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Nuclear Physics from First Principles

Symmetries in Nuclei from Lattice QCD and Effective Theories

! Thorsten Kurth and Evan Berkowitz for the Collaboration

Team

• LLNL: Robert Falgout, Ron Soltz, Pavlos Vranas, Chris Schroeder, Evan Berkowitz, Enrico Rinaldi, Joe Wasem

• LBL/UCB: Wick Haxton, Thorsten Kurth, Ken McElvain, Mark Strother

• SDSU: Calvin Johnson

• nVidia: Michael Clark

• BNL: Sergey Syritsyn

• JLAB/W&M: André Walker-Loud

• JSC/Bonn University: Tom Luu

Motivation

• Historically, nuclear physics has relied on models.

• Nuclei are made of protons and neutrons, which in turn are made of quarks and gluons.

• We can use QCD to extract nucleon properties and interactions,

• connecting model parameters to the Standard Model.

• giving first-principles understanding.

Liquid Drop Shell

Bakken at en.wikipedia CC-BY-SA-3.0

Mean Field Potentials QCD

L = ̄(i /D +m) � 1 4 Tr(F 2)

Nuclei as Laboratories

• There are observables that are hard to measure experimentally.

• Nuclei provide a low-energy environment where high-precision “experiments” happen all the time.

• Can test many-body physics.

• Hadronic electroweak neutral current responsible for parity violation (PV) is the least constrained observable in the SM.

• Weak interaction is compared to strong interaction .

• Nuclear data show enhanced isoscalar and suppressed isovector PV.

PV PV≠

⇠GFF 2⇡=O(10�7)⇠O(1)

What is QCD?

• Quantum Chromodynamics is the fundamental theory of strong/ nuclear interactions (fusion, fission, α-decay, …)

• QCD describes interactions between Quarks and Gluons

• QCD features confinement (small energies) and asymptotic freedom (large energies)

g g g2

Quark-Gluon coupling (QED-like)

Gluon self-interaction

9. Quantum chromodynamics 33

QCD αs(Mz) = 0.1185 ± 0.0006

Z pole fit

0.1

0.2

0.3

αs (Q)

1 10 100 Q [GeV]

Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO)

DIS jets (NLO)

Sept. 2013

Lattice QCD (NNLO)

(N3LO)

τ decays (N3LO)

1000

pp –> jets (NLO)(–)

Figure 9.4: Summary of measurements of αs as a function of the energy scale Q. The respective degree of QCD perturbation theory used in the extraction of αs is indicated in brackets (NLO: next-to-leading order; NNLO: next-to-next-to leading order; res. NNLO: NNLO matched with resummed next-to-leading logs; N3LO: next-to-NNLO).

9.4. Acknowledgments

We are grateful to J.-F. Arguin, G. Altarelli, J. Butterworth, M. Cacciari, L. del Debbio, D. d’Enterria, P. Gambino, C. Glasman Kuguel, N. Glover, M. Grazzini, A. Kronfeld, K. Kousouris, M. Lüscher, M. d’Onofrio, S. Sharpe, G. Sterman, D. Treille, N. Varelas, M. Wobisch, W.M. Yao, C.P. Yuan, and G. Zanderighi for discussions, suggestions and comments on this and earlier versions of this review.

References: 1. R.K. Ellis, W.J. Stirling, and B.R. Webber, “QCD and collider physics,” Camb.

Monogr. Part. Phys. Nucl. Phys. Cosmol. 81 (1996). 2. C. A. Baker et al., Phys. Rev. Lett. 97, 131801 (2006). 3. H. -Y. Cheng, Phys. Reports 158, 1 (1988). 4. G. Dissertori, I.G. Knowles, and M. Schmelling, “High energy experiments and

theory,” Oxford, UK: Clarendon (2003). 5. R. Brock et al., [CTEQ Collab.], Rev. Mod. Phys. 67, 157 (1995), see also

http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.pdf. 6. A. S. Kronfeld and C. Quigg, Am. J. Phys. 78, 1081 (2010). 7. R. Stock (Ed.), Relativistic Heavy Ion Physics, Springer-Verlag Berlin, Heidelberg,

2010. 8. Proceedings of the XXIII International Conference on Ultrarelativistic Nucleus–

Nucleus Collisions, Quark Matter 2012, Nucl. Phys. A, volumes 904–905. 9. Special Issue: Physics of Hot and Dense QCD in High-Energy Nuclear

Collisions, Ed. C. Salgado. Int. J. Mod. Phys. A, volume 28, number 11. [http://www.worldscientific.com/toc/ijmpa/28/11].

