Define: ltn, ltp = live times for n, p helicities; b2n, b2p = Beta2 triggers for n, p helicities; h, hn = scaler counts for all (510), n (538) helicities.

> ltn:=b2n/hn;

ltn := \frac{b2n}{hn}

p helicity counts are c*h -hn = 0.985*h - hn

> ltp:=b2p/(c*h-hn);

ltp := \frac{b2p}{c h − hn}

> Alt:= (ltn-ltp)/(ltn+ltp);

Alt := \frac{\frac{b2n}{hn} − \frac{b2p}{c h − hn}}{\frac{b2n}{hn} + \frac{b2p}{c h − hn}}

> simplify(");

\frac{b2n c h − b2n hn − b2p hn}{b2n c h − b2n hn + b2p hn}

> Alt_b2n:=simplify(diff(Alt,b2n));

Alt b2n := 2 \frac{b2p (c h − hn) hn}{(b2n c h − b2n hn + b2p hn)^{2}}

> Alt_b2p:=simplify(diff(Alt,b2p));

Alt b2p := −2 \frac{b2n (c h − hn) hn}{(b2n c h − b2n hn + b2p hn)^{2}}

> Alt_h:=simplify(diff(Alt,h));

Alt h := 2 \frac{b2n hn c b2p}{(b2n c h − b2n hn + b2p hn)^{2}}

> Alt_hn:=simplify(diff(Alt,hn));

Alt hn := −2 \frac{b2p h c b2n}{(b2n c h − b2n hn + b2p hn)^{2}}

b2n, b2p, h, hn are counts from engine or scalers (h=510, hn =538), so their errors squared are just b2n, etc. counts.

> dAlt:=sqrt(Alt_b2n^2*b2n+Alt_b2p^2*b2p+Alt_h^2*h+Alt_hn^2*hn);

dAlt := 2(\frac{b2p^{2} (c h − hn)^{2} hn^{2} b2n}{%1^{4}} + \frac{b2n^{2} (c h − hn)^{2} hn^{2} b2p}{%1^{4}} + \frac{b2n^{2} hn^{2} c^{2} b2p^{2} h}{%1^{4}}

+ \frac{b2p^{2} h^{2} c^{2} b2n^{2} hn}{%1^{4}} )^{1/2}

%1 := b2n c h − b2n hn + b2p hn

> dAlt2:=collect(dAlt,distributed,factor);

dAlt2 := 2(b2p hn b2n(b2p hn c^{2} h^{2} − 2 b2p hn^{2} c h + b2p hn^{3} + b2n hn c^{2} h^{2} − 2 b2n hn^{2} c h + b2n hn^{3} + b2n hn c^{2} b2p h + b2p h^{2} c^{2} b2n) / (b2n c h − b2n hn + b2p hn)^{4})^{1/2}

> dAlt2_73041:=subs(b2p=360650,b2n=366615,h=792 012,hn=392716,c=0.985,dAlt2);
evalf(dAlt2_73041);

dAlt2 73041 := .1004215685 10^{−10} \sqrt{360650} \sqrt{366615} \sqrt{392716}

.002288307486

> Alt_73041:=subs(b2p=360650,b2n=366615,h=79201 2,hn=392716,c=0.985,Alt);

Alt 73041 := .001408086213