facets of chiral perturbation theory€¦ · e ective lagrangian necessarily nonpolynomial....
TRANSCRIPT
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Facets of Chiral Perturbation Theory
Gerhard Ecker
Univ. Wien
DESY Zeuthen, May 30, 2013
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Contents
1 Motivation and overview
2 Nonleptonic kaon decays
3 Precision physics:
Γ(P → eνe)/Γ(P → µνµ) (P = π,K )
4 Low-energy constants and lattice QCD
5 Carbogenesis: the Hoyle state
6 Conclusions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Motivation and overview
Goal
systematic and quantitative treatmentof the Standard Model at low energies (E < 1 GeV)
Effective Field Theory (EFT)
Lattice Field Theory
main objectives
understand physics of the SM at low energies
look for evidence of new physics
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Motivation and overview
Goal
systematic and quantitative treatmentof the Standard Model at low energies (E < 1 GeV)
Effective Field Theory (EFT)
Lattice Field Theory
main objectives
understand physics of the SM at low energies
look for evidence of new physics
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Motivation and overview
Goal
systematic and quantitative treatmentof the Standard Model at low energies (E < 1 GeV)
Effective Field Theory (EFT)
Lattice Field Theory
main objectives
understand physics of the SM at low energies
look for evidence of new physics
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
E < 1 GeV:
strong-coupling regime of QCD −→not accessible in standard perturbation theory
key concept for EFT: approximate chiral symmetry of QCD
LQCD = −1
2tr(GµνG
µν) +6∑
f =1
qf (iγµDµ −mf 1c) qf
for mf = 0 : chiral components can be rotated separately
qfL =1
2(1− γ5)qf , qfR =
1
2(1 + γ5)qf
−→ chiral symmetry SU(nF )L × SU(nF )R × U(1)V
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
E < 1 GeV:
strong-coupling regime of QCD −→not accessible in standard perturbation theory
key concept for EFT: approximate chiral symmetry of QCD
LQCD = −1
2tr(GµνG
µν) +6∑
f =1
qf (iγµDµ −mf 1c) qf
for mf = 0 : chiral components can be rotated separately
qfL =1
2(1− γ5)qf , qfR =
1
2(1 + γ5)qf
−→ chiral symmetry SU(nF )L × SU(nF )R × U(1)V
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
E < 1 GeV:
strong-coupling regime of QCD −→not accessible in standard perturbation theory
key concept for EFT: approximate chiral symmetry of QCD
LQCD = −1
2tr(GµνG
µν) +6∑
f =1
qf (iγµDµ −mf 1c) qf
for mf = 0 : chiral components can be rotated separately
qfL =1
2(1− γ5)qf , qfR =
1
2(1 + γ5)qf
−→ chiral symmetry SU(nF )L × SU(nF )R × U(1)V
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
mf = 0 :
very good approximation for nF = 2 (u, d)
reasonable approximation for nF = 3 (u, d , s)
in contrast to isospin SU(2) or flavour SU(3):
no sign of chiral symmetry in hadron spectrum
many other arguments in favour of
spontaneous breaking of chiral symmetry
SU(nF )L × SU(nF )R × U(1)V −→ SU(nF )V × U(1)V
Goldstone theorem:
∃ n2F − 1 massless (for mf = 0) Goldstone bosons
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
mf = 0 :
very good approximation for nF = 2 (u, d)
reasonable approximation for nF = 3 (u, d , s)
in contrast to isospin SU(2) or flavour SU(3):
no sign of chiral symmetry in hadron spectrum
many other arguments in favour of
spontaneous breaking of chiral symmetry
SU(nF )L × SU(nF )R × U(1)V −→ SU(nF )V × U(1)V
Goldstone theorem:
∃ n2F − 1 massless (for mf = 0) Goldstone bosons
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Goldstone fields parametrize SU(nF )L × SU(nF )R / SU(nF )V
nF n2F − 1 Goldstone bosons
2 3 π3 8 π,K , η
even in the real world (mq 6= 0):
pseudo-scalar meson exchange dominates amplitudes at low energies
−→ construct EFT for pseudo-Goldstone bosons
nonlinear realization of chiral symmetry −→
effective Lagrangian necessarily nonpolynomial
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Goldstone fields parametrize SU(nF )L × SU(nF )R / SU(nF )V
nF n2F − 1 Goldstone bosons
2 3 π3 8 π,K , η
even in the real world (mq 6= 0):
pseudo-scalar meson exchange dominates amplitudes at low energies
−→ construct EFT for pseudo-Goldstone bosons
nonlinear realization of chiral symmetry −→
effective Lagrangian necessarily nonpolynomial
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Goldstone fields parametrize SU(nF )L × SU(nF )R / SU(nF )V
nF n2F − 1 Goldstone bosons
2 3 π3 8 π,K , η
even in the real world (mq 6= 0):
pseudo-scalar meson exchange dominates amplitudes at low energies
−→ construct EFT for pseudo-Goldstone bosons
nonlinear realization of chiral symmetry −→
effective Lagrangian necessarily nonpolynomial
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
consequence:
EFT nonrenormalizable QFT: Chiral Perturbation Theory (CHPT)
Weinberg, Gasser, Leutwyler,. . .
