Pion Valence Quark Distribution from Lattice Calculable ...J. Badier et all., Z. Phys. C18, 281...
Transcript of Pion Valence Quark Distribution from Lattice Calculable ...J. Badier et all., Z. Phys. C18, 281...
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Pion Valence Quark Distribution from Lattice Calculable Current-Current Correlations
Colin EgererIn Collaboration with R. Sufian, J. Karpie, K. Orginos, J. Qiu & D. Richards
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➔ Models not a complete picture
➔ Global analysis techniques not uniquely defined
➔ Not fully known
An Essential Window into Hadronic Structure
2
➔ Essential for interpretation of high-energy scattering data & BSM searches at energy frontier
DIS
Parton Model
PDFs - non-perturbative
pQCD
M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018)
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Outline
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➔ An essential window
➔ Lattice QCD and Light-Cone Physics?
➔ Lattice “Cross Sections”
➔ The pion - an economical theater
➔ Numerical Investigation
◆ Ensemble specifics
◆ Pion valence distribution
◆ Results and comparison with literature
➔ Progress & Outlook
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A Non-perturbative Study of QCD
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➔ Low-energies & a strong coupling
➔ Real time path integral
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A Non-perturbative Study of QCD
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➔ Low-energies & a strong coupling
➔ Real time path integral
Uncountably infinite parameter space
➔ Lattice QCD discretize and Wick rotate to imaginary time
➔ Importance sampling
Tremendous success in studying QCD spectrum and accessing state-to-vacuum transitions
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Towards the Extraction of PDFs from the Lattice
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➔ All light-cone physics is lost in a Euclidean spacetime
➔ Moments calculations & the OPE
◆ Power-divergent mixing/gauge noise for high moments
➔ Led to quasi/pseudo-PDF proposals
X. Ji, Phys. Rev. Lett. 110, 262002 (2013), arXiv:1305.1539 [hep-ph]
K. Orginos, A. Radyushkin, J. Karpie, and S. Zafeiropoulos, Phys. Rev. D96, 094503 (2017), arXiv:1706.05373 [hep-ph]
?!
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Towards the Extraction of PDFs from the Lattice
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➔ All light-cone physics is lost in a Euclidean spacetime
➔ Moments calculations & the OPE
◆ Power-divergent mixing/gauge noise for high moments
➔ Led to quasi/pseudo-PDF proposals
X. Ji, Phys. Rev. Lett. 110, 262002 (2013), arXiv:1305.1539 [hep-ph]
K. Orginos, A. Radyushkin, J. Karpie, and S. Zafeiropoulos, Phys. Rev. D96, 094503 (2017), arXiv:1706.05373 [hep-ph]
?!
➢ Beyond quasi-/pseudo-PDF approaches
○ Hadronic Tensor (K. F. Liu et al., Phys. Rev. Lett. 72, Phys. Rev. D 59 & D 62)○ Auxiliary quark methods (U. Aglietti et al., Phys. Lett. B441; W. Detmold & C.J. D. Lin, Phys. Rev.
D73; V. Braun & D. Mueller, Eur. Phys. J. C55)○ “OPE without OPE” (A. J. Chambers et al., Phys. Rev. Lett. 118)
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Lattice “Cross Sections” (LCS)
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Y. Q. Ma & J. W. Qiu, Phys. Rev. D 98, no. 7, 074021 (2018), arXiv:1404.6860 [hep-ph]Y. Q. Ma & J. W. Qiu, Phys. Rev. Lett. 120, no. 2, 022003 (2018), arXiv:1709.03018 [hep-ph]
➢ Defining properties:
○ calculable in LQCD with Euclidean time
○ well-defined continuum limit; UV finite
○ share same collinear div. w/ PDFs
➢ Single-hadron matrix elements of renormalized non-local ops.
