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Understanding the large transverse momentum spectrum in SIDIS Nobuo - - PowerPoint PPT Presentation

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Understanding the large transverse momentum spectrum in SIDIS Nobuo Sato University of Connecticut SPIN18 (3D Structure of the Nucleon: TMDs) CERN, 2018 1 / 28 Kinematic regions of SIDIS 2 / 28 Kinematic regions p h p + y h

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SLIDE 1

1 / 28

Understanding the large transverse momentum spectrum in SIDIS Nobuo Sato

University of Connecticut SPIN18 (3D Structure of the Nucleon: TMDs) CERN, 2018

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SLIDE 2

2 / 28

Kinematic regions of SIDIS

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SLIDE 3

Kinematic regions

3 / 28

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions

yh = 1

2 ln

  • p+

h

p−

h

  • Different regions are sensitive to

distinct physical mechanisms

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SLIDE 4

4 / 28

Theory of current fragmentation

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SLIDE 5

Theory framework for current fragmentation

5 / 28

small transverse momentum

W

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

  • utgoing

quark detected hadron

large transverse momentum

FO

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

  • utgoing

quark detected hadron

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SLIDE 6

Theory framework for current fragmentation

6 / 28

small transverse momentum

W

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

  • utgoing

quark detected hadron

large transverse momentum

FO

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

  • utgoing

quark detected hadron

matching region

ASY

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SLIDE 7

Theory framework for current fragmentation

7 / 28

The formulation of is based on a scale separation governed by the ratio qT/Q where z = P · ph P · q , qT = p⊥

h /z

The cross section is built as dσ dxdQ2dzdp⊥

h

= W + FO − ASY + O(m2/Q2) ∼ W for qT ≪ Q ∼ FO for qT ∼ Q

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SLIDE 8

Why qT/Q ?

(J. Gonzalez-Hernandes, T.C Rogers, NS, B. Wang) 8 / 28

q p

              

N k1

q p k1 k

Lets define k ≡ k1 − q Propagators in the blob 1 k2 + O(Λ2

QCD),

1 k2 + O(Q2) Two extreme regions

  • |k2|∼ Λ2

QCD → k is part of PDF

  • |k2|∼ Q2 → k is part of hard blob

|k2|/Q2 is the relevant Lorentz invariant measure of transverse momentum size

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SLIDE 9

Why qT/Q ?

(J. Gonzalez-Hernandes, T.C Rogers, NS, B. Wang) 9 / 28

In terms of partonic variables

  • k2

Q2

  • = (1 − ˆ

z) + ˆ z q2

T

Q2 For qT < Q one can write q2

T

Q2 <

  • k2

Q2

  • < 1 − z
  • 1 − q2

T

Q2

  • One can conclude that
  • qT ≪ Q signals the onset of TMD region
  • qT ∼ Q signals the large transverse momentum region
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SLIDE 10

10 / 28

Phenomenology

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SLIDE 11

Existing phenomenology

11 / 28 Anselmino et al Bacchetta et al

These analyzes used only W (Gaussian, CSS) Samples with qT/Q ∼ 1.63 has been included BUT TMDs are only valid for qT/Q ≪ 1 !

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SLIDE 12

Large pT SIDIS phenomenology

12 / 28

At LO: dσ dxdQ2dzdpT ∼

  • q

e2

q

1

q2 T Q2 xz 1−z +x

dξ ξ − xfq(ξ, µ) dq(ζ(ξ), µ) H(ξ) For collinear distributions we use

  • PDFs: CJ15
  • FFs: DSS07
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SLIDE 13

COMPASS: l + d → l′ + h+ + X

13 / 28 10−3 10−2 10−1 100 2 4 6 10−3 10−2 10−1 100

Q2 (GeV2) xbj

0.007 0.010 0.016 0.03 0.04 0.07 0.15 0.27 1.3 1.8 3.5 8.3 20.0 2 4 6 10−3 10−2 10−1 100

COMPASS 17 h+

dσ dxbjdQ2dzdP 2

T/

dσ dxbjdQ2(GeV−2) vs. qT (GeV)

DDS (LO) DDS (NLO) qT > Q

2 4 6 2 4 6 10−3 10−2 10−1 100

0.24 < z < 0.30 0.30 < z < 0.40 0.40 < z < 0.50 0.65 < z < 0.70

2 4 6 2 4 6 10−3 10−2 10−1 100 2 4 6 2 4 6

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SLIDE 14

COMPASS: l + d → l′ + h+ + X

14 / 28

2 6 10 14 18

data/theory(LO)

xbj = 0.13 Q2 = 5.3 GeV2 xbj = 0.15 Q2 = 9.8 GeV2 xbj = 0.29 Q2 = 22.1 GeV2

20 40

q2

T(GeV2)

2 6 10 14 18

data/theory(NLO)

20 40

q2

T(GeV2)

