h bm rhic collider - Argonne National Laboratory · 2018-10-16 ·...

42
overview on leading-twist chiral-odd TMDs chiral-odd TMDs in πN Drell-Yan chiral-odd TMDs in single polarized pp Drell-Yan Twist-3 TMDs in Drell-Yan processes chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Yan asymmetries Zhun Lu Department of Physics, Southeast University, Nanjing, China Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Transcript of h bm rhic collider - Argonne National Laboratory · 2018-10-16 ·...

Page 1: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

chiral-odd TMDs at twist 2 (and beyond) from(single-/un)polarized Drell-Yan asymmetries

Zhun Lu

Department of Physics, Southeast University, Nanjing, China

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 2: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

1 overview on leading-twist chiral-odd TMDsBoer-Mulders functionT-even chiral-odd TMDs: h1T , h

⊥1T , h

⊥1L

2 chiral-odd TMDs in πN Drell-Yan

3 chiral-odd TMDs in single polarized pp Drell-Yan

4 Twist-3 TMDs in Drell-Yan processes

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 3: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

The TMD correlator for the nucleon (Goeke et.al, 05; Bacchetta et.al,06):

Φ(x, pT ) =1

2

f1 n/+ − f⊥1T

ǫρσT pTρSTσ

Mn/+ + g1sγ5 n/+

+ h1T

[

S/T , n/+]

γ5

2+ h⊥

1s

[

p/T , n/+]

γ5

2M

+ i h⊥1

[

p/T , n/+]

2M

h⊥1s = SLh

⊥1L − pT · ST

Mh⊥1T

The TMD correlator for the pion (twist-2):

Φ(x, pT ) =1

2

f1 n/+ + i h⊥1

[

p/T , n/+]

2M

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 4: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

describe helicity-flipped quark structure.

handbag diagram forbidden by chirality conservation

chiral-odd distributions participate in the processes involving at leasttwo hadrons (SIDIS, Drell-Yan)

chiral-odd TMDs appear as pair in high energy process

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 5: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 6: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders functions: model calculations

T-odd: h⊥1

DY= −h⊥

1

SIDIS. (Collins 02)

model calculations for the nucleon:

spectator model: Gamberg, Goldstein 02; Bacchetta, Schaefer,Yang 03; Gamberg, Goldstein, Schlegel 07; Bacchetta, Conti,Radici 08.constituent (light-cone) quark model: Courtoy, Scopetta, Vento 09;Pasquini and Yuan 10.bag model: Yuan 03; Courtoy, Scopetta, Vento 09baryon-meson fluctuation model for the sea quarks: ZL, Ma,Schmidt 07.

model calculations for the pion: ZL, Ma 04; Meissner, Metz,Schlegel, Goeke 08; Gamberg, Schlegel 10.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 7: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders functions: model calculations

Figure: From arxiv:1108.1713

solid curve: Pasquini and Yuan 10.

dashed curve: Bacchetta, Conti, Radici 08.

dotted curve: Courtoy, Scopetta, Vento 09.

dashed-dotted curve: parametrization by Barone, Melis, Prokudin 10.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 8: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Theoretical status on the Boer-Mulders functions of the proton:

Theoretical approaches and model calculations suggest h⊥u1 and h⊥d

1have the same sign (negative in SIDIS).

Bag modelconstituent (light-cone) quark modelAxia-diquark spectator modelLarge Nc limit (Pobylitsa 03)Lattice calculation (QCDSF/UKQCD 06; Musch et.al 11)GPD approach (Burkardt 05; Pasquini, Boffi 07; Burkardt, Hannafiou08)

h⊥u1 and h⊥d

1 are expected to have the same order of magnitude

The size of Boer-Mulders function is comparable to that of the otherT-odd TMD, the Sivers function

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 9: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders function vs Sivers function:

0.2 0.4 0.6 0.8 1

x

-0.2

-0.1

0

0.1

0.2

xf(x)

xf1T(1/2,u)

xf1T (1/2,d)

xh1⊥(1/2,u)

xh1⊥(1/2,d)

κ = - 0.333

0.2 0.4 0.6 0.8 1

x-0.2

-0.1

0

0.1

0.2

xf(x)

xf1T⊥ (1,u)

xf1T⊥ (1,d)

xh1⊥(1,u)

xh1⊥(1,d)

κ = 1.0

Figure: from Gamberg, Goldstein, Schlegel 2007

X

-0.075

-0.05

-0.025

0

0.025

0.05

0.075

0 0.25 0.5 0.75 1 X

-0.075

-0.05

-0.025

0

0.025

0.05

0.075

0 0.25 0.5 0.75 1

Figure: from Courtoy, Scopetta, Vento 2009

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 10: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders functions: extractions from data

parameterizations for the nucleon:

from anomalous tensor magnetic moment κqT : Barone, Ma, prokudin

08;from pp and pd Drell-Yan data (E866/Nusea): Zhang, ZL, Ma,Schmidt 08 (valence and sea quarks); ZL, Schmidt 09; Barone,Melis, and Prokudin 10 (sea quarks).from SIDIS data (COMPASS, HERMES): Barone, Melis, andProkudin 10.

no existing parametrization for the pion.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 11: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders functions: extraction from DY data

Parameterizations by Zhang, ZL, Ma, Schmidt 08; ZL, Schmidt 10:

h⊥ q1 (x,p2

T ) = h⊥ q1 (x)

1

πp2bmexp

(

− p2T

p2bm

)

.

h⊥ q1 (x) = ωHq x

cq (1− x)b f q1 (x); h⊥ q

1 (x) =1

ωHq x

cq (1− x)b f q1 (x).

0.0 0.2 0.4 0.6 0.8 1.0-0.10

-0.05

0.00

X

xh (1)u1 (x)

0.0 0.2 0.4 0.6 0.8 1.0-0.10

-0.05

0.00xh (1)d

1 (x)

X

The shadow is the region allowed by the positivity bounds (correspondingto 0.48 < ω < 2.1).

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 12: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

parameterizations confront data (qT ≤ 2 GeV).

data from L.Y. Zhu, et,al. (E866/NuSea) 2006 (pd data), 2008 (pp data)

1

σ

dΩ=

3

1

λ+ 3(1 + λ cos2 θ + µ sin 2 θ cos φ+

ν

2sin2 θ cos 2φ).

ν(x1, x2, qT ) =

F[((2h · p1T h · p2T )− (p1T · p2T ))

h⊥ q1 h

⊥ q1

M1M2

]

F [f q1 f q

1 ]

TMD factorization is valid in low qT region. At higher qT , ν is subject to pQCDeffects (Mirkes, Ohnemus 94; Boer, Vogelsang, 06; Berger, Qiu,Rodriguez-Pedraza 07).

Product h⊥ q1 h⊥ q

1 brings uncertainties on the absolute normalization for eachflavor, which is constrained by the positivity bound (Bacchetta 99).

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

Boer-Mulders functions: extraction from SIDIS data

Parameterizations by Barone, Melis, and Prokudin 10:

h⊥q1 (x, k2T ) = λq f

⊥q1T (x, k2T ) = λq ρq(x) η(kT ) f

q1 (x,k

2T ) ,

Extracted from cos 2φ asymmetry in SIDIS (HERMES preliminary 09;COMPASS preliminary 08, 09)

dσ cos 2φ =4πα2

ems

Q4

a

e2a x(1 − y) A[fa1 , D

a1 ] +

1

2B[h⊥a

1 , H⊥a1 ]

0

0.02

0.04

0.06

0.08

0.1

10-2 10-1 1

x |h

1u⊥(1

) (x)|

x

0

0.02

0.04

0.06

0.08

0.1

10-2 10-1 1

x |h

1d⊥(1

) (x)|

x

Knowledge on the Cahn effect A[fa1 , D

a1 ] (Boglinoe, Melis, Prokudin

11)

