Single spin asymmetries in ultra peripheral pa collisions

Transcription

1 Single spin asymmetries in ultra peripheral pa collisions Sanjin Benić (YITP) SB, Hatta, in preparation YKIS2018b, Kyoto, June 11, 2018

2 Single spin asymmetry 1/2 S x y unpolarized π π polarized z A N = dσ dσ dσ + dσ x F = 2P3 h s PHENIX, Phys. Rev. D 90, no. 1, (2014)

3 SSA 2/2 twist-3 observable twist 2 FF hard factor twist 2 PDF initial (Qiu-Sterman) vs final (Collins) fragmentantion contribution dominates? Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)

4 SSA 2/2 twist-3 observable twist 2 FF hard factor twist 3 PDF initial (Qiu-Sterman) vs final (Collins) fragmentantion contribution dominates? Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)

5 SSA 2/2 twist-3 observable twist 2 FF twist 3 FF hard factor hard factor twist 3 PDF twist 2 PDF initial (Qiu-Sterman) vs final (Collins) fragmentantion contribution dominates? Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)

6 Ultra-peripheral collisions p R p b R A A z RHIC already measures p A collisions! a new channel for SSA Z 2 cross section enhancement cleaner than pp, simpler than ep

7 From SIDIS to UPC q 2 = Q 2 0 e2 q 4 L µν g µν dσ pa = 0 dω dn dω dσ photon flux dn dω = 2Z 2 α em πω ξ = ω Rp+R A γ ] [ξk 0 (ξ)k 1 (ξ) ξ2 2 (K 1 2 (ξ) K0 2 (ξ))

8 Cross sections unpolarized Meng, Olness, Soper, Nucl. Phys. B 371, 79 (1992) polarized 1. twist-3 quark-gluon Eguchi, Koike, Tanaka, Nucl. Phys. B 763, 198 (2007) d σ [ x dg ] F (x, x) G F (x, x) ˆσ 1 +G F (0, x) ˆσ 2 + dx G F (0, x) ˆσ 3 2. twist-3 gluon Beppu, Koike, Tanaka, Yoshida, Phys. Rev. D 82, (2010) d σ [ ( ) do(x) δ a O(x) + dn(x) ] N(x) ˆσ g dx dx 3. twist-3 fragmentation Kanazawa, Koike, Phys. Rev. D 88, (2013)

9 Twist-3 frag. contribution 1/3 dx 1 x min d σ frag = αemαs 8 1 M d 2 N sin Φ s à k P h dy h 2ŝ z f x k=1,2 [ ea 2 h1(x) a ê ā 1 (z) ˆσ k 1 + d ( Imẽ a (z) z d(1/z) z a ] dz ImÊF a (z, z) 2 z z 2 1/z 1/z ˆσ4 k z min dz z δ ) ˆσ 2 k + Imẽ a (z) ˆσ 3 k ( ( qt 2 + x 1 1 ) ) ŝ ẑ h1 a (x) transversity Imẽ a (z) (Collins) ImÊ a F (z, z) 0 ψ P h, X P h, X ψf αβ 0 SB, Hatta, in preparation

10 Twist-3 frag. contribution 2/3 equation of motion relation (EOMR) ê ā 1 (z) = zimẽa (z) + z z dz ImÊ F a(z, z) z z z Lorentz invariance relation (LIR) ê ā 1 (z) = 1 ( ) d Imẽ a (z) d(1/z) z z z dz ImÊ F a(z, z) z 2 ( 1 ) 1 2 z z Kanazawa, Koike, Metz, Pitonyak, Schlegel, Phys. Rev. D 93, no. 5, (2016)

11 Twist-3 frag. contribution 3/3 d σ frag = αemαs 16 1 M d 2 N sin Φ s P h dy h 2ŝ z f a e 2 a h a 1(x) [ êā 1 (z) ˆσ 1 + d z d(1/z) dx 1 dz x min x z min ( Imẽ a (z) z ( z δ ) ] ˆσ 2 q 2 T + x ( 1 1 ) ) ŝ ẑ integrals over z completely eliminated (NOT possible in SIDIS!) k = 2 contribution vanishes SB, Hatta, in preparation

12 Calculation scheme extraction of h 1 (x) and Imẽ(z) Wilczek-Wandzura approximation: ê 1(z) = zimẽ(z) µ 2 = 2.4GeV 2 µ 2 = 10.0GeV 2 µ 2 = GeV 2 xh u 1 (x) x Kang, Prokudin, Sun, Yuan, Phys. Rev. D 93, no. 1, (2016)

13 Calculation scheme extraction of h 1 (x) and Imẽ(z) Wilczek-Wandzura approximation: ê 1(z) = zimẽ(z) µ 2 = 2.4GeV 2 µ 2 = 10.0GeV 2 µ 2 = GeV xh d 1 (x) x Kang, Prokudin, Sun, Yuan, Phys. Rev. D 93, no. 1, (2016)

14 Calculation scheme extraction of h 1 (x) and Imẽ(z) Wilczek-Wandzura approximation: ê 1(z) = zimẽ(z) zĥ (3),fav (z) = z 2 MNImẽ fav (z) µ 2 = 2.4GeV 2 µ 2 = 10.0GeV 2 µ 2 = GeV z Kang, Prokudin, Sun, Yuan, Phys. Rev. D 93, no. 1, (2016)

15 Calculation scheme extraction of h 1 (x) and Imẽ(z) Wilczek-Wandzura approximation: ê 1(z) = zimẽ(z) zĥ (3),unfav (z) = z 2 MNImẽ unfav (z) µ 2 = 2.4GeV 2 µ 2 = 10.0GeV 2 µ 2 = GeV z Kang, Prokudin, Sun, Yuan, Phys. Rev. D 93, no. 1, (2016)

16 Results: A N vs. P h π + x F = 0.2 x F = 0.4 x F = AN P h (GeV)

17 Results: A N vs. P h π x F = 0.2 x F = 0.4 x F = AN P h (GeV)

18 Results: A N vs. P h π 0 x F = 0.2 x F = 0.4 x F = AN P h (GeV)

19 Results: A N vs. x F π + π π 0 AN y h = x F

20 Results: nuclear dependence R A = 6R p (pau) R A = 3R p (pal) R A = R p (pp) AN π + y h = x F

21 Conclusions SSA in UPC as a new probe of the polarized proton numerical calculation of the FF contribution does the FF contribution dominate? A N of the order of a few percent very small nuclear dependence