drachenberg dnp2017 mastercopy ·...

Illuminating*QCD*and*Nucleon*Structure*Through*the*Study*of*Hadrons*Within*Jets*

at*STAR

OUTLINE• Introduction• RHIC.and.STAR• Data.and.Models• Near9term.Plans• Summary

James&L.&Drachenbergfor&the&STAR&Collaboration

Lamar&UniversityFall&Meeting&of&the&APS&Division&of&Nuclear&Physics

October&27,&2017

The&study&of&spin&in&particle&physics&has&unlocked&doors&to&a&deeper&understanding&of&nucleon&structure

1Spin.Results.at.STAR.9 Drachenberg

The&Fertile&Field&of&Spin&Physics


• Helicity

Recent&results&enable&a&better&picture&of&gluon&and&sea3quark&helicitySTAR%data%have%played%a%key%role!



NNPDF,&arXiv:1702.05077 DSSV,&PRL&113,&012001e.g.&Gluon&Helicity

5

P(↵), where ↵ is the factor by which the uncertainty onthe new data must be rescaled in order for both the priorand the reweighted sets to be consistent with each other(see Eq. (12) in Ref. [31]). If the modal value of ↵ is closeto unity, the new data is consistent with the old, and itsuncertainties have been correctly estimated.

I perform a simultaneous reweighting of the NNPDF-pol1.1 parton set with all the data sets listed in Tab. I. InTab. II, I show the values of the �

2 per data point afterreweighting, �2

rw

/N

dat

, the number of e↵ective replicas,N

e↵

, and the modal value of the P(↵) distribution, h↵i.The corresponding asymmetries, after reweighting withthe new data, are displayed in Figs. 1-2-3, on top of theircounterparts before reweighting.

The value of the �

2 per data point always decreasesafter reweighting. The improvement is marked for theW -boson production data, moderate for the di-jet pro-duction data and only slight for the neutral pion pro-duction data. This is expected, since the first data sethas the smallest uncertainties, among all, in compari-son to the PDF uncertainties on the theoretical predic-tions. This suggests that this data is bringing in a sig-nificant amount of new information. After reweighting,the �2 per data point is of order one for all the new datasets. However, in the case of W -boson and neutral pionproduction asymmetries, these numbers should be takenwith care, because a complete information on correlatedsystematics is not available. This is the reason why thereweighted �

2 is smaller than one for these sets, exceptfor the W

+ production data. In this case, the value ofthe �2 is raised by a sizable contribution coming from thepoint with the largest positron rapidity, which disagreesby about two sigma with the reweighted theoretical pre-diction and the previous STAR measurement from run2010-2011 (see also Fig. 4 in ref [19]).

The number of e↵ective replicas after reweighting de-pends significantly on the data set. The size of thereweighted parton set is about 90% of the originalNNPDFpol1.1 parton set (made of N

rep

= 100 replicas)for di-jet and pion production data, while it is only about30%-40% for W -boson production data. This result re-flects the di↵erent constraining power of the various datasets, which is maximized in the last case. In principle,a prior ensemble with a larger number of replicas shouldthen be needed for the reweighted ensemble to sample theprobability density in the space of PDFs with as much ac-curacy. However this is not relevant here, as reweightedresults only serve to assess the impact of the new data,and are not used to construct a new parton set.

The modal value of the P(↵) distribution is of orderone for all the new data sets. Values of h↵i slightly largerthan one are found for the W -boson production data: inthe case of W�, this is mostly determined by a sizablefluctuation of one data point (around ⌘

e

� ⇠ 0.25) withrespect to the shape of the corresponding asymmetry; inthe case of W+, this is mostly determined by the fourthdata point (around ⌘

e

+ ⇠ 0.75), which, as already noted,disagrees by about two sigma with the reweighted theo-

-0.1

0

0.1

0.2

0.3 x∆Σ(x,µ2)

µ2=10 GeV

0

0.03

0.06 σx∆Σ NNPDFpol1.1NNPDFpol1.1 (rw)

-0.6

-0.3

0

0.3

0.6x∆g(x,µ2)

NNPDFpol1.1NNPDFpol1.1 (rw)

