Single spin asymmetries in ultra peripheral pA collisionsnfqcd2018/Slide/Benic.pdf · h?dy h = 1 em...

Single spin asymmetries in ultraperipheral pA collisions

Sanjin Benic (YITP)

SB, Hatta, in preparation

YKIS2018b, Kyoto, June 11, 2018

Single spin asymmetry 1/2

ππ

polarized

unpolarized z

x

y

S

AN =dσ↑ − dσ↓

dσ↑ + dσ↓

xF =2P3

h√s

PHENIX, Phys. Rev. D 90, no. 1, 012006 (2014)

Benic - Single spin asymmetries in ultra peripheral pA collisions - NFQCD, Kyoto - 2018/06/11

SSA 2/2

• twist-3 observable

twist 2 PDF

hard factor

twist 2 FF

initial (Qiu-Sterman) vs final (Collins)

fragmentantion contribution dominates?Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)


SSA 2/2


twist 3 PDF

hard factor

twist 2 FF

• initial (Qiu-Sterman) vs final (Collins)

fragmentantion contribution dominates?Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)


SSA 2/2


twist 2 PDF

hard factor

twist 3 FF

twist 3 PDF

hard factor

twist 2 FF

• initial (Qiu-Sterman) vs final (Collins)

• fragmentantion contribution dominates?Gamberg, Kang, Pitonyak, Prokudin, Phys. Lett. B 770, 242 (2017)


Ultra-peripheral collisions

z

p

A

b

Rp

RA

• RHIC already measures p↑A collisions!

• a new channel for SSA

• Z 2 cross section enhancement

• cleaner than pp↑, simpler than ep↑


From SIDIS to UPC

• q2 = −Q2 → 0

• e2

q4Lµν → −g⊥µν• dσpA =

∫∞0 dωdN

dωdσ

• photon flux

dN

dω=

2Z 2αem

πω

[ξK0(ξ)K1(ξ)− ξ2

2(K 2

1 (ξ)− K 20 (ξ))

]ξ = ωRp+RA

γ


Cross sections• unpolarized

Meng, Olness, Soper, Nucl. Phys. B 371, 79 (1992)

• polarized

1. twist-3 quark-gluonEguchi, Koike, Tanaka, Nucl. Phys. B 763, 198 (2007)

d∆σ ∼[xdGF (x , x)

dx− GF (x , x)

]∆σ1 +GF (0, x)∆σ2 +GF (0, x)∆σ3

2. twist-3 gluonBeppu, Koike, Tanaka, Yoshida, Phys. Rev. D 82, 054005 (2010)

d∆σ ∼[δa

(dO(x)

dx− O(x)

)+

dN(x)

dx− N(x)

]∆σg

3. twist-3 fragmentationKanazawa, Koike, Phys. Rev. D 88, 074022 (2013)


Twist-3 frag. contribution 1/3

d∆σfrag

d2Ph⊥dyh=αemαs

2s

8

zfMN sin Φs

∑k=1,2

Ak

∫ 1

xmin

dx

x

∫ 1

zmin

dz

zδ

(q2T + x

(1− 1

z

)s

)

×∑a

e2ah

a1(x)

[ea1 (z)

z∆σ1

k +d

d(1/z)

(Imea(z)

z

)∆σ2

k + Imea(z)∆σ3k

− 2

∫ ∞

z

dz ′

z ′2ImE a

F (z ′, z)

1/z − 1/z ′∆σ4

k

]

• ha1(x) transversity

• Imea(z) (Collins)

• ImE aF (z ′, z) ∼ 〈0|ψ|Ph,X 〉〈Ph,X |ψF αβ|0〉

SB, Hatta, in preparation



• equation of motion relation (EOMR)

ea1 (z) = z Imea(z) + z

∫ ∞

z

dz ′

z ′2ImE a

F (z ′, z)1z ′− 1

z

• Lorentz invariance relation (LIR)

ea1 (z) =1

2

d

d(1/z)

