[PPT] - Quantum Monte Ca Carlo calculations s of neutron ma matter er wi PowerPoint Presentation

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Quantum Monte Ca Carlo calculations s of neutron ma matter er wi with Ch Chiral E Effective F Field Th Theory in interac actio ions

Ingo Tews,

In collaboration with J. Carlson, S. Gandolfi, A. Gezerlis, K. Hebeler, T. Krüger, J. Lynn, A. Schwenk, …

Talk, YITP program: "Nuclear Physics, Compact Stars, and Compact Star Mergers”, Oct.20, 2016, Kyoto

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 2

Equation of state

f neutron matter

Ultracold atoms Neutron-rich nuclei Neutron stars

Antoniadis et al., Science (2013) Credit: S. Rosswog

Gravitational waves from neutron star mergers

Zwierlein et al., Nature (2005) Credit: B.A. Brown

Mo Motivation

Ø The neutron-matter equation

f state at T=0 connects

several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial.

SLIDE 3

Oct. 20, 2016

Ingo Tews, NPCSM workshop 3 Roca-Maza et al., PRC (2013)

Ø Neutron matter at saturation density constrains neutron-skin thickness of neutron-rich nuclei Ø Experiments at RCNP, GSI, … Neutron-rich nuclei

Tamii et al., PRL (2011)

20 40 60 80 100 120 L (MeV) 28 32 36 40 44 J (MeV) EDFs

From αD

exp( 208Pb)

From αD

exp( 68Ni)

From αD

exp( 120Sn)

Credit: B.A. Brown

Ø The neutron-matter equation

f state at T=0 connects

several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial. Equation of state

f neutron matter

Mo Motivation

SLIDE 4

Oct. 20, 2016

Ingo Tews, NPCSM workshop 4

Ø The neutron-matter equation

f state at T=0 connects

several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial. Equation of state

f neutron matter

Lattimer, Lim, ApJ (2013).

Ø Neutron matter equation of state at saturation density and above determines mass-radius relation of neutron stars and gravitational- wave signal of neutron-star mergers Ø EOS properties at saturation density are correlated with neutron-star radii and gravitational wave peak frequency

P [MeV fm()] R,../⊙ [km] Lattimer, Lim

10 11 12 13 14 15 16 1.5 2 2.5 3 3.5 4 4.5 fpeak [kHz] R1.6 [km]

Bauswein et al., PRD (2012)

Mo Motivation

SLIDE 5

Oct. 20, 2016

Ingo Tews, NPCSM workshop 5

Nuclear Forces Many-body methods

Phenomenological forces (e.g. AV18 + UIX) Quantum Monte Carlo:

Very reliable

Equation of state

f neutron matter

Quantum Chromodynamics

Chiral effective field theory Broad range of methods

Mo Motivation

How to obtain the EOS in an ab initio approach?

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 6

Ou Outlin tline

Ø Chiral effective field theory:

Systematic basis for low-energy nuclear forces, connected to QCD
naturally includes many-body forces
Very successful in calculations of nuclei and nuclear matter

Ø Ab-initio calculations using chiral EFT can be used to constrain equation of state of neutron matter Ø Neutron-matter applications:

Symmetry energy
Neutron-star mass-radius relation

Ø Improving neutron-matter results using Quantum Monte Carlo methods Ø Summary

Epelbaum et al., PPNP (2006) and RMP (2009) IT, Krüger, Hebeler, Schwenk, PRL & PRC & PLB (2013) Gezerlis, IT, et al., PRL & PRC (2013, 2014, 2016)

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 7

u d d u d d u d d

R λ≫R

Effective field theory for nuclear forces Basic principle of effective field theory: At low energies (long wavelength) details not resolved! Ø Choose relevant degrees of freedom for low-energy processes Ø Systematic expansion of interactions constrained by symmetries

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 8

Chiral effecti tive field th theory for nuc nuclear fo forces

Separation of scales: Ø Low momenta 1 ≪ breakdown scale Λ4 Ø Expand in powers of

5 67 8

∼

, ) 8

Explicit degrees of freedom: Ø Pions and nucleons Write most general Lagrangian consistent with the symmetries of QCD Power counting: Ø : = 0: leading order (LO), Ø : = 2: next-to-leading order (NLO), ...