nevertheless: CHPT fully renormalized QFT
(to next-to-next-to-leading order)
basis for systematic low-energy expansion:
pseudo-Goldstone bosons decouple for vanishing momenta and masses
systematic approach for low-energy hadron physics
most advanced in meson sector (up to 2 loops)
also single-baryon sector and few-nucleon systems
electroweak interactions can be included
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
consequence:
EFT nonrenormalizable QFT: Chiral Perturbation Theory (CHPT)
Weinberg, Gasser, Leutwyler,. . .
nevertheless: CHPT fully renormalized QFT
(to next-to-next-to-leading order)
basis for systematic low-energy expansion:
pseudo-Goldstone bosons decouple for vanishing momenta and masses
systematic approach for low-energy hadron physics
most advanced in meson sector (up to 2 loops)
also single-baryon sector and few-nucleon systems
electroweak interactions can be included
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
consequence:
EFT nonrenormalizable QFT: Chiral Perturbation Theory (CHPT)
Weinberg, Gasser, Leutwyler,. . .
nevertheless: CHPT fully renormalized QFT
(to next-to-next-to-leading order)
basis for systematic low-energy expansion:
pseudo-Goldstone bosons decouple for vanishing momenta and masses
systematic approach for low-energy hadron physics
most advanced in meson sector (up to 2 loops)
also single-baryon sector and few-nucleon systems
electroweak interactions can be included
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Effective chiral Lagrangian (meson sector)
Lchiral order (# of LECs) loop order
Lp2(2) + Loddp4 (0) + L∆S=1
GF p2 (2) + LemweakG8e2p0 (1) L = 0
+ Leme2p0(1) + Lleptons
kin (0)
+ Lp4(10) + Loddp6 (23) + L∆S=1
G8p4 (22) + L∆S=1G27p4 (28) L ≤ 1
+ LemweakG8e2p2 (14) + Lem
e2p2(13) + Lleptonse2p2 (5)
+ Lp6(90) L ≤ 2
LECs: low-energy constants ≡ coupling constants of CHPTin red: Lagrangians relevant for nonleptonic K decays
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Nonleptonic kaon decays
dominant decays: K → 2π, 3π
LO Cronin
NLO Kambor, Missimer, Wyler
NLO + isospin violation + rad. corrs. Cirigliano, E., Neufeld, PichBijnens, Borg
−→ LO couplings G8,G27 well known
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Effective chiral Lagrangian (meson sector)
Lchiral order (# of LECs) loop order
Lp2(2) + Loddp4 (0) + L∆S=1
GF p2 (2) + LemweakG8e2p0 (1) L = 0
+ Leme2p0(1) + Lleptons
kin (0)
+ Lp4(10) + Loddp6 (23) + L∆S=1
G8p4 (22) + L∆S=1G27p4 (28) L ≤ 1
+ LemweakG8e2p2 (14) + Lem
e2p2(13) + Lleptonse2p2 (5)
+ Lp6(90) L ≤ 2
in red: LO Lagrangian for nonleptonic K decays
in blue: NLO Lagrangian — “ —
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Nonleptonic kaon decays
dominant decays: K → 2π, 3π
LO Cronin
NLO Kambor, Missimer, Wyler
NLO + isospin violation + rad. corrs. Cirigliano, E., Neufeld, PichBijnens, Borg
−→ LO couplings G8,G27 well known
N.B.: all other nonleptonic transitions start at NLO = O(GFp4)
problem: 22 (octet) + 28 (27-plet) LECs
Theorists’ favourite nonleptonic decays
KS → γγ, KL → π0γγ [, KS → π0π0γγ]
no LECs at all at NLO !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Nonleptonic kaon decays
dominant decays: K → 2π, 3π
LO Cronin
NLO Kambor, Missimer, Wyler
NLO + isospin violation + rad. corrs. Cirigliano, E., Neufeld, PichBijnens, Borg
−→ LO couplings G8,G27 well known
N.B.: all other nonleptonic transitions start at NLO = O(GFp4)
problem: 22 (octet) + 28 (27-plet) LECs
Theorists’ favourite nonleptonic decays
KS → γγ, KL → π0γγ [, KS → π0π0γγ]
no LECs at all at NLO !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Status at O(GFp4)
KS → γγ D’Ambrosio, Espriu; GoityKL → π0γγ E., Pich, de Rafael; Cappiello, D’AmbrosioKS → π0π0γγ Funck, Kambor
O(GFp2) no contribution
O(GFp4) LECs do not contribute → finite loop amplitude
KL
0
pre-CHPT: KL → π0γγ vector-meson dominated
compare 2-photon spectra
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Status at O(GFp4)
KS → γγ D’Ambrosio, Espriu; GoityKL → π0γγ E., Pich, de Rafael; Cappiello, D’AmbrosioKS → π0π0γγ Funck, Kambor
O(GFp2) no contribution
O(GFp4) LECs do not contribute → finite loop amplitude
KL
0
pre-CHPT: KL → π0γγ vector-meson dominated
compare 2-photon spectra
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Status at O(GFp4)
KS → γγ D’Ambrosio, Espriu; GoityKL → π0γγ E., Pich, de Rafael; Cappiello, D’AmbrosioKS → π0π0γγ Funck, Kambor
O(GFp2) no contribution
O(GFp4) LECs do not contribute → finite loop amplitude
KL
0
pre-CHPT: KL → π0γγ vector-meson dominated
compare 2-photon spectra
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KL → π0γγ decay distribution in m34 = Mγγ
100
200
300
0. 100. 200. 300. 400.