0

0.1

0.2σx∆g

-0.01

0

0.01

0.02

0.03 x∆u-(x,µ2)

0

0.01

0.02

0.01 0.1 1

x

σx∆u-

-0.03

-0.02

-0.01

0

0.01x∆d-(x,µ2)

0.01 0.1 1 0

0.01

0.02

x

σx∆d-

FIG. 4. A comparison of polarized PDFs before and after thesimultaneous reweighting of NNPDFpol1.1 with the data setslisted in Tab. I. From left to right, top to bottom, the singlet,�⌃, the gluon, �g, and the up and down sea quarks, �uand �d, are displayed. Parton distributions are evaluated atµ2 = 10 GeV. Bands represent one-sigma uncertainties; theyare also shown in the lower inset of each panel.

retical prediction. Values of h↵i slightly smaller than oneare found for the neutral pion production data, thus sug-gesting that experimental uncertainties are likely to beoverestimated, possibly because of the lack of a completeinformation on correlations among systematics.In Fig. 4, I compare the polarized PDFs before and af-

ter the simultaneous reweighting of NNPDFpol1.1 withthe data sets listed in Tab. I. From left to right, topto bottom, I show the singlet (for n

f

active flavors),�⌃ =

Pnf

i=1

(�q

i

+�q

i

), the gluon, �g, and the up anddown sea quarks, �u and �d. Parton distributions areevaluated at µ

2 = 10 GeV2. Bands represent one-sigmauncertainties, which are also displayed separately in thelower inset of each panel.The impact of the wew data on the polarized PDFs of

the proton is twofold. On the one hand, it induces a shiftof the PDF central values, as a consequence of the ad-justment to the shape of the corresponding asymmetries.Specifically, the central value of �g increases by about30% of its original value in the region 0.1 . x . 0.2; thecentral value of �u increases by about 25% and that of�d decreases by about 10% approximately in the sameregion of x wher also �g is a↵ected. On the other hand,the new data induces a reduction of the PDF uncertain-ties, as a consequence of the improved precision of thecorresponding asymmetries. For �g and �d such a re-duction is moderate, and not larger than 5% of its orig-inal value; for �u it is fairly more pronounced, around

5




rw

/N

dat


e↵







rep



e


e


-0.1

0

0.1

0.2

0.3 x∆Σ(x,µ2)

µ2=10 GeV

0

0.03


-0.6

-0.3

0

0.3

0.6x∆g(x,µ2)


0

0.1

0.2σx∆g

-0.01

0

0.01

0.02

0.03 x∆u-(x,µ2)

0

0.01

0.02

0.01 0.1 1

x

σx∆u-

-0.03

-0.02

-0.01

0

0.01x∆d-(x,µ2)

0.01 0.1 1 0

0.01

0.02

x

σx∆d-




f


Pnf

i=1

(�q

i

+�q

i




5




rw

/N

dat


e↵







rep



e


e


-0.1

0

0.1

0.2

0.3 x∆Σ(x,µ2)

µ2=10 GeV

0

0.03


-0.6

-0.3

0

0.3

0.6x∆g(x,µ2)


0

0.1

0.2σx∆g

-0.01

0

0.01

0.02

0.03 x∆u-(x,µ2)

0

0.01

0.02

0.01 0.1 1

x

σx∆u-

-0.03

-0.02

-0.01

0

0.01x∆d-(x,µ2)

0.01 0.1 1 0

0.01

0.02

x

σx∆d-




f


Pnf

i=1

(�q

i

+�q

i





• Helicity• Transversity

Multiple&mechanisms&in&play&to&constrain&transverse&spin3structure



Opportunities%with%!↑ + !…!

