several excited mesons, ie. with radial or orbital excitations, have been observed at non-negligible production rates. Extrapolated to all states a fair fraction of all particle production might proceed through such states. There are big uncertainties, however, since these excited mesons in many cases are extremely poorly known. This also means that the modeling of their production and decay is very primitive, and even that the inclusion of the production of such states may lead to a degraded agreement with data. Currently the default is that all such production is switched off. <p/> Parameters are provided to switch them on. By demand, this machinery has been made more flexible than in the past. Therefore one parameter is provided for each combination of heaviest flavour (<ei>u/d</ei>, <ei>s</ei>, <ei>c</ei> or <ei>b</ei>) and multiplet produced. In each case the production rate is normalized to that of the lowest-lying pseudoscalar of the same flavour content, as for the vector-meson rates introduced above. The multiplets available are the four obtained for one unit of orbital angular momentum, in the nonrelativistic classification. Using <ei>J</ei> to denote the sum of quark spin <ei>S</ei> and orbital angular momentum <ei>L</ei>, i.e. what would normally be called the spin of the meson, one has: <ul> <li>a pseudovector multiplet with <ei>L=1, S=0, J=1</ei>;</li> <li>a scalar multiplet with <ei>L=1, S=1, J=0</ei>;</li> <li>a pseudovector multiplet with <ei>L=1, S=1, J=1</ei>;</li> <li>a tensor multiplet with <ei>L=1, S=1, J=2</ei>.</li> </ul> The maximum allowed rate for each case has been set according to spin-counting rules, but we expect the real rates to be significantly lower, owing to mass suppression. <parm name="StringFlav:mesonUDL1S0J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=0,J=1)</ei>/pseudoscalar for light (<ei>u</ei>, <ei>d</ei>) mesons. </parm> <parm name="StringFlav:mesonUDL1S1J0" default="0.0" min="0." max="1."> the relative scalar production ratio <ei>(L=1,S=1,J=0)</ei>/pseudoscalar for light (<ei>u</ei>, <ei>d</ei>) mesons. </parm> <parm name="StringFlav:mesonUDL1S1J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=1,J=1)</ei>/pseudoscalar for light (<ei>u</ei>, <ei>d</ei>) mesons. </parm> <parm name="StringFlav:mesonUDL1S1J2" default="0.0" min="0." max="5."> the relative tensor production ratio <ei>(L=1,S=1,J=2)</ei>/pseudoscalar for light (<ei>u</ei>, <ei>d</ei>) mesons. </parm> <parm name="StringFlav:mesonSL1S0J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=0,J=1)</ei>/pseudoscalar for strange mesons. </parm> <parm name="StringFlav:mesonSL1S1J0" default="0.0" min="0." max="1."> the relative scalar production ratio <ei>(L=1,S=1,J=0)</ei>/pseudoscalar for strange mesons. </parm> <parm name="StringFlav:mesonSL1S1J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=1,J=1)</ei>/pseudoscalar for strange mesons. </parm> <parm name="StringFlav:mesonSL1S1J2" default="0.0" min="0." max="5."> the relative tensor production ratio <ei>(L=1,S=1,J=2)</ei>/pseudoscalar for strange mesons. </parm> <parm name="StringFlav:mesonCL1S0J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=0,J=1)</ei>/pseudoscalar for charm mesons. </parm> <parm name="StringFlav:mesonCL1S1J0" default="0.0" min="0." max="1."> the relative scalar production ratio <ei>(L=1,S=1,J=0)</ei>/pseudoscalar for charm mesons. </parm> <parm name="StringFlav:mesonCL1S1J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=1,J=1)</ei>/pseudoscalar for charm mesons. </parm> <parm name="StringFlav:mesonCL1S1J2" default="0.0" min="0." max="5."> the relative tensor production ratio <ei>(L=1,S=1,J=2)</ei>/pseudoscalar for charm mesons. </parm> <parm name="StringFlav:mesonBL1S0J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=0,J=1)</ei>/pseudoscalar for bottom mesons. </parm> <parm name="StringFlav:mesonBL1S1J0" default="0.0" min="0." max="1."> the relative scalar production ratio <ei>(L=1,S=1,J=0)</ei>/pseudoscalar for bottom mesons. </parm> <parm name="StringFlav:mesonBL1S1J1" default="0.0" min="0." max="3."> the relative pseudovector production ratio <ei>(L=1,S=1,J=1)</ei>/pseudoscalar for bottom mesons. </parm> <parm name="StringFlav:mesonBL1S1J2" default="0.0" min="0." max="5."