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


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


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


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





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:


4





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:


4





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


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


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


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


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


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


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


backup slides

11


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


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


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



µhadronic

γ

µ

hadronic




↪→ but we want a standard-model prediction

and with a reliable uncertainty estimate!



14



µhadronic

γ

µ

hadronic







14



µhadronic

γ

µ

hadronic






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

(← highest accuracy so far)

14



µhadronic

γ

µ

hadronic







14


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


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


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


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


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


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


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


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


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


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


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


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

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

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