Fu Func nctio tions ns on t on the he La Latt ttic ice - - PowerPoint PPT Presentation

▶
fu func nctio tions ns on t on the he la latt ttic ice
SMART_READER_LITE
LIVE PREVIEW

Fu Func nctio tions ns on t on the he La Latt ttic ice - - PowerPoint PPT Presentation

Jun 14, 2023 39 likes •451 views

Par arto ton n Di Dist stributi ribution on Fu Func nctio tions ns on t on the he La Latt ttic ice Huey-Wen Lin University of Washington Huey-Wen Lin Los Alamos National Lab 1 Outline Introduction to PDFs A brief

slide-1
SLIDE 1

Par arto ton n Di Dist stributi ribution

  • n

Fu Func nctio tions ns

  • n t
  • n the

he La Latt ttic ice

Huey-Wen Lin University of Washington

1 Huey-Wen Lin — Los Alamos National Lab

slide-2
SLIDE 2

Outline

§ Introduction to PDFs

 A brief overview on global analysis

§ Lattice QCD

 Difficulties: why seek a new idea?

§ New Approach on the Lattice

 Preliminary results on nucleon quark, helicity and transversity distributions

2 Huey-Wen Lin — Los Alamos National Lab

slide-3
SLIDE 3

Parton Distribution Functions

§ Structure functions studied through scattering processes

 Deep inelastic scattering beginning in 1960s at SLAC  Depend on energy scale (Q2) and quark momentum fraction (x)

§ “Parton”

 1969 by Feynman: pointlike constituents inside hadron → now known to be quarks and gluons

§ Still limited knowledge

 Many ongoing/planned experiments (EIC, LHeC, …)

3 Huey-Wen Lin — Los Alamos National Lab

slide-4
SLIDE 4

4

Parton Distribution Functions

§ Quark distribution

 Processes: DIS (F2, σ), Drell-Yan,

W-asymmetry, Z-rapidity, (γ+) jet, …

 Experiment: BCDMS, NMC, SLAC, JLab,

HERA, E866, CDF, DØ,…

§ Helicity distribution

 Processes: polarized DIS, semi-inclusive DIS,

photo- and electroproduction of hadrons and charm, pp collisions

 Experiment: EMC, HERMES, Hall A, CLAS,

COMPASS, STAR, PHENIX, …

§ Transversity distribution

 Process: single-spin asymmetry in SIDIS, …  Experiment: HERMES, COMPASS, Belle…

Huey-Wen Lin — Los Alamos National Lab

spin-averaged/unpolarized spin-dep./long. polarized transversely polarized

slide-5
SLIDE 5

§ Experiments cover diverse kinematics of parton variables

 Global analysis takes advantage of all data sets

5

Global Analysis

Theory Input Exp’t Input Global Analysis

  • f PDFs

PDFs Applications Predictions

Huey-Wen Lin — Los Alamos National Lab

slide-6
SLIDE 6

Global Analysis

6

§ Important fundamental QCD property

 Exploration of the valence and sea-quark content of the nucleon

§ Important for BSM searches

 Provides SM cross-section prediction for LHC new-physics search  IceCube PeV neutrinos can be explained by PDF uncertainties  Proton weak charge (medium-modification effects) PDFs Applications Predictions

§ Experiments cover diverse kinematics of parton variables

 Global analysis takes advantage of all data sets

Huey-Wen Lin — Los Alamos National Lab

slide-7
SLIDE 7

Global Analysis

7

Theory Input Exp’t Input Global Analysis

  • f PDFs

+ 1 + + 1 =

5 4 3

2 4 3 a a x a

x e e x a x a x P ) ( ) ( ) ( ) 1 ( = ) , (

2 1

x P x x a μ x f

a a

  • Discrepancies appear when data is scarce

Huey-Wen Lin — Los Alamos National Lab

§ Some choices made for the analysis

 Choice of data sets and kinematic cuts  Strong coupling constant αs(MZ)  Uncertainties in perturbation theory

(depends on process whether LO, NLO or NNLO is known)