m34 [MeV/c2]
N.o
f eve
nts
NA48 (2002)
0
50
100
150
200
250
300
350
400
450
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4m GeV/c2
Eve
nts/
0.02
GeV
/c2
Data
0 + Bkg MC
Bkg MC
KTeV (2008)
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
higher-order corrections (starting at NNLO = O(GFp6))
rescattering (unitarity) corrections largely model independent
Cappiello, D’Ambrosio, Miragliuolo; Cohen, E., Pich;Kambor, Holstein
KS → γγ “trivial” in terms of K → 2π rate
KL → π0γγ more involved but straightforward
resonance contributions
Cohen, E., Pich; D’Ambrosio, Portoles;Buchalla, D’Ambrosio, Isidori
KS → γγ small (vector mesons cannot contribute)
KL → π0γγ vector meson contribution model dependentgood approximation: single parameter aV
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
higher-order corrections (starting at NNLO = O(GFp6))
rescattering (unitarity) corrections largely model independent
Cappiello, D’Ambrosio, Miragliuolo; Cohen, E., Pich;Kambor, Holstein
KS → γγ “trivial” in terms of K → 2π rate
KL → π0γγ more involved but straightforward
resonance contributions
Cohen, E., Pich; D’Ambrosio, Portoles;Buchalla, D’Ambrosio, Isidori
KS → γγ small (vector mesons cannot contribute)
KL → π0γγ vector meson contribution model dependentgood approximation: single parameter aV
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KS → γγ
puzzling result of NA48 (2003):
rate substantially bigger than
O(p4) result
KLOE (2008):
B(KS → γγ) = 2.26(12)(06)× 10−6
−→ perfect agreement1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
BR
x106
PT O(p4 )
NA31NA48/99
NA48/03
KLOE
not a good idea:
PDG averages NA48/03 and KLOE −→B(KS → γγ) = 2.63(17)× 10−6
??
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KS → γγ
puzzling result of NA48 (2003):
rate substantially bigger than
O(p4) result
KLOE (2008):
B(KS → γγ) = 2.26(12)(06)× 10−6
−→ perfect agreement1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
BR
x106
PT O(p4 )
NA31NA48/99
NA48/03
KLOE
not a good idea:
PDG averages NA48/03 and KLOE −→B(KS → γγ) = 2.63(17)× 10−6
??
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KL → π0γγ
for reasonable values of aV :
pion loop dominates 2γ-spectrum
rate more affected both by rescattering corrections and by aV
=⇒ excellent agreement between theory and experiment
B(KL → π0γγ) · 106 =
1.27± 0.04± 0.01 NA48 (2002)1.28± 0.06± 0.01 KTeV (2008)1.273± 0.033 PDG (2012)
aV = −0.43± 0.06 PDG (2012)
important consequence
CP-conserving contribution KL → π0γ∗γ∗ → π0e+e− negligible incomparison with CP-violating amplitudes
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KL → π0γγ
for reasonable values of aV :
pion loop dominates 2γ-spectrum
rate more affected both by rescattering corrections and by aV
=⇒ excellent agreement between theory and experiment
B(KL → π0γγ) · 106 =
1.27± 0.04± 0.01 NA48 (2002)1.28± 0.06± 0.01 KTeV (2008)1.273± 0.033 PDG (2012)
aV = −0.43± 0.06 PDG (2012)
important consequence
CP-conserving contribution KL → π0γ∗γ∗ → π0e+e− negligible incomparison with CP-violating amplitudes
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
KL → π0γγ
for reasonable values of aV :
pion loop dominates 2γ-spectrum
rate more affected both by rescattering corrections and by aV
=⇒ excellent agreement between theory and experiment
B(KL → π0γγ) · 106 =
1.27± 0.04± 0.01 NA48 (2002)1.28± 0.06± 0.01 KTeV (2008)1.273± 0.033 PDG (2012)
aV = −0.43± 0.06 PDG (2012)
important consequence
CP-conserving contribution KL → π0γ∗γ∗ → π0e+e− negligible incomparison with CP-violating amplitudes
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Precision physics:Γ(P → eνe)/Γ(P → µνµ) (P = π,K )
V − A structure of charged currents −→
R(P)e/µ = Γ(P → eνe [γ])/Γ(P → µνµ[γ]) helicity suppressed
−→ sensitive probe for new physics
(charged Higgs exchange, violation of lepton universality, . . . )
PDG 2012 Marciano, Sirlin 1993 Finkemeier 1996
R(π)e/µ · 104 1.230± 0.004 1.2352± 0.0005 1.2354± 0.0002
R(K)e/µ · 105 2.488± 0.012 2.472± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Precision physics:Γ(P → eνe)/Γ(P → µνµ) (P = π,K )
V − A structure of charged currents −→
R(P)e/µ = Γ(P → eνe [γ])/Γ(P → µνµ[γ]) helicity suppressed
−→ sensitive probe for new physics
(charged Higgs exchange, violation of lepton universality, . . . )
PDG 2012 Marciano, Sirlin 1993 Finkemeier 1996
