theoretical hadron physics in sweden - nupecc · stefan leupold theoretical hadron physics in...

Stefan Leupold Theoretical Hadron Physics in Sweden

Theoretical Hadron Physics in Sweden

Stefan Leupold

Uppsala, June 2016

1

Stefan Leupold Theoretical Hadron Physics in Sweden

Disclaimer

this talk covers only Swedish activities intheoretical hadron physics

theoretical heavy-ion physics not covered

↪→ some players:R. Pasechnik, L. Lonnblad, G. Gustafson (Lund U.)E. Perotti, SL (Uppsala U.)

nuclear structure Christian Forssen’s talk

2

Stefan Leupold Theoretical Hadron Physics in Sweden

Challenges of hadron physics

understand structure of matter at the femtometer scale↪→ structure of hadronsfor structure of nuclei Christian’s talk

standard-model tests:

determination of standard-model parameters(light-quark masses, ...)

flavor physicshadronic contributions to high-precisionstandard model predictions (g − 2 of muon, ...)

↪→ quest for physics beyond the standard model

3

Stefan Leupold Theoretical Hadron Physics in Sweden

Towards model independence

mandatory at least for standard-model tests:high precision, reliable uncertainty estimates(does not hurt to achieve this also for hadron-structure studies)

↪→ model independent approaches preferable (not always possible)

lattice QCD:

needs guidance for pions that are not light or not chiral enough

effective field theories:

2-loop chiral perturbation theory; how light are strange quarks?

dispersion theory:

requires close collaboration experiment-theory

4

Stefan Leupold Theoretical Hadron Physics in Sweden

Towards model independence

mandatory at least for standard-model tests:high precision, reliable uncertainty estimates(does not hurt to achieve this also for hadron-structure studies)

↪→ model independent approaches preferable (not always possible)

lattice QCD:needs guidance for pions that are not light or not chiral enougheffective field theories:

2-loop chiral perturbation theory; how light are strange quarks?

dispersion theory:

requires close collaboration experiment-theory

4

Stefan Leupold Theoretical Hadron Physics in Sweden

Towards model independence

mandatory at least for standard-model tests:high precision, reliable uncertainty estimates(does not hurt to achieve this also for hadron-structure studies)

↪→ model independent approaches preferable (not always possible)

lattice QCD:needs guidance for pions that are not light or not chiral enougheffective field theories:2-loop chiral perturbation theory; how light are strange quarks?dispersion theory:

requires close collaboration experiment-theory

4

Stefan Leupold Theoretical Hadron Physics in Sweden

Towards model independence

mandatory at least for standard-model tests:high precision, reliable uncertainty estimates(does not hurt to achieve this also for hadron-structure studies)

↪→ model independent approaches preferable (not always possible)

lattice QCD:needs guidance for pions that are not light or not chiral enougheffective field theories:2-loop chiral perturbation theory; how light are strange quarks?dispersion theory:requires close collaboration experiment-theory

4

Stefan Leupold Theoretical Hadron Physics in Sweden

Structure of hadrons — concrete projects

2-loop chiral

perturbation theory

Bijnens/Ecker/...

chiral logs for

nucleon mass∗

Bijnens/Vladimirov

pion-baryon fluct.

in nucleon

Ghaderi/Ingelman/SL��

��structure of

hadrons

scale separation

Goldstones ↔ vectors∗

Terschlusen/SL

lattice QCD meets

chiral pert. theo.∗

Bijnens/Rossler

hyperon form factors

(how close to nucleon?)