other. One can see that the experimental data indeed showsome tension with the Soffer bound for the d quark in thehigh-x region as predicted in Ref. [94]. This saturationhappens in the region not explored by the current exper-imental data, so future data from Jefferson Lab 12 will bevery important to test the Soffer bound and to constrain thetransversity and tensor charge.The functions themselves are slightly different as can be

seen by comparing solid and dashes lines in Fig. 27(a). Infact Ref. [17] uses the tree-level TMD expression (no TMDevolution) for extraction, and we use the NLL TMDformalism. Results should be different even though inasymmetries, as we saw, at low energies results with NLLTMD are comparable with the tree level. At higher energiesand Q2, the situation changes, and extracted functionsmust be different. At the same time, one should rememberTMD evolution does not act as a universal Q2 suppressionfactor. A complicated Fourier transform should be per-formed that mixes Q2 and b dependence, and thus theresulting functions are different in shape but comparable inmagnitude. It is also very encouraging that tree-level TMDextractions yielded results very similar to our NLL extrac-tion. This makes the previous phenomenological resultsvalid even though the appropriate TMD evolution was nottaken into account. It also means that we need to haveexperimental data on unpolarized cross sections differentialin Ph⊥. As we have seen, the effects of evolution should beevident in the data, and those measurements will help toestablish the validity of the modern formulation of TMDevolution.We compare extracted Collins fragmentation functions

−zHð3ÞðzÞ in Fig. 28 at Q2 ¼ 2.4 GeV2 with the extractionof Torino-Cagliari-JLab 2013 [17]. The resulting CollinsFFs have the same signs, but shapes and sizes are slightlydifferent. Indeed one could expect it as far as Q2 of eþe− isdifferent, and the evolution effect must be more evident. Atthe same time, those functions for both tree-level and NLL

TMD give the same (or similar) theoretical asymmetriesthat are well compared to the experimental data of SIDISand eþe−. The favored Collins fragmentation function ismuch better determined by the existing data, as one cansee from Fig. 28 that the functions at Q2 ¼ 2.4 GeV2 arecompatible within error bands. The unfavored fragmenta-tion functions are different; however, those functions arenot determined very well by existing experimental data.We also compare the tensor change from our and other

extractions in Fig. 29. The contribution to the tensor chargeof Ref. [18] is found by extraction using the so-calleddihadron fragmentation function that couples to the col-linear transversity distribution. The corresponding func-tions have DGLAP-type evolution known at LO and wereused in Ref. [18]. The results plotted in Fig. 29 correspondto our estimates of the contribution to the u quark and dquark in the region of x½0.065; 0.35& at Q2 ¼ 10 GeV2 at68% C.L. (label 1) and the contribution to the u quark andd quark in the same region of x and the same Q2 using the

)2(x

,Q1

x h

ud

x

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1

-0.15-0.1

-0.050

0.05

Kang et al (2015)

Anselmino et al (2013)

(a)

)2(x

,Q1

x h

ud

x

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

-0.2

-0.1

0

0.1

Kang et al (2015)

Radici et al (2015)

(b)

FIG. 27. (a) Comparison of extracted transversity (solid lines and vertical-line hashed region) Q2 ¼ 2.4 GeV2 with the Torino-Cagliari-JLab 2013 extraction [17] (dashed lines and shaded region). (b) Comparison of extracted transversity (solid lines and shadedregion) at Q2 ¼ 2.4 GeV2 with Pavia 2015 extraction [18] (shaded region).

)2(z

,Q(3

)H

-zfa

vun

fav

z

0

0.02

0.04Kang et al (2015)Anselmino et al (2013)

0 0.2 0.4 0.6 0.8 1

-0.04

-0.02

0

FIG. 28. Comparison of extracted Collins fragmentation func-tions (solid lines and vertical-line hashed region) at Q2 ¼2.4 GeV2 with the Torino-Cagliari-JLab 2013 extraction [17](dashed lines and shaded region).