R(π)e/µ · 104 1.230± 0.004 1.2352± 0.0005 1.2354± 0.0002
R(K)e/µ · 105 2.488± 0.012 2.472± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
P → `ν` to O(p2)
T p2
` = −2 i GF Vud F m` uL(pν) v(p`) (P = π)
O(p2n), e = 0 : F → F(2n)P −→ RP
e/µ =m2
e
m2µ
(M2
P −m2e
M2P −m2
µ
)2
−→ nontrivial corrections (hadronic structure) only for e 6= 0
amplitudes of O(e2p2)
one loop −→ T e2p2
` corresponds to point-like approximation
Kinoshita; Marciano, SirlinKnecht, Neufeld, Rupertsberger, Talavera
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
P → `ν` to O(p2)
T p2
` = −2 i GF Vud F m` uL(pν) v(p`) (P = π)
O(p2n), e = 0 : F → F(2n)P −→ RP
e/µ =m2
e
m2µ
(M2
P −m2e
M2P −m2
µ
)2
−→ nontrivial corrections (hadronic structure) only for e 6= 0
amplitudes of O(e2p2)
one loop −→ T e2p2
` corresponds to point-like approximation
Kinoshita; Marciano, SirlinKnecht, Neufeld, Rupertsberger, Talavera
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
O(e2p4) Cirigliano, Rosell
(up to) 2-loop diagrams −→ involve meson structure
loop integration divergent −→ T e2p4
` contains counterterm
Cirigliano, Rosell: counterterm fixed by
matching form factors with large-Nc QCD
inclusion of real photon corrections +
summation of leading logs αn logn(mµ/me) (Marciano, Sirlin )
Cirigliano, Rosell Marciano, Sirlin Finkemeier
R(π)e/µ · 104 1.2352± 0.0001 1.2352± 0.0005 1.2354± 0.0002
R(K)e/µ · 105 2.477± 0.001 2.472± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
O(e2p4) Cirigliano, Rosell
(up to) 2-loop diagrams −→ involve meson structure
loop integration divergent −→ T e2p4
` contains counterterm
Cirigliano, Rosell: counterterm fixed by
matching form factors with large-Nc QCD
inclusion of real photon corrections +
summation of leading logs αn logn(mµ/me) (Marciano, Sirlin )
Cirigliano, Rosell Marciano, Sirlin Finkemeier
R(π)e/µ · 104 1.2352± 0.0001 1.2352± 0.0005 1.2354± 0.0002
R(K)e/µ · 105 2.477± 0.001 2.472± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
=⇒ discrepancy with previous calculation of R(K)e/µ
[asymptotic behaviour of form factors incompatible with QCD]
most recent experimental result for R(K)e/µ
NA62 (2013) Cirigliano, Rosell
R(K)e/µ · 105 2.488± 0.010 2.477± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
=⇒ discrepancy with previous calculation of R(K)e/µ
[asymptotic behaviour of form factors incompatible with QCD]
most recent experimental result for R(K)e/µ
NA62 (2013) Cirigliano, Rosell
R(K)e/µ · 105 2.488± 0.010 2.477± 0.001
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Low-energy constants and lattice QCD
Motto (Laurent Lellouch, John F. Kennedy)
Ask not what CHPT can do for the lattice,
but what the lattice can do for CHPT
CHPT −→ lattice
(chiral) extrapolation to physical quark (meson) masses
still useful, but less needed than 5 years ago
lattice −→ CHPT
determination of LECs (FLAG, . . . )
especially welcome for LECs multiplying quark mass terms
advantage of lattice simulations compared to phenomenology:
quark (and therefore meson) masses can be tuned
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Low-energy constants and lattice QCD
Motto (Laurent Lellouch, John F. Kennedy)
Ask not what CHPT can do for the lattice,
but what the lattice can do for CHPT
CHPT −→ lattice
(chiral) extrapolation to physical quark (meson) masses
still useful, but less needed than 5 years ago
lattice −→ CHPT
determination of LECs (FLAG, . . . )
especially welcome for LECs multiplying quark mass terms
advantage of lattice simulations compared to phenomenology:
quark (and therefore meson) masses can be tuned
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Low-energy constants and lattice QCD
Motto (Laurent Lellouch, John F. Kennedy)
Ask not what CHPT can do for the lattice,
but what the lattice can do for CHPT
CHPT −→ lattice
(chiral) extrapolation to physical quark (meson) masses
still useful, but less needed than 5 years ago
lattice −→ CHPT
determination of LECs (FLAG, . . . )
especially welcome for LECs multiplying quark mass terms
advantage of lattice simulations compared to phenomenology:
quark (and therefore meson) masses can be tuned
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
illustrative example:
chiral SU(3) Lagrangian (strong interactions)
Lp2(2) =F 2
0
4〈DµUDµU† + χU† + χ†U〉
Lp4(10) = · · ·+ L4〈DµUDµU†〉〈χU† + χ†U〉+ . . .