Granados/Husek/Junker/SL

5

Stefan Leupold Theoretical Hadron Physics in Sweden

Standard-model (SM) tests — concrete projects

2-loop chiral

perturbation theory

Bijnens/Ecker/...

quark-mass ratio

Balkestahl/Kupsc/Passemar

towards CP viol.in baryons

hyperon decaysIkegami-A./Johansson/SL/Perotti/Schonning/Thome�

���SM tests

pion transition

form factor∗

Hoferichter/Jansson/Kubis/SL/Niecknig/Schneider

Husek/SL

Bijnens/Pallante/Prades

muon’s g − 2 in

general, error budget

Bijnens/Prades/...

eta transition

form factor

Hanhart/Kupsc/Meißner/Stollenwerk/Wirzba

6

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 1: Chiral logs for nucleon mass

contributions to nucleon masstypes m2n+1 logn−1(µ2/m2) and m2n+2 logn(µ2/m2)using heavy-baryon chiral perturbation theory (χPT)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.02 0.04 0.06 0.08 0.1

Mph

ys-M

[GeV

]

m2 [GeV2]

012345

J. Bijnens, A.A. Vladimirov,

Nucl.Phys. B891 (2015) 700

(with pion mass m)

7

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 2: Importance of vector mesons

three degenerate flavors“kaon” decay constant as function of bare “kaon” masshow important are vector-meson loops (with physical mass)?as compared to one-loop chiral perturbation theory (χPT)

0.6

0.8

1.0

0.1 0.2 0.3 0.4 0.5mP [GeV]

F0 / FKexp

fV = 150 MeV, hP = 1.50fV = √ 2 F(π)exp, hP = 2fV = 150 MeV, hP = 2pure ChPT

C. Terschlusen, SL,

arXiv:1604.01682 [hep-ph]

8

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 3: Lattice QCD meets χPT

explore importance of finite-volume effects, partial quenching,twisted boundary conditions, staggered fermionstwo-loop chiral perturbation theory (χPT)explore different pion masses (and physical kaon mass)

1e-06

1e-05

0.0001

0.001

0.01

0.1

2 2.5 3 3.5 4

−∆VF

π/F

π

mπ0 L

mπ = 100 MeV

mπ = 300 MeV

mπ = 495 MeV

p4

p4+p6

T. Rossler, J. Bijnens,

arXiv:1511.06294 [hep-lat]

J. Bijnens, T. Rossler,

JHEP 1511 (2015) 017;

JHEP 1511 (2015) 097;

JHEP 1501 (2015) 034

9

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 4: Pion transition form factor (TFF)

input: pion phase shifts and

cross section e+e− → 3π

0.6 0.7 0.8 0.9 1.0 1.1

10-2

10-1

100

101

102

103

fit SND+BaBarfit HLMNTSNDBaBar

√q2 [GeV]

σe+

e−→

3π[n

b]

postdiction: e+e− → π0γ

0.5 0.6 0.7 0.8 0.9 1.0 1.1

10-3

10-2

10-1

100

101

102

SNDCMD2

√q2 [GeV]

σe+

e−→

π0γ

[nb]

prediction: spacelike pion TFF

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

CLEOCELLO

Q2 [GeV2]

Q2 F

π0γ∗ γ

(−

Q2 ,

0)/e

2[G

eV]

work in progress: pion-pole

contribution to g − 2 of muonγ

µ

π

M. Hoferichter, B. Kubis, SL, F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 3180

10

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 4: Pion transition form factor (TFF)

input: pion phase shifts and

cross section e+e− → 3π

0.6 0.7 0.8 0.9 1.0 1.1

10-2

10-1

100

101

102

103

fit SND+BaBarfit HLMNTSNDBaBar

√q2 [GeV]

σe+

e−→

3π[n

b]

postdiction: e+e− → π0γ

0.5 0.6 0.7 0.8 0.9 1.0 1.1

10-3

10-2

10-1

100

101

102

SNDCMD2

√q2 [GeV]

σe+

e−→

π0γ

[nb]

prediction: spacelike pion TFF

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

CLEOCELLO

Q2 [GeV2]

Q2 F

π0γ∗ γ

(−

Q2 ,

0)/e

2[G

eV]

work in progress: pion-pole

contribution to g − 2 of muonγ

µ

π

M. Hoferichter, B. Kubis, SL, F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 3180

10

Stefan Leupold Theoretical Hadron Physics in Sweden

Highlight 4: Pion transition form factor (TFF)

input: pion phase shifts and

cross section e+e− → 3π

0.6 0.7 0.8 0.9 1.0 1.1

10-2

10-1

100

101

102

103

fit SND+BaBarfit HLMNTSNDBaBar

√q2 [GeV]

