The Impact of Excited Neutrinos on <svg      style="vertical-align:-4.698pt;width:87.75px;" id="M1" height="21.625" version="1.1" viewBox="0 0 87.75 21.625" width="87.75"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.713)"><path id="x1D708" d="M509 373q0 -52 -42.5 -118.5t-124.5 -159.5l-94 -107h-27q-22 209 -78 342q-21 48 -41 48q-18 0 -63 -62l-22 21q77 111 125 111q30 0 52 -21.5t38 -75.5q37 -130 52 -285q48 62 74.5 99.5t53.5 87t27 76.5q0 43 -17 60q-5 5 -5 15q0 17 12.5 30.5t28.5 13.5
q21 0 36 -22.5t15 -52.5z" /></g>

			<g transform="matrix(1.25,0,0,-1.25,90,90)">
				<path d="m -62.41,70.61 9.54,0" style="fill:none;stroke:#000000;stroke-width:0.89700001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none" />
			</g>
			<g transform="matrix(.022,-0,0,-.022,11.988,15.713)"><use xlink:href="#x1D708"/></g><g transform="matrix(.022,-0,0,-.022,33.866,15.713)"><path id="x2192" d="M901 255q-71 -62 -185 -187l-22 15l102 147h-727v50h727l-102 147l22 15q114 -125 185 -187z" /></g><g transform="matrix(.022,-0,0,-.022,65.204,15.713)"><path id="x1D6FE" d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
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</svg> Process

<table>The decoupling temperature <svg height="15.8375" id="M138" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 16.9 15.8375" width="16.9" 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>
<g transform="matrix(.012,-0,0,-.012,11.388,15.637)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
</svg> as a function of <svg height="20.362499" id="M139" style="vertical-align:-6.53424pt" version="1.1" viewbox="0 0 36.287498 20.362499" width="36.287498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M671 0h-247v28q49 7 60 18.5t0 45.5l-155 438h-2q-21 -61 -74 -204.5t-75 -210.5q-15 -51 -4.5 -65t67.5 -22v-28h-221v28q50 9 69 26.5t45 84.5l202 517l32 9l194 -535q23 -61 42 -78.5t67 -23.5v-28z" id="x39B"></path></g><g transform="matrix(.017,-0,0,-.017,11.724,12.162)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,18.727,12.162)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" id="x1D453"></path></g>
<g transform="matrix(.012,-0,0,-.012,29.638,17.2)"><path d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
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</svg> when the <svg height="11.825" id="M140" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 21.15 11.825" width="21.15" 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="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><path d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5
q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g>
</svg> are equivalent to 250 GeV and 500 GeV.</table>

Advances in High Energy Physics

fig3

Figure 3

Figure 3: The Impact of Excited Neutrinos on <svg      style="vertical-align:-4.698pt;width:87.75px;" id="M1" height="21.625" version="1.1" viewBox="0 0 87.75 21.625" width="87.75"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.713)"><path id="x1D708" d="M509 373q0 -52 -42.5 -118.5t-124.5 -159.5l-94 -107h-27q-22 209 -78 342q-21 48 -41 48q-18 0 -63 -62l-22 21q77 111 125 111q30 0 52 -21.5t38 -75.5q37 -130 52 -285q48 62 74.5 99.5t53.5 87t27 76.5q0 43 -17 60q-5 5 -5 15q0 17 12.5 30.5t28.5 13.5
q21 0 36 -22.5t15 -52.5z" /></g>

			<g transform="matrix(1.25,0,0,-1.25,90,90)">
				<path d="m -62.41,70.61 9.54,0" style="fill:none;stroke:#000000;stroke-width:0.89700001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none" />
			</g>
			<g transform="matrix(.022,-0,0,-.022,11.988,15.713)"><use xlink:href="#x1D708"/></g><g transform="matrix(.022,-0,0,-.022,33.866,15.713)"><path id="x2192" d="M901 255q-71 -62 -185 -187l-22 15l102 147h-727v50h727l-102 147l22 15q114 -125 185 -187z" /></g><g transform="matrix(.022,-0,0,-.022,65.204,15.713)"><path id="x1D6FE" d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
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</svg> Process 

Advances in High Energy Physics

The Impact of Excited Neutrinos on Process

Figure 3