Challenges and recent progress in SIDIS Nobuo Sato ODU/JLab - - PowerPoint PPT Presentation

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Challenges and recent progress in SIDIS Nobuo Sato ODU/JLab - - PowerPoint PPT Presentation

Mar 11, 2024 189 likes •592 views

Challenges and recent progress in SIDIS Nobuo Sato ODU/JLab Workshop on Novel Probes of the Nucleon Structure in SIDIS, e+e- and pp (FF2019) Duke University Durham, 2019 1 / 34 Outline Recent progress in SIDIS large p T o

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SLIDE 1

1 / 34

Challenges and recent progress in SIDIS Nobuo Sato

ODU/JLab Workshop on Novel Probes of the Nucleon Structure in SIDIS, e+e- and pp (FF2019) Duke University Durham, 2019

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SLIDE 2

Outline

2 / 34

Recent progress in SIDIS large pT

  • Gonzalez-Hernandez, Rogers, NS, Wang

( PRD98 2018 )

  • Wang, Gonzalez-Hernandez, Rogers, NS

( arXiv:1903.01529 2019 )

New developments to identify SIDIS regions

  • Boglione, Collins, Gamberg, Gonzalez-Hernandez, Rogers, NS

( PLB 766 2017 )

  • Boglione, Gamberg, Gordon, Gonzalez-Hernandez, Prokudin, Rogers, NS

( in preparation )

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SLIDE 3

Zooming in at the femtometer scale using JLab12

3 / 34

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SLIDE 4

Zooming in at the femtometer scale using JLab12

3 / 34

QED corrections

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SLIDE 5

Zooming in at the femtometer scale using JLab12

3 / 34

QED corrections QCD factorization

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SLIDE 6

Zooming in at the femtometer scale using JLab12

3 / 34

QED corrections QCD factorization

The inverse problem

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SLIDE 7

4 / 34

Recent progress in SIDIS large pT

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SLIDE 8

SIDIS regions

5 / 34

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

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SLIDE 9

SIDIS regions

6 / 34

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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SLIDE 10

SIDIS regions

7 / 34

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)

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SLIDE 11

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

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SLIDE 12

SIDIS regions

8 / 34

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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SLIDE 13

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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SLIDE 14

Toy example

10 / 34

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)

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SLIDE 15

Existing phenomenology

11 / 34 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 !

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SLIDE 16

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

12 / 34 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

?

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SLIDE 17

Trouble with large transverse momentum

13 / 34

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?

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SLIDE 18

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

14 / 34 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

?

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SLIDE 19

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

15 / 34 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

?

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SLIDE 20

Trouble with large transverse momentum

16 / 34

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

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SLIDE 21
  • rder α2

S corrections to FO

17 / 34

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

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SLIDE 22

O(α2

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

18 / 34

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

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SLIDE 23

FO @ LO predictions (JAM18)

19 / 34 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

?

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SLIDE 24

FO @ NLO (JAM18)

20 / 34 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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SLIDE 25

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

21 / 34

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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SLIDE 26

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

22 / 34

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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SLIDE 27

23 / 34

New developments to identify SIDIS regions

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SLIDE 28

SIDIS region indicators

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P PB q ki kf kX kb

i =

  • Q

ˆ xN √ 2, ˆ xN(k2

i + k2 i,b,T)

√ 2Q , ki,b,T

  • kb

f =

k2

f,b,T + k2 f

√ 2ˆ zNQ , ˆ zNQ √ 2 , kf,b,T

  • k = kf − q
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SLIDE 29

SIDIS region indicators

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P PB q ki kf kX R1 ≡ PB · kf PB · ki R2 ≡ |k2| Q2 R3 ≡ |k2

X|

Q2 For TMD factorization to hold one needs R1, R2, R3 ≪ 1

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SLIDE 30

SIDIS region indicators

25 / 34

Web app is available

  • https://sidis.herokuapp.com/
  • use chrom (slow in safary)
  • feedback/questions are

welcomed

  • it might take few seconds to

load be patient

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SLIDE 31

SIDIS region indicators - example

26 / 34

R1 π

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SLIDE 32

SIDIS region indicators - example

27 / 34

R2 π

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SLIDE 33

SIDIS region indicators - example

28 / 34

R3 π

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SLIDE 34

SIDIS region indicators - example

29 / 34

R1 K

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SLIDE 35

SIDIS region indicators - example

30 / 34

R2 K

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SLIDE 36

SIDIS region indicators - example

31 / 34

R3 K

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SLIDE 37

Using the ratios in pheno

32 / 34

Recall the Bayesian regression paradigm P(a|data) = L(a, data)π(a) The likelihood L(a, data) = exp

  • −1

2

  • i

datai − theoryi(a)

δdatai

2

The priors π(a) ∝ Πiθ(amin

i

< ai < amax

i

) E[O] =

  • dna P(a|data)O(a) ,

V[O] =

  • dna P(a|data) (O(a) − E[O])2
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SLIDE 38

Using the ratios in pheno

33 / 34

IDEA: use Ri as priors π(Rk) ∝ exp (−|Rk|p) The full prior becomes π(a) ∝ Πiθ(amin

i

< ai < amax

i

) × Πj exp

 −

  • k=1,2,3

|Rk(a, b, Ωj)|p

  × π(b)

  • parameters a enter directly in TMD factorization
  • parameters b are other parameters that characterizes additional

partonic d.o.f. (i.e. virtualities)

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SLIDE 39

Summary and outlook

34 / 34

SIDIS at large pT

  • 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

  • Inclusion of SIDIS large pT data in PDFs/FFs analysis is required

SIDIS region indicators

  • New tools to map SIDIS regions (web-app)
  • The indicators can be used as Bayesian priors for the regression in

TMD phenomenology