PDFsPseudo-structure Functions
Hard Coefficients
valid for any finite provided
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Pion Structure - A First Numerical LCS Study
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➔ Chiefly from pionic Drell-Yan
➔ Importance of pion cannot be understated
◆ DCSB and long-range interaction◆ nucleon quark sea flavor asymmetry
E.g. J. S. Conway et al., Phys. Rev. D 39, 39 (1989)J. Badier et all., Z. Phys. C18, 281 (1983) B. Betev et al., Z. Phys. C28, 9 (1985)
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PR12-15-006: TDIS @ JLab(pion structure via Sullivan process)
Pion Structure - A First Numerical LCS Study
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➔ Chiefly from pionic Drell-Yan
➔ Importance of pion cannot be understated
◆ DCSB and long-range interaction◆ nucleon quark sea flavor asymmetry
J. S. Conway et al., Phys. Rev. D 39, 39 (1989)
E.g. J. S. Conway et al., Phys. Rev. D 39, 39 (1989)J. Badier et all., Z. Phys. C18, 281 (1983) B. Betev et al., Z. Phys. C28, 9 (1985)
LO Analysis Conflicts with Expectations
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PR12-15-006: TDIS @ JLab(pion structure via Sullivan process)
Pion Structure - A First Numerical LCS Study
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➔ Chiefly from pionic Drell-Yan
➔ Importance of pion cannot be understated
◆ DCSB and long-range interaction◆ nucleon quark sea flavor asymmetry
Can a LCS calculation serve as a discriminator?
J. S. Conway et al., Phys. Rev. D 39, 39 (1989)
E.g. J. S. Conway et al., Phys. Rev. D 39, 39 (1989)J. Badier et all., Z. Phys. C18, 281 (1983) B. Betev et al., Z. Phys. C28, 9 (1985)
LO Analysis Conflicts with Expectations
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Many Wick Contractions
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➔ 4pt function with light-quark currents
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Many Wick Contractions
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➔ 4pt function with light-quark currents
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Many Wick Contractions
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➔ Heavy-light currents
◆ sufficiently small and leading-twist contribution to PDFW. Detmold & C.J. D. Lin, Phys.Rev. D73 (2006) 014501 hep-lat/0507007
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Currents to Consider
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➔ Vector/axial currents pseudo-scalar hadrons
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Currents to Consider
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➔ Vector/axial currents pseudo-scalar hadrons
➔ Isolation of pseudo-structure functions
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Currents to Consider
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➔ Vector/axial currents pseudo-scalar hadrons
➔ Isolation of pseudo-structure functions
➔ Selecting: and
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Matching Kernels
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➔ Factorized relation asymptotic parton state order-by-order in
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Matching Kernels
10
➔ Factorized relation asymptotic parton state order-by-order in
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Matching Kernels
10
➔ Factorized relation asymptotic parton state order-by-order in
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The Essence of the Calculation
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➔ Randomly chosen source point
➔ Momentum projections and src/snk seps.
◆ ...costly inversions
➢ Unrestricted energy flow
➢ Heavy auxiliary quark propagators
W. Detmold & C.J. D. Lin, Phys.Rev. D73 (2006) 014501 hep-lat/0507007
High-momenta essential
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The Essence of the Calculation
11
➔ Randomly chosen source point
➔ Momentum projections and src/snk seps.
◆ ...costly inversions
➢ Unrestricted energy flow
➢ Heavy auxiliary quark propagators
W. Detmold & C.J. D. Lin, Phys.Rev. D73 (2006) 014501 hep-lat/0507007
High-momenta essential
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The Essence of the Calculation
11
➔ Randomly chosen source point
➔ Momentum projections and src/snk seps.
◆ ...costly inversions
➢ Unrestricted energy flow
➢ Heavy auxiliary quark propagators
W. Detmold & C.J. D. Lin, Phys.Rev. D73 (2006) 014501 hep-lat/0507007
High-momenta essential
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The Essence of the Calculation
11
➔ Randomly chosen source point
➔ Momentum projections and src/snk seps.
◆ ...costly inversions
➢ Unrestricted energy flow
➢ Heavy auxiliary quark propagators
W. Detmold & C.J. D. Lin, Phys.Rev. D73 (2006) 014501 hep-lat/0507007
High-momenta essential
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Ensemble & Typical Ratio Fits
12
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The Pseudo-structure Function
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➢ An ill-posed inverse !
➔ How best to extract PDFs?
➢ Extra information needed
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The Pseudo-structure Function
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➢ An ill-posed inverse !
➔ Smooth, physically-motivated models
➔ ROOT for numerical integration Rene Brun & Fons Rademakers, Nucl. Inst. & Meth. in Phys. Res. A 389 (1997) 81-86
➔ How best to extract PDFs?