 Evolution of PDFs to different scales  Parametrization assumptions

slide-8
SLIDE 8

Global Analysis

§ Some choices made for the analysis

 Choice of data sets and kinematic cuts  Strong coupling constant αs(MZ)  Uncertainties in perturbation theory

(depends on process whether LO, NLO or NNLO is known)

 Evolution of PDFs to different scales  Parametrization assumptions

§ Sum rules to constrains the fit

 Quark number, momentum, gA, SU(3) flavor symmetry…

§ Assumptions imposed where theory and exp’t are lacking

 Charge symmetry, (anti-)strange, “sea” (antiquark) distribution…

8

Theory Input Exp’t Input Global Analysis

  • f PDFs

Huey-Wen Lin — Los Alamos National Lab

slide-9
SLIDE 9

Global Analysis

§ Some choices made for the analysis

 Choice of data sets and kinematic cuts  Strong coupling constant αs(MZ)  Uncertainties in perturbation theory

(depends on process whether LO, NLO or NNLO is known)

 Evolution of PDFs to different scales  Parametrization assumptions

§ Sum rules to constrains the fit

 Quark number, momentum, gA, SU(3) flavor symmetry…

§ Assumptions imposed where theory and exp’t are lacking

 Charge symmetry, (anti-)strange, “sea” (antiquark) distribution…

9

Theory Input Exp’t Input Global Analysis

  • f PDFs

Huey-Wen Lin — Los Alamos National Lab

For example,

  • r symmetric

sea in helicity

) ( d u κ s s + = +

slide-10
SLIDE 10

Global Momentum Analysis

10

§ Many groups have tackled the analysis

 CTEQ, MSTW, ABM, JR, NNPDF, etc.

Jimenez enez-Delgad Delgado, , Melnitc lnitchouk, , Owens ns, J.Phys hys. . G40 (2013 13) ) 09310 10

Huey-Wen Lin — Los Alamos National Lab

slide-11
SLIDE 11

Global Momentum Analysis

11

§ Many groups have tackled the analysis

 CTEQ, MSTW, ABM, JR, NNPDF, etc.

Jimenez enez-Delgad Delgado, , Melnitc lnitchouk, , Owens ns, J.Phys hys. . G40 (2013 13) ) 09310 10

Huey-Wen Lin — Los Alamos National Lab

slide-12
SLIDE 12

JAM13 ACC09 DSSV09 BB10 LSS10

Global Helicity Analysis

12

§ Many groups have tackled the analysis

 DSSV, ACC, BB, LSS, JAM, etc.

Huey-Wen Lin — Los Alamos National Lab

JAM, , 1310.3 10.3734 734 [hep ep-ph ph]

slide-13
SLIDE 13

Transversity

§ There have only been 2 attempts (still very preliminary)

 Requires more theory input and experimental data  More assumptions are made to extract the distribution

13

M.

  • M. Anselm

elmino ino, , et al., ., Nucl.P l.Phys. s.Proc. c.Suppl ppl. . 191, 1, 98–10 107 7 (2009)

  • A. Bacchetta

chetta, , A. Courtoy rtoy, , and d M. Radic dici, , Phys. s.Rev ev.L .Let ett. . 107, , 012001 01 (2011 11)

Huey-Wen Lin — Los Alamos National Lab

slide-14
SLIDE 14

§ Lattice QCD is an ideal theoretical tool for investigating strong-coupling regime of quantum field theories

 Ideal tool for studying nonperturbative hadron structure

PDFs on the Lattice

14

§ Physical observables are calculated from the path integral

gluon field quark field

a L

t x, y, z

§ Lattice QCD

 Impose a UV cutoff discretize spacetime  Impose an Infrared cutoff finite volume  Wick rotate to Euclidean  Use compact gauge group

Huey-Wen Lin — Los Alamos National Lab

slide-15
SLIDE 15

§ Many lattice calculations of the moments of the PDFs

 Limited to the lowest few moments  Might provide constraints on models or tests of experiment

§ Also applies to GPDs: limited to 3rd moment § Most progress made in quark contributions

 Very costly to obtain useful gluon signal  Limited by available computational resources