December 18, 2013 12:00

long distance short distance

u d

d

neutron

uu

d

proton

How to solve QCD?

• QCD is described by infinite dimensional integrals

ZE =

Z DUµ D D

¯

exp

0

@�Sg[U ]� Z

R4 d

4 x

¯

(x)D[U ] (x)

1

A

How to solve QCD?

• QCD is described by infinite dimensional integrals

• use (euclidian) 4D lattice as regulator

ZE =

Z DUµ D D

¯

exp

0

@�Sg[U ]� Z

R4 d

4 x

¯

(x)D[U ] (x)

1

A

a

L

Uµ ̄

How to solve QCD?

• QCD is described by infinite dimensional integrals

• use (euclidian) 4D lattice as regulator

• generate configurations and extract observables

ZE =

Z DUµ D D

¯

exp

0

@�Sg[U ]� Z

R4 d

4 x

¯

(x)D[U ] (x)

1

A

N̄

N̄N

N−

hOi⇡ 1 N

NX

n=1

O[Un, D[Un]�1]

How to solve QCD?

• QCD is described by infinite dimensional integrals

• use (euclidian) 4D lattice as regulator

• generate configurations and extract observables

• perform limit a→0, L→∞ to recover continuum QCD

ZE =

Z DUµ D D

¯

exp

0

@�Sg[U ]� Z

R4 d

4 x

¯

(x)D[U ] (x)

1

A

N̄

N̄N

N−

hOi⇡ 1 N

NX

n=1

O[Un, D[Un]�1]

How to solve QCD?

• QCD is described by infinite dimensional integrals

• use (euclidian) 4D lattice as regulator

• generate configurations and extract observables

• perform limit a→0, L→∞ to recover continuum QCD

• but: tCPU~a-5

ZE =

Z DUµ D D

¯

exp

0

@�Sg[U ]� Z

R4 d

4 x

¯

(x)D[U ] (x)

1

A

=

Z DUµ D�D�

† exp

0

@�Sg[U ]� Z

R4 d

4 x�

† (x)D[U ]

� 12 �(x)

1

A

expensive matrix inversions

S(x, y) = (x) ̄(y) = D[U ]�1(x, y)

How to solve QCD?

• QCD is described by infinite dimensional integrals

• use (euclidian) 4D lattice as regulator

• generate configurations and extract observables

• perform limit a→0, L→∞ to recover continuum QCD

• but: tCPU~a-5

• big computers needed

−

N̄N

N̄N

P P̄

P̄P

+ . . .

Nuclear Physics from Bottom Up

• compute multi-nucleon correlation functions

N̄

N̄N

N−

single Nucleon 2!1!=2

deuteron 3!3!=36

He3-scattering 5!4!=2880

Nuclear Physics from Bottom Up

• compute multi-nucleon correlation functions

• measure energy difference between interacting and non- interacting system

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12 14

E e ff(

t/a )

t/a

1S03P03P13P2

�E�e↵(t) = 1

2

log

✓ C�NN (t� 1) C�NN (t+ 1)

C2N (t+ 1)

C2N (t� 1)

◆

Nuclear Physics from Bottom Up

• compute multi-nucleon correlation functions

• measure energy difference between interacting and non- interacting system

• use Lüscher’s finite volume formula to relate measured energies to phase shifts δ(k)

2 3 4 5 6 7 8 M

! L

2

2.5

3

3.5

4

E/ M

!

free theory

Nuclear Physics from Bottom Up

• compute multi-nucleon correlation functions

• measure energy difference between interacting and non- interacting system

• use Lüscher’s finite volume formula to relate measured energies to phase shifts δ(k)

2 3 4 5 6 7 8 M

! L

2

2.5

3

3.5

4

E/ M

!

free theory

2 3 4 5 6 7 8 M

! L

2

2.5

3

3.5

4

E/ M

! interacting theory

Nuclear Physics from Bottom Up

• compute multi-nucleon correlation functions

• measure energy difference between interacting and non- interacting system

• use Lüscher’s finite volume formula to relate measured energies to phase shifts δ(k)

2 3 4 5 6 7 8 M

! L

2

2.5

3

3.5

4

E/ M

!

free theory

2 3 4 5 6 7 8 M

! L

2

2.5

3

3.5

4

E/ M

! interacting theory

�E ! k2 LFV�! �(k2)

Nuclear Physics from Bottom Up