➢ Extra information needed
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Extracted Valence PDF
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Comparison with the Literature
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R. Sufian, J. Karpie, CE et al., (2019) arXiv:1901.03921 [hep-lat]**To appear in PRD**
➔ Appear to be capturing essential physics --- gluons esp. important in pion
P. C. Barry et al., Phys. Rev. Lett. 121, 152001 (2018), arXiv:1804.01965 [hep-ph]
➔ commensurate
➔ consistent w/ NLL threshold soft-gluon resummation effects (ASV)
➔ favors
➔ no statistically meaningful change in distribution as varied
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In Progress
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➔ Populating with off-axis separations
◆ maintaining
◆ improving statistics
Discretization effects...
Momentum projections as a time-slice average
G. S. Bali et al., Phys. Rev. D 98, no. 9, 094507 (2018), arXiv:1807.06671 [hep-lat]G. S. Bali et al., Eur. Phys. J. C78 (2018) no. 3, 217, arXiv:1709.04325 [hep-lat]
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In Progress
16
➔ Populating with off-axis separations
◆ maintaining
◆ improving statistics
➔ Completing isolation of NLO kernels
◆ logarithmic corrections ( and related )
◆ power corrections & higher-twist effects
Discretization effects...
Momentum projections as a time-slice average
G. S. Bali et al., Phys. Rev. D 98, no. 9, 094507 (2018), arXiv:1807.06671 [hep-lat]G. S. Bali et al., Eur. Phys. J. C78 (2018) no. 3, 217, arXiv:1709.04325 [hep-lat]
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In Progress
16
➔ Populating with off-axis separations
◆ maintaining
◆ improving statistics
➔ Completing isolation of NLO kernels
◆ logarithmic corrections ( and related )
◆ power corrections & higher-twist effects
➔ Finite volume effects?
➔ Power of LCS formalism lies in a “global” analysis of calculated matrix elements◆ analyzing
◆ Can LCS data be competitive enough to include in global analyses?
Discretization effects...
Momentum projections as a time-slice average
R. Briceño et al., Phys. Rev. D 98, no. 1, 014511 (2018), arXiv:1805.01034 [hep-lat]
G. S. Bali et al., Phys. Rev. D 98, no. 9, 094507 (2018), arXiv:1807.06671 [hep-lat]G. S. Bali et al., Eur. Phys. J. C78 (2018) no. 3, 217, arXiv:1709.04325 [hep-lat]
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BACKUPS
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More on quasi/pseudo-distributions
18
X. Ji, Phys. Rev. Lett. 110, 262002 (2013), arXiv:1305.1539 [hep-ph]
K. Orginos, A. Radyushkin, J. Karpie, and S. Zafeiropoulos, Phys. Rev. D96, 094503 (2017), arXiv:1706.05373 [hep-ph]
Fourier transform over length of Wilson line
Fourier transform Ioffe time - fixed length Wilson line
K. Cichy & M. Constantinou, arXiv:1811.07248v1 [hep-lat]
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Leading Order Coefficient Functions - Coordinate Space
19
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Matching Kernels & the Pion Valence Distribution
10
➔ Factorized relation asymptotic parton state order-by-order in
➔ To ensure access to valence distribution◆ momentum space pseudo-structure fns.
Y. Q. Ma & J. W. Qiu, Phys. Rev. Lett. 120, no. 2, 022003 (2018), arXiv:1709.03018 [hep-ph]
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➔ Solution of QCD from first-principles
➔ “No free lunch!”
◆ signal-to-noise problems
◆ excited-state contamination
◆ reduced symmetry groups
◆ discretization/finite volume effects
◆ quark mass dependence
➔ Systematics can be systematically removed with further computation...
Physics in a Discretized Euclidean Box
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Momentum Smearing
21
➔ Dilemma >>>>>>> Large Ioffe time large momentum
G. S. Bali et al. Phys. Rev. D93, 094515 (2016), arXiv:1602.05525 [hep-lat]➔ Rotate gauge links
*** But what are these phases? ***
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Scanning for Momentum Phases
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Preliminary E2 Pseudo-structure Functions
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Many Combinations….
Vector-Vector of E1 ensemble
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➔ Correlation fns. carry spacetime signature info
◆ time-indep matrix elements do not
➔ quasi-PDF carries no info about spacetime signature
➔ spacetime signature of ops. only arise when time-evolved
◆ should carry no E vs. M distinction
Euclidean vs. Minkowski Matrix Elements
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➔ With no temporal extent
◆ 1-loop perturbative calculation (scalar field theory)
◆ all-orders derivation of LSZ reduction in Euclidean space
R. A. Briceño et al., Phys. Rev. D 96, no. 1, 014502 (2017), arXiv:1703.06072