Effective nuclear theories

and

lattice QCD

Johannes Kirscher

.א!

Goal:

A derivation of nuclear physics from the Standard Model.

Motivation:

י! Consistent understanding of nature;י! Analysis/exploration/discovery of new phenomena;י! Stability of the universe with respect to variations in

fundamental constants.

.א!

Goal:

A derivation of nuclear physics from the Standard Model.

Motivation:

י! Consistent understanding of nature;י! Analysis/exploration/discovery of new phenomena;י! Stability of the universe with respect to variations in

fundamental constants.

.א!

Goal:

A derivation of nuclear physics from the Standard Model.

Motivation:

י! Consistent understanding of nature;

י! Analysis/exploration/discovery of new phenomena;י! Stability of the universe with respect to variations in

fundamental constants.

.א!

Goal:

A derivation of nuclear physics from the Standard Model.

Motivation:

י! Consistent understanding of nature;י! Analysis/exploration/discovery of new phenomena;

י! Stability of the universe with respect to variations infundamental constants.

.א!

Goal:

A derivation of nuclear physics from the Standard Model.

Motivation:

י! Consistent understanding of nature;י! Analysis/exploration/discovery of new phenomena;י! Stability of the universe with respect to variations in

fundamental constants.

.ב!

Nuclear theory as a combination of EFTs.

A

Q

mπ

140

510806

Cluster

α ?

EFT(π/)

pert.

χEFT

d

t

LQCD

.ג!

The theory of strong interactions, QCD.

L QCD=q (i/∂

+ g s/G) q−1 2Gµνa G µν,a

+m · q (1− 0± τ 3) q+

. . .

global SO flavorand

local SU colorgauge symmetries

basic scales: Λ QCD∼ 1 GeV and

m π∼ 140 MeVq fGa

bound-states

〈0| ∑ xO f(x, t)O i(0)|0〉 =

∑ n〈0|O f|n〉〈

n|O i|0〉2E n

e−E nt

. . . and scattering phase shifts(Luscher).

qq

L

Ga

.ג!

QCD solution in discretized space time.

L QCD=q (i/∂

+ g s/G) q−1 2Gµνa G µν,a

+m · q (1− 0± τ 3) q+

. . .

global SO flavorand

local SU colorgauge symmetries

basic scales: Λ QCD∼ 1 GeV and

m π∼ 140 MeVq fGa

bound-states

〈0| ∑ xO f(x, t)O i(0)|0〉 =

∑ n〈0|O f|n〉〈

n|O i|0〉2E n

e−E nt

. . . and scattering phase shifts(Luscher).

qq

L

Ga

.ד!

Lattice nuclei for various pion masses.

0

20

40

60

80

100

120

140

nn D 3H α

Energy

[MeV

]

mπ

χEFT 190-210 MeV

EFT(π/)

140 MeV

300 MeV

450 MeV

510 MeV

806 MeV

.ד!

mπ dependence of two nucleons (I).

0

5

10

15

20

25

30

140real world

300Yamazaki et al.

430NPLQCD

510Yamazaki et al.

805NPLQCD

b

i

n

d

i

n

g

e

n

e

r

g

y

[

M

e

V

℄

mπ [MeV℄

singlet BNN

(1S0

)

triplet BNN

(3S1

)

.ד!

mπ dependence of two nucleons (II).

-20

-10

0

10

20

140 350 450 490 590 800

s

a

t

t

e

r

i

n

g

l

e

n

g

t

h

a

[

f

m

℄

mπ [MeV℄

3S1

1S0

1anp3anp

real-world data

NPLQCD “data” and EFT extrapolation;

.ה!

χEFT as an effective theory of QCD for mesons

and nuclei.

L QCD=q (i/∂

+ g s/G) q−1 2Gµνa G µν,a

+m · q (1− 0± τ 3) q+

. . .

global SO flavorand

local SU colorgauge symmetries

basic scales: Λ QCD∼ 1 GeV and

m π∼ 140 MeVq fGa

bound-states

〈0| ∑ xO f(x, t)O i(0)|0〉 =

∑ n〈0|O f|n〉〈

n|O i|0〉2E n

e−E nt

. . . and scattering phase shifts(Luscher).

qq

L

Ga

L EFT=L π+

N+( iD 0+

~D2m n) N

+g A2f π

N+~S~τN + C 0N+

NN+ N

+C 2N+N( ~DN+

) ·~DN + . . .Q ∼ m π�Λ QCD

iteration of A-nucleon potential

Weinberg, Ordonez, van Kolck, Epelbaum, etc.πN = (p, n)

.ו!