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 14: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

T-even chiral-odd TMDs: model calculations

spectator model: Jakob, Mulders, Rodrigues, 97; Bacchetta, Conti,Radici 08

constituent quark model: Pasquini and Yuan 10.

bag model: Avakian, Efremov, Schweitzer, Yuan 10.

light-cone diquark (spectator) model: She, Zhu, Ma 09; Zhu, Ma 11.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 15: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

T-even chiral-odd TMDs: model calculations

0

2

4

0 0.25 0.5 0.75 x

hu1

-0.4

-0.2

0

0 0.25 0.5 0.75 x

h ⊥ (1)u1L

-0.6

-0.4

-0.2

0

0 0.25 0.5 0.75 x

h ⊥ (1)u1T

-0.75

-0.5

-0.25

0

0 0.25 0.5 0.75 x

hd1

0

0.1

0.2

0 0.25 0.5 0.75 x

h ⊥ (1)d1L

0

0.1

0.2

0.3

0 0.25 0.5 0.75 x

h ⊥ (1)d1T

Figure: From arxiv:1108.1713

solid curve: Pasquini and Yuan 10.

dashed curve: Jakob, P. J. Mulders, and J. Rodrigues, 97

dotted curve: Avakian, Efremov, Schweitzer, Yuan 10.

Different model results qualitatively agree with each other.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 16: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

T-even chiral-odd TMDs: model calculations

light-cone diquark model: She, Zhu, Ma 09; Zhu, Ma 11:

juv (x, k2T ) =[

fuv

1 (x, k2T )−1

2fdv

1 (x, k2T )]

W jS(x, k

2T )

− 1

6fdv

1 (x, k2T )WjV (x, k

2T ),

jdv(x, k2T ) =− 1

3fdv

1 (x, k2T )WjV (x, k

2T ), j = h1, h

⊥1T , h

⊥1L.

0.0

0.2

0.4

0.0 0.2 0.4 0.6 0.8 x

x huv1

-0.4

-0.2

0.0

0.0 0.2 0.4 0.6 0.8 x

x hdv1

-0.2

-0.1

0.0

0.0 0.2 0.4 0.6 0.8 x

x h⊥ (1)uv1T

0.0

0.1

0.2

0.0 0.2 0.4 0.6 0.8 x

x h⊥ (1)dv1T

-0.2

-0.1

0.0

0.0 0.2 0.4 0.6 0.8 x

x h⊥ (1)uv1L

0.0

0.1

0.2

0.0 0.2 0.4 0.6 0.8 x

x h⊥ (1)dv1L

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 17: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Boer-Mulders functionT-even chiral-odd TMDs: h1T , h⊥

1T , h⊥1L

T-even chiral-odd TMDs: extraction from data

most recent extraction of transversity: Anselmino et.al 08 (fromHERMES and COMPASS SIDIS data on Collins asymmetry)

d(x

)T∆

x u

(x)

T∆x

) d

(x, k

T∆x

) u

(x, k

T∆x

x (GeV)k

−0.1

0

0.1

0.2

0.3

0.4

0.2 0.4 0.6 0.8 1−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

−0.1

0

0.1

0.2

0.3

0.4

x = 0.1

0 0.2 0.4 0.6 0.8 1−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

x = 0.1

Asin(φh+φS)UT = 2

dφS dφh [dσ↑ − dσ↓] sin(φh + φS)

dφS dφh [dσ↑ + dσ↓]

∝∑

q e2q ∆T q(x, k⊥)⊗∆NDh/q↑(z, p⊥)

q e2q fq/p(x, k⊥)⊗Dh/q(z, p⊥)

.

no extractions of pretzelosity and h⊥1L.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 18: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

1 overview on leading-twist chiral-odd TMDsBoer-Mulders functionT-even chiral-odd TMDs: h1T , h

⊥1T , h

⊥1L

2 chiral-odd TMDs in πN Drell-Yan

3 chiral-odd TMDs in single polarized pp Drell-Yan

4 Twist-3 TMDs in Drell-Yan processes

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

h1(P1) + h2(P2) → γ∗(q) +X → ℓ(l) + ℓ(l′) +X.