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer ...

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 8

Explicit degrees of freedom: Ø Pions and nucleons Ø Long-range physics explicit Ø Short-range physics expanded in general operator basis Ø High-momentum physics absorbed into short-range couplings, fit to experiment (phase shifts)

ρ

∼const.

2 LECs 7 LECs 15 LECs

Chiral effecti tive field th theory for nuc nuclear fo forces

Second scale: cutoff Λ (resolution): Ø Interactions Λ-dependent

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 9

Epelbaum et al., Eur. Phys. J (2015)

Systematic expansion of the nuclear forces: Ø Can work to desired accuracy Ø Can obtain systematic error estimates

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 10

Natural hierarchy of nuclear forces: Ø Two-body (NN) forces start at first order Ø Three-body (3N) forces start at third order (2 LECs) Many-body forces: Ø Have been found to be crucial ingredient to describe nuclear physics Fitting: Ø NN forces in NN system (NN phase shifts, …) Ø 3N forces in 3N/4N system (Binding energies, radii, …)

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 10

Consistent interactions: Ø Same couplings for two-nucleon and many-body sector Ø In contrast to phenomenological interactions

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 11

Chiral effecti tive field th theory for nuc nuclear fo forces

Many-body forces are crucial:

Calcium

Gallant et al., PRL (2012)

NN + 3N forces: Ø Give correct physics of neutron-rich nuclei

Oxygen

Otsuka et al., PRL (2010)

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 12

Many-body forces are crucial: NN + 3N forces: Ø Give correct saturation with theoretical uncertainties in nuclear matter

Drischler et al., PRC (2016) N Drischler et al., PRC (2016) Coraggio, Holt, Itaco, Machleidt, Marcucci, Sammarruca, PRC (2014)

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 13

Neutron matter: Ø Complete calculation at N3LO using many-body perturbation theory (MBPT)

IT, Krüger, Hebeler, Schwenk, PRL (2013)

Calculation is simpler in neutron matter: Ø Only certain parts of the many- body forces contribute Ø Chiral many-body forces completely predicted from NN sector

Chiral effecti tive field th theory for nuc nuclear fo forces

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 14

0.05 0.1 0.15

n [fm-3]

5 10 15 20

E/N [MeV]

EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV IT, Krüger, Hebeler, Schwenk, PRL (2013)

NN+3N interactions: Ø Have large impact on energy and uncertainty: 14-21 MeV NN interactions: Ø E/N at saturation density: 12-15 MeV Bands: Ø Include several sources of uncertainty: Ø Chiral Hamiltonians (cutoff, 3N LECs) Ø Many-body method

Ne Neutron

n matter

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 14

0.05 0.1 0.15

n [fm-3]

5 10 15 20

E/N [MeV]

EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV NLO lattice (2009) QMC (2010) APR (1998) GCR (2012) IT, Krüger, Hebeler, Schwenk, PRL (2013)

Good agreement with other calculations Ø but in those no theoretical uncertainties

Akmal et al., PRC (1998) Gandolfi et al., PRC (2012)

Chiral EFT puts constraints on neutron matter EOS

Ne Neutron

n matter

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 14

Lines from Hempel, Lattimer, G. Shen

0.05 0.1 0.15

n [fm-3]

5 10 15 20

E/N [MeV]

this work LS 180 LS 220 LS 375 FSU2.1 NL3 TM1 DD2 SFHo SFHx

Good agreement with other calculations Ø but in those no theoretical uncertainties

Akmal et al., PRC (1998) Gandolfi et al., PRC (2012)

