/
neutrino_ellipse_calc.go
269 lines (225 loc) · 6.28 KB
/
neutrino_ellipse_calc.go
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package tbuilder
import (
"fmt"
"math"
"go-hep.org/x/hep/fmom"
"gonum.org/v1/gonum/mat"
)
type neutrinoEllipseCalculator struct {
bjet fmom.PxPyPzE
lep fmom.PxPyPzE
bjetBeta, bjetBeta2, bjetGamma, bjetGamma2 float64
lepBeta, lepBeta2, lepGamma, lepGamma2 float64
// particle masses
mw, mt, mnu float64
mw2, mt2, mnu2 float64
// numbers
x0, x0p float64
sx, sy float64
epsilon2 float64
cos, sin float64 //cosine and sine of theta_{b,mu}
omega float64
Omega float64
x1, y1 float64
z2 float64
ab *mat.Dense
al *mat.Dense
ht *mat.Dense
h *mat.Dense
hperp *mat.Dense
hperpInv *mat.Dense
nperp *mat.Dense
}
func newNeutrinoEllipseCalculator(
bjet, lepbar fmom.PxPyPzE,
mt, mw, mnu float64,
) *neutrinoEllipseCalculator {
nec := &neutrinoEllipseCalculator{
bjet: bjet,
lep: lepbar,
bjetBeta: betaOf(&bjet),
bjetGamma: gammaOf(&bjet),
lepBeta: betaOf(&lepbar),
lepGamma: gammaOf(&lepbar),
mw: mw,
mt: mt,
mnu: mnu,
mw2: mw * mw,
mt2: mt * mt,
mnu2: mnu * mnu,
cos: fmom.CosTheta(&lepbar, &bjet),
ab: mat.NewDense(4, 4, nil),
al: mat.NewDense(4, 4, nil),
ht: mat.NewDense(3, 3, nil),
h: mat.NewDense(3, 3, nil),
hperp: mat.NewDense(3, 3, nil),
hperpInv: mat.NewDense(3, 3, nil),
nperp: mat.NewDense(3, 3, nil),
}
nec.bjetBeta2 = nec.bjetBeta * nec.bjetBeta
nec.bjetGamma2 = nec.bjetGamma * nec.bjetGamma
nec.lepBeta2 = nec.lepBeta * nec.lepBeta
nec.lepGamma2 = nec.lepGamma * nec.lepGamma
nec.sin = math.Sqrt(1 - nec.cos*nec.cos)
return nec
}
func (nec *neutrinoEllipseCalculator) getNeutrinoEllipse() *mat.Dense {
nec.Wsurface()
nec.leptonEllipsoid()
nec.bJetEllipsoid()
nec.neutrinoSolution()
nec.labSystemTransform()
return nec.nperp // FIXME(sbinet): clone?
}
func (nec *neutrinoEllipseCalculator) Wsurface() {
nec.x0p = -(0.5 / nec.bjet.E()) * (nec.mt2 - nec.mw2 - nec.bjet.M2())
nec.x0 = -(0.5 / nec.lep.E()) * (nec.mw2 - nec.lep.M2() - nec.mnu2)
nec.sx = (1. / nec.lepBeta2) * (nec.x0*nec.lepBeta - nec.lep.P()*(1.-nec.lepBeta2))
nec.epsilon2 = (1. - nec.lepBeta2) * (nec.mw2 - nec.mnu2)
}
func (nec *neutrinoEllipseCalculator) leptonEllipsoid() {
nec.al.Set(0, 0, 1.-nec.lepBeta2)
nec.al.Set(1, 0, 0)
nec.al.Set(2, 0, 0)
nec.al.Set(3, 0, nec.sx*nec.lepBeta2)
nec.al.Set(0, 1, 0)
nec.al.Set(1, 1, 1)
nec.al.Set(2, 1, 0)
nec.al.Set(3, 1, 0)
nec.al.Set(0, 2, 0)
nec.al.Set(1, 2, 0)
nec.al.Set(2, 2, 1)
nec.al.Set(3, 2, 0)
nec.al.Set(0, 3, nec.sx*nec.lepBeta2)
nec.al.Set(1, 3, 0)
nec.al.Set(2, 3, 0)
nec.al.Set(3, 3, nec.mw2-nec.x0*nec.x0-nec.epsilon2)
}
func (nec *neutrinoEllipseCalculator) bJetEllipsoid() {
nec.ab.Set(0, 0, 1-nec.cos*nec.cos*nec.bjetBeta2)
nec.ab.Set(1, 0, -nec.cos*nec.sin*nec.bjetBeta2)
nec.ab.Set(2, 0, 0)
nec.ab.Set(3, 0, nec.cos*nec.x0p*nec.bjetBeta)
nec.ab.Set(0, 1, -nec.cos*nec.sin*nec.bjetBeta2)
nec.ab.Set(1, 1, 1-nec.sin*nec.sin*nec.bjetBeta2)
nec.ab.Set(2, 1, 0)
nec.ab.Set(3, 1, nec.sin*nec.x0p*nec.bjetBeta)
nec.ab.Set(0, 2, 0)
nec.ab.Set(1, 2, 0)
nec.ab.Set(2, 2, 1)
nec.ab.Set(3, 2, 0)