15

PDFs on the Lattice

Huey-Wen Lin — Los Alamos National Lab

slide-16
SLIDE 16

§ Leading moment x, hypercubic decomposition

 4141 = 11  31  61  63: O44−(O11+O22+O33)/3 O14+O41, (requires p≠0)  Both operators go to same continuum limit

§ No mixing with operators of same or lower dimension § To improve to O(a)

 Consider all irrelevant operators of same symmetry:

§ Higher moments x2

 41: O111 mixes with q

―γ1q with coefficient ~ 1/a2

 42: O{123} requires all momentum components to be nonzero  81: O{441}−(O{221}+O{331})/2 mixes under renormalization

§ For higher spin, all ops mix with lower-dimension ops

xn Moments

16 Huey-Wen Lin — Los Alamos National Lab

slide-17
SLIDE 17

§ Leading moment x, hypercubic decomposition

 4141 = 11  31  61  63: O44−(O11+O22+O33)/3 O14+O41, (requires p≠0)  Both operators go to same continuum limit

§ No mixing with operators of same or lower dimension § To improve to O(a)

 Consider all irrelevant operators of same symmetry:

§ Higher moments x2

 41: O111 mixes with q

―γ1q with coefficient ~ 1/a2

 42: O{123} requires all momentum components to be nonzero  81: O{441}−(O{221}+O{331})/2 mixes under renormalization

§ For higher spin, all ops mix with lower-dimension ops

xn Moments

17 Huey-Wen Lin — Los Alamos National Lab

slide-18
SLIDE 18

§ For higher spin, all ops mix with lower-dimension ops

 Tricks: subtraction to remove divergent terms, heavy fields, four-point functions… None is practical enough

§ Relative error grows in higher moments

 Calculation would be costly

xn Moments

x2q x3q

Dolgov lgov et al. . PRD66, 6, 034506 6 (2002) ) Göckel eler er et al. . PRD71, 71, 1145 4511 11 (2005) LHPC C (SCRI, CRI, SESAM): AM): 2f, Wilson lson and clove lover QCDSF SF: : 0f

18 Huey-Wen Lin — Los Alamos National Lab

slide-19
SLIDE 19

Limited Access

§ What can we learn about the x-distribution?

 Make an ansatz of some smooth form for the distribution and fix the parameters by matching to the lattice moments

  • W. Detmol
  • ld

d et al, , Eur.Ph .Phys ys.J.d .J.direct irect C3 (2001) 1) 1–15 15

Cannot separate valence- quark contribution from sea

New idea needed to access the sea!

19 Huey-Wen Lin — Los Alamos National Lab

slide-20
SLIDE 20

§ Lightcone nucleon quark distribution

 Transform lab coordinates to light-cone ones x± = z±t

Quark Distribution

Nucleon momentum P

µ

Lightcone coordinate ξ±=(t±z)/√

―

2

Renormalization scale µ Gluon potential A+

20 Huey-Wen Lin — Los Alamos National Lab

slide-21
SLIDE 21

Nucleon momentum P

µ

Lightcone coordinate ξ±=(t±z)/√

―

2

Renormalization scale µ Gluon potential A+

§ Lightcone nucleon quark distribution

 Transform lab coordinates to light-cone ones x± = z±t

Quark Distribution

21

 Massive particles lie on hyperboloids invariant under Lorentz transformation

Huey-Wen Lin — Los Alamos National Lab

slide-22
SLIDE 22

§ Lightcone nucleon quark distribution

The Idea

Nucleon momentum P

µ

Lightcone coordinate ξ±=(t±z)/√

―

2

Renormalization scale µ Gluon potential A+

§ Approaching lightcone with large P

 Just another limit to take, like taking a→0

Xian angd gdong

  • ng Ji, Phys.
  • s. Rev.

. Lett tt. . 111 11, , 039103 3 (2013 13)

22 Huey-Wen Lin — Los Alamos National Lab

slide-23
SLIDE 23

§ Finite-momentum quark distribution

The Idea

Lattice z coordinate x=kz/P

z

Product of lattice gauge links  In P

z limit,

parton distribution is recovered  For finite P

z, corrections are needed

Nucleon momentum P

µ={P 0,0,0,P z}

Xian angd gdong

  • ng Ji, Phys.
  • s. Rev.