Figure: kinematics of Drell-Yan process in the Collins-Soper frame

Left: Definition of φ and φS by Boer (99).

right: Definition of φ and φS by Arnold, Metz, Schlegel (08).

Two conventions are connected by φ ↔ −φ and φS ↔ φS − φ

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 20: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

cross-section contributed by Chiral-odd TMDs: (Boer 99; Arnold,Metz, Schlegel 09)

dσ(h1h2 → l+l−X)

dx1 dx2 d2qT dΩ=

α2em

12Q2

sin2 θ cos 2φF cos 2φUU + SLsin

2 θ sin 2φF sin 2φLU

+|ST |sin2 θ[

sin(2φ+ φS)Fsin(2φ+φS)TU + sin(2φ− φS)F

sin(2φ−φS)TU

]

+ · · ·

.

F cos 2φUU = C

[2(h · p1T )(h · p2T )− p1T · p2T

M1M2h⊥1 h

⊥1

]

,

Fsin(2φ−φS)TU = C

[h · p1T

M1h1h

⊥1

]

,

Fsin(2φ+φS)TU = C

[2(h · p1T )[2(h · p1T )(h · p2T )− p1T · p2T ]− p21T (h · p2T )

2M1M22

×h⊥1T h

⊥1

]

,

F sin 2φLU = C

[2(h · p1T )(h · p2T )− p1T · p2T

M1M2h⊥1Lh

⊥1

]

.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 21: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πN DY at COMPASS

The azimuthal asymmetries are defined as

Asin(2φ±φS)UT =

2∫ 2π

0dφ sin(2φ± φS) [dσ

↑ − dσ↓]∫ 2π

0 dφ[dσ↑ + dσ↓]

for transversely polarized target, and

Asin(2φ)UL =

2∫ 2π

0 dφ sin 2φ [dσ⇒ − dσ⇐]∫ 2π

0dφ[dσ⇒ + dσ⇐]

.

for longitudinally polarized target.

Fsin(2φ−φS)UT (h1, h2) = −F

sin(2φ−φS)TU (h2, h1)

Fsin(2φ+φS)UT (h1, h2) = −F

sin(2φ+φS)TU (h2, h1)

F sin 2φUL (h1, h2) = −F sin 2φ

LU (h2, h1)

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 22: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πN DY at COMPASS

Kinematics:

√s = 18.9 GeV, 0.1 < x1 < 1, 0.05 < x2 < 0.5,

4 6 M 6 8.5 GeV, 0 6 qT 6 2 GeV.

190 GeV pion beams collide on nucleon target

isospin symmetry and charge conjugation(Φq [Γ] = Φq [Γ]for γµ, iσµνγ5) ⇒ simple flavor structure of the pion:

f u/π−

= fd/π−

= f d/π+

= fu/π+

, f = f1 or h⊥1

ideal in unraveling the flavor content of nucleon TMDs:

f1 ⊗ f⊥1T ; h⊥

1 ⊗ h⊥1 ; h⊥

1 ⊗ h⊥1T ; h⊥

1 ⊗ h1; h⊥1 ⊗ h⊥

1L

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πp↑ DY at COMPASS by h⊥1T

4 6 8 0.5 1.0 1.5 2.00.2 0.4 0.6 0.8-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

h 1 h

1T

qT/GeV

xF

Asin(

2S

UT

-

+

- with qT cut

+ with qT cut

M/GeV

Asin(2φ+φS)UT in π−p DY: positive. (−h

⊥u/π−

1 ⊗ h⊥u1T )

Asin(2φ+φS)UT in π+p DY: negative, consistent with zero

(−h⊥d/π+

1 ⊗ h⊥d1T ). Suppressed by the smaller size of h⊥d

1T

Blue curves: qT is integrated from 1 GeV to 2 GeV, increase theasymmetries.