〈. . . 〉 flavour trace
F0 = limmu ,md ,ms→0 Fπ, χ = 2B0Mq (B0 ∼ quark condensate)
U = 1 + meson fields
gauge-covariant derivative DµU (contains Aµ,W±µ )
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Lp2(2) + Lp4(10) =1
4〈DµUDµU†〉
[F 2
0 + 8L4
(2
◦M2
K +◦M2π
)]+ . . .
◦MP lowest-order meson mass
F 2π/(16M2
K ) = 2× 10−3 ∼ typical size of NLO LEC
consequences
strong anticorrelation
between F0 and L4
in global fits
Bijnens, Jemos
Out[7]=
50 60 70 80 90 100F0 HMeVL
0.0
0.5
1.0
1.5
L4r HM·L 103
J . Bijnens, I. Jemos : Global fit for SU H3L LECsNucl. Phys. B854 H2012L 631
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Lp2(2) + Lp4(10) =1
4〈DµUDµU†〉
[F 2
0 + 8L4
(2
◦M2
K +◦M2π
)]+ . . .
◦MP lowest-order meson mass
F 2π/(16M2
K ) = 2× 10−3 ∼ typical size of NLO LEC
consequences
strong anticorrelation
between F0 and L4
in global fits
Bijnens, Jemos
Out[7]=
50 60 70 80 90 100F0 HMeVL
0.0
0.5
1.0
1.5
L4r HM·L 103
J . Bijnens, I. Jemos : Global fit for SU H3L LECsNucl. Phys. B854 H2012L 631
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
“convergence” of SU(3) CHPT depends (also) on value of F0
but LO LEC F0 less known than many higher-order LECs
rather wide spread in F0 also from lattice studies −→FLAG (2011) does not perform an average
L4 is large-Nc suppressed −→ in Gasser, Leutwyler (1985)set to zero (more precisely: Lr
4(Mη) = 0± 0.5× 10−3)
FLAG (2011): published lattice determinations (for Lr4(Mρ))
-1
-1
0
0
1
1
RBC/UKQCD 08
PACS-CS 08
MILC 09A
GL 85
Bijnens 09
103 L4
Nf=
2+1
MILC 09
MILC 10
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
“convergence” of SU(3) CHPT depends (also) on value of F0
but LO LEC F0 less known than many higher-order LECs
rather wide spread in F0 also from lattice studies −→FLAG (2011) does not perform an average
L4 is large-Nc suppressed −→ in Gasser, Leutwyler (1985)set to zero (more precisely: Lr
4(Mη) = 0± 0.5× 10−3)
FLAG (2011): published lattice determinations (for Lr4(Mρ))
-1
-1
0
0
1
1
RBC/UKQCD 08
PACS-CS 08
MILC 09A
GL 85
Bijnens 09
103 L4
Nf=
2+1
MILC 09
MILC 10
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
“convergence” of SU(3) CHPT depends (also) on value of F0
but LO LEC F0 less known than many higher-order LECs
rather wide spread in F0 also from lattice studies −→FLAG (2011) does not perform an average
L4 is large-Nc suppressed −→ in Gasser, Leutwyler (1985)set to zero (more precisely: Lr
4(Mη) = 0± 0.5× 10−3)
FLAG (2011): published lattice determinations (for Lr4(Mρ))
-1
-1
0
0
1
1
RBC/UKQCD 08
PACS-CS 08
MILC 09A
GL 85
Bijnens 09
103 L4
Nf=
2+1
MILC 09
MILC 10
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
“convergence” of SU(3) CHPT depends (also) on value of F0
but LO LEC F0 less known than many higher-order LECs
rather wide spread in F0 also from lattice studies −→FLAG (2011) does not perform an average
L4 is large-Nc suppressed −→ in Gasser, Leutwyler (1985)set to zero (more precisely: Lr
4(Mη) = 0± 0.5× 10−3)
FLAG (2011): published lattice determinations (for Lr4(Mρ))
-1
-1
0
0
1
1
RBC/UKQCD 08
PACS-CS 08