. Lett tt. . 111 11, , 039103 3 (2013 13)

23 Huey-Wen Lin — Los Alamos National Lab

slide-24
SLIDE 24

§ Exploratory study

 Nf = 2+1+1 clover/HISQ lattices (MILC) Mπ ≈ 310 MeV, a ≈ 0.12 fm (L ≈ 2.88 fm)  Isovector only (“disconnected” suppressed)

gives us flavor asymmetry between up and down quark

 2 source-sink separation (tsep≈0.96 and 1.2 fm) used

Some Lattice Details

§ Properties known on these lattices

 Lattice ZΓ for bilinear operator ~ 1 (with HYP-smearing)  Mπ L ≈ 4.6 large enough to avoid finite-volume effects

tsep

§ Feasible with today’s computational resources!

 8/16 nodes on UW Hyak cluster Hyak @ UW

24 Huey-Wen Lin — Los Alamos National Lab

slide-25
SLIDE 25

§ Exploratory study

 Nf = 2+1+1 clover/HISQ lattices (MILC) Mπ ≈ 310 MeV, a ≈ 0.12 fm (L ≈ 2.88 fm)

Warning!

tsep

25

nO sYSTEMATICS YET!

Huey-Wen Lin — Los Alamos National Lab

slide-26
SLIDE 26

§ Exploratory study

Quark Distribution

P

z {1, 2, 3} 2π⁄L

 Lattice momenta discretized by finite size of volume  How many links are needed?

26 Huey-Wen Lin — Los Alamos National Lab

slide-27
SLIDE 27

§ Exploratory study

Quark Distribution

Uncorrected bare lattice results

Preliminary

x=kz/P

z

P

z {1, 2, 3} 2π⁄L

27 Huey-Wen Lin — Los Alamos National Lab

slide-28
SLIDE 28

§ Exploratory study

Quark Distribution

Preliminary

Distribution gets sharper as P

zincreases

Artifacts due to finite P

z

  • n the lattice

Improvement?

Work out leading-P

z

corrections

P

z {1, 2, 3} 2π⁄L

28 Huey-Wen Lin — Los Alamos National Lab

slide-29
SLIDE 29

§ Back to the continuum

Quark Distribution

What we want What we calculate

  • n the lattice

P

z  {1, 2, 3} 2π⁄L

Dominant correction (for nucleon); known scaling form

J. J.-W. . Chen en et al. . (in prepara arati tion) n) J. J.-H.

  • H. Zhang,

ang, Y . Zha hao, J.-W. . Chen en et al. . (in preparat ration)

  • n)

Xiangdong Ji, Phys. Rev. Lett. 111, 039103 (2013)

Smaller P

z correction but

complicated twist-4

  • perator

(extrapolate it away)

29

  • X. Xion
  • ng,

g, X. Ji, , J. Zhang, ang, 1310.7 10.747 471 1 [hep ep-ph ph]

Finite Pz → ∞ Estimate O(20%) effect

Huey-Wen Lin — Los Alamos National Lab

slide-30
SLIDE 30

Quark Distribution

§ Exploratory study

 Take ratios (partially cancel statistical and systematic errors)

No significant finite-momentum effect seen for P

z>1

§ Renormalization needed

Preliminary

30

Removing O(MN

n/P z n) errors + O(αs)

Huey-Wen Lin — Los Alamos National Lab

slide-31
SLIDE 31

Quark Distribution

§ Compare with experiments Compared with E866

Too good to be true?

