Studying Evolution with Jets at STAR. Renee Fatemi University of Kentucky May 28 th, PDF Free Download

Studying Evolution with Jets at STAR Renee Fatemi University of Kentucky May 28 th, 2015

Relativistic Heavy Ion Collider Absolute Polarimeter (H jet) RHIC pc Polarimeters Siberian Snakes PHOBOS PHENIX Siberian Snakes Siberian Snakes BRAHMS STAR Spin Rotators (longitudinal polarization) Pol. H - Source Solenoid Partial Siberian Snake LINAC BOOSTER AGS 200 MeV Polarimeter Rf Dipole Spin flipper Spin Rotators (longitudinal polarization) Helical Partial Siberian Snake AGS Internal Polarimeter AGS pc Polarimeters Strong Helical AGS Snake The Relativistic Heavy Ion Collider is the worlds first and only polarized proton colider. It can provide both longitudinal and transversely polarized proton beams.

STAR s large acceptance allows for jet reconstruction and charged hadron particle identification. η = -ln[tan(θ/2)] Barrel Electromagnetic Calorimeter Time Projection Chamber Endcap Electromagnetic Calorimeter

Parton distribution functions in the Proton f (x) Δf (x) Δ T f (x) Number density of partons with flavor f and momentum fraction x inside a nucleon Number density of longitudinally polarized partons inside longitudinally polarized nucleons (Helicity) Number density of transversely polarized partons inside a transversely polarized nucleon (Transversity) Nucleon Momentum

CT10 NNLO Momentum Distributions Phys. Rev. D 89 033009 (2014)

Inclusive Jet Cross- sections http://projects.hepforge.org/fastnlo/form/index.html STAR inclusive jet crosssection data accesses lowest Q 2 scales to date. Currently Tevatron Run-I inclusive jet data are excluded from CT10 NNLO. STAR data is not included. What impact could we provide?

CT10 NNLO & CT10W NLO Comparison Phys. Rev. D 89 033009 (2014) At large x g(x,q) is reduced in CT10 NNLO compared to CT10W due to removal of Run-I Tevatron data. At s = 200 GeV high p T jets from pp collisions at RHIC push into the high x region where PDF uncertainties start to quickly rise.

Jet Reconstruction at STAR Before 2009 STAR used Mid-point cone algorithm Adapted from Tevatron II hep-ex/ 0005012 o Seed E = 0.5 GeV o Cone Radius R = 0.7 in η-φ space o Split/merge fraction f = 0.5 Starting in 2009 STAR moves to Anti-k T algorithm Cacciari, Salam, and Soyez, JHEP 0804, 063 o Recombination radius R = 0.6 for 200 GeV o Recombination radius R = 0.5 for 500 GeV

STAR 2009 inclusive jet cross section η <1.0

STAR 2009 inclusive jet cross section η <0.5

STAR 2009 inclusive jet cross section 0.5< η <1.0

Comparisons of STAR data to C10 NLO QCD Evolution Workshop 2015

Gluon Helicity Distributions DSSV NNPDF 1.1 Phys. Rev. Lett. 113 (2014) 012001 Nucl. Phys. B, Volume 887 (2014) 276-308

Recent s = 200 GeV jet A LL arxiv:1405.5134 2009 STAR inclusive jet A LL measurements are a factor of 3 4 more precise than the 2006 results. A LL falls in the middle among several recent polarized PDF fit predictions A LL is somewhat larger than predictions from the 2008 DSSV and NNPDF1.0 indicating a positive Δg in the accessible x region.

First s = 500 GeV jet A LL! Provides first access to lower x Results are in excellent agreement with newest DSSV and NNPDF NLO predictions!