σe+

e−→

3π[n

b]

postdiction: e+e− → π0γ

0.5 0.6 0.7 0.8 0.9 1.0 1.1

10-3

10-2

10-1

100

101

102

SNDCMD2

√q2 [GeV]

σe+

e−→

π0γ

[nb]

prediction: spacelike pion TFF

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

CLEOCELLO

Q2 [GeV2]

Q2 F

π0γ∗ γ

(−

Q2 ,

0)/e

2[G

eV]

work in progress: pion-pole

contribution to g − 2 of muonγ

µ

π

M. Hoferichter, B. Kubis, SL, F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 3180

10

Stefan Leupold Theoretical Hadron Physics in Sweden

backup slides

11

Stefan Leupold Theoretical Hadron Physics in Sweden

g − 2 of the muon — status

290

240

190

140140

190

240

290

1979CERN

Theory

KN

O(1

985)

1997

µ+

1998

µ+

1999

µ+

2000

µ+

2001

µ−

Average

Theory

(2009)

(aµ-1

1659000)×

10−1

0A

nom

alo

us

Magnetic

Mom

ent

BNL Running Year

Jegerlehner/Nyffeler, Phys. Rept. 477, 1 (2009)12

Stefan Leupold Theoretical Hadron Physics in Sweden

g − 2 of the muon — theory

Largest uncertainty of standard model: hadronic contributions

γ

µhadronic

γ

µ

hadronic

vacuum polarization light-by-light scattering∼ α2 ∼ α3

13

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model prediction

and with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data”

(← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic contribution to g − 2 of the muonγ

µhadronic

γ

µ

hadronic

how to determine size of hadronic fluctuations?

↪→ develop a phenomenological hadronic modelor quark model P(?)

↪→ this would yield a P-model prediction

↪→ but we want a standard-model predictionand with a reliable uncertainty estimate!

↪→ need a model independent approach

↪→ lattice QCD, effective field theory or“data” (← highest accuracy so far)

14

Stefan Leupold Theoretical Hadron Physics in Sweden

Data-driven approach

vacuum polarization (now dominant uncertainty)

directly related to cross sect. e+e− → hadrons(by dispersion relation)

measurable

ongoing improvements by international efforts

γ

µhadronic

light-by-light scattering(soon dominant uncertainty)

γ

µ

hadronic

γ∗γ∗ ↔ hadron(s) not so easily accessible by experiment

↪→ crank dispersive machinery furtherColangelo/Hoferichter/Kubis/Procura/Stoffer, Phys.Lett. B738 (2014) 6

↪→ defines extensive experimental and theoretical program15

Stefan Leupold Theoretical Hadron Physics in Sweden

Hadronic light-by-light contribution

true for all hadronic contributions:

γ

µ

hadronic

the lighter the hadronic system, the more important(though high-energy contributions not unimportant for light-by-light)

↪→ γ(∗)γ(∗) ↔ π0 γ(∗)γ(∗) ↔ 2π, . . .

γ

µ

π

γ

µ

π

π

16

Stefan Leupold Theoretical Hadron Physics in Sweden

Unitarity and analyticity

constraints from quantum field theory:partial-wave amplitudes for reactions/decays must be

unitary:

S S† = 1 , S = 1 + iT ⇒ 2 ImT = T T †

↪→ note that this is a matrix equation:ImTA→B =

∑X TA→X T †X→B

in practice: use most relevant intermediate states Xanalytical (dispersion relations):