Lost resolution in small-x region

Future improvement to have larger lattice volume

  • R. Towell

ell et al. . (E866/NuSe /NuSea), a), Phys ys.R .Rev ev. . D64, 052002 (2001) 1)

31

ⅆ𝑦 𝑣 𝑦 − ⅆ(𝑦) 𝑕𝑊 ≈ −0.16(12)

Huey-Wen Lin — Los Alamos National Lab

slide-32
SLIDE 32

Helicity Distribution

§ Exploratory study

Preliminary

32 Huey-Wen Lin — Los Alamos National Lab

slide-33
SLIDE 33

Helicity Distribution

§ Exploratory study Larger O(Λ2

QCD/P z 2) seen

but well fit by extrapolation

Preliminary

33

Removing O(MN

n/P z n) errors + O(αs)

ⅆ𝑦 Δ 𝑣 𝑦 − Δ ⅆ(𝑦) 𝑕𝐵 ≈ 0.19(5)

Huey-Wen Lin — Los Alamos National Lab

slide-34
SLIDE 34

Helicity Distribution

§ Experimental comparison

  • A. Airap

apet etian an et al. . (HERM RMES) ES), Phys. s.Rev ev. . D71, , 012003 03 (2005)

§ Model: large-Nc predicts larger polarized antiquark asymmetry

chiral quark-soliton model

  • B. Dressl

sler er et al, , hep-ph/980 ph/9809487 9487

  • D. De Florian
  • rian et al.,

., Phys.R s.Rev ev. . D80, (2009) 034030

34 Huey-Wen Lin — Los Alamos National Lab

slide-35
SLIDE 35

Helicity Distribution

§ Experimental comparison § Model: large-Nc predicts larger polarized antiquark asymmetry

chiral quark-soliton model

  • B. Dressl

sler er et al, , hep-ph/980 ph/9809487 9487

35

  • D. De Florian
  • rian et al.,

., Phys. s.Rev ev. . D80, (2009) ) 034030

Huey-Wen Lin — Los Alamos National Lab

slide-36
SLIDE 36

Transversity Distribution

§ Exploratory study § Renormalization needed

Preliminary

Uncorrected bare lattice results

36 Huey-Wen Lin — Los Alamos National Lab

slide-37
SLIDE 37

Transversity Distribution

§ Exploratory study Removing O(MN

n/P z n) errors + O(αs)

§ Renormalization needed

Preliminary

37 Huey-Wen Lin — Los Alamos National Lab

slide-38
SLIDE 38

Transversity Distribution

§ Exploratory study

 We found δu

― < δd ―with

large sea asymmetry  Chiral quark-soliton model

P . Schwe weitzer r et al. PRD 64, 034013 13 (2001) 1)

CQS model

Preliminary

38

ⅆ𝑦 𝜀 𝑣 𝑦 − 𝜀 ⅆ(𝑦) 𝑕𝑈 ≈ −0.23(9)

Huey-Wen Lin — Los Alamos National Lab

slide-39
SLIDE 39

Pion Distribution Amplitude

§ Exploratory study

Preliminary

P

z {1, 2, 3} 2π⁄L

Only leading mass correction applied Dominated by O(Λ2

QCD/P z 2) errors

39 Huey-Wen Lin — Los Alamos National Lab

slide-40
SLIDE 40

§ Overcoming longstanding obstacle to x-distribution

 New idea by Ji for studying full x dependence of PDFs  Promising results on unpolarized and polarized sea asymmetry compared with experiments, even at non-physical pion mass

§ Caveats

 Not a precision calculation yet  Need to complete the other pz corrections (on-going; possibly done in a couple weeks)  Systematics due to large momenta (some ideas to improve it)

§ Need improvement for large-momentum sources

 Better overlapping boosted hadron smearing (asymmetric source)  Applications: large-q form factors, hadronic and flavor physics, …

Exciting time for hadron structure on the lattice

40 Huey-Wen Lin — Los Alamos National Lab

slide-41
SLIDE 41

§ Overcoming longstanding obstacle to x-distribution

 New idea by Ji for studying full x dependence of PDFs  Promising results on unpolarized and polarized sea asymmetry compared with experiments, even at non-physical pion mass

§ Hope this study motivates others to give Ji’s method a try § Caveats

 Not a precision calculation yet , proper renormalization,…  Systematics due to large momenta (some ideas to improve it)

§ Need improvement for large-momentum sources

 Applications: large-q form factors, hadronic and flavor physics, …

§ Many more quantities to study

 strange/charm/beauty sea distributions, gluons, TMD…

Summary and Outlook

Exciting time for hadron structure on the lattice

41 Huey-Wen Lin — Los Alamos National Lab