nec.ab.Set(0, 3, nec.cos*nec.x0p*nec.bjetBeta)
nec.ab.Set(1, 3, nec.sin*nec.x0p*nec.bjetBeta)
nec.ab.Set(2, 3, 0)
nec.ab.Set(3, 3, nec.mw2-nec.x0p*nec.x0p)
}
func (nec *neutrinoEllipseCalculator) neutrinoSolution() {
nec.sy = (1. / nec.sin) * (nec.x0p/nec.bjetBeta - nec.cos*nec.sx)
nec.omega = (1. / nec.sin) * (nec.lepBeta/nec.bjetBeta - nec.cos) //only the positive slope
nec.Omega = math.Sqrt(math.Max(0, nec.omega*nec.omega+1.-nec.lepBeta2))
Omega2 := nec.Omega * nec.Omega
nec.x1 = nec.sx - (1./Omega2)*(nec.sx+nec.omega*nec.sy)
nec.y1 = nec.sy - (1./Omega2)*nec.omega*(nec.sx+nec.omega*nec.sy)
nec.z2 = nec.x1*nec.x1*Omega2 - (nec.sy-nec.omega*nec.sx)*(nec.sy-nec.omega*nec.sx) - (nec.mw2 - nec.x0*nec.x0 - nec.epsilon2)
Z := math.Sqrt(math.Max(0, nec.z2))
nec.ht.Set(0, 0, Z/nec.Omega)
nec.ht.Set(0, 1, 0)
nec.ht.Set(0, 2, nec.x1-nec.lep.P())
nec.ht.Set(1, 0, nec.omega*Z/nec.Omega)
nec.ht.Set(1, 1, 0)
nec.ht.Set(1, 2, nec.y1)
nec.ht.Set(2, 0, 0)
nec.ht.Set(2, 1, Z)
nec.ht.Set(2, 2, 0)
}
func (nec *neutrinoEllipseCalculator) labSystemTransform() {
Rz := rotationMatrix(2, -nec.lep.Phi())
Ry := rotationMatrix(1, 0.5*math.Pi-thetaOf(&nec.lep))
bJetP := fmom.VecOf(&nec.bjet)
bJet_xyz := mat.NewVecDense(3, []float64{bJetP.X, bJetP.Y, bJetP.Z})
var rM mat.Dense
rM.Mul(Rz, bJet_xyz)
rM.Mul(Ry, &rM)
rA := rM.RawMatrix().Data
phi := -math.Atan2(rA[2], rA[1])
Rx := rotationMatrix(0, phi)
var R = mat.NewDense(3, 3, nil)
R.Mul(Ry.T(), Rx.T())
R.Mul(Rz.T(), R)
nec.h.Reset()
nec.h.Mul(R, nec.ht)
h := nec.h.RawMatrix().Data
hp := nec.hperp.RawMatrix().Data
copy(hp[:6], h[:6])
hp[6] = 0
hp[7] = 0
hp[8] = 1
det := mat.Det(nec.hperp) // FIXME(sbinet): work in log-space?
if det == 0 {
return
}
copy(nec.hperpInv.RawMatrix().Data, hp)
nec.hperpInv.Inverse(nec.hperpInv)
U := mat.NewDense(3, 3, []float64{
1, 0, 0,
0, 1, 0,
0, 0, -1,
})
nec.nperp.Reset()
nec.nperp.Mul(U, nec.hperpInv)
nec.nperp.Mul(nec.hperpInv.T(), nec.nperp)
// Rz := r3.NewRotation(-nec.lepton_.Phi(), r3.Vec{Z: 1})
// Ry := r3.NewRotation(0.5*math.Pi-thetaOf(&nec.lepton_), r3.Vec{Y: 1})
// bJetP := fmom.VecOf(&nec.bJet_)
// //bJet_xyz := mat.NewVecDense(3, []float64{bJetP.X, bJetP.Y, bJetP.Z})
// rA := Ry.Rotate(Rz.Rotate(bJetP))
// phi := -math.Atan2(rA.Z, rA.Y)
//
// Rz := r3.NewRotation(phi, r3.Vec{X:1})
// R := Rz.Rotate(Ry.Rotate(
// var rM mat.Dense
// rM.Mul(Rz, bJet_xyz)
}
func betaOf(p4 fmom.P4) float64 {
return p4.P() / p4.E()
}
func gammaOf(p4 fmom.P4) float64 {
b := betaOf(p4)
return 1.0 / math.Sqrt(1-b*b)
}
func thetaOf(p4 fmom.P4) float64 {
var (
px = p4.Px()
py = p4.Py()
pz = p4.Pz()
)
if px == 0 && py == 0 && pz == 0 {
return 0
}
return math.Atan2(p4.Pt(), pz)
}
func rotationMatrix(axis int, angle float64) *mat.Dense {
sin, cos := math.Sincos(angle)
switch axis {
case 0:
return mat.NewDense(3, 3, []float64{
1, 0, 0,
0, +cos, -sin,
0, +sin, +cos,
})
case 1:
return mat.NewDense(3, 3, []float64{
+cos, 0, +sin,
0, 1, 0,
-sin, 0, +cos,
})
case 2:
return mat.NewDense(3, 3, []float64{
+cos, -sin, 0,
+sin, +cos, 0,
0, 0, 1,
})
default:
panic(fmt.Errorf("invalid axis=%d", axis))
}
}