[PPT] - Lattice QCD for Nuclear Physics Saul D. Cohen (for NPLQCD PowerPoint Presentation

SLIDE 1

Lattice QCD for Nuclear Physics

Saul D. Cohen (for NPLQCD Collaboration)

International Workshop on Lattice QCD 2013 October 18

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 1 / 38

SLIDE 2

Outline

1 Lattice QCD for Nuclear Spectroscopy

2 Quarkonia in Nuclei

3 Nuclear Sigma Term

4 Nuclear Equation of State

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 2 / 38

SLIDE 3

Nuclear LQCD

Section 1 Lattice QCD for Nuclear Spectroscopy

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 3 / 38

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Nuclear LQCD

NPLQCD Collaboration

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 4 / 38

SLIDE 5

Nuclear LQCD Strategy

The Trouble with Nucleons Nucleons are more complicated than mesons because...

Noise Signal diminishes at large t relative to noise Excited-state contamination Nearby excited state Roper N(1440) Hard to extrapolate in pion mass ∆ resonance nearby; multiple expansions, poor convergence Requires large volume and high statistics Ensembles are not always generated with nuclear physics in mind Quark contractions Naively scale like Nu!Nd!Ns! For a typical nucleus: ((3A/2)!)2, α: 518400, 12C: 4 × 1031

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 5 / 38

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Nuclear LQCD Strategy

Signal-to-Noise Ratio

Why is noise such a problem for nucleons?

Recall that variance is σ2

O = O2 − O2.

For a nucleon correlator, our operator is a correlator: O ∝ qqq(t) ¯ q¯ q¯ q(0) What you want p

u u d

p

u u d

p

u u d

p

u u d

S/N ∼ e−MNt/e−2MNt/2 ∼ const What you get Π Π Π

u u d

Π Π Π

u u d u u d u u d

∼ e−MNt/e−3Mπt/2 ∼ e−(MN− 3

2 Mπ)t

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 6 / 38

SLIDE 7

Nuclear LQCD Strategy

The Golden Window

Things don’t always have to go wrong

Although the exponential behavior is known, the coefficients are not. Suppose there is suppression of the overlap of the N†N onto the 3π state. σ2 = Z0e−2AMNt + A2 (MπL)3 Z1e−(2(A−1)MN+3Mπ)t + . . .

n nn 0 0 0 0n 10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 tbt bt E

For Zn ≪ Zn+1, tgold ∼

2 2MN−3Mπ ln

(MπL)3

A2

Momentum-projected
perators cover full volume;

pions only form if N and N† coincide spatially.

[PRD80,074501 (2009)]

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 7 / 38

SLIDE 8

Nuclear LQCD Strategy

Excited-State Contamination

Trade-off: We must remain at small t to avoid noise, but we must wait for large t for excited states to die away Use large t, defeat noise with enormous statistics Craft sources that improve overlap with ground state or reduce overlap with noise or both Directly address excited states in analysis

Multistate fitting Variational method or matrix Prony

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 8 / 38

SLIDE 9

Nuclear LQCD Strategy

Contractions

Building a multibaryon operator

Need to tame squared-factorial behavior

Symmetries give substantial improvements: Triton: 2880 → 93, 4He: 518400 → 1107 Consider A =

a wa1,a2,...,anq(a1)q(a2) . . . q(an)

Use total antisymmetry: A = N

k=1 ˜

wa1,a2,...,an

k

i ǫi1,i2,...,inq(ai1)q(ai2) . . . q(ain)

Constrain wavefunction to include only 3-quark baryon subblocks Ba1,a2,a3 = NB

k=1 ˜

wc1,c2,c3

k

i ǫi1,i2,i3S(ci1, a1)S(ci2, a2)S(ci3, a3)

[PRD87,114512 (2013)]

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 9 / 38

SLIDE 10

Nuclear LQCD Strategy

Contractions

Assembling blocks

Use recursion and save intermediate blocks

Connect each baryon in all possible ways to the quarks at the source. With M terms in the baryon side and N on the quark side Final cost: M × N × Nu!Nd!Ns! 2A−NΣ/Λ

[PRD80,074501 (2009)]

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 10 / 38

SLIDE 11

Nuclear LQCD Results

H Dibaryon

Is it bound?