MILC 09A
GL 85
Bijnens 09
103 L4
Nf=
2+1
MILC 09
MILC 10
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
comparison between SU(2) and SU(3)
F = limmu ,md→0 Fπ
F0 = F − F−1
{(2M2
K −M2π
)(4Lr
4(µ) +1
64π2logµ2/M2
K
)+
M2π
64π2
}+ O(p6)
“paramagnetic” inequality (Descotes-Genon,Girlanda,Stern )
F0 < F −→ Lr4(Mρ) > −0.4× 10−3
FLAG (2011): F = Fπ/1.073(15)
−→ linear relation between F0 and L4
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
comparison between SU(2) and SU(3)
F = limmu ,md→0 Fπ
F0 = F − F−1
{(2M2
K −M2π
)(4Lr
4(µ) +1
64π2logµ2/M2
K
)+
M2π
64π2
}+ O(p6)
“paramagnetic” inequality (Descotes-Genon,Girlanda,Stern )
F0 < F −→ Lr4(Mρ) > −0.4× 10−3
FLAG (2011): F = Fπ/1.073(15)
−→ linear relation between F0 and L4
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
comparison between SU(2) and SU(3)
F = limmu ,md→0 Fπ
F0 = F − F−1
{(2M2
K −M2π
)(4Lr
4(µ) +1
64π2logµ2/M2
K
)+
M2π
64π2
}+ O(p6)
“paramagnetic” inequality (Descotes-Genon,Girlanda,Stern )
F0 < F −→ Lr4(Mρ) > −0.4× 10−3
FLAG (2011): F = Fπ/1.073(15)
−→ linear relation between F0 and L4
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
suggestion:
determine F0, L4 from SU(3) lattice data for Fπ
essential: CHPT to NNLO = O(p6) (Amoros,Bijnens,Talavera)
drawback: only available in numerical form
in addition: need some knowledge of L5 and LECs of O(p6)
(e.g.: from analysis of FK/Fπ)
with large-Nc motivated approximation for 2-loop calculation
E.,Masjuan,Neufeld
Out[25]=
-0.4 -0.2 0.0 0.2 0.4L4
r HM·L 103
70
75
80
85
90
95
F0 HMeVL
Blue : fitting FΠ with RBC�UKQCD data H2011LRed: F0 IF,L4
r IM·MM with FΠ�F = 1.073 H15L HFLAG 2011L
preliminary
RBC/UKQCD data (2011)
F0 = (86.7± 8.2) MeV
Lr4(Mρ) = (0.0±0.3) ·10−3
SU(2) constraint ?
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
suggestion:
determine F0, L4 from SU(3) lattice data for Fπ
essential: CHPT to NNLO = O(p6) (Amoros,Bijnens,Talavera)
drawback: only available in numerical form
in addition: need some knowledge of L5 and LECs of O(p6)
(e.g.: from analysis of FK/Fπ)
with large-Nc motivated approximation for 2-loop calculation
E.,Masjuan,Neufeld
Out[25]=
-0.4 -0.2 0.0 0.2 0.4L4
r HM·L 103
70
75
80
85
90
95
F0 HMeVL
Blue : fitting FΠ with RBC�UKQCD data H2011LRed: F0 IF,L4
r IM·MM with FΠ�F = 1.073 H15L HFLAG 2011L
preliminary
RBC/UKQCD data (2011)
F0 = (86.7± 8.2) MeV
Lr4(Mρ) = (0.0±0.3) ·10−3
SU(2) constraint ?
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
suggestion:
determine F0, L4 from SU(3) lattice data for Fπ
essential: CHPT to NNLO = O(p6) (Amoros,Bijnens,Talavera)
drawback: only available in numerical form
in addition: need some knowledge of L5 and LECs of O(p6)
(e.g.: from analysis of FK/Fπ)
with large-Nc motivated approximation for 2-loop calculation
E.,Masjuan,Neufeld
Out[25]=
-0.4 -0.2 0.0 0.2 0.4L4
r HM·L 103
70
75
80
85
90
95
F0 HMeVL
Blue : fitting FΠ with RBC�UKQCD data H2011LRed: F0 IF,L4
r IM·MM with FΠ�F = 1.073 H15L HFLAG 2011L
preliminary
RBC/UKQCD data (2011)
F0 = (86.7± 8.2) MeV
Lr4(Mρ) = (0.0±0.3) ·10−3
SU(2) constraint ?