Chiral EFT puts constraints on neutron matter EOS

Ne Neutron

n matter

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 15

Lattimer, Lim, ApJ (2013)

Put constraints on symmetry energy and its density dependence L: Ø >? = 28.9 − 34.9 MeV Ø E = 43.0 − 66.6 MeV Good agreement with experimental constraints

Sy Symmetry energy and L parameter

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 16

Drischler, Soma, Schwenk, PRC (2014)

Put constraints on symmetry energy and its density dependence L: Ø >? = 28.9 − 34.9 MeV Ø E = 43.0 − 66.6 MeV Good agreement with experimental constraints

Sy Symmetry energy and L parameter

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Ne Neutron

n Star

ars

Oct. 20, 2016

Ingo Tews, NPCSM workshop 17

Equation of state for neutron star matter: extend results to small Ye,p Agrees with standard crust EOS after inclusion of many-body forces

13.0 13.5 14.0

log 10 [g / cm3]

31 32 33 34 35 36 37

log 10 P [dyne / cm2]

1 2 3

with ci uncertainties

crust

crust EOS (BPS) neutron star matter

12 23 1

Extend to higher densities using polytropic expansion

Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013)

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 18

Constrain resulting EOS: causality and observed 1.97 M neutron star

Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013)

Ne Neutron

n Star

ars

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 19

8 10 12 14 16

Radius [km]

0.5 1 1.5 2 2.5 3

Mass [M°

.]

this work RG evolved

causality

IT, Krüger, Hebeler, Schwenk, PRL (2013)

Radius for 1.4 M neutron star: Ø G = 9.7 − 13.9 km Maximum mass neutron star: Ø JKLM ≤ 3.05J⊙ (14 km) Uncertainties from many-body forces and polytropic expansion Ø How to reduce uncertainties?

Ne Neutron

n Star

ars

SLIDE 24

Oct. 20, 2016

Ingo Tews, NPCSM workshop 20

If a 2.4 M neutron star was observed:

Hebeler et al., PRL (2010) and APJ (2013)

Ne Neutron

n Star

ars

SLIDE 25

Oct. 20, 2016

Ingo Tews, NPCSM workshop 21

Radius for 1.4 M neutron star: Ø G = 11.5 − 13.9 km Maximum mass neutron star: Ø JKLM ≤ 3.05J⊙ (14 km) Uncertainties from many-body forces and polytropic expansion

IT, Krüger, Gezerlis, Hebeler, Schwenk (2013)

Ne Neutron

n Star

ars

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 22

Nuclear Forces Many-body methods

Status: Ø Sizeable uncertainty for chiral EFT calculations of neutron matter Ø Phenomenological interactions provide a good description of light nuclei and nulear matter Ø But it is not clear how to systematically improve their quality Ø No systematic uncertainty estimates

Im Improvi ving g neu eutron-ma matter r ba band nd

Quantum Monte Carlo:

Very reliable

Quantum Chromodynamics

Chiral effective field theory Broad range of methods Phenomenological forces (e.g. AV18 + UIX)

SLIDE 27

Oct. 20, 2016

Ingo Tews, NPCSM workshop 22

Nuclear Forces Many-body methods Quantum Chromodynamics

Status: Ø Sizeable uncertainty for chiral EFT calculations of neutron matter Goal: Combine QMC methods and chiral EFT Ø Minimize uncertainty to enable precision studies of nuclear matter Ø Check convergence of MBPT calculations and other approaches

Im Improvi ving g neu eutron-ma matter r ba band nd

Quantum Monte Carlo:

Very reliable

Chiral effective field theory

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 23

0.05 0.1 0.15

n [fm-3]

5 10 15 20 25 30

E/N [MeV]

Hartree Fock 2nd order 3rd order

EGM 450/500 MeV

0.05 0.1 0.15

n [fm-3]

Hartree Fock 2nd order 3rd order

EGM 450/700 MeV

0.05 0.1 0.15

n [fm-3]