EXTRACTION OF QUARK TRANSVERSITY DISTRIBUTION … PHYSICAL REVIEW D 93, 014009 (2016)

014009-33

PRD.93,.014009.(2016)

Collins&from&SIDIS

IFF&from&SIDIS(Preliminary%update%atDIS2017)

Collins&from&SIDIS

Collins&Effect&in&Hadroproduction• Asymmetry.in.distribution%of%hadrons%within%jets%∼ sin () − (+



Anselmino et.al.,.PRD.73,.014020.(2006)F..Yuan,.PRL.100,.032003.(2008)D’Alesio et.al.,.PRD.83,.034021.(2011)

φH–pbeam

pbeamS�

pπ

PJET

jT

φSA

Terms in&Numerator&of&TMD&SSA&for&qq Scattering English&Names Modulation

Δ-.//1↑ ⋅ .3/4 ⋅ 56/7 Sivers •.PDF •.FF sin ()8ℎ:/ ⋅ Δ-.3↑/4 ⋅ 56/7 Transversity •.Boer9Mulders.•.FF sin ()8ℎ:;</ ⋅ Δ-.3↑/4 ⋅ 56/7 Pretzelocity •.Boer9Mulders.•.FF sin ()8ℎ:/ ⋅ .3/4 ⋅ Δ-56/7↑ Transversity •.PDF.•.Collins sin ()8 − (+

Δ-.//1↑ ⋅ Δ-.3↑/4 ⋅ Δ

-56/7↑ Sivers •.Boer9Mulders.•.Collins sin ()8 − (+

ℎ:;</ ⋅ .3/4 ⋅ Δ-56/7↑ Pretzelocity •.PDF •.Collins sin ()8 + (+

Δ-.//1↑ ⋅ Δ-.3↑/4 ⋅ Δ

-56/7↑ Sivers •.Boer9Mulders.•.Collins sin ()8 + (+

Transverse&Momentum&Dependent&(TMD)&Approach

Collins&Effect&in&Hadroproduction• Asymmetry.in.distribution%of%hadrons%within%jets%∼ sin () − (+




φH–pbeam

pbeamS�

pπ

PJET

jT

φSA

Terms in&Numerator&of&TMD&SSA&for&qq Scattering English&Names Modulation

Δ-.//1↑ ⋅ .3/4 ⋅ 56/7 Sivers •.PDF •.FF sin ()8ℎ:/ ⋅ Δ-.3↑/4 ⋅ 56/7 Transversity •.Boer9Mulders.•.FF sin ()8ℎ:;</ ⋅ Δ-.3↑/4 ⋅ 56/7 Pretzelocity •.Boer9Mulders.•.FF sin ()8ℎ:/ ⋅ .3/4 ⋅ Δ-56/7↑ Transversity •.PDF.•.Collins sin ()8 − (+

Δ-.//1↑ ⋅ Δ-.3↑/4 ⋅ Δ

-56/7↑ Sivers •.Boer9Mulders.•.Collins sin ()8 − (+

ℎ:;</ ⋅ .3/4 ⋅ Δ-56/7↑ Pretzelocity •.PDF •.Collins sin ()8 + (+

Δ-.//1↑ ⋅ Δ-.3↑/4 ⋅ Δ

-56/7↑ Sivers •.Boer9Mulders.•.Collins sin ()8 + (+


Collins&Effect&in&Hadroproduction• Asymmetry.in.distribution%of%hadrons%within%jets%∼ sin () − (+• Do.TMD.jet(h).observables.factorize%in%p+p? [arXiv:1705.08443]• How.do.TMDs.evolve,.e.g..with. =, ?@ ?• Enhance.A9quark.sensitivity




φH–pbeam

pbeamS�

pπ

PJET

jT

φSA






)2(x

,Q1

x h

ud

x

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1

-0.15-0.1

-0.050

0.05

Kang et al (2015)


(a)

)2(x

,Q1

x h

ud

x

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

-0.2

-0.1

0

0.1

Kang et al (2015)

Radici et al (2015)

(b)


)2(z

,Q(3

)H

-zfa

vun

fav

z

0

0.02


0 0.2 0.4 0.6 0.8 1

-0.04

-0.02

0



014009-33

PRD.93,.014009.(2016)

NIM.A499,.245.(2003)

Relativistic&Heavy&Ion&ColliderRHIC&as&PolarizedXproton&Collider• “Siberian.Snakes”.!mitigate.depolarization.resonances• Spin.rotators.provide.choice.of.spin.orientation.

independent&of&experiment• Spin.direction.varies.bucket9to9bucket.(9.4.MHz)• Spin.pattern.varies.fill9to9fill


NIM.A499,.245.(2003)