Long predicted by Jaffe to be bound-state of ΛΛ [PRL38,195 (1977)] Experiments inconclusive NPLQCD Calculation [PRD85,054511 (2011)]

Anisotropic 2+1-flavor 390-MeV O(a)-improved Wilson-clover fermions as = 0.1227 fm, as/at ≈ 3.5 2 volumes: 3 fm and 4 fm Very high statistics: 178 × 2215 (3 fm), 174 × 739 (4 fm)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 11 / 38

SLIDE 12

Nuclear LQCD Results

H Dibaryon

Is it bound?

Long predicted by Jaffe to be bound-state of ΛΛ [PRL38,195 (1977)] Experiments inconclusive NPLQCD Calculation [PRD85,054511 (2011)]

10 20 30 40 0.015 0.010 0.005 0.005 0.010 0.015

t t.l.u.

k 2 s.l.u.2 10 20 30 40 0.02 0.010 0.010 0.02

t t.l.u.

k 2 s.l.u.2

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 11 / 38

SLIDE 13

Nuclear LQCD Results

H Dibaryon

Is it bound?

Long predicted by Jaffe to be bound-state of ΛΛ [PRL38,195 (1977)] Experiments inconclusive NPLQCD Calculation [PRD85,054511 (2011)]

200 400 600 800 20 10 10 20 30 40 50

mΠ MeV BH MeV

nf 3 nf 21

with HALQCD

[PRL106,162002 (2011)]

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 11 / 38

SLIDE 14

Nuclear LQCD Results

d Deuteron

Is it bound?

Very weakly bound Expect strong finite-volume effects NPLQCD Calculation [PRD85,054511 (2011)]

10 20 30 40 0.03 0.02 0.01 0.01 0.02 0.03

t t.l.u.

k 2 s.l.u.2 10 20 30 40 0.02 0.01 0.01 0.02

t t.l.u.

k 2 s.l.u.2

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 12 / 38

SLIDE 15

Nuclear LQCD Results

d Deuteron

Is it bound?

Very weakly bound Expect strong finite-volume effects NPLQCD Calculation [PRD85,054511 (2011)]

200

400 600 800 5 5 10 15 20 25

mΠ MeV Bd MeV

Experiment

nf 0 nf 21

with PACS-CS

[PRD84,054506 (2011)]

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 12 / 38

SLIDE 16

Nuclear LQCD Results

SU(3)-Symmetric QCD

Move to the SU(3) symmetric point: Mπ ≈ 800 MeV NPLQCD Calculation [PRD87,034506 (2012)]

Isotropic 2+1-flavor 800-MeV O(a)-improved Wilson-clover fermions as = 0.145 fm 3 volumes: 3.4 fm, 4.5 fm and 6.7 fm Very high statistics: 72 × 3822 (3.4 fm), 48 × 3050 (4.5 fm), 54 × 1905 (6.7 fm)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 13 / 38

SLIDE 17

Nuclear LQCD Results

SU(3)-Symmetric QCD

−200 −180 −160 −140 −120 −100 −80 −60 −40 −20

−B [MeV]

1+ 0+ 1+ 0+ 1+ 0+

1 2 + 1 2 + 3 2 + 1 2 + 3 2 +

0+ 0+ 0+ 0+

d nn nΣ H-dib nΞ

3He 3 ΛH 3 ΛHe 3 ΣHe 4He 4 ΛHe 4 ΛΛ He

s = 0 s = −1 s = −2

2-body 3-body 4-body

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 14 / 38

SLIDE 18

Nuclear LQCD Results

SU(3)-Symmetric QCD

−200 −180 −160 −140 −120 −100 −80 −60 −40 −20

−B [MeV]

1+ 0+ 1+ 0+ 1+ 0+

1 2 + 1 2 + 3 2 + 1 2 + 3 2 +

0+ 0+ 0+ 0+

d nn nΣ H-dib nΞ

3He 3 ΛH 3 ΛHe 3 ΣHe 4He 4 ΛHe 4 ΛΛ He

s = 0 s = −1 s = −2 2-body 3-body 4-body

H-dibaryon deeply bound: BH = 74.6(3.3)(3.3)(0.8) MeV Deuteron clearly bound: Bd = 19.5(3.1)(0.2) MeV more bound than quenched Small d-nn splitting