EFT(π↗) = EFT(/π) for mπ > 140 MeV.

100

300

500

800

950

1400

1600

140real world

300Yamazaki et al.

450NPLQCD

510Yamazaki et al.

806NPLQCD

Energy

[MeV

]

mπ [MeV]

mπ

mN√2mN(m∆ −mN)√

2mNB/A

.ז!

EFT(π↗) = EFT(/π) for mπ > 140 MeV.

L QCD=q (i/∂

+ g s/G) q−1 2Gµνa G µν,a

+m · q (1− 0± τ 3) q+

. . .

global SO flavorand

local SU colorgauge symmetries

basic scales: Λ QCD∼ 1 GeV and

m π∼ 140 MeVq fGa

bound-states

〈0| ∑ xO f(x, t)O i(0)|0〉 =

∑ n〈0|O f|n〉〈

n|O i|0〉2E n

e−E nt

. . . and scattering phase shifts(Luscher).

qq

L

Ga

L EFT=L π+

N+( iD 0+

~D2m n) N

+g A2f π

N+~S~τN + C 0N+

NN+ N

+C 2N+N( ~DN+

) ·~DN + . . .Q ∼ m π�Λ QCD

iteration of A-nucleon potential

Weinberg, Ordonez, van Kolck, Epelbaum, etc.πN = (p, n)

EFT(π↗)

Lorentz symmetry

scales: ℵ ∼B NN�

Λ QCD

m π∼ 510, 805 MeVnp

.ח!

EFT = loop and vertex expansion.

+ + . . .

+

+

+

+

...

↔ ~∇2

2m +~∇4

8m3 + . . .

V = C0 + C0,0 + C2q2 + . . .

י! Leading order:

V = ˚˚C0,s P(1S0) +˚˚C0,t P(3S1) + ˚˚D(∗) P(S)

י! Next-to-leading order:

V = VLO +

(C2,s + C q2

2,s

)P(1S0) +

(C2,t + C q2

2,t

)P(3S1) + D(∗) P(S)

+CppP(1S0)pp + e2

4|r|

“Natural”, renormalized LECs:

C2n = 4πO(1)mℵ(Mℵ)n C

′2n = 4πO(1)

mM2n+1

This program is incomplete for A > 2 (even physical mπ)!

.ח!

EFT = loop and vertex expansion.

+ + . . .

+

+

+

+

...

↔ ~∇2

2m +~∇4

8m3 + . . .

V = C0 + C0,0 + C2q2 + . . .

י! Leading order:

V = ˚˚C0,s P(1S0) +˚˚C0,t P(3S1) + ˚˚D(∗) P(S)

י! Next-to-leading order:

V = VLO +

(C2,s + C q2

2,s

)P(1S0) +

(C2,t + C q2

2,t

)P(3S1) + D(∗) P(S)

+CppP(1S0)pp + e2

4|r|

“Natural”, renormalized LECs:

C2n = 4πO(1)mℵ(Mℵ)n C

′2n = 4πO(1)

mM2n+1

This program is incomplete for A > 2 (even physical mπ)!

.ח!

EFT = loop and vertex expansion.

+ + . . .

+

+

+

+

...

↔ ~∇2

2m +~∇4

8m3 + . . .

V = C0 + C0,0 + C2q2 + . . .

י! Leading order:

V = ˚˚C0,s P(1S0) +˚˚C0,t P(3S1) + ˚˚D(∗) P(S)

י! Next-to-leading order:

V = VLO +

(C2,s + C q2

2,s

)P(1S0) +

(C2,t + C q2

2,t

)P(3S1) + D(∗) P(S)

+CppP(1S0)pp + e2

4|r|

“Natural”, renormalized LECs:

C2n = 4πO(1)mℵ(Mℵ)n C

′2n = 4πO(1)

mM2n+1

This program is incomplete for A > 2 (even physical mπ)!