Solenoidal Tracker&at&RHIC

Jets,&diXhadrons,&weak&bosonsTPC.+.Barrel.+.Endcap.EMC

RHIC&as&PolarizedXproton&Collider• “Siberian.Snakes”.!mitigate.depolarization.resonances• Spin.rotators.provide.choice.of.spin.orientation.

independent&of&experiment• Spin.direction.varies.bucket9to9bucket.(9.4.MHz)• Spin.pattern.varies.fill9to9fill


Trigger on.calorimeter.energy

Year B� [GeV] STAR D [%]2006 200 8.5.pb91 57

2006 62.4 0.2.pb91 48

2008 200 7.8.pb91 45

2011 500 25.pb91 53/54

2012 200 22.pb91 61/58

2015 200 53.pb91 53/57

2015 200 pAu 0.42.pb91 60

2015 200.pAl 1.0.pb91 54

2017 510 320.pb91 56

PolarizedXproton&Datasets&at&RHIC


Unique&opportunities&to&probe&nucleon&spin&structure!

Dramatically%increased%figure%of%merit%in%recent%years

Transverse%Luminosity%Recorded

Arbi

trary

Uni

ts

0

0.05

0.1

0.15

0.2 > 0η, JP2, QQ+x

< 0η, JP2, QQ+x

< 55 GeV/c

T22.7 < p

Log(x)3− 2.5− 2− 1.5− 1− 0.5− 00

0.05

0.1

0.15

0.2

0 > 0η, VPDMB, Gx

< 0η, VPDMB, Gx

points: unbiased; histogram: triggered

< 13.8 GeV/c

T6 < p

0

arXiv:1708.07080

B� = 500 GeV

Kinematic&Sensitivity&at&STAR


Access&to&transversity in&interesting&region!• Limited.constraints• Potentially.large.effects• Sensitivity.to.evolution• Insight%into%nature%of%Collins%mechanism!






)2(x

,Q1

x h

ud

x

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1

-0.15-0.1

-0.050

0.05

Kang et al (2015)


(a))2

(x,Q

1x

hu

d

x

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

-0.2

-0.1

0

0.1

Kang et al (2015)

Radici et al (2015)

(b)


)2(z

,Q(3

)H

-zfa

vun

fav

z

0

0.02


0 0.2 0.4 0.6 0.8 1

-0.04

-0.02

0



014009-33

PRD.93,.014009.(2016)


First%Collins%asymmetry%observations%in%hadroproduction!New&500&GeV&Paper:&arXiv:1708.07080

STAR&Collins&Results&at& B� = 200 and 500 GeV

+ X±π jet + → + p ↑p

= 1

.3 G

eV

/c⟩

T,je

tp⟨

×m

inR

∆

z0.2 0.4 0.6

UT

)Hφ-

Sφsi

n(

A

0.05−

0

0.05

-π; Open points: +πClosed points:

STAR = 12.9 GeV/c (Preliminary)⟩

T,jetp⟨ = 200 GeV, s

= 31.0 GeV/c⟩T,jet

p⟨ = 500 GeV, s

At&the&current&precision,results&from&! + ! exhibit&=; scaling

200&GeV:&Int.&J.&Mod.&Phys.&Conf.&Ser.&40,&1660040

Comparison&to&Models


z0.1 0.2 0.3 0.4 0.5 0.6

UT

)Hφ-

Sφsi

n(

A

0.05−

0

0.05

+ X±π jet + → + p ↑p = 500 GeVs < 1

jetη0 < = 31.0 GeV/c⟩

T,jetp⟨

+πSTAR 2011

-πSTAR 2011

+πModel Curves Positive: -πModel Curves Negative:

DMP+2013 KPRY KPRY-NLL

arXiv:1708.07080

Models%based%on%SIDIS/IJIK• Assume universality%and.