T (s) = T (0) +s

π

∞∫−∞

ds ′ImT (s ′)

s ′ (s ′ − s − iε),

can be used to calculate whole amplitude from imaginary part

17

Stefan Leupold Theoretical Hadron Physics in Sweden

Using lowest-mass states

hadronic light-by-light contribution

γ

µ

hadronic →γ

µ

π

need pion transition form factor

π0

→ π0

π−

π+

18

Stefan Leupold Theoretical Hadron Physics in Sweden

Dispersive reconstruction I

pion transition form factor

π0

→ π0

π−

π+

need pion vector form factor

π−

π+

→ very well measured

and amplitude γ∗–3-pion

π0 π−

π+

19

Stefan Leupold Theoretical Hadron Physics in Sweden

Pion vector form factor

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-2

10-1

100

101

102

√s [GeV]

|FV π(s

)|2

Belle data [25]Ref. [23]Ref. [24]Fit π−

π+

↓

π−

π+

π−

π+

pion phase shift very well known; fits to pion vector form factorSebastian P. Schneider, Bastian Kubis, Franz Niecknig, Phys.Rev.D86:054013,2012

20

Stefan Leupold Theoretical Hadron Physics in Sweden

Dispersive reconstruction II

amplitude γ∗–3-pion

π0 π−

π+

contains two-body correlations(depend on s, t, u), e.g.

π0 π−

π+

and genuine three-body correlations(depend on m2

3π = m2γ∗)

π0 π−

π+

21

Stefan Leupold Theoretical Hadron Physics in Sweden

Dispersive reconstruction II

amplitude γ∗–3-pion

π0 π−

π+

contains two-body correlations(depend on s, t, u), e.g.

π0 π−

π+

and genuine three-body correlations(depend on m2

3π = m2γ∗)

π0 π−

π+

21

Stefan Leupold Theoretical Hadron Physics in Sweden

Required input

for

π0 π−

π+

need pion phase shift

π

π

π

π

very well measured

and genuine three-body correlations(one-parameter function!)

π0 π−

π+

fit to cross section of e+e− → π+π−π0

22

Stefan Leupold Theoretical Hadron Physics in Sweden

Fit to e+e− → π+π−π0

dominated by narrow resonances ω, φ

↪→ use Breit-Wigners plus background forgenuine three-body correlations

↪→ fully include cross-channel rescatteringof pion pairs (two-body correlations) π0 π−

π+

0.6 0.7 0.8 0.9 1.0 1.1

10-2

10-1

100

101

102

103

fit SND+BaBarfit HLMNTSNDBaBar

√q2 [GeV]

σe+

e−→

3π[n

b]

M. Hoferichter, B. Kubis, S.L., F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 318023

Stefan Leupold Theoretical Hadron Physics in Sweden

Results

so far: single-virtual pion transition form factor

time-like: cross section e+e− → π0γ↪→ compare to experimental data (postdiction)space-like: reaction γ∗γ → π0

↪→ prediction for low energies

final aim: double-virtual pion transition form factor

↪→ relevant for g − 2

γ

µ

π

24

Stefan Leupold Theoretical Hadron Physics in Sweden

Time-like pion transition form factor

0.5 0.6 0.7 0.8 0.9 1.0 1.1

10-3

10-2

10-1

100

101

102

SNDCMD2

√q2 [GeV]

σe+

e−→

π0γ

[nb]

theory uncertainties from

different data sets fore+e− → 3π

different pion phase shifts

other intermediate statesthan 2π neglected

↪→ explored by differentcutoff for range where2π dominates

excellent agreementM. Hoferichter, B. Kubis, S.L., F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 3180

25

Stefan Leupold Theoretical Hadron Physics in Sweden

Space-like pion transition form factor

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

CLEOCELLO

Q2 [GeV2]

Q2 F

π0γ∗ γ

(−

Q2 ,

0)/e

2[G

eV] this is a prediction, no datayet at low energies

expect new measurementsfrom BESIII

final aim: double virtualtransition form factor

↪→ relevant for g − 2

M. Hoferichter, B. Kubis, S.L., F. Niecknig, S. P. Schneider, Eur.Phys.J. C74 (2014) 11, 3180

26