Hartree-Fock 2nd order 3rd order

EM 500 MeV

0.05 0.1 0.15

n [fm-3]

5 10 15 20 25 30 Hartree-Fock 2nd order 3rd order

POUNDerS N2LO NN

0.05 0.1 0.15

n [fm-3]

5 10 15 20 25 30

E/N [MeV]

Hartree-Fock 3rd order 2nd order

EGM 550/600 MeV

0.05 0.1 0.15

n [fm-3]

Hartree-Fock 3rd order 2nd order

EGM 600/600 MeV

0.05 0.1 0.15

n [fm-3]

Hartree-Fock 3rd order 2nd order

EGM 600/700 MeV

0.05 0.1 0.15

n [fm-3]

5 10 15 20 25 30 Hartree-Fock 3rd order 2nd order

EM 600 MeV

Im Improvi ving g neu eutron-ma matter r ba band nd

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 24

Solve the many-body Schrödinger equation Basic steps: Ø Choose trial wavefunction which overlaps with the ground state Ø Evaluate propagator for small timestep ΔQ, feasible only for local potentials Ø Make consecutive small time steps using Monte Carlo techniques to project out ground state

More details: Carlson, Gandolfi, Pederiva, Pieper, Schiavilla, Schmidt, Wiringa, RMP (2015)

Qua Quantum tum Mo Monte Carl rlo me metho thod

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 25

Particle in a 1D box, solution: RS T = 2

sin YZT , \S = Y]Z]

2 Basic steps: Ø Choose parabolic trial wavefunction which overlaps with the ground state

Animation by Joel Lynn, TU Darmstadt

Qua Quantum tum Mo Monte Carl rlo me metho thod

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 25

Particle in a 1D box, solution: RS T = 2

sin YZT , \S = Y]Z]

2 Ø Make consecutive small timesteps, Q = 1.4

, ^_`a

Animation by Joel Lynn, TU Darmstadt

Qua Quantum tum Mo Monte Carl rlo me metho thod

SLIDE 32

Oct. 20, 2016

Ingo Tews, NPCSM workshop 26

S. Pieper and R. Wiringa

Qua Quantum tum Mo Monte Carl rlo me metho thod

SLIDE 33

Oct. 20, 2016

Ingo Tews, NPCSM workshop 27

Nuclear Forces Many-body methods Equation of state

f neutron matter

Quantum Chromodynamics

Krüger, IT, Hebeler, Schwenk, PRC (2013)

Problems: 1) Regulator → choose local regulator 2) Contact operators → use Fierz freedom

Chiral effective field theory:

Systematic, generally nonlocal

Quantum Monte Carlo:

Precise, needs local interactions

Lo Local ch chiral interact ctions

SLIDE 34

Oct. 20, 2016

Ingo Tews, NPCSM workshop 28

Lo Local ch chiral interact ctions

Ø Leading order f(h) = f

jklm h

+ fopq Ø Pion exchange local → local regulator Ø Contact potential:

→ Only two independent (Pauli principle)

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer ...

r

sklt(u) = 1 − exp(−u./Gh .)

r

yzk{m(u) = | exp(−u./Gh .)

SLIDE 35

Oct. 20, 2016

Ingo Tews, NPCSM workshop 28

Lo Local ch chiral interact ctions

Ø Choose local set of short-range operators at NLO (7 out of 14)

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer ...

v v v

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Oct. 20, 2016

Ingo Tews, NPCSM workshop 28

Ø Choose local set of short-range operators at NLO (7 out of 14) Ø Pion exchanges up to N2LO are local Ø This freedom can be used to remove all nonlocal operators up to N²LO Ø LECs fit to phase shifts

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer ... Gezerlis, IT, Epelbaum, Gandolfi, Hebeler, Nogga, Schwenk, PRL (2013) Gezerlis, IT, Epelbaum, Freunek, Gandolfi, Hebeler, Nogga, Schwenk, PRC (2014)