0.24 < z < 0.30 0.30 < z < 0.40 0.40 < z < 0.50 0.65 < z < 0.70

20 40

q2

T(GeV2)

qT > Q

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SLIDE 15

HERMES: l + p → l′ + π+ + X

15 / 28 10−2 10−1 100 101

dσ dxbjdQ2dzdP 2

T/

dσ dxbjdQ2

xbj = 0.04 Q2 = 1.2 (GeV2) xbj = 0.06 Q2 = 1.5 (GeV2) xbj = 0.10 Q2 = 1.8 (GeV2)

< z >= 0.1 < z >= 0.2 < z >= 0.3 < z >= 0.5 < z >= 0.9 2 4 6

qT(GeV)

10−2 10−1 100 101

xbj = 0.15 Q2 = 2.9 (GeV2)

2 4 6

qT(GeV)

xbj = 0.25 Q2 = 5.2 (GeV2)

2 4 6

qT(GeV) HERMES π+

xbj = 0.41 Q2 = 9.2 (GeV2)

DDS (LO) DDS (NLO) qT > Q

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SLIDE 16

HERMES: l + p → l′ + π+ + X

16 / 28

10 20 30

data/theory(LO)

xbj = 0.15 Q2 = 2.9 GeV2 xbj = 0.25 Q2 = 5.2 GeV2 xbj = 0.41 Q2 = 9.2 GeV2

20 40

q2

T(GeV2)

10 20 30

data/theory(NLO)

< z >= 0.1 < z >= 0.2 < z >= 0.3 < z >= 0.5 < z >= 0.9 20 40

q2

T(GeV2)

qT > Q 20 40

q2

T(GeV2)

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SLIDE 17

The large pT puzzle

17 / 28

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions

?

What are we missing?

  • perturtative parts : power corrections, threshold corrections
  • non-perturbative parts : PDFs, FFs
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SLIDE 18

The role of non perturbative input

18 / 28

For pT integrated @ LO: dσ dxdQ2dz ∼

  • q

e2

qfq(x, µ) dq(z, µ)

For pT differential @ LO: dσ dxdQ2dzdpT ∼

  • q

e2

q

1

q2 T Q2 xz 1−z +x

dξ ξ − xfq(ξ, µ) dq(ζ(ξ), µ) H(ξ) Note:

  • gluon PDFs/FFs are involved in pT differential but not in the

integrated case

  • For pT differential, the qT factor in the integrand provides

point-by-point in qT constraints on PDF/FF

  • The pT spectrum is very sensitive to the shape of PDF/FF
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SLIDE 19

19 / 28

Revisiting charged hadron FFs (in JAM)

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SLIDE 20

Revisiting charged hadron FFs (in JAM)

20 / 28

Data sets:

  • SIDIS(h+, h−) qT integrated data from COMPASS
  • e+e− → h± + X (work with the 0.2 < z < 0.8 samples)
  • PDFs: JAM18 (see my talk at spin physics in nuclear reactions

and nuclei)

Extracted FFs:

0.2 0.4 0.6 0.8 z 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Dh+

JAM18/Dh+ DSS07

Q2 = 10GeV2 u d s ¯ u ¯ d ¯ s g c

The gluon fragmentation is significantly different → recently observed by the NNPDF

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SLIDE 21

Revisiting charged hadron FFs (in JAM)

21 / 28 0.2 0.4 0.6 0.8 z 10−1 100 101

1 σT dσ dz TPC

0.2 0.4 0.6 0.8 z 100 101

TASSO

0.2 0.4 0.6 0.8 z 10−1 100 101

ALEPH

0.2 0.4 0.6 0.8 z 100 101

DELPHI

0.2 0.4 0.6 0.8 z 10−1 100 101

SLD

0.2 0.4 0.6 0.8 z 100 101

OPAL

0.2 0.4 0.6 0.8 z 10−2 10−1 100 101

OPAL(c)

0.2 0.4 0.6 0.8 z 10−1 100 101

OPAL(b)

χ2/npts = 0.53

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SLIDE 22

Revisiting charged hadron FFs (in JAM)

22 / 28

0.2 0.4 0.6 0.8 z 1 2 3 4

Mh+ + α pd → h+ + X

0.2 0.4 0.6 0.8 z 1 2 3 4 0.2 0.4 0.6 0.8 z 1 2 3 4 0.2 0.4 0.6 0.8 z 1 2 3 4 0.2 0.4 0.6 0.8 z 1 2 3 4

y ∈ [0.10, 0.15], α = 0.00 y ∈ [0.15, 0.20], α = 0.25 y ∈ [0.20, 0.30], α = 0.50 y ∈ [0.30, 0.50], α = 0.75