(Imea(z)

z

)+

1

z

∫ ∞

z

dz ′

z ′2ImE a

F (z ′, z)(1z− 1

z ′

)2

Kanazawa, Koike, Metz, Pitonyak, Schlegel, Phys. Rev. D 93, no. 5, 054024 (2016)



d∆σfrag

d2Ph⊥dyh=αemαs

2s

16

zfMN sin Φs

∫ 1

xmin

dx

x

∫ 1

zmin

dz

zδ

(q2T + x

(1− 1

z

)s

)×∑a

e2ah

a1(x)

[ea1 (z)

z∆σ1 +

d

d(1/z)

(Imea(z)

z

)∆σ2

]

• integrals over z ′ completely eliminated

(NOT possible in SIDIS!)

• k = 2 contribution vanishesSB, Hatta, in preparation


Calculation scheme

• extraction of h1(x) and Ime(z)

• Wilczek-Wandzura approximation: e1(z) = z Ime(z)

0.2 0.4 0.6 0.8 1.0x

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35xh

u 1(x)

µ2 = 2.4GeV2

µ2 = 10.0GeV2

µ2 = 1000.0GeV2

Kang, Prokudin, Sun, Yuan, Phys. Rev. D 93, no. 1, 014009 (2016)


Calculation scheme



0.2 0.4 0.6 0.8 1.0x

−0.16

−0.14

−0.12

−0.10

−0.08

−0.06

−0.04

−0.02

0.00xh

d 1(x)

µ2 = 2.4GeV2

µ2 = 10.0GeV2

µ2 = 1000.0GeV2



Calculation scheme



0.2 0.4 0.6 0.8 1.0z

0.00

0.01

0.02

0.03

0.04

0.05

0.06−

zH(3

),fa

v (z)

=−

z2 MN

Imefa

v (z) µ2 = 2.4GeV2

µ2 = 10.0GeV2

µ2 = 1000.0GeV2



Calculation scheme



0.2 0.4 0.6 0.8 1.0z

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

0.00−

zH(3

),un

fav (

z)=−

z2 MN

Imeun

fav (

z)

µ2 = 2.4GeV2

µ2 = 10.0GeV2

µ2 = 1000.0GeV2



Results: AN vs. Ph⊥

2 3 4 5 6 7 8Ph⊥ (GeV)

0.000

0.005

0.010

0.015

0.020

0.025

0.030A

Nπ+ xF = 0.2

xF = 0.4xF = 0.6



2 3 4 5 6 7 8Ph⊥ (GeV)

−0.030

−0.025

−0.020

−0.015

−0.010

−0.005

0.000A

Nπ−

xF = 0.2xF = 0.4xF = 0.6



2 3 4 5 6 7 8Ph⊥ (GeV)

0.000

0.005

0.010

0.015

0.020

0.025

0.030A

Nπ0 xF = 0.2

xF = 0.4xF = 0.6


Results: AN vs. xF

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60xF

−0.03

−0.02

−0.01

0.00

0.01

0.02

0.03

0.04A

N

yh = 3.0

π+

π−

π0


Results: nuclear dependence

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60xF

0.000

0.005

0.010

0.015

0.020

0.025

0.030A

N

π+ yh = 3.0

RA = 6Rp (pAu)

RA = 3Rp (pAl)

RA = Rp (pp)


Conclusions

• SSA in UPC as a new probe of the

polarized proton

• numerical calculation of the FF

contribution

does the FF contribution dominate?

• AN of the order of a few percent

• very small nuclear dependence


Single spin asymmetries in ultra peripheral pA collisionsnfqcd2018/Slide/Benic.pdf · h?dy h = 1 em...

Documents

Transcript of Single spin asymmetries in ultra peripheral pA collisionsnfqcd2018/Slide/Benic.pdf · h?dy h = 1 em...