robust%factorization• DMP&KPRY:&no&TMD&evol.• KPRYXNLL:&TMD&evolution&up&

to&NLLDMP:&PLB&773,&300&(2017)KPRY:&arXiv:1707.00913



Consistency&between&models&and&STAR&data&at&95%&confidence&level! Suggests&robust&factorization&and&universality

z0.1 0.2 0.3 0.4 0.5 0.6

UT

)Hφ-

Sφsi

n(

A

0.05−

0

0.05

+ X±π jet + → + p ↑p = 500 GeVs < 1

jetη0 < = 31.0 GeV/c⟩

T,jetp⟨

+πSTAR 2011

-πSTAR 2011



arXiv:1708.07080







Slight&preference&for&no&evolution?

z0.1 0.2 0.3 0.4 0.5 0.6

UT

)Hφ-

Sφsi

n(

A

0.05−

0

0.05

+ X±π jet + → + p ↑p = 500 GeVs < 1

jetη0 < = 31.0 GeV/c⟩

T,jetp⟨

+πSTAR 2011

-πSTAR 2011



arXiv:1708.07080







Slight&preference&for&no&evolution?L@/M = 14/10 (w/o).vs..17.6/10 (with)

For&now,&“Beauty&is&in&the&eye&of&the&beholder!”(a.k.a..need.more.data!)

z0.1 0.2 0.3 0.4 0.5 0.6

UT

)Hφ-

Sφsi

n(

A

0.05−

0

0.05

+ X±π jet + → + p ↑p = 500 GeVs < 1

jetη0 < = 31.0 GeV/c⟩

T,jetp⟨

+πSTAR 2011

-πSTAR 2011



arXiv:1708.07080





Asymmetries&appear&to&decrease&with&S;Consistent&between&energies?


< 1jet

η0 <

UT

) Hφ- Sφsi

n(A

0.05−

0

0.05

< 0jet

η-1 <

= 0.13⟩z

⟨

+ X±π jet + → + p ↑p = 500 GeVs = 31.0⟩

T,jetp⟨

0.05−

0

0.05

= 0.23⟩z

⟨

1−10 1

0.05−

0

0.05STAR 2011

+π-π

= 0.37⟩z

⟨

[GeV/c]Tj

1−10 1

) Hφ - Sφ

sin(

UT

A

+π-π

STAR Preliminary > 0Fx

= 200 GeVs + X at ±π jet + → + p ↑p5.6% Scale Uncertainty Not Shown

0.04

0

-0.04

)Hφ

- Sφ

sin(

UT

A

+π-π < 0Fx0.04

0

-0.04

TJe

t p

< 31.6 GeV/cT

10 < Jet p16

12

8

[GeV/c]Tj

-110 1Z

0.1 < z < 0.60.750.5

0.25

Dependence&on&S; (momentum&transverse&to&jet)

arXiv:1708.07080

Int..J..Mod..Phys..Conf..Ser..40,.1660040


Further&investigation&of&low&TU region&needede.g.&unpolarized TMD&data,&model&parameterization,&etc.


) Hφ - Sφ

sin(

UT

A

+π-π



0.04

0

-0.04

)Hφ

- Sφ

sin(

UT

A

+π-π < 0Fx0.04

0

-0.04

TJe

t p

< 31.6 GeV/cT

10 < Jet p16

12

8

[GeV/c]Tj

-110 1Z

0.1 < z < 0.60.750.5

0.25

Dependence&on&S; (momentum&transverse&to&jet)

Compare&to&DMP&modelsPLB.773,.300.(2017)

Int..J..Mod..Phys..Conf..Ser..40,.1660040

The&NearXterm&Future:&Collins&Evolution&


+ X±π jet + → + p(Au) ↑p

z0.2 0.4 0.6

UT) Hφ- Sφ

sin(

A

0.05−

0

0.05

STAR 0.13≈ TJet x


= 200 GeV (Preliminary 2012)sp+p, = 200 GeV (proj. stat. 2012+2015)sp+p,

= 200 GeV (proj. stat. 2015)sp+Au, = 500 GeV (STAR 2011)sp+p, = 500 GeV (proj. stat. 2017)sp+p,

2011.and.Preliminary.2012.Collins.asymmetries.suggest.=; scalingImplications%for%TMD%evolution?

