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diff --git a/current_generator/W_extremal_qqbar.frm b/current_generator/W_extremal_qqbar.frm
index 856fb9f..7305403 100644
--- a/current_generator/W_extremal_qqbar.frm
+++ b/current_generator/W_extremal_qqbar.frm
@@ -1,102 +1,105 @@
*/**
* \brief Calculation of W + extremal qqbar current contraction
*
* TODO: unify conventions with developer manual
* the current dictionary is as follows:
*
* code | manual
* pq | p_2
* pqbar | p_1
* pg | p_a
*
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2020
* \copyright GPLv2 or later
*/
#include- include/helspin.frm
#include- include/write.frm
s h,sgb,sgn,sqqbarW;
v pq,pqbar,pg,pl,plbar,pn,pb,pW,pr,q1,q2;
i mu,nu,rho,sigma;
i mu1,...,mu20;
cf epsg,m2,m2inv,sqrt;
#do h1={+,-}
* eq:U1tensorX in developer manual, up to factors 1/sij, 1/tij
l [U1X `h1'] = (
+ Current(`h1'1, pq, nu, pg-pq, mu, pqbar+pW, rho, pqbar)
+ Current(`h1'1, pq, nu, pg-pq, rho, pg-pq-pW, mu, pqbar)
- Current(`h1'1, pq, rho, pq+pW, nu, pg-pq-pW, mu, pqbar)
);
* eq:U2tensorX in developer manual, up to factors 1/sij, 1/tij
l [U2X `h1'] = (
- Current(`h1'1, pq, mu, pg-pqbar-pW, nu, pqbar+pW, rho, pqbar)
+ Current(`h1'1, pq, mu, pg-pqbar-pW, rho, pg-pqbar, nu, pqbar)
+ Current(`h1'1, pq, rho, pq+pW, mu, pg-pqbar, nu, pqbar)
);
* eq:LtensorX in developer manual, up to factors 1/sij, 1/tij
l [LX `h1'] = (
- Current(`h1'1, pq, sigma, pqbar+pW, rho, pqbar) +
+ Current(`h1'1, pq, rho, pq+pW, sigma, pqbar)
)*(
+ (-(pb(nu)/sgb + pn(nu)/sgn)*m2(q1 + pg) + 2*q1(nu) - pg(nu))*d_(mu, sigma)
- (2*pg(sigma) + q1(sigma))*d_(mu, nu)
+ 2*pg(mu)*d_(nu, sigma)
)/sqqbarW;
#enddo
.sort
* restore kinematic factors
id Current(h?, pq, mu?, q1?, nu?, q2?, rho?, pqbar) = (
Current(h, pq, mu, q1, nu, q2, rho, pqbar)*m2inv(q1)*m2inv(q2)
);
id Current(h?, pq, mu?, q1?, nu?, pqbar) = (
Current(h, pq, mu, q1, nu, pqbar)*m2inv(q1)
);
.sort
drop;
* multiply with polarisation vector and other currents
#do h1={+,-}
#do h2={+,-}
#do hg={+,-}
#do TENSOR={U1X,U2X,LX}
l [`TENSOR' `h1'`h2'`hg'] = (
[`TENSOR' `h1']
*epsg(`hg'1, nu)
*Current(`h2'1, pn, mu, pb)
*Current(-1, pl, rho, plbar)
);
#enddo
#enddo
#enddo
#enddo
-* TODO: choice of best reference vector (pn or pb)
-id epsg(h?, mu?) = epsg(h, mu, pn);
+* choice of reference vector (pn or pb)
+* this is not exactly the optimal choice for all helicities,
+* but it's pretty close and the logic is simple
+id epsg(h?, nu?)*Current(h?, pn, mu?, pb) = epsg(h, nu, pn)*Current(h, pn, mu, pb);
+also epsg(h?, nu?) = epsg(h, nu, pb);
id epsg(-1, mu?, pr?) = sqrt(2)/2*SpinorChain(pr, mu, pg)/AngleChain(pg,pr);
id epsg(+1, mu?, pr?) = sqrt(2)/2*SpinorChain(pg, mu, pr)/SquareChain(pg,pr);
multiply replace_(q1,-(pq+pqbar+pW));
multiply replace_(pW,pl+plbar);
.sort
#call ContractCurrents
multiply replace_(
sgn,m2(pg+pn),
sgb,m2(pg+pb),
sqqbarW,m2(pq+pqbar+pW)
);
id m2inv(q1?) = 1/m2(q1);
multiply replace_(pW,pl+plbar);
.sort
format O4;
format c;
#call WriteHeader(`OUTPUT')
#call WriteOptimised(`OUTPUT',U1X,3,pg,pq,plbar,pl,pqbar,pn,pb)
#call WriteOptimised(`OUTPUT',U2X,3,pg,pq,plbar,pl,pqbar,pn,pb)
#call WriteOptimised(`OUTPUT',LX,3,pg,pq,plbar,pl,pqbar,pn,pb)
#call WriteFooter(`OUTPUT')
.end

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