Strong interactions for the precision frontier in …...Strong interactions for the precision...

Strong interactions for the precision frontierin particle and nuclear physics

Bastian Kubis

Helmholtz-Institut fur Strahlen- und Kernphysik (Theorie)

Bethe Center for Theoretical Physics

Universitat Bonn, Germany

ColloquiumIndiana University, Bloomington, March 10th 2014

B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics – p. 1

Outline

Introduction: why the strong interactions are difficult

Strong and weak interactions

• Spectroscopy, CP violation, and Dalitz plots

Strong interactions and electromagnetism

• The anomalous magnetic moment of the muon

Summary / Outlook


The Standard Model of particle physics

uup

2.4 MeV/c

⅔ ccharm

1.27 GeV/c

⅔ ttop

171.2 GeV/c

⅔

ddown

4.8 MeV/c

- sstrange

104 MeV/c

- bbottom

4.2 GeV/c

-

ν<2.2 eV/c

νμ<0.17 MeV/c

ντ<15.5 MeV/c

eelectron

0.511 MeV/c

- μmuon

105.7 MeV/c

- τtau

1.777 GeV/c

γphoton

ggluon

Z91.2 GeV/c

80.4 GeV/c

±

mass

spin

charge

Qu

ark

sL

ep

ton

s

Ga

ug

e b

oso

ns

I II III

name

electronneutrino

muonneutrino

tauneutrino

Z boson

W boson

Three generations

of matter (fermions)

Wμ ±

2 2 2

2 2 2

2 2 2

2 2 2 2

2

~125 GeV/c

Higgs boson

H*

2

0

*Yet to be confirmed

• matter particle:quarks and leptons

• force carriers: gauge bosons

• how did we find these?how to find something beyond?



uup

2.4 MeV/c

ccharm

1.27 GeV/c

⅔ ttop

171.2 GeV/c

⅔

ddown

4.8 MeV/c

- sstrange

104 MeV/c

- bbottom

4.2 GeV/c

-

νe<2.2 eV/c

0 νμ<0.17 MeV/c

0 ντ<15.5 MeV/c

0

eelectron

0.511 MeV/c

-1 μmuon

105.7 MeV/c

-1 τtau

1.777 GeV/c

-1

γphoton

0

0

1

ggluon

0

1

0

Z91.2 GeV/c

0

1

80.4 GeV/c

1

±1

mass→

spin→

charge→

Qu

ark

sL

ep

ton

s

Ga

ug

e b

oso

ns

I II III

name→

electronneutrino

muonneutrino

tauneutrino

Z boson

W boson

Three generations


Wμ

0

±

2 2 2

2 2 2

2 2 2

2 2 2 2

2

~125 GeV/c

0

Higgs boson

H*

2

0





• discoveries at high energies:production of new particles

g

g

t

t



uup

2.4 MeV/c

⅔ ccharm

1.27 GeV/c

⅔ ttop

171.2 GeV/c

⅔

ddown

4.8 MeV/c

- sstrange

104 MeV/c

- bbottom

4.2 GeV/c

-

νe<2.2 eV/c

0 νμ<0.17 MeV/c

0 ντ<15.5 MeV/c

0

eelectron

0.511 MeV/c

-1 μmuon

105.7 MeV/c

-1 τtau

1.777 GeV/c

-1

γphoton

0

0

1

ggluon

0

1

0

Z91.2 GeV/c

0

1

80.4 GeV/c

1

±1

mass→

spin→

charge→

Qu

ark

sL

ep

ton

s

Ga

ug

e b

oso

ns

I II III

name→

electronneutrino

muonneutrino

tauneutrino

Z boson

W boson

Three generations


Wμ

0

±

2 2 2

2 2 2

2 2 2

2 2 2 2

2

~125 GeV/c

0

Higgs boson

H*

2

0





• discoveries at high energies:production of new particles

• discoveries in precision experi-ments: effects of virtual particles

s

d

du, c, t

W

d

g


Why the strong interactions are difficult

Perturbation theory and coupling constants

• expand amplitudes in powers of coupling constants α

scattering amplitude ∝ α(. . .)