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
suggestion:
determine F0, L4 from SU(3) lattice data for Fπ
essential: CHPT to NNLO = O(p6) (Amoros,Bijnens,Talavera)
drawback: only available in numerical form
in addition: need some knowledge of L5 and LECs of O(p6)
(e.g.: from analysis of FK/Fπ)
with large-Nc motivated approximation for 2-loop calculation
E.,Masjuan,Neufeld
Out[25]=
-0.4 -0.2 0.0 0.2 0.4L4
r HM·L 103
70
75
80
85
90
95
F0 HMeVL
Blue : fitting FΠ with RBC�UKQCD data H2011LRed: F0 IF,L4
r IM·MM with FΠ�F = 1.073 H15L HFLAG 2011L
preliminary
RBC/UKQCD data (2011)
F0 = (86.7± 8.2) MeV
Lr4(Mρ) = (0.0±0.3) ·10−3
SU(2) constraint ?
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Carbogenesis: the Hoyle state
almost all carbon produced in stellar nucleosynthesis via
triple-α process
Hoyle (1954): to explain observed carbon abundance
−→ ∃ excited 0+ state of 12C near 8Be-α threshold
observed soon afterwards
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Carbogenesis: the Hoyle state
almost all carbon produced in stellar nucleosynthesis via
triple-α process
Hoyle (1954): to explain observed carbon abundance
−→ ∃ excited 0+ state of 12C near 8Be-α threshold
observed soon afterwards
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
properties of Hoyle state
ε = 379.47(18) keV (above 3α threshold)
Γtot = 8.3(1.0) eV, Γγ = 3.7(5) meV
triple-α rate ∼ Γγ exp−ε/kT −→ mainly sensitive to ε
example of anthropic principle?
Livio et al. (1989), Oberhummer et al. (2004)
∆ε ∼< 100 keV tolerable to explain abundance of 12C, 16O
−→ not exactly severe fine-tuninghowever:
more interesting issue:
dependence of ε on fundamental parameters ofstrong and electromagnetic interactions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
properties of Hoyle state
ε = 379.47(18) keV (above 3α threshold)
Γtot = 8.3(1.0) eV, Γγ = 3.7(5) meV
triple-α rate ∼ Γγ exp−ε/kT −→ mainly sensitive to ε
example of anthropic principle?
Livio et al. (1989), Oberhummer et al. (2004)
∆ε ∼< 100 keV tolerable to explain abundance of 12C, 16O
−→ not exactly severe fine-tuninghowever:
more interesting issue:
dependence of ε on fundamental parameters ofstrong and electromagnetic interactions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
properties of Hoyle state
ε = 379.47(18) keV (above 3α threshold)
Γtot = 8.3(1.0) eV, Γγ = 3.7(5) meV
triple-α rate ∼ Γγ exp−ε/kT −→ mainly sensitive to ε
example of anthropic principle?
Livio et al. (1989), Oberhummer et al. (2004)
∆ε ∼< 100 keV tolerable to explain abundance of 12C, 16O
−→ not exactly severe fine-tuning
however:
more interesting issue:
dependence of ε on fundamental parameters ofstrong and electromagnetic interactions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
properties of Hoyle state
ε = 379.47(18) keV (above 3α threshold)
Γtot = 8.3(1.0) eV, Γγ = 3.7(5) meV
triple-α rate ∼ Γγ exp−ε/kT −→ mainly sensitive to ε
example of anthropic principle?
Livio et al. (1989), Oberhummer et al. (2004)
∆ε ∼< 100 keV tolerable to explain abundance of 12C, 16O
−→ not exactly severe fine-tuninghowever:
more interesting issue:
dependence of ε on fundamental parameters ofstrong and electromagnetic interactions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
one-parameter (p) nuclear cluster model Oberhummer et al.
tolerances
∆p/p ∼< 0.5% ∆FCoulomb/FCoulomb ∼< 4%
open question:
relation to fundamental parameters of QCD and QED?
chiral EFT of nuclear forces Weinberg (1990), . . .
expansion of nuclear potential (2-,3-,4-nucleon forces)
successful approach for small nuclei (A ∼< 3)
more recent development
nuclear lattice simulations (Muller, Lee, Borasoy, . . . )
lattice dofs: nucleons (not quarks!) and pions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
one-parameter (p) nuclear cluster model Oberhummer et al.
tolerances
∆p/p ∼< 0.5% ∆FCoulomb/FCoulomb ∼< 4%
open question:
relation to fundamental parameters of QCD and QED?
chiral EFT of nuclear forces Weinberg (1990), . . .
expansion of nuclear potential (2-,3-,4-nucleon forces)
successful approach for small nuclei (A ∼< 3)
more recent development
nuclear lattice simulations (Muller, Lee, Borasoy, . . . )
lattice dofs: nucleons (not quarks!) and pions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
one-parameter (p) nuclear cluster model Oberhummer et al.