Lo Local ch chiral interact ctions

SLIDE 37

Oct. 20, 2016

Ingo Tews, NPCSM workshop 29 Gezerlis, IT, Epelbaum, Freunek, Gandolfi, Hebeler, Nogga, Schwenk, PRC (2014) Ekström et al., PRL (2013)

Compare to NNLOopt:

Ph Phase sesh shifts ts for

r loc

local al po potentials

SLIDE 38

Oct. 20, 2016

Ingo Tews, NPCSM workshop 30

NN-only calculation: Ø QMC: Statistical uncertainty of points negligible Ø Bands include NN cutoff variation Gh = 1.0 − 1.2 fm Ø Order-by-order convergence up to saturation density

Q Q Q

Gezerlis, IT, Epelbaum, Freunek, Gandolfi, Hebeler, Nogga, Schwenk, PRL (2013) and PRC (2014)

QMC QMC re results for

r NN

NN force ces

SLIDE 39

Oct. 20, 2016

Ingo Tews, NPCSM workshop 31 Gezerlis, IT, Epelbaum, Freunek, Gandolfi, Hebeler, Nogga, Schwenk, PRC (2014)

Many-body perturbation theory: Ø Excellent agreement with QMC for soft potentials (Gh = 1.2 fm) Ø Validates perturbative calculations for those interactions

Bench chmark of

f MB

MBPT

SLIDE 40

Oct. 20, 2016

Ingo Tews, NPCSM workshop 32

NN-only calculation Ø Good agreement with other approaches: MBPT with N]LO EGM

IT, Krüger, Hebeler, Schwenk, PRL (2013)

CC with N]LOkÄm

Hagen, Papenbrock, Ekström, Wendt, Baardsen, Gandolfi, Hjorth-Jensen, Horowitz, PRC (2013)

MBPT with N]LOkÄm

IT, Krüger, Gezerlis, Hebeler, Schwenk, NTSE (2013)

CIMC with N]LOkÄm

Roggero, Mukherjee, Pederiva, PRL (2014) 0.05 0.1 0.15

n [fm-3]

5 10 15

E/N [MeV]

AFDMC N2LO MBPT (N2LO EGM) CC (N2LOopt) MBPT (N2LOopt) CIMC (N2LOopt)

Gezerlis, IT, Epelbaum, Freunek, Gandolfi, Hebeler, Nogga, Schwenk, PRC (2014)

QMC QMC re results for

r NN

NN force ces

SLIDE 41

Oct. 20, 2016

Ingo Tews, NPCSM workshop 33

Next: inclusion of leading 3N forces Three topologies: Ø Two-pion exchange f

Å

Ø One-pion-exchange contact f

Ç

Ø Three-nucleon contact f

^

f

Ç

f

Å

f

^

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer ...

QMC QMC with ith ch chiral 3N 3N force ces

Only two new couplings: ÉÇ and cq

SLIDE 42

Oct. 20, 2016

Ingo Tews, NPCSM workshop 34

QMC QMC with ith ch chiral 3N 3N force ces

Two-pion-exchange most important in PNM, usually f

Ç and f ^ vanish in neutron matter:

ÉÇ due to spin-isospin structure, É^ due to Pauli principle Only true for regulator symmetric in particle labels like commonly used nonlocal regulators, not for local regulators É, term: Tucson-Melbourn S-wave interaction É),. term: Fujita-Miyazawa interaction

Ø Only three-nucleon two-pion exchange ∼ É, and É) Ø Auxiliary-field diffusion Monte Carlo: Ø NN + 3N TPE forces Ø Gh = 1.0 − 1.2 fm Ø G)á = 1.0 − 1.2 fm Ø 3N cutoff dependence small Ø TPE 3N contributions ≈ 1 − 2 MeV at Yh

QMC QMC resul sults ts wi with th 3N TPE TPE

SLIDE 44

Oct. 20, 2016

Ingo Tews, NPCSM workshop 35

0.05 0.1 0.15

n [fm

3]

