[PPT] - Understanding the large pT spectrum in SIDIS Nobuo Sato In PowerPoint Presentation

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Understanding the large pT spectrum in SIDIS Nobuo Sato

ODU/JLab

27th Workshop on Deep-Inelastic Scattering and Related Subjects DIS 2019 Turin, Italy

In collaboration with: Gonzalez-Hernandez, Rogers, NS, Wang

PRD98 2018
arXiv:1903.01529 2019

SLIDE 2

SIDIS regions

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p⊥

h

yh

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

Breit frame

identified hadron pµ

h

incoming lepton lµ incoming proton P µ

utgoing lepton l′µ

exchanged photon q = l − l′ p⊥

h

SLIDE 3

SIDIS regions

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p⊥

h

yh

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

⊗

incoming quark

utgoing

quark detected hadron

small transverse momentum aka W

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SIDIS regions

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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 aka FO (=fixed order)

SLIDE 5

SIDIS regions

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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

SLIDE 6

SIDIS regions

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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 aka ASY (=asymptotic)

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SIDIS regions

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dσ dxdQ2dzdp⊥

h

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

h /z)/Q → scale separation

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Toy example

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

qT (GeV)

10−4 10−3 10−2 10−1 100 Q = 2.0 (GeV) FO |AY| Y |W| W + Y

Γ(x, z, Q, qT)

SLIDE 9

Existing phenomenology

8 / 20 Anselmino et al Bacchetta et al

These analyses used only W (Gaussian, CSS) → no FO nor ASY Samples with qT/Q ∼ 1.63 have been included BUT TMDs are only valid for qT/Q ≪ 1 !

SLIDE 10

FO @ LO predictions (DSS07) Gonzalez, Rogers, NS, Wang PRD98 (2018)

9 / 20 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

p⊥

h

yh

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

?

SLIDE 11

Trouble with large transverse momentum

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FO =

q

e2

q

1

q2 T Q2 xz 1−z +x

dξ ξ − x H(ξ) fq(ξ, µ) dq(ζ(ξ), µ) + O(α2

S) + O(m2/q2)

+ FFs needs to be updated?

SLIDE 12

FO @ LO predictions (DSS07) Gonzalez, Rogers, NS, Wang PRD98 (2018)

11 / 20 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

p⊥

h

yh

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

?

SLIDE 13

FO @ LO predictions (JAM18) Gonzalez, Rogers, NS, Wang PRD98 (2018)

12 / 20 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

data/theory(LO) vs. qT GeV

p⊥

h

yh

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

?

SLIDE 14

Trouble with large transverse momentum

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FO =

q

e2

q

1

q2 T Q2 xz 1−z +x

dξ ξ − x H(ξ) fq(ξ, µ) dq(ζ(ξ), µ) + O(α2

S) + O(m2/q2)

+ O(α2

S) corrections might be important

SLIDE 15

rder α2

S corrections to FO

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dsp/dpT (pb/GeV)

2 £ Q2 £ 4.5 GeV2 1 10 102

KKP NLO KKP LO K NLO K LO

4.5 £ Q2 £ 15 GeV2 1 10 102

pT (GeV)

15 £ Q2 £70 GeV2 1 10 102 3 4 5 6 7 8 9 10 15

ff ff fi

Daleo,et al. (2005) PRD.71.034013

There are strong indications that order α2

S corrections are

very important An order of magnitude correction at small pT . As a sanity check, we need to have an independent calculation

SLIDE 16

O(α2

S) calculation (Wang, Gonzalez-Hernandes, Rogers, NS - arXiv:1903.01529)

15 / 20

W µν(P, q, PH) = 1+

x−

dξ ξ 1+

z−

dζ ζ2 ˆ W µν

ij (q, x/ξ, z/ζ)fi/P (ξ)dH/j(ζ)

{Pµν

g

ˆ W (N)

µν ; Pµν P P ˆ

W (N)

µν } ≡

1 (2π)4

{|M 2→N

g

|2; |M 2→N

pp

|2} dΠ(N) − Subtractions Born/Virtual Real Generate all 2 → 2 and 2 → 3 squared amplitudes Evaluate 2 → 2 virtual graphs (Passarino-Veltman) Integrate 3-body PS analytically Check cancellation of IR poles

SLIDE 17

FO @ LO predictions (JAM18)

16 / 20 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

data/theory(LO) vs. qT GeV

p⊥

h

yh

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

?

SLIDE 18

FO @ NLO (JAM18)

17 / 20 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

p⊥

h

yh

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

?

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Understanding the large x (Wang, Gonzalez-Hernandes, Rogers, NS - arXiv:1903.01529)

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2 4 6

F NLO

1

/F LO

1

z = 0.2 qT = Q z = 0.8 qT = Q

0.01 0.1 2 4 6

z = 0.2 qT = 2Q

0.01 0.1

x

z = 0.8 qT = 2Q

Q = 2 GeV Q = 20 GeV

Large corrections threshold corrections are observed The x at the minimum can be used as an indicator of where such corrections are expected to be large

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Understanding the large x (Wang, Gonzalez-Hernandes, Rogers, NS - arXiv:1903.01529)

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COMPASS kinematics

0.01 0.1

x

1 2 3 4 5 6 7

qT/Q

< z >= 0.24

0.01 0.1

x

1 2 3 4 5 6 7

< z >= 0.48

0.01 0.1

x

1 2 3 4 5 6 7

< z >= 0.69

x > x0 x ≤ x0

The blue region might receive large threshold corrections This can potential explain why the O(α2

S) fail to describe the data at

large x

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Summary and outlook

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O(α2

S) corrections are important to describe SIDIS at COMPASS

The large x region receives large threshold corrections which can explain the difficulty to describe the data Potential impact of SIDIS large pT data on PDFs/FFs global analysis