ZL, Ma and She, 11

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 24: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πp↑ DY at COMPASS by h1

4 6 8 0.5 1.0 1.5 2.00.2 0.4 0.6 0.8

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12 h 1 h

1

qT/GeV

xF

Asin(

2S

UT

-

+

M/GeV

Asin(2φ−φS)UT in π−p DY: negative (− h

⊥u/π−

1 ⊗ hu1 ).

Asin(2φ−φS)UT in π+p DY: positive (− h

⊥d/π+

1 ⊗ hd1).

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 25: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πp⇒ DY at COMPASS by h⊥1L

4 6 8 0.5 1.0 1.5 2.00.2 0.4 0.6 0.8

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12 h 1 h1L

qT/GeV

xF

Asin2

UL

-

+

M/GeV

Asin 2φUL in π−p DY: positive (− h

⊥u/π−

1 ⊗ h⊥u1L ).

Asin 2φUL in π+p DY: negative (− h

⊥d/π+

1 ⊗ h⊥d1L ).

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 26: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Asymmetries in πD⇒ DY at COMPASS by h⊥1L

4 6 8 0.5 1.0 1.5 2.00.2 0.4 0.6 0.8

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12 h 1 h1L

qT/GeV

xF

Asin2

UL

-

+

M/GeV

Asin(2φ)UL in π−D DY: positive (−h

⊥u/π−

1 ⊗ (h⊥u1L + h⊥d

1L )).

Asin(2φ)UL in π+D DY: positive (−h

⊥d/π+

1 ⊗ (h⊥u1L + h⊥d

1L )).

Asymmetries for the π− and π+ beams are similar.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 27: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

qT weighted asymmetries

Bacchetta, Conti, Radici, Guagnelli 10 :

AqT sin(2φ−φS2

)

UT= 2

⟨qTM1

sin(2φ − φS2)⟩

UT

〈1〉UU

= −2B(y)

A(y)

∑a e2a x1h

⊥(1)a1 (x1)x2ha

1(x2)∑a e2a x1fa

1 (x1)x2fa1 (x2)

,

Aq3T sin(2φ+φS2

)

UT= 2

⟨q3T

6M1M22

sin(2φ + φS2)⟩

UT

〈1〉UU

=− 2B(y)

A(y)

∑a e2a x1h

⊥(1)a1 (x1)x2h

⊥(2)a1T (x2)∑

a e2a x1fa1 (x1)x2fa

1 (x2),

AqT sin 2φUL

= 2

⟨q2T

4M1M2sin 2φ

UL

〈1〉UU

= −2B(y)

A(y)

∑a e2a x1h

⊥(1)a1 (x1)x2h

⊥(1)a1L (x2)∑

a e2a x1fa1 (x1)x2fa

1 (x2),

ZL, Ma, Schmidt 06:

Aq2T cos 2φ

UU= 2

⟨q2T

4M1M2cos(2φ)

UU

〈1〉UU

=2B(y)

A(y)

∑a e2a x1h

⊥(1)a1 (x1)x2h

⊥(1)a1 (x2)∑

a e2a x1fa1 (x1)x2fa

1 (x2),

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 28: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

A(y) and B(y) are defined as:

A(y) =1

2− y + y2

cm=

1

4(1 + cos2 θ), B(y) = y(1− y)

cm=

1

4sin2 θ.