5 10 15 20

E/N [MeV]

Local N2LO (this work) MBPT EGM N2LO pp ladder EM N2LO CC N2LOopt SCGF N2LOopt IT, Gandolfi, Gezerlis, Schwenk, PRC (2016)

Ø Only three-nucleon two-pion exchange ∼ É, and É) Ø Auxiliary-field diffusion Monte Carlo: Ø NN + 3N TPE forces Ø Gh = 1.0 − 1.2 fm Ø G)á = 1.0 − 1.2 fm Ø 3N cutoff dependence small Ø TPE 3N contributions ≈ 1 − 2 MeV at Yh Ø smaller than for nonlocal regulators

QMC QMC resul sults ts wi with th 3N TPE TPE

SLIDE 45

Oct. 20, 2016

Ingo Tews, NPCSM workshop 35

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

R3N [fm]

10 10.5 11 11.5 12 12.5 13

E/N [MeV]

n1=4, n2=1 n1=2, n2=2 n1=2, n2=4 n1=4, n2=2 n1=8, n2=1

NN only R0=1.2 fm n = 0.16 fm-3

flong=(1-e-(r/R3N)n1)n2

IT, Gandolfi, Gezerlis, Schwenk, PRC (2016)

Ø Only three-nucleon two-pion exchange ∼ É, and É) Ø Auxiliary-field diffusion Monte Carlo: Ø NN + 3N TPE forces Ø Gh = 1.0 − 1.2 fm Ø G)á = 1.0 − 1.2 fm Ø 3N cutoff dependence small Ø TPE 3N contributions ≈ 1 − 2 MeV at Yh Ø smaller than for nonlocal regulators Ø Independent of exact regulator form

QMC QMC resul sults ts wi with th 3N TPE TPE

SLIDE 46

Oct. 20, 2016

Ingo Tews, NPCSM workshop 36

Lo Local NN NN force ces in HF

Ø Example: two-body regulators at Hartree-Fock: r

{àt /âä = exp − ã

Λ

]S

, r

{àt /âáä = exp −2 å

Λ

]S

Ø After antisymmetrization we have a direct and an exchange term. Ø Spin-dependent interactions at Hartree-Fock: only exchange term survives Ø Effective cutoff smaller for local regulators! Direct term: ã = å − åç = 0 → r

{àt /âä = 1,

r

{àt /âáä = exp −2 å

Λ

]S

Exchange term: ã = å − åç = 2å → r

{àt /âä = exp − 2å

Λ

]S

, r

{àt /âáä = exp −2 å

Λ

]S

SLIDE 47

Oct. 20, 2016

Ingo Tews, NPCSM workshop 37 Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016)

Ø Fit É^ and ÉÇ to 4He binding energy and n-| scattering

Fi Fits of 3N LECs Cs

SLIDE 48

0.05 0.1 0.15

n [fm

3]

5 10 15 20

E/N [MeV]

Local N2LO (this work) MBPT EGM N2LO pp ladder EM N2LO CC N2LOopt SCGF N2LOopt

Oct. 20, 2016

Ingo Tews, NPCSM workshop 38 9 8 7 6 5 E (MeV)

3H 3He 4He

31 25 19 13

3H 3He 4He

0.8 1.0 1.2 1.4 1.6 1.8 2.0

q hr2

pti (fm)

NLO N2LO (D2, Eτ) Exp.

Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016)

Ø Chiral interactions at N]LO simultaneously reproduce the properties of A=3, 4, 5 systems and of neutron matter Ø Commonly used phenomenological 3N interactions fail for neutron matter

Sarsa, Fantoni, Schmidt, Pederiva, PRC (2003)

Re Results

SLIDE 49

Oct. 20, 2016

Ingo Tews, NPCSM workshop 39 IT, Krüger, Hebeler, Schwenk, PRL (2013) Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016)

Comparing to N)LO calculation:

Re Results

Chiral EFT forces with the Quantum Monte Carlo method: Ø Energies agree well with MBPT result within uncertainty bands Ø Many-body uncertainty negligible Ø uncertainties comparable but QMC band only at N2LO and includes also hard interactions

Ø Improve local chiral interactions: Ø Develop N3LO potentials

SLIDE 50

Ne Next step: : N3LO

LO

Ø Problem: only 8 out of 30 possible operators local Ø But: work in progress!

