Baryon Spectroscopy from Experiment and Theory

Michael Doring

Seminar @ Yale. March 31, 2016

with B. Hu, M. Mai, U.-G. Meißner, R. Molina, K. Nakayama, D. Ronchen, A. Rusetsky, R. Workman et al.

supported by NSF/CAREER, NSF/PIF

HPC support by

Elementary particles of the Standard Model

Strong interaction

Questions

Q: How many quarks or gluons have ever been directly observed?

A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Questions

Q: How many quarks or gluons have ever been directly observed?A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Questions

Q: How many quarks or gluons have ever been directly observed?A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Questions

Q: How many quarks or gluons have ever been directly observed?A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Questions

Q: How many quarks or gluons have ever been directly observed?A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Questions

Q: How many quarks or gluons have ever been directly observed?A: 0 (zero)

Q: The mass of a down quark is 5 MeV and that of an up quark is 2 MeV.Then, the mass of the proton (uud) should be mP ∼ 9 MeV, right?

A: mP = 938.272 MeV

It is obviously a long way from our “periodic table” of quarks and gluonsto matter and its properties as we know them.

and this is the topic of this Seminar.

Even these 4% notwell understood

The full complexity: Parton shower and hadronization

Only colorless final states ↔ confinement

Quark-gluon interaction: QCDRemember from Mechanics:L=T-Vdescribes your physical system [T: Kinetic energy, V: potential energy]

e.g.: Gaµν = ∂µGa

ν − ∂νGaµ + g f abcGb

µGcν

One fundamental coupling strength αS =g2

4π 1.

For small αS , one can solve QCD in a controlled way (perturbation theory).

The running coupling

←− Energy decreases

Deur, Burkert, Chen, Korsch, PLB665 (2008)

No easy solution of QCD at lower energies!

Lattice QCD for hadrons

Simulate the complexity of QCD at low energies with the help ofsupercomputersAb-initio approach: QCD → hadron massesDiscretization in space and time, in a finite volume, to make the problemnumerically treatable

The baryon spectrum: N ∗ and ∆ resonances

Many resonances predicted in lattice calculations[Edwards et al., Phys.Rev. D84 (2011)]:

JP=

Nucleon

Δ(1232)

Interme diate

Energie s

mπ = 396MeV (!)

Search for these states in dedicated experimental programs

Photoproduction experiments: Jefferson Lab , MAMI, ELSA,. . .

Photoproduction cross sections

[data: JLab, ELSA, MAMI]

Partial wave analysis from many observables: γN → πN

Differential cross section γp → nπ+

[CLAS measurements, PRC 79 (2009); Solid (dashed) lines:

SAID (MAID) analysis; filled: CLAS, triangles: MAMI

Photon: Spin 1Nucleon: Spin 1/2

Single, double, triple polarizationobservables

Order principle in the chaos:Conserved quantum numbers, e.g.,J P : Total angular momentumParity

Partial wave analysisDecompose experimental data with respectto conserved quantum numbers.Resonances have a certain, conserved J P .

The Julich approach – Principles from scattering theory[M.D., Haberzettl, Hanhart, Huang, Krewald, Meißner, Nakayama, Ronchen]

Field-theoretical approach; TOPT unitarized; implemented on supercomputers.Example:

Selected results: Two partial waves for πN → πN[Ronchen, M.D., Haberzettl, Hanhart, Huang, Krewald, Meißner, Nakayama, EPJA 49 (2013)]

-0.4

-0.2

0

0.2

0.4

0.2

0.4

0.6

0.8

1

1200 1400 1600 1800 2000

E [MeV]

-0.4

-0.2

0

0.2

0.4

1200 1400 1600 1800 2000

E [MeV]

0.2

0.4

0.6

0.8Im P

11

Im S11

Re S11

Re P11

N(1535)

N(1650)

N(1440) "Roper"

??

JP = 1/2

+

JP = 1/2

-

E=939 MeVNucleon

[Data points: SAID (Arndt, Briscoe, Strakovsky, Workman, PRC 74 (2006))]

Fit to world data on πN → πN , ηN ,KΛ,KΣ (∼ 105 exp. points)[Ronchen, M.D. et al., EPJA 49 (2013)]

Selected results for π−p → K0Λ [almost complete experiment]

-1 -0.5 0 0.5 1

cosΘ

0

40

80

120

dσ

/dΩ

[µ

b/s

r]

E = 1626 MeV

-1 -0.5 0 0.5 1

cosΘ

1707 MeV

-1 -0.5 0 0.5 1

cosΘ

1938 MeV

-1 -0.5 0 0.5 1

cosΘ

2316 MeV

-1 -0.5 0 0.5 1

cosΘ

-1

-0.5

0

0.5

1

1.5

2

P

1661 MeV

-1 -0.5 0 0.5 1

cosΘ

1845.5 MeV

-1 -0.5 0 0.5 1

cosΘ

1939 MeV

-1 -0.5 0 0.5 1

cosΘ

2159 MeV

-2

0

2

4

6

β [ra

d]

E = 1852 MeV

-1 -0.5 0 0.5 1

cosΘ

-2

0

2

4

6

β [ra

d]

2107 MeV

π−p → K 0Λ: Total cross section

1700 1800 1900 2000 2100 2200 2300

E [MeV]

0

0.2

0.4

0.6

0.8

1

σ [

mb

]

1625 1650 1675 1700 17250

0.2

0.4

0.6

0.8

1

KΣ threshold

KΣ Result: Partial wave content.