Forward A LL accesses x ~ 10-3 region Neutral pion A LL at s= 500 GeV in the STAR Forward Meson Spectrometer ( 2.5 < η < 4)

1 dx g(x,q 2 ) x min 1 0.8 0.6 Q 2 = 10 GeV 2 DSSV 2014 with 90% C.L. band projection with RHIC data 2015: STAR: 1-jet 200 & 510 GeV PHENIX: incl. π 0 510 GeV at mid & fwd rapidity RHIC impact on ΔG DSSV Phys.Rev.Lett. 113 1, 012001 (2014) 0.4 ΔG (x > 0.05) = 0.2 (+0.06/- 0.07) NNPDF 0.2 Nucl.Phys.B887, 276-308 (2014) 0 ΔG (0.2 > x > 0.05) = 0.17 (+/- 0.06) 10-6 10-5 10-4 10-3 10-2 10-1 1 x min RHIC Spin Whitepaper arxiv:1501.01220

Transversity Distributions COLLINS : Simulatneous fit of HERMES p, COMPASS p & d and Belle data è IFF: Simulatneous fit of HERMES p, COMPASS p & d and Belle data ê Phys.Rev. D87 (2013) 094019 JHEP 1303 (2013)

What about pp Collisions? Since Δ T f(x) is CHIRAL ODD must access it by coupling to a second chiral odd function. Ralston and Soper proposed Drell- Yan but ú ú low rates compared to other hadronic processes anti- quark transversity is likely very small Could also look at inclusive jet A TT in pp collisions, however ú ú Gluons are abundant and have ZERO transversity A TT < A LL due to Soffer bound Phys.Rev. D65 (2002) 114024

STAR Inclusive Jet A TT In 2006 STAR collected 2 pb -1 of transversly polarized s= 200 GeV data Data integrates over 7.5 < jet pt < 40 GeV Data Precision ~0.005 Maximized signal for jet pt = 10 GeV is ~0.001 Requires at LEAST x25 more data to make a significant measurement. Possibly 2015 RHIC run? Phys.Rev. D86 (2012) 32006

Look Instead to the Final State! Couple a chiral odd fragmentation function with quark Δ T f(x) Correlation between spin of transversely polarized quark and transverse momentum kick given to fragmentation hadron. S Q S Q (P Q P H ) P H S Q P H+ Correlation between spin of transversely polarized quark and momentum cross- product of dihadron pair. P H- S Q ( xp H+ )

Look Instead to the Final State! Couple a chiral odd fragmentation function with quark Δ T f(x) Does not survive integration over transverse momentum of hadron j T with respect to the jet axis. Needs Transverse Momentum Dependent framework! S Q S Q (P Q P H ) P H j T S Q P H+ The center of mass of the hadron pair is traveling collinear with the jet axis. IFF survives integration over j T of hadrons and therefore works in collinear framework. P H- R = ½ S Q ( +P H+ ) R

Unique contributions from pp? 0.2 0.18 0.16 ± p + p jet + π PYTHIA 6.4.22 Perugia 0 Tune + X at s = 200 GeV x F x F > 0 < 0 0.14 *Excluded: 0.12 qq q'q' qq gg 0.1 gg qq 0.08 0.06 0.04 0.02 Phys. Rev. D 87 094019 (2013) 0-3 -2.5-2 -1.5-1 -0.5 0 Log(x) How do Collins and Interference FF evolve with Q 2? Are the Collins and Interference FF universal? What are the size of factorization breaking effects for Collins in pp?

Full Disclosure Subprocess Fraction 0.6 0.5 0.4 0.3 0.2 gg qq+qq' qg pp jet+x NLO CTEQ6M Anti-kT R=0.6 η <1 0.1 Solid: Dotted: s=200 GeV s=500 GeV 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Jet x (= 2p / s) T T GLUONS dominate at low jet transverse momentum - need to place cut to minimize dilution to asymmetries.