Oct. 20, 2016

Ingo Tews, NPCSM workshop 40

Improve local chiral interactions: Ø Develop maximally local N3LO potentials Ø Inclusion of Delta degree of freedom

SLIDE 51

Finite Volume Calcu culations

Oct. 20, 2016

Ingo Tews, NPCSM workshop 41

Ø Long-term goal: Matching of chiral EFT couplings to lattice QCD results Ø Enable chiral EFT predictions from first principles Motivation: Ø Lattice QCD is the only ab initio method available to solve QCD directly at low energies but computational costs too high to compute more than a few particles Ø Connect ab-initio nuclear physics to the underlying theory of QCD by studying, e.g., few-neutron systems in a box

Credit: P. Klos

SLIDE 52

Oct. 20, 2016

Ingo Tews, NPCSM workshop 42

Use Luescher formula to extract infinite-volume scattering data from finite volume calculations:

Finite Volume Calcu culations

Klos, Lynn, IT, Gandolfi, Gezerlis, Hammer, Hoferichter, Schwenk, arXiv:1604:01387, accepted for PRC

10 20 30 40 50 60

L [fm]

0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

q

2

AFDMC, sph. node AFDMC, non-sph. node Lüscher, a=−18.9 fm, re=2.01 fm Lüscher fit, a=-19.1(3) fm 1st excited state LO R0=1.0 fm 10 20 30 40 50 60

L [fm]

0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05

q

2

AFDMC, NLO R0=1.0 fm Lüscher, a=−18.9 fm, re=2.71 fm (NLO) AFDMC, N2LO R0=1.0 fm Lüscher, a=−18.9 fm, re=2.79 fm (N2LO) Lüscher fit to ground state, N2LO, a=−18.8(3) fm ground state

Ø Easy to extend to larger systems or, e.g., systems with hyperons

SLIDE 53

Oct. 20, 2016

Ingo Tews, NPCSM workshop 43

Sum Summary

Chiral effective field theory: ØProvides constraints on symmetry energy, neutron star EOS ØImprovement of neutron-matter EOS work in progress ØUsing QMC methods with higher order interactions expected to reduce theoretical uncertainties by a factor of two Constraints on symmetry energy and neutron stars: Ø >? = 28.9 − 34.9 MeV Ø E = 43.0 − 66.6 MeV Ø Radius for 1.4 M neutron star: 9.7 − 13.9 km

Gezerlis, IT, Epelbaum, Gandolfi, Hebeler, Nogga, Schwenk, PRL (2013) & PRC (2014) IT, Gandolfi, Gezerlis, Schwenk, PRC (2016) Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016)

8 10 12 14 16

Radius [km]

0.5 1 1.5 2 2.5 3

Mass [M°

.]

this work RG evolved

causality

IT, Krüger, Hebeler, Schwenk, PRL & PRC (2013)

SLIDE 54

Thanks to my collaborators: Ø Technische Universität Darmstadt: H.-W. Hammer, K. Hebeler, P. Klos, J. Lynn, A. Schwenk Ø Universität Bochum: E. Epelbaum Ø Ohio State University: A. Dyhdalo, D. Furnstahl Ø Los Alamos National Laboratory: J. Carlson, S. Gandolfi Ø University of Guelph: A. Gezerlis Ø Forschungszentrum Jülich: A. Nogga Ø Institute for Nuclear Theory: M. Hoferichter Thanks to FZ Jülich for computing time and NIC excellence project.

Oct. 20, 2016

Ingo Tews, NPCSM workshop 44