Significance

Significance estimations

ProfileLikelihood Calculator (roostats)

nominal case / no systematics:

using the entire mass range 7-14

x2 = 0.213796 +/- 0.0881078 x23 = 0.148275 +/- 0.0576889

the significance of this is 6.3 sigma

modified case i: restrict fit range

truncating the range to 8-14

x2 = 0.185549 +/- 0.0896092 x23 = 0.126762 +/- 0.064579

the significance goes down to 5.4 sigma

modified case ii: discard events

performing the nominal fit to a sub-set of the data (to inflate stat errors)

Toy-based p-value estimtation

plan: generate about 10**6 pseudo-experiments with either no systematics or latest evaluations (15% for X23 and 10% for X2)

Profile likelihood ratio

Force x2 = 1, x3 = 1

Importance Sampling

RooFitResult: minimized FCN value: -79598.1, estimated distance to minimum: 0.000187477

covariance matrix quality: Full, accurate covariance matrix

Constant Parameter Value

——————– ————

mscale_hi 1.0000e+00 mscale_pp 1.0000e+00

npow 2.3000e+00

x2 1.0000e+00 x3 1.0000e+00

Floating Parameter InitialValue FinalValue +/- Error GblCorr.

——————– ———— ————————– ——–

alpha 1.1178e+00 1.0872e+00 +/- 1.16e-01 <none>

bkg_a1_pp 3.6390e-01 2.9483e-01 +/- 8.27e-02 <none> bkg_a2_pp -4.3799e-01 -5.8112e-01 +/- 9.17e-02 <none>

decay_hi 6.0756e+00 6.5805e+00 +/- 7.83e-01 <none>

f2 1.1883e-01 1.6712e-01 +/- 2.62e-02 <none> f3 2.4369e-02 7.1444e-02 +/- 2.42e-02 <none>

mean_hi 9.4552e+00 9.4555e+00 +/- 4.18e-03 <none> mean_pp 9.4457e+00 9.4512e+00 +/- 1.12e-02 <none> nbkg_hi 1.1670e+04 1.1546e+04 +/- 1.44e+02 <none> nbkg_pp 3.3735e+02 3.8035e+02 +/- 2.32e+01 <none>

nsig1_hi 1.3177e+03 1.3158e+03 +/- 7.35e+01 <none> nsig1_pp 8.8229e+01 1.0544e+02 +/- 1.29e+01 <none>

sigma1 7.9382e-02 7.9284e-02 +/- 4.38e-03 <none>

turnOn_hi 7.8960e+00 7.7720e+00 +/- 1.89e-01 <none>

width_hi 2.2974e+00 2.2925e+00 +/- 2.56e-01 <none>

chi2/ndf = (74.997 + 71.282)/125 = 1.170 chi2 prob = 0.0938 min nll = -79598.11763910

the delta of S is : 20.1263 the delta of ndof is : 2 the C.L. is : 1 the significance level is : 6.01342 (one side)

the C.L. is : 1, the significance level is : 6.01342 sigma (one side)

evaluate significance for systematic variations back of the envelope checks

based on nominal fit results

from individual fits:

PbPb

N_{2S+3S}/N_{1S} 0.155 +/- 0.038

N_{2S}/N_{1S} 0.127 +/- 0.027

pp

N_{2S+3S}/N_{1S} 0.879 +/- 0.17 N_{2S}/N_{1S} 0.496 +/- 0.12

pp-PbPb

N_{2S+3S}/N_{1S} 0.724 +/- 0.17 N_{2S}/N_{1S} 0.369 +/- 0.12

pp-PbPb: #sigmas away from zero [note this assumes gaussian errors] 0.72/0.17 = 4.3 0.37/0.12 = 3.1

maximum significance allowed by pp data alone (assume full suppression in PbPb):

0.879/0.17=5.2 0.496/0.12=4.1

from simultaneous fit:

x23 = 0.147 +/- 0.048

x2 = 0.214 +/- 0.069

x3 = 0.059 +/- 0.060

#sigmas away from unit [note however ratio of gaussian pdf’s is not gaussian!]

(1 - 0.147) / 0.048 ~ 18

(1 - 0.214) / 0.069 ~14

Importance Sampling

#
#Guillermo Breto Rangel UPC xsection vs root(s)
#
import math
from ROOT import TCanvas, TGraph, TGraphErrors, TF1, TLegend
from ROOT import gROOT
from math import pow
from array import array

gROOT.Reset()

c1 = TCanvas( 'c1', 'A parameter as funtion of \sqrt{s}', 400, 400, 700, 500 )

#c1.SetFillColor( 42 )
#c1.SetGrid()

#n = 3
lumi = 134000
p_T = array( 'd',[0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.5] )
yields_dpT = array( 'd',[3062,2989,6050, 2426, 1687] )
dsigma_dy = array( 'd',[20539./lumi,7251./lumi,3062./lumi,2989./lumi,3191./lumi, 2426./lumi, 1734./lumi] )
err_x = array( 'd',[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.3])
err_y = array('d',[167./lumi, 70./lumi, 56./lumi, 56./lumi, 59./lumi, 50./lumi, 42./lumi])

def cross_section(eff, lumi, weighted_jpsi_yield):
    xsection = weighted_jpsi_yield/(eff*lumi)
    return xsection

lumi = 134/math.pow(10,-3)
eff_list = [1, 0.98, 0.95, 0.90, 0.85, 0.80]

weighted_jpsi_yield = round(sum(dsigma_dy),4)*lumi

for i in range(len(eff_list)):
    eff = eff_list[i]
    print "The value of the cross section for "+ eff*100+"% efficiency is "+ str(round(cross_section(eff,lumi,weighted_jpsi_yield),3))+ "mb"



print "the total cross ssection is", round(sum(dsigma_dy),4)
print dsigma_dy
n = len(p_T)
gr_dsigma_pT = TGraphErrors(7)

for i in range(7):
    gr_dsigma_pT.SetPoint(i,p_T[i],dsigma_dy[i]/(2.0*math.pi*0.2*p_T[i]))
    print p_T[i]
    print dsigma_dy[i]/(0.2*p_T[i])
    gr_dsigma_pT.SetPointError(i, 0.1, err_y[i])
    if (i == n - 1):
        gr_dsigma_pT.SetPoint(i,p_T[i],dsigma_dy[i]/(2.0*math.pi*0.6*p_T[i]))
        gr_dsigma_pT.SetPointError(i, 0.3, err_y[i])

gr = TGraphErrors(7)

for i in range(7):
    gr.SetPoint(i,p_T[i],dsigma_dy[i])
    gr.SetPointError(i, 0.1, err_y[i])
    if (i == n - 1):
        gr.SetPoint(i,p_T[i],dsigma_dy[i]/(0.6*p_T[i]))
        gr.SetPointError(i, 0.3, err_y[i])


#gr = TGraphErrors( 7, p_T, dsigma_dy, err_x, err_y )
#gr.SetLineColor( 2 )
gr.SetLineWidth( 1 )
gr_dsigma_pT.SetLineWidth( 1 )
gr_dsigma_pT.SetMarkerColor(6)
gr.SetMarkerColor( 4 )
gr.SetMarkerStyle( 21 )
gr_dsigma_pT.SetMarkerStyle( 24 )

gr.SetTitle( 'p_{T} Spectra' )
gr_dsigma_pT.SetTitle( 'UPC J/#Psi, p_{T} Spectra L = 134 #mub^{-1}' )

gr.GetXaxis().SetTitle( 'p_{T} GeV/c' )
gr_dsigma_pT.GetXaxis().SetTitle( 'p_{T} GeV/c ' )

gr.GetXaxis().SetRangeUser(0, 2)
#c1.SetLogx()
gr.GetYaxis().SetTitle( '#frac{d#sigma}{dy} (#mub)' )
gr_dsigma_pT.GetYaxis().SetTitle( 'mb or mb/(GeVc^{-1})^{2}' )
gr.GetYaxis().SetTitleOffset(1.2)
gr.GetYaxis().SetRangeUser(0, 10)
gr_dsigma_pT.GetYaxis().SetRangeUser(-10, 2)

gr_dsigma_pT.Draw('AP')
gr.Draw("psame")
#gr_dsigma_pT.Draw('same')
c1.SetLogy()

leg = TLegend(0.53,0.63,0.85,0.85)
leg.SetBorderSize(0)
leg.SetFillColor(0)
leg.SetTextSize(0.03)
leg.AddEntry(gr,"#frac{d#sigma}{dy}","P")
leg.AddEntry(gr_dsigma_pT,"#frac{d#sigma}{2#pip_{T}dydp_{T}}","P")
leg.AddEntry(gr, "the total #sigma = "+ str(round(sum(dsigma_dy),4))+" mb")
leg.Draw('same')

# TCanvas.Update() draws the frame, after which one can change it
c1.Update()
#c1.GetFrame().SetFillColor(0)
#c1.GetFrame().SetBorderSize( 12 )
#c1.Modified()
#c1.Update()
c1.Print('UPC_pt_graphlog.png')
c1.Print('UPC_pt_graphlog.pdf')

(Source code)

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