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Lattice Nuclear Physics Investigations of Fundamental Symmetries
Advisor: Tom Luu | Begin of Work: November 2014
31. July 2015 | Christopher Körber | Forschungszentrum Jülich & University of Bonn
ECT* Talent — Training in Advanced Low Energy Nuclear Theory
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Christopher Körber — ECT* Talent — 31. July 2015
Asymmetry of Matter and Antimatter
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Images by TED-Ed original: What happened to antimatter? Rolf Landua
Pair annihilation and radiation
Observed asymmetry of matter
Symmetry of baryonic matter and antimatter after beginning of universe?
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Christopher Körber — ECT* Talent — 31. July 2015 3
Need for Charge-Parity Violation
Sakharov conditions for explaining asymmetry
Processes violate baryon or lepton number conservation
Processes violate Charge and Charge-Parity symmetry (Weak interactions violate both)
Generation of antisymmetry outside of thermal equilibrium
Weak Standard Model interactions (CKM matrix) not sufficient to explain amount of asymmetry
X ‘æ B + Y
T-Symmetry
‘æ
Y + B ‘æ X
X ‘æ B + Y
‘æ
X ‘æ B + Y
‘æ
NB = NB
C-Symmetry
CP: Phase space cancellationsCP
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Christopher Körber — ECT* Talent — 31. July 2015 4
Hadronic Hints for CP Violations:
Electric Dipole Moment
Electric Dipole Moment as a CP violating quantity
d :=
⁄d3
r r fl(r ) = d S
Charge distribution Total nucleus spin
H = −B · (µ S) − E · (d S)
Magnetic Dipole Moment
= −(−B) · (µ (−S)) − (+E) · (d (−S))
T
EDM violates CP CPT
P
S
d
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EDMs and Matter Asymmetry?Analysis of EDMs
Analysis of CP violating interactions
Sources of CP violating interactions
Strong Interactions (QCD, theta)
Weak Interactions (CKM matrix)
New Physics (SUSY,…)
Christopher Körber — ECT* Talent — 31. July 2015
Experimental Status
• Background free • Complementary to LHC (order of magnitudes?)
• Less expensive than high energy physics • Non-vanishing measurement: Nobel price?
proton & deuteron, Storage Ring EDM, JEDI
CryoEDM, ILL
dp ∼ 10−29
dn ∼ 10−29
Planned Bounds:
dp ∼ 7.9 · 10−25
dn ∼ 2.9 · 10−26
de ∼ 8.7 · 10−29
ThO, ACME
ultracold neutrons, ILL
Hg, UWash199
Current Bounds:
if θ = 1
Source: “NEDM limit history" by Andreas Knecht - Wikipedia: Neutron electric dipole moment
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Christopher Körber — ECT* Talent — 31. July 2015 6
Computation of EDMs…
Nuclear Level Hadronic Level SM/QCD Level BSM Level
… is essential for understanding CP violating structure on fundamental level
… on fundamental level is important for controlled model-independent predictions
SUSY
Multi-Higgs
Quark-Gluon Int.
Gluon Int.
Quark EDMs
Pion Int.
LR Symmetric
Nuclear EDMs
Nucleon EDMs
Pion Nucleon Int.
Theta Term QCD
Currently large uncontrolled uncertainties
Nuclear Models
Chiral Perturbation Theory & Lattice QCD
Effective Field Theories
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Christopher Körber — ECT* Talent — 31. July 2015 7
Chiral Perturbation Theory:
An Effective Field Theory for QCD
Chiral Perturbation Theory: Most general Lagrangian which respects the symmetries of QCD in chiral limit and has hadrons as degrees of freedom
e
Â-
-
- d
-
-
- Âf
Final Objective
Nucleus wave function
EDM operator
Lχ
= LNπ + Lπ + LNN + Lχ
��CP· · ·
Compute bound states (non perturbative)
+ · · ·
NN +
NN +NN +
NN +NN +
NN +
Nπ ++ · · ·
NN +
NN +
Nπ ++ · · ·P
NP
3
2πγ
3
2π
E
100 MeV
1 GeVPerturbative treatment of QCD in low energy sector not possible (confinement) and Lattice QCD not able to access light nuclear systems yet
q
q
g
g
g
g
q
q
q
q
CP violating
CP conserving
g
gg
g
g
g
g
q
q
g
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Christopher Körber — ECT* Talent — 31. July 2015 8
Nuclear Lattice Effective Field Theory:
The Transfer Matrix
Transfer Matrix Interpretation (Triton)
Transfer matrix evolves states by accounting all possible paths and interactions (path integral of chiral Lagrangian)
Eigenstates of transfer matrix correspond to wave function of physical state
Èψ(t + δt) | Mδt| ψ(t)Í
Èψ(t + δt) | Mδt| ψ(t)Í &
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N3
L
2
NP
Path integral identities and stochastically methods
Statistical errorsGreatly reduced dimensionality
0
1000
2000
3000
4000
5000
6000
0 4 8 12 16 20
Tim
e fo
r 100 H
MC
tra
j. p
er p
roce
ss [
s]
A
Nucleon Number Scaling for L = 6, Ltin = 8, L
tout
= 8
2014 Code
79.7 A + 7.11 A2
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Christopher Körber — ECT* Talent — 31. July 2015 9
Why NLEFT for EDMs?
SUSY
Multi-Higgs
Quark-Gluon Int.
Gluon Int.
Quark EDMs
Pion Int.
LR Symmetric
Nuclear EDMs
Nucleon EDMs
Pion Nucleon Int.
Theta Term QCD
NLEFT
ChPT + LQCD
EFT
Nuclear Models
Nuclear EDM calculations systematically connected to fundamental theory
Extend calculations to uncharted territories
Crucial to interpret experimental signal
Crucial to interpret matter-antimatter asymmetry…
Why NLEFT for EDMs?
Improvement of precision and accessibility
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