SSA in pp sensitive to Transversity: Azimuthal distributions of pions in Jets φ S is defined as the angle between proton spin and reaction plane S ΦS pπ jt Φh pbeam j T defines particle transverse momentum in jet φ H defines angle between jet particle transverse momentum and reaction plane φ C = φ S - φ H (Collins Angle) pbeam PJET N N N + N ϕ sinϕ ( C ) = A C UT sin( ϕ C ) Δ T q H 1

2006 A UT COLLINS of Leading Charged Pions in Mid- Rapidity Jets at STAR in 200 GeV AIP Conf. Proc. 1441, 233 (2012) Average π + asymmetry = 0.02082 +/- 0.0064 +/- 0.02306 Average π - asymmetry = - 0.0040 +/- 0.0068 +/- 0.02306

Mid- rapidity Predictions from D Alesio, Murgia and Pisano Presented at Transversity 2014 and based on work from PRD 83 034021 (2011)

2012 A UT COLLINS vs. j T at 200 GeV (xf>0) 0.04 π + π - x F > 0 STAR Preliminary s p x F < 0 ) H p beam - p beam φ - S sin(φ A UT 0 x F > 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Jet p T 16 12 8 10 < Jet p T < 31.6 GeV/c Z 0.75 0.5 0.25 0.1 < z < 0.6-1 10 1 j [GeV/c] T

2012 A UT COLLINS vs. j T at 200 GeV (x F <0) 0.04 π + π - x F < 0 STAR Preliminary s p x F < 0 ) H p beam - p beam φ - S sin(φ A UT 0 x F > 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Jet p T 16 12 8 10 < Jet p T < 31.6 GeV/c Z 0.75 0.5 0.25 0.1 < z < 0.6-1 10 1 j [GeV/c] T

200 GeV A UT COLLINS vs. z x F < 0 s p p beam - p beam 0.04 π + π - x F > 0 STAR Preliminary x F > 0 - φ H ) S sin(φ A UT 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Jet p j T T 16 12 8 1.5 1 0.5 10 < Jet p T 0.125 < j T < 31.6 GeV/c < 4.5 GeV/c 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Z

200 GeV A UT COLLINS vs. z x F < 0 s p p beam - p beam 0.04 π + π - x F < 0 STAR Preliminary x F > 0 - φ H ) S sin(φ A UT 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Jet p j T T 16 12 8 1.5 1 0.5 10 < Jet p T 0.125 < j T < 31.6 GeV/c < 4.5 GeV/c 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Z

Higher Q 2 and same x T? s= 200 vs 500 GeV p ± + p jet + π + X ) -φ H S sin(φ UT A 0.05 0 STAR Preliminary R min p = 1.3 GeV/c T,jet Once scaled to same x T and average j T the 200 and 500 GeV asymmetries are similar. -0.05 0.05 0-0.05 - Closed points: π + ; Open points: π s = 200 GeV, p T,jet s = 500 GeV, p T,jet = 12.9 GeV/c = 31.0 GeV/c 0.2 0.4 0.6 z 3.2 GeV/c Is this evidence for small evolution effects?

Reduced uncertainties with additional data s=200 GeV in 2015 and s=500 GeV in 2017

Collecting first data set of p+au at s=200!

Additional moments can be and have been measured! Linearly polarized gluons Sensitive to Sivers

SSA in pp sensitive to Transversity: Di- hadron pairs R = ½ ϕ S : Angle between scattering plane and spin ϕ R : Angle between scattering plane and R vector ϕ SR = ϕ S - ϕ R N N N + N ϕ sinϕ ( SR) = A SR UT sin( ϕ SR ) Δ T q H q

arxiv: 1504.00415 2006 A UT IFF vs. M inv s = 200 GeV

200 GeV A UT IFF vs. M inv

AUT 0.08 0.06 0.04 0.02 2012 A UT IFF vs. M inv s = 200 GeV x10 more data than before! P + T,M + inv hp T i =10.49 0 hp T i =7.16 hp T i =5.66 hp T i =4.47 hp T i =3.57 > 0 0 0.02 1.5 1 M π + π inv GeV/c 2 0.5 4 6 8 P π + π T GeV/c 10 QCD Evolution Workshop 2015

2012 A UT IFF vs. M inv s = 200 GeV x10 more data than before! AUT 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 P + hp T i =10.49 hp T i =7.16 hp T i =5.66 hp T i =4.47 hp T i =3.57 T,M + > 0 inv AUT 0.08 0.06 0.04 0.02 0 0 0.01 P " P! + + X at p s =200GeV STAR preliminary 0.02 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 M π + π inv GeV/c 2 0.02 1.5 1 M π + π inv GeV/c 2 0.5 4 6 8 P π + π T GeV/c 10 QCD Evolution Workshop 2015