+ X±π jet + → + p(Au) ↑p

z0.2 0.4 0.6

UT) Hφ- Sφ

sin(

A

0.05−

0

0.05

STAR 0.13≈ TJet x




The&NearXterm&Future:&Collins&Evolution&


Higher&precision&in&2015&and&2017&will&allow&more&

precise&comparison!


+ X±π jet + → + p(Au) ↑p

z0.2 0.4 0.6

UT) Hφ- Sφ

sin(

A

0.05−

0

0.05

STAR 0.13≈ TJet x




The&NearXterm&Future:&! + V Collins


Higher&precision&in&2015&and&2017&will&allow&more&

precise&comparison!

First&!↑ + VW run!Should&allow&for&first&

glimpse&of&Collins&in&! + V! Explore&hadronization


Summary

21Recent.Transverse.Spin.Developments.at.RHIC.9 Drachenberg

• Spin&physics&is&a&fertile&field&and&! + ! plays&a&critical&role

Summary


• Spin&physics&is&a&fertile&field&and&! + ! plays&a&critical&role• First.observations.of.Collins.effect.in.polarized.! + !

9 Possible.=; scaling9 Consistency.with.models.suggests.robust.factorization.and.

universality9 Evolution.effects.slow.(more.precise.data.needed.to.quantify)

Summary





• Recent&and&nearXfuture&runs&offer&even&more&potential9 Substantially.increased.precision.for.Collins.at.200.and.510.GeV9 First.investigation.of.Collins.in.! + V

Summary




• Recent&and&nearXfuture&runs&offer&even&more&potential9 Substantially.increased.precision.for.Collins.at.200.and.510.GeV9 First.investigation.of.Collins.in.! + V

Stay%tuned%for%more%new%results%from%STAR!


BackXup&Slides


STAR&Results&at& B� = 500 GeV


< 1jet

η0 <

UT

) Hφ- Sφsi

n(A

0.05−

0

0.05

< 0jet

η-1 <

= 10.6 GeV/c

⟩T,jet

p⟨

0.05−

0

0.05STAR 2011

+π-π = 20.6 G

eV/c⟩

T,jetp⟨

+ X±π jet + → + p ↑p = 500 GeVs

0.2 0.4 0.6

0.05−

0

0.05

= 31.0 GeV/c

⟩T,jet

p⟨

z0.2 0.4 0.6

< 1jet

η0 <

UT

) Hφ- Sφsi

n(A

0.05−

0

0.05STAR 2011

+π-π

< 0jet

η-1 <

= 0.14⟩z

⟨

+ X±π jet + → + p ↑p = 500 GeVs

0.05−

0

0.05

= 0.24⟩z

⟨

10 20 30 40 50

0.05−

0

0.05

= 0.38⟩z

⟨

[GeV/c]T

Particle-jet p10 20 30 40 50

) Hφ - Sφ

sin(

UT

A

+π-π



0.04

0

-0.04

)Hφ

- Sφ

sin(

UT

A

+π-π < 0Fx0.04

0

-0.04

TJe

t p

< 31.6 GeV/cT

10 < Jet p16

12

8

[GeV/c]Tj

-110 1

Z

0.1 < z < 0.60.750.5

0.25) Hφ

- Sφsi

n(U

TA

+π-π



0.04

0

-0.04

)Hφ

- Sφ

sin(

UT

A

+π-π < 0Fx0.04

0

-0.04

Z

0.1 < z < 0.60.75

0.5

0.25

[GeV/c]T

Particle Jet p5 10 15 20 25 30

Tj

< 4.5 GeV/cT

0.125 < j1.51

0.5



Transverse&Asymmetries&for&Gluon&Jets

φH

–pbeam

pbeamS�

pπ

PJET

jT

φSA



Terms in&Numerator&of&TMD&SSA&for&gg Scattering English&Names Modulation

Sivers •.PDF •.FF

Transversity9like•.Boer9Mulders9like.•.FF

Pretzelocity9like•.Boer9Mulders9like.•.FFTransversity9like.•.PDF

•.Collins9likeSivers •.Boer9Mulders9like

• Collins9likePretzelocity9like.•.PDF

•.Collins9likeSivers •.Boer9Mulders9like.•.