tolerances
∆p/p ∼< 0.5% ∆FCoulomb/FCoulomb ∼< 4%
open question:
relation to fundamental parameters of QCD and QED?
chiral EFT of nuclear forces Weinberg (1990), . . .
expansion of nuclear potential (2-,3-,4-nucleon forces)
successful approach for small nuclei (A ∼< 3)
more recent development
nuclear lattice simulations (Muller, Lee, Borasoy, . . . )
lattice dofs: nucleons (not quarks!) and pions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
one-parameter (p) nuclear cluster model Oberhummer et al.
tolerances
∆p/p ∼< 0.5% ∆FCoulomb/FCoulomb ∼< 4%
open question:
relation to fundamental parameters of QCD and QED?
chiral EFT of nuclear forces Weinberg (1990), . . .
expansion of nuclear potential (2-,3-,4-nucleon forces)
successful approach for small nuclei (A ∼< 3)
more recent development
nuclear lattice simulations (Muller, Lee, Borasoy, . . . )
lattice dofs: nucleons (not quarks!) and pions
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Monte-Carlo techniques
−→ energies of low-lying states of 12C (in MeV)
0+1 2+
1 (E+) 0+2
LO −96(2) −94(2) −89(2)NLO −77(3) −74(3) −72(3)
NNLO −92(3) −89(3) −85(3)
Exp −92.16 −87.72 −84.51
Epelbaum et al.
0+2 : Hoyle state
method allows to study dependence on
quark masses (via Mπ ∼ (mu + md))
fine-structure constant αem (not αQCD )
final conclusion for tolerances
∆mq/mq ∼< 3% ∆αem/αem ∼< 2.5%
−→ fine-tuning in mq, αem much more severe than in ε
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Monte-Carlo techniques
−→ energies of low-lying states of 12C (in MeV)
0+1 2+
1 (E+) 0+2
LO −96(2) −94(2) −89(2)NLO −77(3) −74(3) −72(3)
NNLO −92(3) −89(3) −85(3)
Exp −92.16 −87.72 −84.51
Epelbaum et al.
0+2 : Hoyle state
method allows to study dependence on
quark masses (via Mπ ∼ (mu + md))
fine-structure constant αem (not αQCD )
final conclusion for tolerances
∆mq/mq ∼< 3% ∆αem/αem ∼< 2.5%
−→ fine-tuning in mq, αem much more severe than in ε
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Monte-Carlo techniques
−→ energies of low-lying states of 12C (in MeV)
0+1 2+
1 (E+) 0+2
LO −96(2) −94(2) −89(2)NLO −77(3) −74(3) −72(3)
NNLO −92(3) −89(3) −85(3)
Exp −92.16 −87.72 −84.51
Epelbaum et al.
0+2 : Hoyle state
method allows to study dependence on
quark masses (via Mπ ∼ (mu + md))
fine-structure constant αem (not αQCD )
final conclusion for tolerances
∆mq/mq ∼< 3% ∆αem/αem ∼< 2.5%
−→ fine-tuning in mq, αem much more severe than in ε
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Monte-Carlo techniques
−→ energies of low-lying states of 12C (in MeV)
0+1 2+
1 (E+) 0+2
LO −96(2) −94(2) −89(2)NLO −77(3) −74(3) −72(3)
NNLO −92(3) −89(3) −85(3)
Exp −92.16 −87.72 −84.51
Epelbaum et al.
0+2 : Hoyle state
method allows to study dependence on
quark masses (via Mπ ∼ (mu + md))
fine-structure constant αem (not αQCD )
final conclusion for tolerances
∆mq/mq ∼< 3% ∆αem/αem ∼< 2.5%
−→ fine-tuning in mq, αem much more severe than in ε
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Conclusions
main objectives
understand physics of the SM at low energies
look for evidence of new physics
objectives accomplished?
we have gone some way in understanding theSM at low energies
on the other hand: we have not foundevidence for new physics
but neither has the LHC !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Conclusions
main objectives
understand physics of the SM at low energies
look for evidence of new physics
objectives accomplished?
we have gone some way in understanding theSM at low energies
on the other hand: we have not foundevidence for new physics
but neither has the LHC !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Conclusions
main objectives
understand physics of the SM at low energies
look for evidence of new physics
objectives accomplished?
we have gone some way in understanding theSM at low energies
on the other hand: we have not foundevidence for new physics
but neither has the LHC !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Conclusions
main objectives
understand physics of the SM at low energies
look for evidence of new physics
objectives accomplished?
we have gone some way in understanding theSM at low energies
on the other hand: we have not foundevidence for new physics
but neither has the LHC !
Motivation Nonleptonic K decays Precision physics Lattice QCD Carbogenesis Conclusions
Conclusions
main objectives
understand physics of the SM at low energies
look for evidence of new physics
objectives accomplished?
we have gone some way in understanding theSM at low energies
on the other hand: we have not foundevidence for new physics
but neither has the LHC !