In the region where x1 and x2 are not small (ZL, Ma, Schmidt 06):

Aq2T cos 2φ

UU,π−D

Aq2T

cos 2φ

UU,π−p

≈1 +

h⊥(1)d1 (x2)

h⊥(1)u1 (x2)

1 +fd1 (x2)

fu1 (x2)

;A

q2T cos 2φ

UU,π+p

Aq2T

cos 2φ

UU,π−p

≈h⊥(1)d1 (x2)

h⊥(1)u1 (x2)

fd1 (x2)

fu1 (x2)

.

similarly:

AqT sin(2φ−φS2)

UT,π−D

AqT sin(2φ−φS2)

UT,π−p

≈1 +

hd1(x2)

hu1 (x2)

1 +fd1 (x2)

fu1 (x2)

;A

qT sin(2φ−φS2)

UT,π+p

AqT sin(2φ−φS2)

UT,π−p

≈hd1(x2)

hu1 (x2)

fd1 (x2)

fu1 (x2)

.

Apply different beams/targets to explore the flavor contents ofTMDs

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 29: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

1 overview on leading-twist chiral-odd TMDsBoer-Mulders functionT-even chiral-odd TMDs: h1T , h

⊥1T , h

⊥1L

2 chiral-odd TMDs in πN Drell-Yan

3 chiral-odd TMDs in single polarized pp Drell-Yan

4 Twist-3 TMDs in Drell-Yan processes

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

p↑/→(P1) + p(P2) → γ∗(q) +X → ℓ(l) + ℓ(l′) +X.

Figure: kinematics of Drell-Yan process in the Collins-Soper frame

current/planned polarized pp program

c.m. energy (GeV) mode

RHIC 200, 510 colliderRHIC 22 fixed-target

J-PARC 10 fixed-targetE906 15 fixed-targetNICA 12÷ 27 collider

SPASCHARM 10.7 fixed-target

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

In PRD84 074036 (ZL, Ma, Zhu 11), the asymmetries is defined as

Asin(2φ−φS)TU (x1, x2, qT ) =

Fsin(2φ−φS)TU

F 1UU

,

Asin(2φ+φS)TU (x1, x2, qT ) =

Fsin(2φ+φS)TU

F 1UU

,

Asin 2φLU (x1, x2, qT ) =

F sin 2φLU

F 1UU

.

In an analogy with the definition of the cos 2φ: ν = 2F cos 2φUU /F 1

UU

AW (φ,φS)PU =

2A(y)∫ 2π

0dφW (φ, φS)[dσ

↑/⇒ − dσ↑/⇐]

B(y)∫ 2π

0dφ[dσ↑/⇒ + dσ↑/⇐]

, P = L, T

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 32: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

-0.2

0.0

0.2

0.4

ATUsin(2φ - φS) ∼ h1⊗ h⊥

1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2

0.4 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.4

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 5.0 6.0 7.0 Q

ω = 2.0

-0.2

0.0

0.2

ATUsin(2φ + φS) ∼ h⊥

1T⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 5.0 6.0 7.0 Q

ω = 2.0

-0.2

0.0

0.2

ALUsin2φ ∼ h⊥

1L⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 5.0 6.0 7.0 Q

ω = 2.0

h⊥

1 from the parametrization by ZL, Schmidt 09; T-even chiral-odd TMDs fromlight-cone diquark model (She, Zhu, Ma 09; Zhu, Ma 11)

Dashed line in the left panels: calculated from the parameterization for h1 byAnselmino et.al., 08

Shaded regions: ranges of the asymmetries by considering the additional

contribution from hq1, h

⊥q1T and h⊥q

1L√s = 15 GeV, 0.3 < x1 < 0.7, 0.1 < x2 < 0.3,

0 < qT < 1 GeV, 4 GeV < Q < 7 GeV,

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 33: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

-0.2

0.0

0.2

0.4

ATUsin(2φ - φS) ∼ h1⊗ h⊥

1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2

0.4 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.4

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 4.2 4.4 4.6 4.8 5.0 Q

ω = 2.0

-0.2

0.0

0.2

ATUsin(2φ + φS) ∼ h⊥

1T⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 4.2 4.4 4.6 4.8 5.0 Q

ω = 2.0

-0.2

0.0

0.2

ALUsin2φ ∼ h⊥

1L⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.0 0.2 0.4 0.6 y

ω = 2.0

4.0 4.2 4.4 4.6 4.8 5.0 Q

ω = 2.0

kinematical cuts at J-PARC:

4 GeV < Q < 5 GeV, 0 < qT < 1 GeV,

0.5 < x1 < 0.9,

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 34: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

-0.2

0.0

0.2

0.4

ATUsin(2φ - φS) ∼ h1⊗ h⊥

1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2

0.4 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.4

-1.0 -0.5 0.0 0.5 1.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

-0.2

0.0

0.2

ATUsin(2φ + φS) ∼ h⊥

1T⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-1.0 -0.5 0.0 0.5 1.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

-0.2

0.0

0.2

ALUsin2φ ∼ h⊥

1L⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-1.0 -0.5 0.0 0.5 1.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

The kinematics cuts at NICA:√s = 27 GeV, 4 GeV < Q < 9 GeV,

0 < qT < 1 GeV, 0.1 < x1 < 0.8,

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

-0.2

0.0

0.2

0.4

ATUsin(2φ - φS) ∼ h1⊗ h⊥

1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2

0.4 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.4

-0.6 -0.3 0.0 0.3 0.6 0.9 y

ω = 2.0

5.0 6.0 7.0 8.0 Q

ω = 2.0

-0.2

0.0

0.2

ATUsin(2φ + φS) ∼ h⊥

1T⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-0.6 -0.3 0.0 0.3 0.6 0.9 y

ω = 2.0

5.0 6.0 7.0 8.0 Q

ω = 2.0

-0.2

0.0

0.2

ALUsin2φ ∼ h⊥

1L⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-0.6 -0.3 0.0 0.3 0.6 0.9 y

ω = 2.0

5.0 6.0 7.0 8.0 Q

ω = 2.0

RHIC kinematics for the fixed-target experiment:

√s = 22 GeV, 4.5 GeV < Q < 8 GeV,

0 < qT < 1 GeV, 0.2 < x1 < 0.6,

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 36: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

-0.2

0.0

0.2

0.4

ATUsin(2φ - φS) ∼ h1⊗ h⊥

1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2

0.4 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

0.4

-1.0 0.0 1.0 2.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

-0.2

0.0

0.2

ATUsin(2φ + φS) ∼ h⊥

1T⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-1.0 0.0 1.0 2.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

-0.2

0.0

0.2

ALUsin2φ ∼ h⊥

1L⊗ h⊥1

ω = 0.5 ω = 0.5

-0.2

0.0

0.2 ω = 1.0 ω = 1.0

-0.2

0.0

0.2

-1.0 0.0 1.0 2.0 y

ω = 2.0

4.0 5.0 6.0 7.0 8.0 9.0 Q

ω = 2.0

kinematics for collider experiment at RHIC-STAR:

√s = 200 GeV, 4 GeV < Q < 9 GeV,

0 < qT < 1 GeV, − 1 < y < 2.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

1 overview on leading-twist chiral-odd TMDsBoer-Mulders functionT-even chiral-odd TMDs: h1T , h

⊥1T , h

⊥1L

2 chiral-odd TMDs in πN Drell-Yan

3 chiral-odd TMDs in single polarized pp Drell-Yan

4 Twist-3 TMDs in Drell-Yan processes

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

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overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

angular dependence of DY at O(1/Q) (Arnold, Metz, Schlegel 09, ZL, Schmidt11):

dσtwist-3

dx1dx2d2qT dΩ=α2em

3Q2sin 2θ

cos φF cosφ

UU+ S1L sinφF sinφ

LU+ S2L sinφF sinφ

UL

+ |~S1T |[sin(φ1 + φ)F

sin(φS1+φ)

TU+ sin(φS1

− φ)Fsin(φS1

−φ)

TU

]

+ |~S2T |[sin(φS2

+ φ)Fsin(φS2

+φ)

UT+ sin(φS2

− φ)Fsin(φS2

−φ)