Collins9like

ΔN fa/A↑

• fb/B •Dπ /g sin φSA( )sin φSA( )sin φSA( )

sin φSA − 2φH( )sin φSA − 2φH( )sin φSA + 2φH( )sin φSA + 2φH( )

ImF+−a+− •Δ

N fTb1/B

•Dπ /g

ΔN fa/A↑

•ΔN fTb1/B

•ΔNDπ /T g1

ImF−+a+− • fb/B •Δ

NDπ /T g1

ΔN fa/A↑

•ΔN fTb1/B

•ΔNDπ /T g1

ImF−+a+− •Δ

N fTb1/B

•Dπ /g

ImF+−a+− • fb/B •Δ

NDπ /T g1

Anselmino et.al.,.PRD.73,.014020.(2006)F..Yuan,.PRL.100,.032003.(2008)

D’Alesio et.al.,.PRD.83,.034021.(2011)

UNCONSTRAINED!

Asymmetry&modulations&sensitive&to&various&contributions

(often.involving.transversely&polarized&quarks or.linearly&

polarized&gluons)

VX; – Transverse.single9spin.asymmetry.(also.written.V-)



[GeV/c]T

Particle-jet p5 6 7 8 9 10 11 12 13 14 15

UT

) Hφ-2 Sφ

sin(

A

0.02−

0

0.02

+ X±π jet + → + p ↑p = 500 GeVs| < 1

jetη| = 0.18⟩z⟨

STAR 2011DMP+KretzerDMP+DSS

z0.1 0.2 0.3 0.4 0.5 0.6

UT

) Hφ-2 Sφ

sin(

A

0.02−

0

0.02

+ X±π jet + → + p ↑p = 500 GeVs| < 1

jetη| = 10.6 GeV/c⟩

T,jetp⟨

STAR 2011DMP+KretzerDMP+DSS

UT

) Sφsi

n(A

0.02−

0

0.02

< -0.5jet

η-1 <

10 20 30 40 50

0.02−

0

0.02

< 0.5jet

η0 <

STAR 2011

jet + X→ + p ↑p = 500 GeVs

< 0jet

η-0.5 <

[GeV/c]T

Particle-jet p10 20 30 40 50

< 1jet

η0.5 <

Jet&Reconstruction&at&RHIC

e.g..Anti9Y; algorithmJHEP.0804,.063.(2008)

Radius.parameter.Z = 0.5 or.0.6

Use.PYTHIA +.GEANT to.quantify.detector.response

STAR&DiXjet&event&at&detector&level

!"

#0

!0!+

eC

e+

Detector

GEANT

PYTHIA

etcpe

,,,π

γν ,,

gq,

Data&jets&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MC&jets

Particle

Parton

[± Kinematic&Variables] – [ momentum./.jet.momentumS; – [ !; relative.to.jet.axis


Non9zero.asymmetry.from.multi9partoncorrelation.functions

e.g..Qiu and.Sterman,.PRL.67,.2264.(1991); PRD.59,.014004.(1998)

Correlators closely%related%to%kTmoments%of%TMDs

Boer,.Mulders,.Pijlman,.NPB.667,.201.(2003)

Formalisms&for&Transverse&SingleXspin&Asymmetries

Sivers mechanism: asymmetry.in.e.g..jet.or.γ productionD..Sivers,.PRD.41,.83.(1990);.43,.261.(1991)

Collins*mechanism: asymmetry.in.the.jet.fragmentationJ..Collins,.NP.B396,.161.(1993)

Sensitive.to proton&spin–parton transverse&motioncorrelations.(needs.Lz)

SP kT,parton

p

p

⟨SP � (p × kT,parton) ⟩ ≠.0 SP

p

p

Sq kT,π

Sensitive.to.transversity (h1)

⟨Sq� (p × kT,π) ⟩ ≠.0

π± Kinematic&Variablesz = pπ / pjet

jT (kT, π) = π pT relative.to.jet.axis

!p !p !p

p p p

! ! !

Y..Koike,.RSC.Discussion.(2004)

Transverse&Momentum&Dependent&(TMD)&PDFs&and&FFs

Collinear&TwistX3&Correlators


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