Chiral two- and three-nucleon forces with explicit Delta degree of … · 2017. 3. 1. · A. M....
Transcript of Chiral two- and three-nucleon forces with explicit Delta degree of … · 2017. 3. 1. · A. M....
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Chiral two- and three-nucleon forces Chiral two- and three-nucleon forces with explicit Delta degree of freedomwith explicit Delta degree of freedomChiral two- and three-nucleon forces Chiral two- and three-nucleon forces with explicit Delta degree of freedomwith explicit Delta degree of freedom
A. M. Gasparyan, Ruhr-Universität Bochum
in collaboration with
H. Krebs, E. Epelbaum,D. Siemens, V. Bernard, Ulf-G. Meißner
February 28, 2017, TRIUMF
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989OutlineOutlineOutlineOutline
➔Introduction&Motivation
➔2-N forces with explicit
➔3-N forces with explicit
➔N scattering with explicit
➔Summary and Outlook
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EFT with explicit EFT with explicit EFT with explicit EFT with explicit
➔Standard chiral expansion:
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EFT with explicit EFT with explicit EFT with explicit EFT with explicit
➔Standard chiral expansion:
➔Small scale expansion: Hemmert, Holstein, Kambor '98
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EFT with explicit EFT with explicit EFT with explicit EFT with explicit
➔Standard chiral expansion:
➔Small scale expansion: Hemmert, Holstein, Kambor '98
➔ gives a large contribution to LEC (c3,c
4) via resonance saturation
Bernard, Kaiser, Meißner '97
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EFT with explicit EFT with explicit EFT with explicit EFT with explicit
➔Standard chiral expansion:
➔Small scale expansion: Hemmert, Holstein, Kambor '98
➔ gives a large contribution to LEC (c3,c
4) via resonance saturation
Bernard, Kaiser, Meißner '97
➔Explicit decoupling of makes comparison with less theory more transparent Bernard, Fearing, Hemmert, Meißner '98
finite parts of LECs can be always chosen such that Appelquist, Carrazone '74 (Decoupling theorem)
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Small scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NF
Δ-less theory Δ-full theory: additional graphs
...
... Krebs, Epelbaum, Meißner '07
Keiser, Gerstendorfer, Weise '98
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Small scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NF
Δ-less theory Δ-full theory: additional graphs
...
... Krebs, Epelbaum, Meißner '07
Keiser, Gerstendorfer, Weise '98
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Small scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NF
Δ-less theory Δ-full theory: additional graphs
...
... Krebs, Epelbaum, Meißner '07
Keiser, Gerstendorfer, Weise '98
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Small scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NFSmall scale expansion of 2NF
Δ-less theory Δ-full theory: additional graphs
...
...
Higher orders
Krebs, Epelbaum, Meißner '07
Keiser, Gerstendorfer, Weise '98
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Preliminary results for NPreliminary results for N33LOLO2N forces with explicit 2N forces with explicit
Preliminary results for NPreliminary results for N33LOLO2N forces with explicit 2N forces with explicit
➔Only 2-pion-exchange contribution are considered (the long range part)
➔1/mN corrections are not yet included
➔Results for peripheral phases, no refitting of LEC's, no cut offs
➔No additional parameters, h
A and g
1 (N and )
are extracted from the fit to N scattering
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F and G wavesF and G wavesF and G wavesF and G waves
LO
NLO
N2LO
N3LO
N4LO
-less -full -less -full
Data:Nijmegen PWA
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F and G wavesF and G wavesF and G wavesF and G waves
LO
NLO
N2LO
N3LO
N4LO
-less -full -less -full F-waves might be sensitive to the short-range physics
Data:Nijmegen PWA
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F and G wavesF and G wavesF and G wavesF and G waves
LO
NLO
N2LO
N3LO
N4LO
-less -full -less -full F-waves might be sensitive to the short-range physics
Significant improvement compared with -less case
Data:Nijmegen PWA
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H and I wavesH and I wavesH and I wavesH and I waves
LO
NLO
N2LO
N3LO
N4LO
-less -full -less -full
Data:Nijmegen PWA
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ixing angles ixing angles , , , , , , ixing angles ixing angles , , , , , ,
LO
NLO
N2LO
N3LO
N4LO
-less -full
Data:Nijmegen PWA
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NLO
N2LO
Δ-less theory Δ-full theory: additional graphs
N3LO
N4LO
Small scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NF
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NLO
N2LO
Δ-less theory Δ-full theory: additional graphs
N3LO
N4LO
Small scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NF
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NLO
N2LO
Δ-less theory Δ-full theory: additional graphs
N3LO
N4LO
Small scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NFSmall scale expansion of 3NF
Large contributions to the ringand 2 topologies saturating some of the N5,6LO graphs in the less theory
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Long-range 3NFLong-range 3NFLong-range 3NFLong-range 3NF
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exchange
ringexchange
Long-range 3NFLong-range 3NFLong-range 3NFLong-range 3NF
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exchange
ringexchange
Long-range 3NFLong-range 3NFLong-range 3NFLong-range 3NF
➔Only the long range part considered (coordinate space)
➔Scheme independent
➔No unknown parameters
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Most general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NF
Krebs, Gasparyan, Epelbaum '13
Constraints:➔ Locality➔ Isospin symmetry➔ Parity and time-reversal invariance
Up to N4LO all considered contribution are local
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Most general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NF