UT

]

TMD correlator at twist-3 (Goeke et.al, 05; Bacchetta et.al, 06):

Φ(x, pT ) = . . .+M

2P+

e− i es γ5 − e⊥T

ǫρσT

pTρ

STσ

M

+ f⊥p/T

M− f ′

T ǫρσT

γρSTσ − f⊥

s

ǫρσT

γρpTσ

M

+ g′T γ5 S/T + g⊥s γ5p/T

M− g⊥γ5

ǫρσT

γρpTσ

M

+ hs[ n/+, n/−]γ5

2+ h⊥

T

[S/T , p/T

]γ5

2M+ i h

[n/+, n/−

]

2

.

hL, hT , h⊥

T, and h might be probed in Drell-Yan process

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 39: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

un/single-polarized structure functions at twist-3

F cosφUU

=2

QC[(h · k1T )

(f⊥f1 − M2

M1h⊥

1 h

)− (h · k2T )

(f1 f

⊥ − M1

M2h h⊥

1

)]

F sinφLU

=2

QC[(h · k1T )

(f⊥

L f1 +M2

M1h⊥

1L h

)− (h · k2T )

(g1Lg

⊥ +M1

M2hL h

1

)]

Fsin(φS1

−φ)

TU=

1

QC[2M1 fT f1 + 2M2 h1h

+(k1T · k2T )

f⊥

1T f⊥

M1− g1T g⊥

M1− hTh⊥

1

M2+

h⊥

Th⊥

1

M2

Fsin(φS1

+φ)

TU=

1

QC

−(2 (h · k1T )2 − k2

1T

)

f⊥

Tf1

M1+

M2 h⊥

1T h

M21

+(2h · k1Th · k2T − k1T · k2T )

f⊥

1T f⊥

M1+

g1T g⊥

M1+

hTh⊥

1

M2+

h⊥

T h⊥

1

M2

f = x1

((1 − c) f + c f

), f = x2

(c f + (1− c) f

). c =

1

2: CS frame

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 40: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Accessible in DY?

lesson from SIDIS

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

LUhφ

sin

A

-0.05

0

0.05

0.10.1< x <0.2

(GeV)TP0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.05

0

0.05

0.1

0.3< x <0.40.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.2< x <0.3

(GeV)TP0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.4< x <0.6

Figure: sin φ asymmetry measured by CLAS (arxiv:1106.2293) for Q > 1 GeV,W 2 > 4 GeV2 and 0.4 < z < 0.7

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 41: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

SIDIS at twist-3 (Bacchetta et.al,06)

F sinφh

LU =2M

QC

PT · pT

M

[

Mh

Mh⊥1

E

z+ x g⊥D1

]

PT · kT

Mh

[

Mh

Mf1

G⊥

z+ x eH⊥

1

]

.

Drell-Yan at low mass (2.0 < Q < 2.5GeV) region (COMPASS,SPASCHARM)?

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y

Page 42: h bm rhic collider - Argonne National Laboratory · 2018-10-16 · overviewonleading-twistchiral-odd TMDs chiral-odd TMDsinπN Drell-Yan chiral-odd TMDsinsinglepolarizedpp Drell-Yan

overview on leading-twist chiral-odd TMDschiral-odd TMDs in πN Drell-Yan

chiral-odd TMDs in single polarized pp Drell-YanTwist-3 TMDs in Drell-Yan processes

Summary

The πN Drell-Yan program at COMPASS provides greatopportunity to explore the flavor contents of chiral-odd TMDs

Single polarized pp Drell-Yan programme at E906, RHIC, J-PARC,NICA is vital to access h1, h1L in the valence and sea region,

through asymmetries Asin(2φ−φS)TU and Asin 2φ

LU .

Possibility for accessing twist-3 TMDs by Drell-Yan is explored.

Zhun Lu chiral-odd TMDs at twist 2 (and beyond) from (single-/un)polarized Drell-Y