Perturbation theory and coupling constants

• expand amplitudes in powers of coupling constants α

scattering amplitude ∝ α(. . .) + α2(. . .)

• works well for electromagnetic and weak interactions: α ≈ 10−2



The running coupling constant in Quantum Chromodynamics

QCDO(α )

245 MeV

181 MeV

ΛMS(5) α (Μ )s Z

0.1210

0.1156

0.1

0.2

0.3

0.4

0.5

αs(Q)

1 10 100Q [GeV]

Heavy QuarkoniaHadron Collisionse+e- AnnihilationDeep Inelastic Scattering

NL

O

NN

LO

TheoryData L

attic

e

211 MeV 0.1183s4

• asymptotic freedom athigh energies ("weak QCD")

• confinement at low energies("strong QCD"):

no quarks + gluons, only(colour-neutral) hadrons

baryons (rgb) + mesons (rr)



The running coupling constant in Quantum Chromodynamics

QCDO(α )

245 MeV

181 MeV

ΛMS(5) α (Μ )s Z

0.1210

0.1156

0.1

0.2

0.3

0.4

0.5

αs(Q)

1 10 100Q [GeV]

Heavy QuarkoniaHadron Collisionse+e- AnnihilationDeep Inelastic Scattering

NL

O

NN

LO

TheoryData L

attic

e

211 MeV 0.1183s4

• asymptotic freedom athigh energies ("weak QCD")

• confinement at low energies("strong QCD"):

no quarks + gluons, only(colour-neutral) hadrons

baryons (rgb) + mesons (rr)

Perturbative QCD notapplicable for

• hadron spectroscopy

• hadron scattering, decays

• nuclear physics



Alternative methods

Effective field theories

−→ symmetries, scale separation

Λχ

π,K, η



Alternative methods



Λχ

π,K, η

Dispersion relations

−→ analyticity, unitarity, crossing symmetry



Alternative methods



Λχ

π,K, η

Dispersion relations

−→ analyticity, unitarity, crossing symmetry

Lattice QCD

−→ solve discretized version of QCDnumerically


Part I:

Strong and weak interactions:

Spectroscopy, CP violation,

and Dalitz plots


Modern spectroscopy

qq~L

• mesons in the quark model: qq states

−→ certain quantum numbers JPC not allowed:

0+−, 0−−, 1−+, 2+−, . . . “exotics”

• lattice QCD: 1−+ state ≈ 1.3 GeV above the ρ Dudek et al. 2013


Modern spectroscopy

qq~L



0+−, 0−−, 1−+, 2+−, . . . “exotics”


• experiments:

p

π ??

COMPASS@CERN

p

γ??

CLAS, GlueX@JLab


Modern spectroscopy

qq~L



0+−, 0−−, 1−+, 2+−, . . . “exotics”


• experiments:

p

π ??

COMPASS@CERN

p

γ??

CLAS, GlueX@JLab

Things to control using dispersion relations:

• (exotic) phases interfere with known reference phases

• effects of three-/many-body final-state interactions?

• resonances = poles in the complex scattering-energy plane


CP violation in weak interactions

• CP violation: one of the prerequisites for matter–antimatterasymmetry in the universe




• in the Standard Model: embedded in the weak interactions,Cabibbo–Kobayashi–Maskawa matrix

VCKM =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

CP-violation given by a complex phase in V




• in the Standard Model: embedded in the weak interactions,Cabibbo–Kobayashi–Maskawa matrix

VCKM =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

CP-violation given by a complex phase in V

• Standard-Model CP violation too small−→ search for new/unconventional sources of CP violation⊲ charm D / beauty B decays⊲ electric dipole moments (proton/neutron/deuteron. . . )



CP violation in partial widths Γ(P → f) 6= Γ(P → f)

• at least two interfering decay amplitudes

• different weak (CKM) phases

• different strong (final-state-interaction) phases







two-body decays: D → ππ, KK

• decay at fixed total energy −→fixed strong phase







two-body decays: D → ππ, KK

• decay at fixed total energy −→fixed strong phase

three-body decays: D → 3π, ππK

• Dalitz plot = density distributionin two kinematical variables

• resonances −→ rapid phase vari-ation enhances CP-violation inparts of the decay region


Amplitude analyses in Dalitz plots

The traditional picture: isobar model / Breit–Wigner resonances

B, D

π

π

K

κ, K∗ . . .

