On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

<table>The product <svg height="16.049999" id="M213" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 24.6875 16.049999" width="24.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M484 406q0 -21 -22 -38q-10 -7 -18 -1q-15 11 -30 11q-30 0 -77.5 -37t-74.5 -67l79 -168q11 -23 19.5 -34.5t13 -14t10.5 -2.5q9 0 30 17.5t40 42.5l17 -23q-31 -45 -57.5 -69.5t-40.5 -29.5t-31 -5q-18 0 -32 13.5t-35 55.5q-34 71 -69 160q-36 -32 -59 -56
q-12 -27 -36 -158q-44 -7 -77 -15l-5 7l82 349q6 25 -2 25q-16 0 -72 -41l-14 22q44 41 89 69.5t66 28.5q19 0 19 -32q0 -16 -6 -43l-35 -160l146 143q94 92 136 92q20 0 33 -12t13 -30z" id="x1D705"></path></g><g transform="matrix(.017,-0,0,-.017,8.681,15.775)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
<g transform="matrix(.012,-0,0,-.012,18.288,7.613)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> is given as a function of <svg height="11.6125" id="M214" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.45 11.6125" width="11.45" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
</svg> at various <svg height="12.175" id="M215" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 9.5625 12.175" width="9.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310
q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" id="x1D707"></path></g>
</svg>-values for hadronic (a), bosonic (b), and fermionic (c) resonance gas.</table>

Advances in High Energy Physics

fig7

Figure 7

Figure 7: On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint 