Latest results on J/ψ produc6on in pp collisions from the ALICE experiment

Transcription

1 Latest results on J/ψ produc6on in pp collisions from the ALICE experiment Claudio Geuna CEA Saclay Irfu/SPhN on behalf of the ALICE Collabora1on J/ψ candidate (3.4 GeV/c ) in pp collisions at 7 ev in the ALICE Muon Spectrometer (01/04/0) Heavy- ion Mee,ng ( IPN Orsay) 1

2 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons Results of J/ψ ev: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions

3 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons Results of J/ψ ev: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions 3

4 Physics mo1va1on: the quarkonium puzzle in pp collisions Need to understand the quarkonium produc1on mechanisms in pp collisions the hadroproduc1on of heavy quarkonium states is governed by both perturba1ve and non- perturba1ve aspects of Quantum Chromodynamics (QCD) Various theore1cal approaches have been proposed to describe the data CEM (Color evapora1on model) COM (NRQCD) (Color octet model) CSM (Color singlet model) hey mainly differ in the details of the non- perturba1ve evolu1on of the heavy quark pair towards a bound state he quarkonium produc1on has been already extensively studied at the evatron and RHIC hadron colliders he models are not able to consistently reproduce at same,me the produc,on cross sec,on, the transverse momentum (p ) distribu,ons and the polariza,on dσ/dp in pp collisions at various order in α S at s = 1.96 ev in the central ( y < 0.6 ) rapidity region compared to the CDF data ( evatron ) 4

5 Physics mo1va1on: J/ψ polariza?on he different models make different predic1ons on the degree of polariza1on of the quarkonium state CEM (Color evapora1on model) No predic1on on polariza1on (*) COM (NRQCD) (Color octet model) ransverse polariza1on at high p CSM (Color singlet model) Longitudinal polariza1on at high p Polariza1on is a good way to discriminate among the different hypothesis J/ p+p J/ +X s=00 GeV y <0.35 Helicity Frame s-channel cut CSM COM (**) 0 (*) A. Abulencia et al., he CDF Collabora1on, Phys. Rev. Lek. 99, (007) (**) Phenix Collabora1on, Phys. Rev. D 8, (0) p [GeV/c] 5

6 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons J/ψ ev, results: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions 6

7 J/ψ measurement in ALICE J/ψ in ALICE can be measured in two ways: in the central barrel in the e + e - decay channel (BR = 5.94%) in the forward spectrometer in the µ + µ - decay channel (BR = 5.93%) 3 sources of J/Ψ Inclusive J/Ψ Prompt J/Ψ Direct produc,on : ~50% J/Ψ from b- hadron decay: ~% Feed down from heavier states (χ c, Ψ ) : ~40% feasible in the central barrel, thanks to the good impact parameter resolu1on (σ rφ < 75 µm for p >1 GeV/c) ALICE results refer to inclusive J/ψ produc1on Acceptance coverage at both central and forward rapidi1es down to zero p (unique at LHC at y=0) forward detec1on more difficult 3- muon event B cross sec1on from single muon measurement 7

8 he ALICE experiment Central barrel ( η <0.9) Forward Muon spectrometer (- 4<η<-.5) he barrel detectors used in this analysis are: the Inner racking System (IS) a cylindrically- shaped silicon tracker that surrounds the central beam pipe the ime Projec1on Chamber (PC) a large cylindrical dris detector the VZERO detector consists of two scin1llator (V0A & V0C) arrays covering the range.8 < η < 5.1 and 3.7 < η < 1.7 riggers: Minimum Bias interac1on trigger (SPD or V0A or VOC) Muon trigger: required one muon in the Muon rigger chambers in coincidence with a Minimum bias trigger VZERO PC Claudio Geuna IS 8 Heavy- ion Mee1ng IPN Orsay, hu th November 011

9 he Forward Muon Spectrometer Forward MUON Spectrometer the components: Front absorber to suppress all par1cles except muons from IP (λi) Dipole magnet (B = 0.7 ) MUON tracking system: 5 sta1ons ( quadrant type and 3 slat type) chambers ( chambers/sta1on with 156 detec1on elements) required spa1al resolu1on: x (1 mm) non bending plane y (0.1 mm) bending plane Claudio Geuna racking chambers (Cathode Pad Chambers) Muon filter (7λI) rigger chambers (Resis1ve PlateChambers) 4 planes with p cut It is designed in order to have: large geometrical acceptance (- 4<η<-.5): to increase dimuon sta?s?cs acceptance down to pj/ Ψ= 0: where direct J/ψ produc?on dominates good nominal invariant mass resolu1on: ~ 70 MeV/c (J/ψ region) and ~0 MeV/c (ϒ region) tracking/trigger high granularity read- out: to cope with the high mul?plicity 9 Heavy- ion Mee1ng IPN Orsay, hu th November 011

10 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons Result of J/ψ ev: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions

11 - Data Sample J/ψ - > μ + μ - in s =.76 ev 18 runs, collected during 3 days of data taking ( pp ev ) in March 011 Runs are selected according to quality checks on the stability of the muon spectrometer tracking and trigger performances ( QA check ) he total data sample available for physics analysis corresponds to ~ 9 6 μ- MB triggers (where a Muon trigger requires one muon in the Muon rigger chambers in coincidence with a pp Minimum Bias trigger) µ + dn/dm µ 4 3 Dimuon opposite sign Mass Spectrum 0-5 GeV/c, before any Selec1on cuts L= 17.8 ± 1.4 (syst) nb - 1 Selec,on cuts at least one interac1on vertex in the silicon pixel detector (SPD) at least one muon reconstructed in the tracking and trigger chambers sa1sfying the trigger algorithm cut on the track posi1on at the end of the front absorber 17.6 < R abs < 89.5 cm.5 < y μ+μ- < 4, p J/ψ > 0 GeV/c Physics Selec,on is applied to remove beam- halo and beam- gas events Dimuon Invariant Mass M µ - [GeV/c ] + µ 11

12 Signal extrac1on (I) he J/ψ yield, N J/ψ, is extracted by fizng the invariant mass spectra (1.5 < m μμ < 6 GeV/c ) assuming: a sum of two exponen6als for the underlying con,nuum (background) different shapes for the J/ψ signal have been used Integrated spectrum 1. Crystal Ball shape with free tail. Crystal Ball shape with tail fixed to MC simula1ons 3. Double Crystal Ball shape with tails fixed to MC simula1ons 4. NA60 func1on m J/ψ and σ J/ψ are kept as free parameters Differen,al spectra ( p and y ) Crystal Ball shape with tail fixed to MC simula1ons with different approaches for σ J/ψ 1. σ J/ψ free. σ J/ψ fixed taking into account the MC evolu1on bin by bin m J/ψ kept as free parameter Reminder, Crystal Ball func?on: f(x; α,n, x, σ) =N A =( n α )n exp( α ), B = n α α, exp( (x x) σ ), for x x σ > -α A (B x x σ ) n, for x x σ -α he Crystal Ball func1on is a probability density func1on and it consists of a Gaussian core por1on and a power- law low- end tail, below a certain threshold. Prac1cally, the Gaussian shape is connected to a power- law tail at α sigma of the Gaussian. 1

13 dn/dm µµ Integrated spectrum 3 pp, s =.76 ev Signal extrac1on (II) ALICE Performance N J/ 1/05/011 = 187 ± 48 Dimuon opposite sign Mass Spectrum ( GeV/c, all cuts applied ) Fit performed between GeV/c J/ψ signal: Crystal Ball shape with tail fixed to MC simula1ons ψ parameters bound to the J/ψ J/ψ yield coming from the different extrac1on methods Raw Yield J/! (GeV/c ) M µµ m J/ψ = 3.14 ± GeV/c σ J/ψ = 91 ± 3 MeV/c N J/ψ = 187 ± 48 (stat) ± 77 (syst) S/B (3σ) CB tail MC fixed used to extract the J/ψ cross sec1on Double CB tails MC fixed CB tail MC fixed CB free tail NA60 function Different extrac1on methods - > systema,cs on signal extrac1on 13

14 Acceptance and efficiency correc1ons o obtain the J/ψ yield required for the cross sec1on, the number of raw J/ψ events extracted must be corrected with a MC procedure: correc1on for the acceptance of the apparatus and for reconstruc1on and triggering efficiencies simula,on of a large sample of J/ψ signal events (~ 1 x 6 J/ψ generated in total ) with : Acc ε vs p (1D correc6on) p distribu6on extrapolated from CDF measurements y distribu6on parameterized from Color Evapora6on Model (CEM) calcula6ons Simula1ons are performed run by run : taking into account the realis1c condi1on of the detector genera1ng a number of J/ψ propor1onal to the integrated luminosity the acceptance and efficiency correc1ons are calculated separately for p and y (1D) J/ψ produc1on done with 3 different polariza,on scenarios 14

15 Acceptance and efficiency correc1ons o obtain the J/ψ yield required for the cross sec1on, the number of raw J/ψ events extracted must be corrected with a MC procedure: correc1on for the acceptance of the apparatus and for reconstruc1on and triggering efficiencies simula,on of a large sample of J/ψ signal events (~ 1 x 6 J/ψ generated in total ) with : Acc ε vs y (1D correc6on) p distribu6on extrapolated from CDF measurements y distribu6on parameterized from Color Evapora6on Model (CEM) calcula6ons Simula1ons are performed run by run : taking into account the realis1c condi1on of the detector genera1ng a number of J/ψ propor1onal to the integrated luminosity the acceptance and efficiency correc1ons are calculated separately for p and y (1D) J/ψ produc1on done with 3 different polariza,on scenarios 15

16 J/ψ - > e + e - in s =.76 ev Analysis is based on L= 1.1±0.1 nb - 1 y J/ψ <0.9, p J/ψ >0 GeV/c rack selec,on: η e+,e- <0.9 and y J/ψ <0.9 p e+,e- > 1 GeV/c racks with hits in the PC and IS (at least one in the pixel detector) Electron PID based on PC de/dx Signal extrac,on: Yield extracted from bin coun1ng (above like- sign background) in M e+e- = GeV/c N J/ψ = 41 ± 9 16

17 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons Result of J/ψ ev: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions 17

18 J/ψ in s =.76 ev: integrated cross sec1on! J " = N J " (Acc J "!#)! BR! 1 L o get the integrated produc1on cross sec1on, σ J/ψ, the ra1o N J/ψ corr = N J/ψ /(Acc J/ψ ε) BR must be normalized to the integrated luminosity L L is calculated using, as reference, the cross sec1on of minimum bias collisions σ MB ( derived from a Van der Meer scan) J/ψ à µ + µ - N J/ψ = 187 ± 48 (stat) ± 77 (syst) Axε = 0.35 ± (stat) ± (syst) BR (J/ψà µ + µ - ) = ± (syst) L int = 17.8 ± 1.4 (syst) nb - 1 J/ψ à e + e - N J/ψ = 41 ± 9 (stat) ± 3 (syst) Axε= ± (stat) ± (syst) BR (J/ψà e + e - ) = ± (syst) L int = 1.1 ± 0.1 (syst) nb (.5 < y < 4) = 3.46 ± 0.13( stat) ± 0.3( syst) ± 0. ( lumi) ( pol) b 55 σ J / ψ µ + 0. ( y < 0.9) = 6.44 ± 1.4( stat) ± 0.88( syst) ± 0. ( lumi) ( pol) b 64 σ J / ψ µ σ J/ψ is obtained at the same energy as the PbPb data it is used as the pp reference in the J/ψ R AA evalua,on 18

19 J/ψà µ + µ - : invariant mass in p and y bins A differen1al study of J/ψ produc1on has been performed in the two kinema1c variables : y and p separately dσ J/ψ /dp is studied in 7 bins { 0-1, 1-, - 3, 3-4, 4-5, 5-6, 6-8 GeV/c } dσ J/ψ /dy is studied in 6 bins {.5 < y < 4 } dn/dm µµ 3 0< p <1 GeV/c N J/ =14 ± 18 dn/dm µµ 3 1< p < GeV/c N J/ =373 ± 3 dn/dm µµ 3 < p <3 GeV/c N J/ =39 ± 1 dn/dm µµ 3 3< p <4 GeV/c N J/ =193 ± 16 pp, s =.76 ev ALICE Performance 1/05/ M µµ (GeV/c ) M µµ (GeV/c ) M µµ (GeV/c ) M µµ (GeV/c ) dn/dm µµ 3 4< p <5 GeV/c N J/ =90 ± 11 dn/dm µµ 3 5< p <6 GeV/c N J/ =53 ± 8 dn/dm µµ 3 6< p <8 GeV/c N J/ =9 ± 6 Fit between GeV/c J/ψ signal: Crystal Ball shape tail fixed to MC simula1ons σ J/ψ fixed taking into account the σ s MC evolu1on bin by bin M µµ (GeV/c ) M µµ (GeV/c ) M µµ (GeV/c ) 19

20 J/ψà µ + µ - : differen1al p distribu1on he differen1al cross s =.76 ev d σ J/ψ /dydp, averaged over the interval.5 < y < 4, for the transverse momentum range 0 < p < 8 GeV/c is presented below (µb / GeV/c) J/ /dydp d 1-1 he results are compared with the previously published s = 7 ev (K. Aamodt et al. (ALICE Collabora1on), Phys. Lek. B (011)) he predic1ons of a NRQCD calcula1on (*), which includes both colour singlet and colour octet terms at NLO order, are ploked for the two energies in the range 3 < p < 8 GeV/c. - pp,.5<y<4-1 s=7 ev, L=13.3 nb -1 s=.76 ev, L=0. nb (preliminary) s=7 ev, CS+CO NLO (M. Butenschoen et al., arxiv:15.080) s=.76 ev, CS+CO NLO (M. Butenschoen et al., priv. comm.) (GeV/c) p Good agreement between the model (NLO NRQCD calcula1ons) and both sets of experimental data (*) M. Butenschoen and B.A. Kniehl, Phys. Rev. D84, (011) and priv. comm. Boxes: systema1c uncertain1es on Luminosity Bars: quadra1c sum of the sta1s1cal errors and the other sources of systema1c uncertainty 0

21 J/ψ à µ + µ - : <p > and <p > Using the results shown in the previous slide we can compute the <p > and <p > for inclusive J/ψ produc1on at forward rapidity y by fizng d σ J/ψ /dydp with the following func1on: with C, p 0 and x as free parameters (this func1on is widely used in the literature for such a kind of fits ) > (GeV/c) <p he ALICE results can be compared to results from other experiments Inclusive J/ production ALICE.5<y<4, p <8 GeV/c LHCb.5<y<4, p <14 GeV/c (prompt J/ ) LHCb.5<y<4, p <14 GeV/c (J/ from B) PHENIX 1.< y <. PHENIX y <0.35 HERAB NA3 > (GeV/c) <p Inclusive J/ production ALICE.5<y<4, p <8 GeV/c PHENIX 1.< y <. PHENIX y <0.35 HERAB E866 NA50 NA3 NA ALICE Preliminary 3 s 1/ ALICE Preliminary Approximately logarithmic increase with s con1nues up to LHC energy 3 s 1/ 4

22 J/ψà µ + µ - : differen1al y distribu1on he differen1al cross sec1on dσ J/ψ s =.76 ev is presented below with the previously published s = 7 ev (K. Aamodt et al. (ALICE Collaboration), Phys. Lett. B (011)) J/ψ produc1on cross sec1on measured in the two rapidity ranges covered by the ALICE experiment Boxes: systema1c uncertain1es on Luminosity Bars: quadra1c sum of the sta1s1cal errors and the other sources of systema1c uncertainty

23 Plan Physics mo1va1on he ALICE experiment Analysis of the J/ψ ev Data sample & Selec1on cuts Signal extrac1on Acceptance and efficiency correc1ons Result of J/ψ ev: Integrated cross sec1on Differen1al p and y cross sec1ons Report on other J/ψ studies Conclusions 3

24 Physics mo,va,on J/ψ produc1on versus dn ch ev (I) ALICE has measured the charged par1cle mul1plicity distribu1on at s = 7 ev pp collisions (*) he highest charged par1cle mul1plicity (dn ch /dη max ~30) reached in 7 ev is comparable with CuCu collisions (50-55%, semi peripheral 00 GeV (RHIC) Quarkonia, bound states of heavy (charm or bokom) quarks such as the J/ψ, are important probes of QGP Analysis: Studying the mul,plicity dependence of J/ψ produc,on in pp collisions at LHC energies might unveil the final- state effects present in heavy- ion collisions Conclusions on QGP- induced phenomena require all non- QGP effects influencing quarkonia yields are well understood. ALICE performs the measurement of the mul1plicity dependence of J/ψ in both leptonic decay channel ( e + e - in the central barrel and μ + μ - in the Forward Muon Spectrometer ) he number of tracklets in the SPD (part of IS) within the pseudorapidity range of η < 1.6 is used for the measurement of the mul1plicity in this analysis. he variable of choice for the mul1plicity is the rela1ve charged par1cle density : dn ch R d! = dn ch / d!!=0 < dn ch / d!!=0 > his study will go up to dn ch /dη η=0 5.5 <dn ch /dη η=0 > (*) K. Aamodt et al.: Charged- Par1cle Mul1plicity Measurement in pp Collisions at s = 7 ev with ALICE at LHC, EPJ C68 (0) 345 4

25 Result: Y R = Y (dn R J/! ch / d") J/! inclusive Y J/! Y R Highp µ = Y Highp µ (dn R ch / d!) inclusive Y Highp µ J/ψ produc1on versus dn ch ev (II) wo observables have been considered he rela1ve yield Y R J/ψ is the J/ψ yield as a func1on of the mul1plicity over the J/ψ inclusive yield per pp inelas1c collisions he rela1ve yield Y R High p μ is the High p μ yield as a func1on of the mul1plicity over the High p μ inclusive yield per pp inelas1c collisions = J/ yield over inclusive J/ yield R J/ Y 9 ALICE Preliminary pp at s = 7 ev J/ ee ( y < 0.9) J/ µµ (.5 < y < 4.0) Global systematic error : 8% µ High p over Y R J/ Y R < y J/ p J/ ALICE Preliminary s = 7 ev pp at < 4.0 > 0.0 GeV/c.5 < High P µ 4.0 < p High p µ < 4.0 < 8.0 GeV/c µ composition : ~18%, K, ~8% HF R dn ch /d = dn ch /d =0 <dn ch /d > =0 he rela1ve J/ψ yield, to a good approxima1on, linearly increases with charged par1cle mul1plicity (similar results in e + e - μ + μ - ) R dn ch /d = dn ch /d =0 <dn ch /d J/ψ yield increases more slowly wrt High p muons (from heavy flavour decays). his result is not expected, since the J/ψ and High p μ share the same ini1al effects. > =0 heore,cal interpreta,ons needed! he limited sta1s1cs of the present results do not allow for a final conclusion 5

26 Latest ALICE results on J/ψ 7 ev EUROPEAN ORGANIZAION FOR NUCLEAR RESEARCH CERN-PH-EP v1, 7 November 011 J/! polarization in pp collisions at s=7 ev arxiv: v1 [hep-ex] 7 Nov 011 he ALICE Collaboration Abstract he ALICE Collaboration has studied J/! production in pp collisions at s = 7eVattheLHC through its muon pair decay. he polar and azimuthal angle distributions of the decay muons were measured, and results on the J/! polarization parameters "# and "$ were obtained. he study was performed in the kinematic region.5 < y < 4, < pt < 8GeV/c, inthehelicityandcollins-soper reference frames. he results for "# in the helicity frame show a longitudinal polarization at low pt, vanishingwith increasingtransverse momentum. All the other polarizationparametersareconsistent with zero, within uncertainties. submiued on Monday 7 November 011 arxiv: See Appendix A for the list of collaboration members 6

27 J/ψ 7 ev (I) he J/ψ polariza1on is a crucial observable for comparison between data and theory Puzzling results from previous experiment (CDF, Phenix, ) he analysis release by the ALICE has been carried out on a significant frac1on of the 0 data integrated luminosity L int 0 nb 1 the J/ψ polariza,on can be obtained measuring the polar and azimuthal angle distribu,ons (full angular distribu,on) of the decay muons he distribu,on of the J/ψ decay products can be expressed in its general form as: W (!,")! 1 3+ #! (1+ #! cos! + # " sin! cos" + #!" sin! cos") where θ (φ) are the polar (azimuthal) angles in a given reference frame. wo reference frames, Collins- Soper (CS) and Helicity (HE) considered in the analysis he three parameters λ θ, λ φ and λ θ φ enable us to quan1fy the degree of polariza1on In par1cular, a transverse polariza1on gives λ θ > 0 a longitudinal polariza1on gives λ θ < 0. Due to the limited J/ψ sta1s1cs (about signal events in the p range under study) the study of the angular distribu1ons was separately performed on the polar and azimuthal variables 7

28 J/ψ 7 ev (II) Fizng the acceptance corrected angular distribu1ons for the J/ψ decay muons we can finally obtain the parameters λ θ and λ φ for inclusive J/ψ produc1on in the kinema1cal region.5 < y < 4, < p < 8 GeV/c Result: he results for λ θ in the Helicity reference frame show a longitudinal polariza1on at low pt, vanishing with increasing transverse momentum. In the Collins- Soper frame λ θ is consistent with no polariza1on he λ φ parameter is found to be consistent with zero within errors, in both reference frames. hese results can be used as a constraint on the commonly adopted QCD framework for heavy quarkonium produc1on 8

29 Conclusion he latest ALICE results on J/ψ produc1on in pp collisions have been presented integrated produc1on cross sec1on σ J/ψ at s =.76 ev both in the dimuon and dielectron decay channels. Results are used as reference for the PbPb R AA evalua1on d σ/dydp and dσ/dy for inclusive J/ψ produc1on in the dimuon decay channel. Results are in good agreement with NLO NRQCD calcula1ons J/ψ yield shows a linear increase as a func1on of dn ch /dη. heore1cal interpreta1on needed New ALICE publica1on on J/ ψ polariza1on measurement: the results for λ θ in the helicity frame show a longitudinal polariza1on at low p, vanishing with increasing transverse momentum. All the other polariza1on parameters are consistent with zero, within uncertain1es. Paper in prepara,on updated results very soon Paper in prepara,on updated results very soon Merci! 9

30 Backup slides 30

31 J/ψà µ + µ - : dσ J/ψ /dy wo ALICE measurements: central and forward rapidity range One CMS point: the rapidity coverage is complementary with the ALICE s one heore1cal predic1ons: CEM predic1on vs CSM predic1on 31

32 Crystal Ball defini1on Reminder : f(x; α,n, x, σ) =N exp( (x x) σ ), for x x σ > -α A (B x x σ ) n, for x x σ -α where A =( n α )n exp( α ), B = n α α, he Crystal Ball func1on is a probability density func1on and it consists of a Gaussian core por1on and a power- law low- end tail, below a certain threshold. Prac1cally, the Gaussian shape is connected to a power- law tail at α sigma of the Gaussian. he sign of α determines if it happens on the les or right side. he n parameter control the slope of the power- law part ( n should be posi1ve for the func1on to make sense as a p.d.f ). 3

33 Double Crystal Ball defini1on 33

34 Signal extrac1on (p and y) 34

35 J/ψ in s =.76 ev: systema1cs uncertain1es Summary table Source of systema1c uncertainty J/ψà µ + µ - J/ψà e + e - signal extrac1on 6 % 8.5 % Acceptance inputs.5% 1 % rigger efficiency 4% - Reconstruc1on efficiency 4% 11 % rigger enhancement 3% - Luminosity 8% 8 % otal systema1c uncertainty 1.1 % 16.1% Polariza1on λ=- 1 λ=+1 λ=- 1 λ=+1 Collins- Soper % % Helicity +4-1 % % 35