Polarized Fragmentation Functions Anselm Vossen Research supported - PowerPoint PPT Presentation

CPHI-2020, CERN, February 2020 Polarized Fragmentation Functions Anselm Vossen Research supported by the

Single Hadron production In SIDIS is a well travelled path Observables: z: fractional energy of the quark carried by the hadron p h,T : transverse momentum of the hadron wrt the quark direction: TMD FFs Parton polarization à Spin averaged longitudinal transverse Hadron Polarization ⇣ $/& (𝑨, 𝑞 + ) .$/& (𝑨, 𝑞 + ) spin averaged 𝐸 # 𝐼 # longitudinal Transverse (here L ) 2

Transverse momentum dependent distributions (TMDs) • In addition to the spin-spin correlations can have spin momentum correlations! Spin-orbit correlations 3

PDF in SIDIS ⇔ 𝐺𝐺 in 𝑓 2 𝑓 3 • E.g. Sivers ⇔ Λ ↑ production X X • Spacelike SIDIS Timelike SIA • GPDs ⇔ GDAs (not discussed here) 4

“You think you understand something?---Now add spin…in Hadronization!” • à polarized final states π + • à di-hadron correlations π – • Explore spin-orbit correlation in hadronization • Additional degrees of freedom in final state make targeted extraction of nucleon structure possible à see h 1 (x), e(x) • New Fragmentation Functions 5

Enter polarization in the final States Observables: z: fractional energy of the quark carried by the hadron p h,T : transverse momentum of the hadron wrt the quark direction: TMD FFs Parton polarization à Spin averaged longitudinal transverse Hadron Polarization ⇣ .𝒊/𝒓 (𝒜, 𝒒 𝑼 ) spin averaged $/& (𝑨, 𝑞 + ) 𝐸 # 𝑰 𝟐 𝚳/𝒓 𝒜, 𝒒 𝑼 𝒊/𝒓 𝒜, 𝒒 𝑼 longitudinal 𝑯 𝟐 𝑰 𝟐𝑴 Transverse (here L ) .𝚳/𝒓 ( 𝒜, 𝒒 𝑼 ) 𝑬 𝟐𝑼 𝚳/𝐫 ( 𝒜, 𝒒 𝑼 ) = 𝑰 𝟐 𝒊/𝒓 𝒜, 𝒒 𝑼 = 𝑯 𝟐𝑼 .𝚳/𝐫 ( 𝒜, 𝒒 𝑼 ) = 𝑰 𝟐𝑼 • Analogue à similar to PDFs encoding spin/orbit correlations Determining final state polarization needs self analyzing decay ( Λ) • • Gluon FFs similar but with circular/linear polarization (not as relevant for e+e-) 6

DI-HADRON FRAGMENTATION FUNCTIONS Additional Observable: 𝑆 = 𝑄 # − 𝑄 W : The relative momentum of the hadron pair is an additional degree of freedom: the orientation of the two hadrons w.r.t. each other and the jet direction can be an indicator of the quark transverse spin Parton polarization à Spin averaged longitudinal transverse Hadron Polarization ⇣ .𝒊/𝒓 (𝒜, 𝒒 𝑼 M, (Ph), q ) ‘Di-hadron spin averaged $/& (𝑨, 𝑁) 𝑰 𝟐 𝐸 # Collins’ longitudinal G 1 ⊥ (z,M,P h , q )= H 1 ∢ (z,M, (P h ), q )=. Transverse Type eq Ty equat ation he here. T -odd, chiral-even T -odd, chiral-odd à jet handedness Colinear QCD vaccum strucuture • Relative momentum of hadrons can carry away angular momentum • Partial wave decomposition in q à Needs to be mapped completely!! (no information yet) • Energy dependence? ( à VM fractions….) • Relative and total angular momentum à In principle endless tower of FFs 7

Some specific points of interest . ) • Spin orbit correlations in hadronization (e.g. 𝐻 # • Interference patterns of different relative partial waves • Access to aspects of the nucleon structure difficult in single hadrons • Examples: • Boer-Mulders w/o Cahn, twist3 • e(x) à See T. Hayward’s talk • Λ production • sensitive to s quarks • FF counterpart to Sivers à universality etc • Test twist3 calculations • Additional degrees of freedom à Need large statistics 8

Role of B-factories •Asymmetric-energy e + e - collider • √s ∿ 10.6 GeV (ϒ(4S)) • βγ=0.425 • L ∿ 1 ab -1 + + - - World Data (Sel.) for e World Data (Sel.) for e e e ± ± +X Production +X Production → → π π ) 13 s S • Dominated by B 10 L D 9 1 G e V ( 1 1 c( × 0 2 12 ) 10 D factories E L P H I NIMA 729 ,615(2013) × 9 1 G 11 e 10 V ( /dz 5 × ALEPH 91GeV ( 1 10 × 0 ) 10 10 3 × 10 9 × • Limited lever arm ) σ NIMA 479 ,117(2002) 9 TASSO 34GeV, 44GeV ( 10 d tot.had. in 𝑡 in particular 8 10 7 × 10 7 × ) T P C 2 9 G 7 e V 10 ( 2 × 1 6 × 0 at high z ) σ 6 10 1/ this meas., Belle 11 GeV ( 5 10 CLEO 10GeV ( • Precision data 0.04) × 4 10 3000) × A R G 3 U includes charged S 10 9 G e V , 1 0 G e V ( 1 2 × 5 10 0 ) single hadrons p , R o n a n e t a 10 l . 3 G e V ( 1 ) × K, p, D, Λ, charmed 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 baryons… z Phys.Rev.Lett. 111 (2013) 062002 (Belle) • Well described at •Asymmetric-energy e + e - collider Phys.Rev. D88 (2013) 032011 (BaBar) NNLO • √s ∿ 10.6 GeV (ϒ(4S)) (e.g. DSS, NNFF) • βγ=0.65 • L ∿ 500 fb -1 9