Krebs, Gasparyan, Epelbaum '13
Constraints:➔ Locality➔ Isospin symmetry➔ Parity and time-reversal invariance
Up to N4LO all considered contribution are local
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Most general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NFMost general structure of a local 3NF
Krebs, Gasparyan, Epelbaum '13
Constraints:➔ Locality➔ Isospin symmetry➔ Parity and time-reversal invariance
Up to N4LO all considered contribution are local
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dTwo-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)Two-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)
TPE “structure functions” Fi in MeV”
in equilateral-triangle configuration
Krebs, Gasparyan, Epelbaum, in preparation
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dTwo-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)Two-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)
TPE “structure functions” Fi in MeV”
in equilateral-triangle configuration
Krebs, Gasparyan, Epelbaum, in preparation
➔similar results for large contributions
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dTwo-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)Two-pion-exhcange 3NF in Two-pion-exhcange 3NF in full andfull and
less approach (preliminary)less approach (preliminary)
TPE “structure functions” Fi in MeV”
in equilateral-triangle configuration
Krebs, Gasparyan, Epelbaum, in preparation
➔similar results for large contributions➔slightly different for small contributions
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Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
Bands indicate physicsnot described by explicitcontributions
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Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
➔Dominant effects come from N3LO-N4LO
Bands indicate physicsnot described by explicitcontributions
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Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
Two-pion-one-pion-exhcange 3NF in Two-pion-one-pion-exhcange 3NF in full full andand less approach (preliminary)less approach (preliminary)
➔Dominant effects come from N3LO-N4LO➔The largest N4LO contribution is saturated by
Bands indicate physicsnot described by explicitcontributions
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Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
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Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
➔Narrow bands:higher order contributionsbeyond are small
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Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
➔Narrow bands:higher order contributionsbeyond are small
➔Strong central isoscalar 3NFdue to double- excitation
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Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
Ring-topology 3NF in Ring-topology 3NF in full andfull and less approach (preliminary)less approach (preliminary)
➔Narrow bands:higher order contributionsbeyond are small
➔Strong central isoscalar 3NFdue to double- excitation
➔Explicit-approach is more efficient !
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exchange
ringexchange
N input for 3-Nucleon ForcesN input for 3-Nucleon ForcesN input for 3-Nucleon ForcesN input for 3-Nucleon Forces
➔Longest-range contributions
➔ Intermediate-range contributions
➔Short-range contributions
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exchange
ringexchange
N input for 3-Nucleon ForcesN input for 3-Nucleon ForcesN input for 3-Nucleon ForcesN input for 3-Nucleon Forces
➔Longest-range contributions
➔ Intermediate-range contributions
➔Short-range contributions
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N scattering up to N scattering up to N scattering up to N scattering up to
11
Siemens et al. In preparation
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N scattering up to N scattering up to N scattering up to N scattering up to
11
redundant, can be absorbed by redefining other LEC's
Siemens et al. In preparation
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N scattering up to N scattering up to N scattering up to N scattering up to
11
redundant, can be absorbed by redefining other LEC's
only two new parameters
Siemens et al. In preparation
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N differential cross sectionN differential cross section N differential cross sectionN differential cross section
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N differential cross sectionN differential cross section N differential cross sectionN differential cross section
➔Theoretical error-bands are narrower
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Quality of the fit to Quality of the fit to N data N data in the in the less and less and full full PT(without theoretical errors)PT(without theoretical errors)
Quality of the fit to Quality of the fit to N data N data in the in the less and less and full full PT(without theoretical errors)PT(without theoretical errors)
HB-NN HB-N covariant
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Quality of the fit to Quality of the fit to N data N data in the in the less and less and full full PT(without theoretical errors)PT(without theoretical errors)
Quality of the fit to Quality of the fit to N data N data in the in the less and less and full full PT(without theoretical errors)PT(without theoretical errors)
sizable reduction of the for a wider energy range
HB-NN HB-N covariant
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eSummarySummarySummarySummary
➔Preliminary results for -full chiral 2-nucleon and 3-nucleon forces at N3LO are presented
➔ 2-nucleon forces (peripheral phases): significant improvement compared to the -less case
➔3-nucleon forces: indication of a better convergence; sizable -contributions missing in -less N4LO 3NF ~O(1/)
➔New results for N scattering at order 4: much better fit to data
➔Completing construction of -full chiral 2N and 3N forces at N3LO and moving forward to even more precise nuclear forces.
OutlookOutlook