ther splittings larger

α also more bound than 0f Bα = 107(12)(21)(1) MeV

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 14 / 38

SLIDE 19

Quarkonia in Nuclei

Section 2 Quarkonia in Nuclei

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 15 / 38

SLIDE 20

Quarkonia in Nuclei Models and Experiment

Unique Probe of QCD Effects

Heavy quarkonia share no valence quarks with nuclei Normally dominant quark exchange suppressed to second order Dominated by two-gluon exchange (color van der Waals) Color Stark effect: Chromoelectric field induces dipoles in neutral hadrons that interact

p

u u d

Ψ c

c

p

u u d

Ψ

c c

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 16 / 38

SLIDE 21

Quarkonia in Nuclei Models and Experiment

Unique Probe of QCD Effects

Heavy quarkonia share no valence quarks with nuclei Normally dominant quark exchange suppressed to second order Dominated by two-gluon exchange (color van der Waals) Color Stark effect: Chromoelectric field induces dipoles in neutral hadrons that interact

p

u u d

Ψ c

c

p

u u d

Ψ

c c D D

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 16 / 38

SLIDE 22

Quarkonia in Nuclei Models and Experiment

Unique Probe of QCD Effects

Heavy quarkonia share no valence quarks with nuclei Normally dominant quark exchange suppressed to second order Dominated by two-gluon exchange (color van der Waals) Color Stark effect: Chromoelectric field induces dipoles in neutral hadrons that interact

p

u u d

Ψ c

c

p

u u d

Ψ

c c

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 16 / 38

SLIDE 23

Quarkonia in Nuclei Models and Experiment

Model History

Brodsky et al. [PRL64,1011 (1990)] noted features of pp scattering near

pen-charm threshold

No Pauli blocking; no quark-exchange ηch: 19 MeV, ηc9Be: 407 MeV(!) Wasson [PRL67,2237 (1991)] points out the nucleus is not pointlike Charm binding saturates for large A ηch: 0.8 MeV, ηc208Pb: 27 MeV Z,A

p p p p p p p p p p n n n n n n n n n n n

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 17 / 38

SLIDE 24

Quarkonia in Nuclei Models and Experiment

Model History

Brodsky et al. [PRL64,1011 (1990)] noted features of pp scattering near

pen-charm threshold

No Pauli blocking; no quark-exchange ηch: 19 MeV, ηc9Be: 407 MeV(!) Wasson [PRL67,2237 (1991)] points out the nucleus is not pointlike Charm binding saturates for large A ηch: 0.8 MeV, ηc208Pb: 27 MeV Z,A

p p p p p p p p p p n n n n n n n n n n n c c

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 17 / 38

SLIDE 25

Quarkonia in Nuclei Models and Experiment

Model History

Brodsky et al. [PRL64,1011 (1990)] noted features of pp scattering near

pen-charm threshold

No Pauli blocking; no quark-exchange ηch: 19 MeV, ηc9Be: 407 MeV(!) Wasson [PRL67,2237 (1991)] points out the nucleus is not pointlike Charm binding saturates for large A ηch: 0.8 MeV, ηc208Pb: 27 MeV Z,A

p p p p p p p p p p n n n n n n n n n n n c c

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 17 / 38

SLIDE 26

Quarkonia in Nuclei Models and Experiment

Model History II

Luke, Manohar, Savage [PLB288,355

(1992)] use heavy-quark expansion and

look at leading Stark effect using OPE At saturation: ΥA: 4 MeV, J/ψA: 11 MeV Induced dipole depends on radius of quarkonium like r3; excited ψ′ has huge radius Excited state becomes ground state in nuclear matter! ψ′(2s)A: 700 MeV(!!) Z,A

p p p p p p p p p p n n n n n n n n n n n c c

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 18 / 38

SLIDE 27

Quarkonia in Nuclei Models and Experiment

Model History II

Luke, Manohar, Savage [PLB288,355

(1992)] use heavy-quark expansion and

look at leading Stark effect using OPE At saturation: ΥA: 4 MeV, J/ψA: 11 MeV Induced dipole depends on radius of quarkonium like r3; excited ψ′ has huge radius Excited state becomes ground state in nuclear matter! ψ′(2s)A: 700 MeV(!!)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 18 / 38

SLIDE 28

Quarkonia in Nuclei Models and Experiment

Experimental Prospects

Long history of proposals to measure charmonium-nucleus binding

ATHENNA 12-GeV upgrade at CEBAF (JLab) (ep scattering) PANDA at FAIR (GSI) (¯ pp scattering)