B, D

π

π

K

f0, ρ . . .

0.0 0.2 0.4 0.6 0.8 1.0

s [GeV2]

0

5

10

15

modulus

0.0 0.2 0.4 0.6 0.8 1.0

s [GeV2]

0

90

180

phase [o]




B, D

π

π

K

κ, K∗ . . .

B, D

π

π

K

f0, ρ . . .

. . . so what’s not to like?

• some resonances don’t looklike Breit–Wigners at all!

−→ use exact scatteringphase shifts instead

400 600 800 1000 1200 1400

s1/2

(MeV)

0

50

100

150

200

250

300

CFDOld K decay dataNa48/2K->2 π decayKaminski et al.Grayer et al. Sol.BGrayer et al. Sol. CGrayer et al. Sol. DHyams et al. 73

δ0

(0)

PPP"σ"

f0




B, D

π

π

K

κ, K∗ . . .

B, D

π

π

K

f0, ρ . . .

. . . so what’s not to like?

• some resonances don’t looklike Breit–Wigners at all!

−→ use exact scatteringphase shifts instead

• 3-particle rescattering 400 600 800 1000 1200 1400

s1/2

(MeV)

0

50

100

150

200

250

300

CFDOld K decay dataNa48/2K->2 π decayKaminski et al.Grayer et al. Sol.BGrayer et al. Sol. CGrayer et al. Sol. DHyams et al. 73

δ0

(0)

PPP"σ"

f0

+++ . . .


A simple Dalitz plot: φ → 3π

• 2×106 events in 1834 binsKLOE 2003

• analyzed in terms of:

sum of 3 Breit–Wigners (ρ±, ρ0)

+ constant background term

+ crossed +φ

ρ

π

π

π

φ

π

π

π

Problem:

−→ unitarity fixes Im/Re parts

−→ adding a contact term destroys this relation


A simple Dalitz plot: φ → 3π

• 2×106 events in 1834 binsKLOE 2003

• analyzed in terms of:

sum of 3 Breit–Wigners (ρ±, ρ0)

+ constant background term

+ crossed +φ

ρ

π

π

π

φ

π

π

π

Problem:

−→ unitarity fixes Im/Re parts

−→ adding a contact term destroys this relation

−→ reconcile data with dispersion relations? Niecknig, BK, Schneider 2012


Experimental comparison to φ → 3π

• successive slices through Dalitz plot: Niecknig, BK, Schneider 2012

750 800 850 900 950 1000 1050 1100 1150 1200 1250bin number

0

2000

4000

6000

8000

χ2/ndof 1.7 . . . 2.1

−→ pairwise interaction only (with correct ππ scattering phase)




750 800 850 900 950 1000 1050 1100 1150 1200 1250bin number

0

2000

4000

6000

8000

χ2/ndof 1.7 . . . 2.1 1.2 . . . 1.5

−→ full 3-particle rescattering, only overall normalization adjustable




750 800 850 900 950 1000 1050 1100 1150 1200 1250bin number

0

2000

4000

6000

8000

χ2/ndof 1.7 . . . 2.1 1.2 . . . 1.5 1.0

−→ full 3-particle rescattering, 2 adjustable parameters(additional "subtraction constant" to suppress inelastic effects)




750 800 850 900 950 1000 1050 1100 1150 1200 1250bin number

0

2000

4000

6000

8000

χ2/ndof 1.7 . . . 2.1 1.2 . . . 1.5 1.0

• perfect fit respecting analyticity and unitarity possible

• contact term emulates neglected rescattering effects

• no need for "background" — inseparable from "resonance"


Heavier decays: D+ → π+π+K−

0.5

1

1.5

2

2.5

3

0.5 1 1.5 2 2.5 3

s [GeV2]

t[G

eV2]

CLEO 2008

c

d

s

D+ K−

π+

π+

u

u

W+

u

d

d



0.5

1

1.5

2

2.5

3

0.5 1 1.5 2 2.5 3

s [GeV2]

t[G

eV2]