.ח!

EFT = loop and vertex expansion.

+ + . . .

+

+

+

+

...

↔ ~∇2

2m +~∇4

8m3 + . . .

V = C0 + C0,0 + C2q2 + . . .

י! Leading order:

V = ˚˚C0,s P(1S0) +˚˚C0,t P(3S1) + ˚˚D(∗) P(S)

י! Next-to-leading order:

V = VLO +

(C2,s + C q2

2,s

)P(1S0) +

(C2,t + C q2

2,t

)P(3S1) + D(∗) P(S)

+CppP(1S0)pp + e2

4|r|

“Natural”, renormalized LECs:

C2n = 4πO(1)mℵ(Mℵ)n C

′2n = 4πO(1)

mM2n+1

This program is incomplete for A > 2 (even physical mπ)!

.ח!

EFT = loop and vertex expansion.

+ + . . .

+

+

+

+

...

↔ ~∇2

2m +~∇4

8m3 + . . .

V = C0 + C0,0 + C2q2 + . . .

י! Leading order:

V = ˚˚C0,s P(1S0) +˚˚C0,t P(3S1) + ˚˚D(∗) P(S)

י! Next-to-leading order:

V = VLO +

(C2,s + C q2

2,s

)P(1S0) +

(C2,t + C q2

2,t

)P(3S1) + D(∗) P(S)

+CppP(1S0)pp + e2

4|r|

“Natural”, renormalized LECs:

C2n = 4πO(1)mℵ(Mℵ)n C

′2n = 4πO(1)

mM2n+1

This program is incomplete for A > 2 (even physical mπ)!

.ט!

The Phillips 3-nucleon characteristicum.

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

6 7 8 9 10 11 12

2an−d

[

f

m

℄

BT

[MeV℄

π/EFT Λ = 2 . . . 8 fm

−1

π/EFT STM

experiment

.ט!

The Phillips 3-nucleon characteristicum.

1

1.5

2

2.5

3

3.5

4

14 16 18 20 22 24 26

2an−d

[

f

m

℄

BT

[MeV℄

π/EFT Λ = 2 . . . 8 fm

−1

mπ = 510 MeV

.ט!

The Phillips 3-nucleon characteristicum.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

30 35 40 45 50 55 60 65 70

2an−d

[

f

m

℄

BT

[MeV℄

π/EFT Λ = 4 . . . 8 fm

−1

Λ = 2 fm

−1

mπ = 805 MeV

.י!

The Tjon 4-nucleon characteristicum.

0

50

100

150

200

250

300

10 20 30 40 50 60 70 80 90 100

Bα

[

M

e

V

℄

Bt [MeV℄

experiment

mπ = 137 MeV

mπ = 510 MeV

mπ = 805 MeV

!K.

The future.

י! mπ dependence of other nuclear characteristics:

י! 5 and 6 nucleons and reactions;י! Electro-weak interactions (moments and decays);י! Emergence of strange nuclei.

י! Nuclei under extreme conditions(magnetic and gravitational fields close to neutron stars).

י! Refinement of multi-nucleon EFTs for physical and largepion masses.

!K.

The future.

י! mπ dependence of other nuclear characteristics:

י! 5 and 6 nucleons and reactions;י! Electro-weak interactions (moments and decays);י! Emergence of strange nuclei.

י! Nuclei under extreme conditions(magnetic and gravitational fields close to neutron stars).

י! Refinement of multi-nucleon EFTs for physical and largepion masses.

!K.

The future.

י! mπ dependence of other nuclear characteristics:

י! 5 and 6 nucleons and reactions;י! Electro-weak interactions (moments and decays);י! Emergence of strange nuclei.

י! Nuclei under extreme conditions(magnetic and gravitational fields close to neutron stars).

י! Refinement of multi-nucleon EFTs for physical and largepion masses.

!K.

The future.

י! mπ dependence of other nuclear characteristics:

י! 5 and 6 nucleons and reactions;י! Electro-weak interactions (moments and decays);י! Emergence of strange nuclei.

י! Nuclei under extreme conditions(magnetic and gravitational fields close to neutron stars).

י! Refinement of multi-nucleon EFTs for physical and largepion masses.