The future is now: Next Generation B factory SuperKEKB • Belle/KEKB recorded ~1000 fb -1 . Now have to change units on the y-axis to ab -1 Close to Belle lumi before winter shutdown ∫ 𝑀 ≈ 11 𝑔𝑐 3# “nano-beams” are the Beam currents only a key; vertical beam size factor of two higher is 50nm at the IP than KEKB (~PEPII) • ∫ 𝑀 needed to map out fully differential 𝑒𝜏 of polarized FF • 𝜄 , flavor dependence for di-hadrons • 𝑞 + , 𝑨, 𝑨 d,e for Λ (also correction for feed-down needs statistics)

Belle II Detector (comp. to Belle) 11

2019: First Collisions in Phase 3, the Physics Run Clear signals for B à J/ψ X in ~1/2 of Phase 3 data.

Collins FFs IN 𝑓 2 𝑓 3 • First non-zero independent measurement of the Collins effect for pion pairs in e + e - annihilation by Belle Collaboration @ √s ∼ 10.6 GeV ( PRL 111,062002(2008), PRD 88,032011(2013) ) leads to first extraction of transversity (Phys.Rev. D75 (2007) 054032 ) from SIDIS and e+e- j 2 • Confirmed by BaBar @ √s ∼ 10.6 GeV ( PRD 90,052003 (2014); p + PRD 92,111101(R)(2015) for KK and Kπ ) z 2 • Measured at BESIII @ √s = 3.65 GeV ( PRL 116,42001(2016) ) q 2 q 1 p - j 1 quark-2 quark-1 z 1 spin spin z 1,2 relative pion pair momenta Cross-section 𝑓 2 𝑓 3 → ℎ # ℎ W ℎ # ℎ W + 𝑌 . 𝐸 # . + 𝐼 # . 𝐼 # . cos 𝜚 # + 𝜚 W ∝ 𝐸 # • Access spin dependence and p T dependence (convolution or in jet) without PDF complication • Made possible by B-factory luminosities 13

New: P t dependence of charged pions from Belle BaBar U nlike/ L ikesign Ratios to cancel acceptance effects Preliminary Unlike: fav*fav+dis*dis Like: fav*dis • Trend consistent with BaBar • Direct comparison difficult due to different correction schemes (thrust vs 𝑟p 𝑟 − axis) 14

<latexit sha1_base64="Fmfzj0FecUk1cyEGHeimBsewYTk=">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</latexit> <latexit sha1_base64="Zyi8lNnW0azNoYQ5/Ck3gcBksc=">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</latexit> New: 𝜌 r /𝜃 from Belle = π 0 π + + π 0 π − 12 = R 0 ± R π 0 12 π + π + + π − π − R L 12 12 = R η ± ηπ + + ηπ − 12 R η = π + π + + π − π − R L 12 • Rise with 𝒜 𝟐,𝟑 , similar to charged pions 0.07 12 h A h 0.06 A with stat. uncertainties 12 h 0.05 A systematic uncertainties 12 0.04 0.03 0.02 1 0.01 5 0 0.4 0.5 0.6 0.7 0.8 z 1 𝜃 almost flat except large z •

Consistency between Neutral and charged pions 0.06 12 A p 0 Preliminary 0.05 A 12 UL UC 0.04 A -A 12 12 0.03 𝐕𝐌 − 𝑩 𝟐𝟑 𝑽𝑫 (𝑱𝒕𝒑𝒕𝒒𝒋𝒐) = 𝐁 𝟐𝟑 0.02 0.01 0 - 0.01 0.3 0.4 0.5 0.6 0.7 0.8 z 1 16

Measuring transverse spin dependent di-Hadron Correlations In unpolarized e + e - Annihilation into Quarks Interference effect in e + e - electron quark fragmentation will lead to azimuthal asymmetries in di-hadron correlation measurements! - + p p - + ( ) p p ( ) j 2 j 1 q 1 Experimental requirements: z 2 q 2 z 1 § Small asymmetries è quark-2 quark-1 very large data sample! spin spin § Good particle ID to high momenta. z 1,2 relative pion pair momenta § Hermetic detector positron 17

First measurement of Interference Fragmentation ∠ ( 𝑟 ↑ → 𝜌 2 𝜌 3 ) Function 𝐼 # arXiv:1104.2425 AV, RS et. al, PRL 107, 072004(2011) a 12 µ H 1< • H 1< 18