CLEO 2008

c

d

s

D+ K−

π+

π+

u

u

W+

u

d

d

pion–pion S2ππ P 1

ππ

pion–kaon S1/2πK P

1/2πK

S3/2πK P

3/2πK

0

50

100

150

200

0 0.5 1 1.5 2

|Ω1/2

0|

√s [GeV]

"κ"

K∗0 (1430)

K∗0 (1950)



0.5

1

1.5

2

2.5

3

0.5 1 1.5 2 2.5 3

s [GeV2]

t[G

eV2]

CLEO 2008

c

d

s

D+ K−

π+

π+

u

u

W+

u

d

d

pion–pion S2ππ P 1

ππ

pion–kaon S1/2πK P

1/2πK

S3/2πK P

3/2πK

0

50

100

150

200

250

300

0 0.5 1 1.5 2

|Ω1/2

1|

√s [GeV]

K∗(892)



0.5

1

1.5

2

2.5

3

0.5 1 1.5 2 2.5 3

s [GeV2]

t[G

eV2]

CLEO 2008

c

d

s

D+ K−

π+

π+

u

u

W+

u

d

d

Fit in the elastic region:

• "improved isobar model" χ2/ndof ≈ 1.4

• full three-body rescattering χ2/ndof ≈ 1.1

−→ visible improvement similar to φ → 3π Niecknig, BK in progress


Part II:

Strong interactions and electromagnetism:

The anomalous magnetic moment of the muon



• gyromagnetic ratio: magnetic moment ↔ spin

~µ = ge

2m~S

• Dirac theory for spin-1/2 fermions: gµ = 2

rad. corr.: gµ = 2(1 + aµ), aµ “anomalous magnetic moment”

• one of the most precisely measured quantities in particle physics

aµ = (116 592 089± 63)× 10−11BNL E821 2006



• gyromagnetic ratio: magnetic moment ↔ spin

~µ = ge

2m~S

• Dirac theory for spin-1/2 fermions: gµ = 2

rad. corr.: gµ = 2(1 + aµ), aµ “anomalous magnetic moment”

• one of the most precisely measured quantities in particle physics

aµ = (116 592 089± 63)× 10−11BNL E821 2006

-700 -600 -500 -400 -300 -200 -100 0

aµ – a

µ exp ×

10

–11

BN

L-E

82

1 2

00

4

HMNT 07 (e+e

–-based)

JN 09 (e+e

–)

Davier et al. 09/1 (τ-based)

Davier et al. 09/1 (e+e

–)

Davier et al. 09/2 (e+e

– w/ BABAR)

HLMNT 10 (e+e

– w/ BABAR)

DHMZ 10 (τ newest)

DHMZ 10 (e+e

– newest)

BNL-E821 (world average)

–285 ±

51

–299 ±

65

–157 ±

52

–312 ±

51

–255 ±

49

–259 ±

48

–195 ±

54

–287 ±

49

0 ±

63

• . . . and one with a signif-icant (??) deviation fromthe Standard Model:

aexpµ −aSMµ = (27.6±8.6)×10−11

Davier et al. 2011

• new g − 2 experiment atFermilab: reduce experi-mental error by factor 4


The Standard Model prediction for aµ

aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.

QED O(α) 116 140 973.21 0.03QED O(α2) 413 217.63 0.01QED O(α3) 30 141.90 0.00QED O(α4) 381.01 0.02QED O(α5) 5.09 0.01QED total 116 584 718.85 0.04

electroweak 153.2 1.8

had. VP (LO) 6923. 42.had. VP (NLO) –98. 1.

had. LbL 116. 40.

total 116 591 813. 58.



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ µ

γ

Schwinger 1948



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ µ

µ µ

e, µ, τ

Petermann 1957

Sommerfield 1957



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

I(a) I(b) I(c) I(d) I(e)

I(f) I(g) I(h) I(i) I(j)

II(a) II(b) II(c) II(d) II(e)

II(f) III(a) III(b) III(c) IV

V VI(a) VI(b) VI(c) VI(d) VI(e)

VI(f) VI(g) VI(h) VI(i) VI(j) VI(k)

Kinoshita et al. 2012



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ µ

Z0, H

W W

ν



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ µ

hadrons



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ µ

µ µ



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

µ

hadrons



aµ [10−11] ∆aµ [10−11]

experiment 116 592 089. 63.




had. LbL 116. 40.

total 116 591 813. 58.