Also attempts to measure nucleus-bound φ, ω, η′ or η ηh: 4(4) MeV(??) at MAMI [PRL92,252001 (2004)] not confirmed by COSY; some theoretical problems COSY-GEM [PRC79,012201 (2009)] found 25

ηMg: 12(2) MeV

Models of other mesic nuclei

[PRC34,1845 (1986)]: A < 12 unbound, ηA: 17 MeV Thomas predicts ηA: 90 MeV at saturation [Prog.Th.Phys.124,147 (2010)]: φA: 4–40 MeV at saturation

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 19 / 38

SLIDE 29

Quarkonia in Nuclei Lattice Data

Gluonic-Interaction Data

Many correlators for nuclei, hypernuclei, strange and light mesons Ideal for gluonic interactions First, apply method to strange quarkonia: ηs, φ No free quark lines = ⇒ no quark exchange No spin degrees of freedom = ⇒ limited to η or α Several sources and smearings available for each correlator Extract binding energies using three methods:

One-state fit to ratio of correlators (gray bar) time-extent of bar does not indicate fit range Splitting between energies extracted from one-state fits (red) Splitting between energies extracted from two-state fits (green)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 20 / 38

SLIDE 30

Quarkonia in Nuclei Lattice Data

ηs-N Binding Effective Mass

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 21 / 38

SLIDE 31

Quarkonia in Nuclei Lattice Data

ηs-A Binding Effective Masses

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 22 / 38

SLIDE 32

Quarkonia in Nuclei Lattice Data

ηs-Nucleus Binding vs A

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 23 / 38

SLIDE 33

Quarkonia in Nuclei Lattice Data

φ-α Binding Effective Mass

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 24 / 38

SLIDE 34

Quarkonia in Nuclei Lattice Data

φ-α Binding

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 25 / 38

SLIDE 35

Nuclear Sigma Term

Section 3 Nuclear Sigma Term

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 26 / 38

SLIDE 36

Nuclear Sigma Term

Dark Matter

Unknown form of matter making up ≈ 23% of the universe

Cluster velocity dispersion, rotation curves, lensing Acoustic oscillations in CMB Big Bang nucleosynthesis Supernovae at extreme distances

Must be cold (thus, not neutrinos), must be nonbaryonic Thus, whatever it is, it must be new physics!

0.25 0.26 YP Aver et al. (2012) Standard BBN 0.018 0.020 0.022 0.024 0.026 ωb 2.2 2.6 3.0 3.4 yDP Iocco et al. (2008) Pettini & Cooke (2012) Planck+WP+highL 0.24 0.32 0.40 0.48

Ωm

0.56 0.64 0.72 0.80

ΩΛ

+lensing +lensing+BAO 40 45 50 55 60 65 70 75

H0

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 27 / 38

SLIDE 37

Nuclear Sigma Term

Dark Matter Detection

Nuclei play central role in detectors constructed to probe dark matter For example, neutralino DM interacts via Higgs exchange Nuclei are dominated by the contributions from individual nucleons (the impulse approximation): gZ,N = Zgp + NgN Nuclear interactions expected to correct at the few-% level (e.g. meson-exchange currents) However, it has been suggested that 10–60% effects might arise and be responsible for some experimental inconsistencies

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 28 / 38

SLIDE 38

Nuclear Sigma Term

Scalar Isoscalar Nuclear σ Terms

Assume isospin symmetry σZ,N = ¯ mZ, N|¯ uu + ¯ dd|Z, N = ¯ m d d ¯ mEZ,N ≈ Mπ 2 d dMπ EZ,N Express in terms of the nuclear binding energies E = AMN − B σZ,N = AσN − Mπ 2 d dMπ BZ,N The impulse approximation is the first term, call the ratio of terms δσZ,N

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 29 / 38

SLIDE 39

Nuclear Sigma Term

Scalar Isoscalar Nuclear σ Terms

Binding Energies vs Pion Mass

Collect all the binding energies generated by lattice groups; extract the discrete derivatives

2 3 4 5 10 15 20 25 30 35

A BA MeV

Experiment mΠ 510 MeV Yamazaki et al mΠ 806 MeV NPLQCD

[PRD81,054505 (2010)] [PRD85,054511 (2012)] [PRD87,034506 (2013)]

(NPLQCD)

[PRD86,074514 (2012)]