> the relative tensor production ratio <ei>(L=1,S=1,J=2)</ei>/pseudoscalar for bottom mesons. </parm> <p/> In addition, an octet-singlet mixing angle is needed for each multiplet, as for the pseudoscalar and vector multiplets above. Only for the tensor multiplet does any determination exist; for the other multiplets default has been chose so that <ei>ssbar</ei> does not mix with the light quarks, and so that the <ei>ssbar</ei> state is the heavier of the two. <parm name="StringFlav:thetaL1S0J1" default="35.3" min="-90." max="90."> gives the mixing angle <ei>theta</ei> in the <ei>(L=1,S=0,J=1)</ei> pseudovector meson sector, expressed in degrees. </parm> <parm name="StringFlav:thetaL1S1J0" default="35.3" min="-90." max="90."> gives the mixing angle <ei>theta</ei> in the <ei>(L=1,S=1,J=0)</ei> scalar meson sector, expressed in degrees. </parm> <parm name="StringFlav:thetaL1S1J1" default="35.3" min="-90." max="90."> gives the mixing angle <ei>theta</ei> in the <ei>(L=1,S=1,J=1)</ei> pseudovector meson sector, expressed in degrees. </parm> <parm name="StringFlav:thetaL1S1J2" default="28.0" min="-90." max="90."> gives the mixing angle <ei>theta</ei> in the <ei>(L=1,S=1,J=2)</ei> tensor meson sector, expressed in degrees. </parm> <h3>Baryon production</h3> The relative rate of baryon production is mainly given by the quark and diquark production parameters above, plus SU(6) Clebsch-Gordans. The one modifiable parameter related to these coefficients is <parm name="StringFlav:decupletSup" default="1.0" min="0.0" max="1.0"> the suppression, relative to default SU(6) factors, of decuplet baryon production. Default corresponds to no suppression, while 0 corresponds to no decuplet production at all. </parm> <p/> In addition, if popcorn production is allowed, wherein a set of mesons (<ei>M</ei>) may be produced in between the baryon (<ei>B</ei>) and the antibaryon (<ei>Bbar</ei>), a set of further parameters is introduced. Currently only the simplest scenario is implemented, wherein at most one intermediate meson may be produced. <parm name="StringFlav:popcornRate" default="0.5" min="0." max="2.0"> gives the relative rates of <ei>B Bbar</ei> and <ei>B M Bbar</ei> production, roughly as <eq> Prob(B M Bbar) / (Prob(B Bbar) + Prob(B M Bbar)) = popcornRate / (0.5 + popcornRate) </eq> (the complete expression depends on all the quark and diquark production parameters and is therefore not so useful). </parm> <parm name="StringFlav:popcornSpair" default="0.5" min="0." max="1.0"> extra suppression for having an <ei>s sbar</ei> pair shared between the <ei>B</ei> and <ei>Bbar</ei> in a <ei>B M Bbar</ei> configuration. </parm> <parm name="StringFlav:popcornSmeson" default="0.5" min="0." max="1.0"> extra suppression for having a strange meson <ei>M</ei> in a <ei>B M Bbar</ei> configuration. </parm> <p/> Finally, there are some indications that leading-baryon production may be further suppressed. A proper description should probably be based on a suppression of early production times <ref>Ede97</ref>, but we here only implement a simpler version where production near the end of a string, as defined by rank, is suppressed. The more detailed studies suggest that leading <ei>c</ei> and <ei>b</ei> baryon production will be less suppressed, so we leave it open to set light- and heavy-baryon suppression separately. <flag name="StringFlav:suppressLeadingB" default="off"> Suppress leading-baryon production. <option value="off">No suppression.</option> <option value="on">Suppress the production of a diquark in the string breaking closest to a quark end of a string, by either of the factors below. This suppresses the production of first-rank baryons by the same amount. Indirectly also the second-rank and, if popcorn production is switched on, third-rank (anti)baryon production is affected. </option> </flag> <parm name="StringFlav:lightLeadingBSup" default="0.5" min="0." max="1.0"> extra suppression of leading-baryon production for a light-quark jet, i.e. <ei>d</ei>, <ei>u</ei> or <ei>s</ei>, when <code>suppressLeadingB = on</code>. Thus 0 means no leading-baryon production at all, while 1 means full rate. </parm> <parm name="StringFlav:heavyLeadingBSup" default="0.9" min="0." max="1.0"> extra suppression of leading-baryon production for a heavy-quark jet, i.e. <ei>c</ei> or <ei>b</ei>, when <code>suppressLeadingB = on</code>. Thus 0 means no leading-baryon production at all, while 1 means full rate. </parm> </chapter> <!-- Copyright (C) 2014 Torbjorn Sjostrand -->