2012 A UT IFF vs. M inv s = 200 GeV x10 more data than before! 0.08 AUT 0.07 0.06 0.05 0.04 0.03 0.02 0.01 hp T i =10.49 hp T i =7.16 hp T i =5.66 hp T i =4.47 hp T i =3.57 AUT 0.08 0.06 0.04 0.02 0 0 0.01 P " P! + + X at p s =200GeV STAR preliminary 0.02 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 M π + π inv GeV/c 2 0.02 1.5 1 M π + π inv GeV/c 2 0.5 4 6 8 P π + π T GeV/c 10 QCD Evolution Workshop 2015

2011 π+π- IFF at s = 500 GeV Increasing asymmetry with increasing pt - similar to 200 GeV but overall suppression in magnitude

2012 π+π- IFF at s = 500 GeV Trend is same as 200 GeV but asymmetries are smaller. Again due to higher gluon dilution and effective lower x values.

Conclusions INCLUSIVE JET CROSS- SECTION at s= 200 GeV - Good agreement with CT10 NLO calculations - First STAR inclusive jet cross- section with anti- kt algorithm - Investigation into constraints placed on gluon momentum distribution ongoing. STAR inclusive jet A LL from 2009 run, together with PHENIX π 0 A LL, gives first evidence of non- zero ΔG in the range of x g > 0.05. First inclusive jet A LL and forward π 0 A LL at s=500 GeV opens the door to lower x measurements at STAR. STAR s measurements of IFF and Collins SSA over a range of s provide insight Q 2 evolution of the transversity PDF, Collins FF & IFF. QCD Evolution Workshop 2015

Thank you QCD Evolution Workshop 2015

STAR Transverse pp Running è è è YEAR s [GeV] STAR Pol [%] 2001 (Run 1) 200 0.15 pb -1 15 2003 (Run 3) 200 0.25 pb -1 30 2005 (Run 5) 200 0.1 pb -1 47 2006 (Run 6) 200 8.5 pb -1 57 2006 (Run 6) 62.4 / 53 2008 (Run8) 200 7.8 pb -1 45 2011 (Run11) 500 25 pb -1 48 2012 (Run12) 200 22 pb -1 59 2015 (Run15) 200 53 pb -1 55 RHIC provides a wide range of center of mass collision energies allowing for the study of transversity and fragmentation FF evolution.

1.5 DIS + SIDIS 90% C.L. constraint DSSV 2014 with 90% C.L. band RHIC projection data 2015 EIC projection s = 78 GeV RHIC impact on ΔG 1 dx g x min 1 0.5 proton spin DSSV Phys.Rev.Lett. 113 1, 012001 (2014) ΔG (x > 0.05) = 0.2 (+0.06/- 0.07) 0 NNPDF Nucl.Phys.B887, 276-308 (2014) Q 2 = 10 GeV 2-0.5 10-5 10-4 10-3 10-2 10-1 x min 1 ΔG (0.2 > x > 0.05) = 0.17 (+/- 0.06) Special thanks to DSSV for this plot!

Charged pion identification Pions identified from TPC track de/dx Use - 1 < n σ (π) < 2.5 cut to identify pions 2012 Tranverse Data n σ (π) (+ Particles) 6 10 16 14 12 10 8 6 4 2 All Particles + K, p π + + e Accepted Range n σ ( π ) = 1! ln de dx $ obs σ # exp " de dx & π,calc % 0-10 -8-6 -4-2 0 2 4 6 8 10 Kaons, protons, and electrons contaminate the pion sample This contamination is p T independent for Collins (3% of sytematic err) and ranges from 3 17% for IFF. Nucl.Instrum.Meth. A558:419-429,2006

- S φ H ) 2012 200 GeV A UT COLLINS vs. p T (x F > 0) 0.04 π + π - x F > 0 STAR Preliminary sin(φ A UT 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Z 0.75 0.5 0.25 0.1 < z < 0.6 j T 1.5 1 0.5 0.125 < j T < 4.5 GeV/c 5 10 15 20 25 30 Particle Jet p [GeV/c] T