(HALQCD)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 30 / 38

SLIDE 40

Nuclear Sigma Term

Scalar Isoscalar Nuclear σ Terms

Impulse Corrections

100 200 300 400 500 600 700 800 900 700 800 4 3 2 1

mΠ MeV ∆Σd

All the corrections are at the order of a few percent

100 200 300 400 500 600 700 800 900 700 800 10 8 6 4 2

mΠ MeV ∆Σ3He

100 200 300 400 500 600 700 800 900 700 800 10 8 6 4 2

mΠ MeV ∆Σ4He

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 31 / 38

SLIDE 41

Nuclear Equation of State

Section 4 Nuclear Equation of State

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 32 / 38

SLIDE 42

Nuclear Equation of State

Neutron Stars

Excellent astrophysical probes of extreme-density nuclear matter Mass-radius relation of NS set by nuclear equation of state Maximum mass also provides constraints: MNS = 1.97(4)M⊙ discovered [Nature 467, 1081 (2010)]

7 8 9 10 11 12 13 14 15 Radius (km) 0.0 0.5 1.0 1.5 2.0 2.5 Mass (solar)

AP4 MS0 MS2 MS1 MPA1 ENG AP3 GM3 PAL6 GS1 PAL1 SQM1 SQM3 FSU G R P <

causality

rotation J1614-2230

J1903+0327 J1909-3744 Double NS Systems

Nucleons Nucleons+ExoticStrange Quark Matter

“effectively rules out the presence of hyperons, bosons, or free quarks”

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 33 / 38

SLIDE 43

Nuclear Equation of State

YN Interactions

Precise NN interactions are well constrained by experiment Small but important NNN interactions are less well known YN scattering constrained by few hypernucleus studies Nijmegen and J¨ ulich models fit data but disagree on phase shifts NPLQCD Calculation [PRL109,172001 (2012)]

Anisotropic 2+1-flavor 390-MeV O(a)-improved Wilson-clover fermions as = 0.1227 fm, as/at ≈ 3.5 2 volumes: 3 fm and 4 fm Very high statistics: 178 × 2215 (3 fm), 174 × 739 (4 fm)

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 34 / 38

SLIDE 44

Nuclear Equation of State

Scattering on the Lattice

Use L¨ uscher method to extract scattering parameters in a Euclidean space by using the finite volume. Extract binding energies from two-point correlators at finite L: GAB(p, t) ≡ CAB(p, t) CA(t)CB(t) → B0 e−∆E t Determine the binding momentum defined by ∆E ≡ E − MA − MB =

k2 + M2

A +

k2 + M2

B − MA − MB

The phase shift at this momentum is k cot δ(k) = 1 πL S kL 2π 2 , where S(x) ≡

|

j|<Λ
j

1 | j|2 − x − 4πΛ

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 35 / 38

SLIDE 45

Nuclear Equation of State

YN Interactions

EFT and Model Comparisons

Nijmegen and J¨ ulich models fit data but disagree on phase shifts Use a lowest-order EFT to describe scattering Tune parameters to match experimental data and lattice data

100 200 300 400 500

pLAB (MeV)

10 20 30 40 50 60

δ (degrees)

NSC97f Juelich '04 EFT

100 200 300 400 500

pLAB (MeV)

60
50
40
30
20
10

10 20 30

δ (degrees)

NSC97f Juelich '04 EFT

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 36 / 38

SLIDE 46

Nuclear Equation of State

YN Interactions

Implications for Equation of State

Apply Fumi’s theorem to find the energy shift due to a static impurity (the hyperon) in a non-interacting Fermi system (neutron-star matter) ∆E = − 1 πµ kf dk k 3 2δ3S1(k) + 1 2δ1S0(k)

At ρn = 0.4 fm−3, ∆E = 46(13)(24) MeV

0.1 0.2 0.3 0.4 0.5

ρn (fm)

3

20 40 60 80 100

∆E (MeV) Σ

−

Nuclear matter

µn ∼ Mn + 150 MeV µe ∼ 200 MeV MΣ − µn − µe ∼ 100 MeV insufficient to exclude Σ− from neutronium

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 37 / 38

SLIDE 47

Conclusions

Lattice QCD has demonstrated capability for single baryons Matrix elements, form factors and structure are becoming available Obstacles to light nuclei are currently being overcome (at relatively heavy masses) Accelerated solvers and efficient contraction algorithms are paving the way for very high-statistics measurements

S. D. Cohen (U Washington)

NPLQCD 2013 Oct 18 38 / 38