−→ hadronic partdominates the un-certainty by far!

Jegerlehner, Nyffeler 2009

Davier et al. 2011

and references therein


Hadronic vacuum polarization

• how to control hadronic vacuum polarization?

• characteristic scale set by muon mass−→ this is not a perturbative QCD problem!

• dispersion relations to the rescue:use the optical theorem!

µ µ

hadrons






µ µ

hadrons

Im

hadrons hadrons

2

⇔ ∝ σtot(e+e− → hadrons)

γ γ γ






µ µ

hadrons

ahad VP

µ ∝∫ ∞

4M2π

K(s)σtot(e+e− → hadrons)

• K(s): kinematical function, for large s: K(s) ∝ 1/s,σtot(e

+e− → hadrons) ∝ 1/s






µ µ

hadrons

ahad VP

µ ∝∫ ∞

4M2π

K(s)σtot(e+e− → hadrons)

• K(s): kinematical function, for large s: K(s) ∝ 1/s,σtot(e

+e− → hadrons) ∝ 1/s

• more than 75% of ahad VPµ given by

energies s ≤ 1GeV2 Jegerlehner, Nyffeler 2009

• dominated by e+e− → π+π−

−→ pion electromagnetic form factor

• well constrained by data KLOE, BABAR. . .

0.0 GeV, ∞

ρ, ω

1.0 GeV

φ, . . . 2.0 GeV

3.1 GeV

ψ 9.5 GeVΥ


Hadronic light-by-light scattering

• hadronic light-by-light soon to dominateStandard Model uncertainty

µ

hadrons




• different contributions estimated (in 10−11):µ

hadrons

π0, η, η′

µ µ

π±, K± axials,

µ

scalars

µ

quarks

99±16 –19±13 15±7 21±3

−→ hadronic modelling at its worst. . . Jegerlehner, Nyffeler 2009




• different contributions estimated (in 10−11):µ

hadrons

π0, η, η′

µ µ

π±, K± axials,

µ

scalars

µ

quarks

99±16 –19±13 15±7 21±3

−→ hadronic modelling at its worst. . . Jegerlehner, Nyffeler 2009

• largest (and unambiguous!) individual contribution: π0 pole term−→ depends on π0 → γ∗γ∗ form factor (doubly virtual in general!)


On the road to a dispersive analysis of π0 → γ∗γ∗

The Wess–Zumino–Witten (chiral) anomaly

• π0 → γγ fixed by the chiral anomaly: Fπ0γγ =e2

4π2Fπ

Fπ: pion decay constant −→ measured at % level PrimEx 2011





4π2Fπ


• analyze the leading hadronic intermediate states:see also Gorchtein, Guo, Szczepaniak 2012

γ(∗)s

π0

γ∗v

π+

π−

γ(∗)v

π0

γ∗s

π+

π−

π0





4π2Fπ



γ(∗)s

π0

γ∗v

π+

π−

γ(∗)v

π0

γ∗sω, φ





4π2Fπ



γ(∗)s

π0

γ∗v

π+

π−

γ(∗)v

π0

γ∗sω, φ

• important ingredients:⊲ anomalous process γπ → ππ

⊲ vector-meson radiative decays ω/φ → π0γ

transition form factors ω/φ → π0ℓ+ℓ−

−→ analyze these in turn, using dispersion relations


The anomalous process γπ → ππ

• γπ → ππ at zero energy: F3π =e

4π2F 3π

= (9.78± 0.05)GeV−3

how well can we test this low-energy theorem?