- S φ H ) 2012 200 GeV A UT COLLINS vs. p T (x F < 0) 0.04 π + π - x F < 0 STAR Preliminary sin(φ A UT 0-0.04 p + p jet + ± π + X at 5.6% Scale Uncertainty Not Shown s = 200 GeV Z 0.75 0.5 0.25 0.1 < z < 0.6 j T 1.5 1 0.5 0.125 < j T < 4.5 GeV/c 5 10 15 20 25 30 Particle Jet p [GeV/c] T

2011 A UT COLLINS vs. Z at s= 500 GeV ) - sin( H S UT ± 0.1 p + p jet + + X at s = 500 GeV Anti-k T, R = 0.6 0.01 sin(φ A S φ H π ) N A 0-0.1 0 < < 1 jet p = 9.5 GeV/c T,jet -1 < < 0 jet p = 9.5 GeV/c T,jet 0.005 π + 0.1 + - 0 0-0.1 0-0.1 0 < < 1 jet p = 20.1 GeV/c T,jet 0.1 0 < < 1 jet p = 29.6 GeV/c T,jet 0.2 0.4 0.6-1 < < 0 jet p = 20.1 GeV/c T,jet -1 < < 0 jet p = 29.6 GeV/c T,jet 0.2 0.4 0.6 z -0.005 0 < η SIDIS 1 j < 1 SIDIS 2-0.01 0 0.2 0.4 0.6 0.8 1 z π Low p T projection for s = 500 GeV Based on work in PRD 83 034021 (2011) Asymmetries consistent with zero across the board - BUT gluon dilution larger and average x is smaller for given jet pt! Need more statistics for definitive answer! Projections for 500 GeV predict nothing larger than 1% at high z

Partial Wave Expansion sin H^1 (z,cos,m + inv 2 ) H^1,ot (z,m + inv +H^1,lt (z,m + inv 2 )sin 2 )sin cos P/P wave interference Interference of L=1 unpolarized pair and L=1 transversely polarized pair S/P wave interference Interference of L=0 unpolarized pair and L=1 transversely polarized pair P wave contributions come from a spin-1 resonance ( 770 MeV ) expect higher asymmetry around.8 GeV 58

Asymmetry as function of < expected to show minimal asymmetry. From unpolarized beam. 0.04 M + inv, 0.05 0.04 0.03 P " P! + + X at p s =200GeV STAR preliminary + h i =0.84 h i =0.25 h i = 0.25 h i = 0.84 AUT 0.02 0 AUT 0.02 0.01 0 0.01 0.02 1 0.5 0 η π + π 0.5 0.02 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 M π + π 1 0.2 0.4 inv GeV/c 2 0.6 0.8 1 1.2 M π + π inv GeV/c 2 1.4 QCD Evolution Workshop 2015

Asymmetry as function of AUT 0.08 0.06 0.04 0.02 0 P + T, AUT 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.01 P " P! + + X at p s =200GeV STAR preliminary h i =0.84 h i =0.25 h i = 0.25 h i = 0.84 + 0.02 1 0.5 0 η π + π 0.5 0.02 3 4 5 6 7 8 9 10 11 P π + π T GeV/c 1 3 4 5 6 7 8 9 P π + π T GeV/c 10 11 QCD Evolution Workshop 2015

2011 500 GeV IFF Extract A UT Particle p T > 1.5 GeV/c STAR Preliminary fit = A UT sin ( φ RS ) Pair p T > 3.75 GeV/c For a given M Inv, p T bin the asymmetry is calculated for 8 φ RS bins The asymmetry is the amplitude extracted from a single- parameter fit Example shown here is one M Inv, p T bin

2011 π+π- IFF at s = 500 GeV Increasing asymmetry with increasing pt - similar to 200 GeV but overall suppression in magnitude

Studying Evolution with Jets at STAR. Renee Fatemi University of Kentucky May 28 th, 2015