0.2 0.4 0.6 0.8 z 1 2 3 4 0.2 0.4 0.6 0.8 z 1 2 3

Mh− + α pd → h− + X

0.2 0.4 0.6 0.8 z 1 2 3 0.2 0.4 0.6 0.8 z 1 2 3 0.2 0.4 0.6 0.8 z 1 2 3 0.2 0.4 0.6 0.8 z 1 2 3 0.2 0.4 0.6 0.8 z 1 2 3

χ2/npts = 0.48

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SLIDE 23

23 / 28

New predictions for the SIDIS qT spectrum

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SLIDE 24

Old predictions (DSS07) @ LO

24 / 28 2 4 6 8 10 2 4 6 2 4 6 8 10

Q2 (GeV2) xbj

0.007 0.010 0.016 0.03 0.04 0.07 0.15 0.27 1.3 1.8 3.5 8.3 20.0 2 4 6 2 4 6 8 10

COMPASS 17 h+ data/theory(LO) vs. qT (GeV)

PDF : CJ15 FF : DSS07

qT > Q

2 4 6 2 4 6 2 4 6 8 10

< z >= 0.24 < z >= 0.34 < z >= 0.48 < z >= 0.68

2 4 6 2 4 6 2 4 6 8 10 2 4 6 2 4 6

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SLIDE 25

New predictions (JAM18) @ LO

25 / 28 2 4 6 8 10 2 4 6 2 4 6 8 10

Q2 (GeV2) xbj

0.007 0.010 0.016 0.03 0.04 0.07 0.15 0.27 1.3 1.8 3.5 8.3 20.0 2 4 6 2 4 6 8 10

COMPASS 17 h+ data/theory(NLO) vs. qT (GeV)

PDF : JAM18 FF : JAM18

qT > Q

2 4 6 2 4 6 2 4 6 8 10

< z >= 0.24 < z >= 0.34 < z >= 0.48 < z >= 0.68

2 4 6 2 4 6 2 4 6 8 10 2 4 6 2 4 6

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SLIDE 26

New predictions (JAM18) @ NLO (DDS)

26 / 28 2 4 6 8 10 2 4 6 2 4 6 8 10

Q2 (GeV2) xbj

0.007 0.010 0.016 0.03 0.04 0.07 0.15 0.27 1.3 1.8 3.5 8.3 20.0 2 4 6 2 4 6 8 10

COMPASS 17 h+ data/theory(NLO) vs. qT (GeV)

PDF : JAM18 FF : JAM18

qT > Q

2 4 6 2 4 6 2 4 6 8 10

< z >= 0.24 < z >= 0.34 < z >= 0.48 < z >= 0.68

2 4 6 2 4 6 2 4 6 8 10 2 4 6 2 4 6

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SLIDE 27

Lessons

27 / 28

It is possible to restore the predictive power of pQCD for the SIDIS large pT by retunning the FFs Conversely the large qT SIDIS spectrum can be used constrain more accurately FFs in particular the gluon These results opens up the possibility to for the first time start the TMD phenomenology within the full W + Y

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SLIDE 28

Summary and outlook

28 / 28

dσ dx dy dΨ dz dφh dP 2

hT

= α2 xyQ2 y2 2(1 − ε)

  • 1 + γ2

2x

18

  • i=1

Fi(x, z, Q2, P 2

hT )βi

Fi Standard label βi F1 FUU,T 1 F2 FUU,L ε F3 FLL S||λe √ 1 − ε2 F4 F sin(φh+φS)

UT

| S⊥|ε sin(φh + φS) F5 F sin(φh−φS)

UT,T

| S⊥|sin(φh − φS) F6 F sin(φh−φS)

UT,L

| S⊥|ε sin(φh − φS) F7 F cos 2φh

UU

ε cos(2φh) F8 F sin(3φh−ψS)

UT

| S⊥|ε sin(3φh − φS) F9 F cos(φh−φS)

LT

| S⊥|λe √ 1 − ε2 cos(φh − φS) F10 F sin 2φh

UL

S||ε sin(2φh) F11 F cos φS

LT

| S⊥|λe

  • 2ε(1 − ε) cos φS

F12 F cos φh

LL

S||λe

  • 2ε(1 − ε) cos φh

F13 F cos(2φh−φS)

LT

| S⊥|λe

  • 2ε(1 − ε) cos(2φh − φS)

F14 F sin φh

UL

S||

  • 2ε(1 + ε) sin φh

F15 F sin φh

LU

λe

  • 2ε(1 − ε) sin φh

F16 F cos φh

UU

  • 2ε(1 + ε) cos φh

F17 F sin φS

UT

| S⊥|

  • 2ε(1 + ε) sin φS

F18 F sin(2φh−φS)

UT

| S⊥|

  • 2ε(1 + ε) sin(2φh − φS)

The apparent disagreement between data and FO can be resolved by tunning FFs It provides for the first time the possibility to describe FUU in the full W + FO − ASY This is important as all the structure functions that are typically provided in a form of asymmetries Ai = Fi/FUU