4π2F 3π

= (9.78± 0.05)GeV−3


Primakoff reaction:

π−π−

π0γ∗

Z

[GeV]0π-πm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

coun

ts

0

100

200

300

400

500

600

700

preliminary

-ρ-beam K

hadron dataCOMPASS 2004

COMPASS, work in progress




4π2F 3π

= (9.78± 0.05)GeV−3


Primakoff reaction:

π−π−

π0γ∗

Z

[GeV]0π-πm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

coun

ts

0

100

200

300

400

500

600

700

preliminary

-ρ-beam K



• same quantum numbers as φ → 3π:

+ + + . . .

Truong 2002, Hoferichter, BK, Sakkas 2012




4π2F 3π

= (9.78± 0.05)GeV−3


Primakoff reaction:

π−π−

π0γ∗

Z

[GeV]0π-πm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

coun

ts

0

100

200

300

400

500

600

700

preliminary

-ρ-beam K



• same quantum numbers as φ → 3π:

−→ extract F3π from the complete spectrum

model-independently, using ππ phase shift!Hoferichter, BK, Sakkas 2012


Transition form factors ω(φ) → π0ℓ+ℓ−

• π0 → γ∗γ∗ form factor linked to ω(φ) → π0γ∗ transition:

e+

e−

π0e−

e+




e+

e−

π0e−

e+

ω(φ)




ω

π0 π0

ωπ+

π−

=Im

• ω transition form factor related to

pion vector form factor × ω → 3π decay amplitude︸︷︷︸

calculate like φ→3π

• form factor normalization yields rate Γ(ω → π0γ)

(2nd most important ω decay channel)−→ works at 95% accuracy Schneider, BK, Niecknig 2012


Numerical results: ω → π0µ+µ−

0 0.1 0.2 0.3 0.4 0.5 0.6

1

10

100

√s [GeV]

|Fωπ0(s)|2

NA60 ’09NA60 ’11Lepton-GVMDTerschlüsen et al.f1(s) = aΩ(s)full dispersive

0.2 0.3 0.4 0.5 0.6 0.70

1

2

3

4

5

6

7

8

9

√s [GeV]

dΓω→

π0µ+µ−/d

s[10−6

GeV

−1]

• unable to account for steeprise in data (from heavy-ioncollisions) NA60 2009, 2011

• more "exclusive" data?! CLAS?

• ω → 3π Dalitz plot? CLAS?


Towards a dispersive analysis of e+e− → π0γ

e+

e−

γ

π0e+

e−

γ

π0

e+

e−

γ

π0 γ∗

• combine isoscalar and isovector contribution to e+e− → π0γ:⊲ parameterise e+e− → 3π

e.g. in terms of (dispersively improved)

ω+ φ Breit–Wigner propagators with good analytic propertiesLomon, Pacetti 2012; Moussallam 2013

⊲ prediction for e+e− → π0γ


Fit to e+e− → 3π data

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10-2

10-1

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σ(q) e

+e−

→3π[nb]

q [GeV]

dispersive FitSND

Hoferichter, BK, Leupold, Niecknig, Schneider preliminary

• one subtraction/normalisation at q2 = 0 fixed by γ → 3π

• fitted: ω, φ residues, one additional (linear) subtraction


Comparison to e+e− → π0γ data

0.5 0.6 0.7 0.8 0.9 1 1.110-3

10-2

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VEPP-2MCMD-2

σ(q) e

+e−

→π0γ[nb]

q[GeV]

Hoferichter, BK, Leupold, Niecknig, Schneider preliminary

• "prediction"—no further parameters adjusted

• data well reproduced


Summary

2 pieces of modern strong-interaction physicsusing dispersion relations :

• Dalitz plot analyses⊲ rigorous using modern phase shift input⊲ allow to understand ad-hoc "background"⊲ methods applicable for many kinds of "amplitude analyses":

CP violation, spectroscopy issues


Summary

2 pieces of modern strong-interaction physicsusing dispersion relations :

• Dalitz plot analyses⊲ rigorous using modern phase shift input⊲ allow to understand ad-hoc "background"⊲ methods applicable for many kinds of "amplitude analyses":

CP violation, spectroscopy issues

• The muon anomalous magnetic moment⊲ hadronic physics needs to be constrained well before

claiming "new physics"⊲ interrelate as much experimental information as possible


Strong interactions for the precision frontier in …...Strong interactions for the precision...

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