1700 1800 1900 2000 2100 2200 2300

E [MeV]

0.0001

0.001

0.01

0.1

1

σ [m

b]

P11

S11

P13

D13

D15

F15

F17

G17

G19

H19

Resonance content: Nucleon-like resonances

Future data challenges: FROST, HD-ICE at JLabfrom: Eugene Pasyuk @ Meson 2012

!" #" $" %" &" '" (" )" $*"

$+"

,*"

,+"

-*"

-+"

.*"

.+"

!"#$#%&$'"()$&

pπ0 !" "" "" "" "" "" "" ""

nπ+ !" "" "" "" "" "" "" ""

pη !" "" "" "" "" "" "" ""

pη’ !" "" "" "" "" "" "" ""

pω !" "" "" "" "" "" ""

K+Λ !" "" "" !" "" "" "" "" "" "" "" "" "" "" !" !"

K+Σ0 !" "" "" !" "" "" "" "" "" "" "" "" "" "" !" !"

K0*Σ+ !" " "" "" "" "" "" ""

“Neutron” target

pπ- ! " " " " " "

pρ- " " " " " " "

K+Σ- " " " " " " "

K0Λ " " " " " " " " " " " " " " " "

K0Σ0 " " " " " " " " " " " " " " " "

K0*Σ0 " "

! - published ! - acquired

FROST E in γp → ηp [Senderovich, M.D., D. Ronchen et al. (CLAS), PLB 755 (2016)]First-ever measurement of this observable

+ global fit of world data on pion photoproduction and pion-induced reactions.[EPJA 50 (2015) 101, EPJA 51 (2015) 70, PLB 750 (2015)]

FROST E in γp → ηp: Excitation function

-1

-0.5

0

0.5

1

1600 1800 2000

1600 1800 2000-1

-0.5

0

0.5

1

1600 1800 2000

Experiment

Fit

Fit; (W,cosθ) averaged

Rebinning included

Rebinning & averaged

cosθ=-0.9 / 154° cosθ=-0.6 / 127°cosθ=-0.2 / 102°

cosθ=0.2 / 78° cosθ=0.6 / 53°

E

W [MeV]

Structure at W = 1.68 GeV: Conventional Resonances plus KΣ Cusp

-1

-0.5

0

0.5

1

E0

+, E

1

+, M

1

+, E

2

-, M

2

-, M

2

+

E0

+,M

2

+

1600 1800 2000-1

-0.5

0

0.5

1

E0

+, M

1

+, E

2

-

E0

+, M

1

+

1600 1800 2000W [MeV]

Solution C’ (not averaged)

cosθ=-0.9 / 154°

cosθ=-0.6 / 127°

cosθ=-0.2 / 102°

cosθ=0.2 / 78°

cosθ=0.6 / 53°

E

NO additional structure (non-exotic pentaquark) at W = 1.68 GeV →interferences & KΣ threshold.

Photon-induced vs. Pion-induced reactions

Perspectives

Applications for excited meson spectroscopy @ GlueX

Hadronic approaches to analyze resonances on the lattice

Next-generation experiments @ JLab

Beyond the isobar model: Three-body unitarity

M*

R

(a) (b)

+

(c)

+ + . . .Z

We know from baryon analysis: the importance of three-body unitarity.

Going beyond the Breit-Wigner parameterization of the ππ amplitudes.

Coupled-channels (c.f. also GlueX proposal: Kaon identification).

Transfer of methods from baryon to meson analysis.

Feasible for complex systems with many partial waves?

Technical simplification of the present approach needed(tool for experimentalists).

The world as lattice sees it

Finite volume L3

Finite lattice spacing a

mq(Lattice) 6= mq

Resonances decaying on the lattice

Eigenvalues in the finite volume

L (box size)

En

erg

y

Resonance

energy

Avoided level crossing

incr

easi

ng

ly d

iffi

cult

to

mea

sure

Extracting resonances from lattice data – meson sector[M.D., Meißner, Oset/Rusetsky, EPJA 47 (2011)]

Three unknownpotentials

V (ππ → ππ)V (ππ → KK)V (KK → KK)

Expand a two-channel potential V in energy(i, j: ππ, KK):

Vij(E) = aij + bij(E2 − 4M 2K )

to extract phase shifts/resonances

lattice data & fit extracted phase shift f0(980) pole position

1.6 1.8 2 2.2 2.4 2.6

L [Mπ

-1]

850

900

950

1000

1050

1100

1150

E [

MeV

]

KK

850 900 950 1000 1050 1100E [MeV]

100

150

200

250δ

0

0 (

ππ

−−

> π

π)

[deg

]

KK

980 990 1000 1010Re E [MeV]

0

5

10

15

20

25

Im E

[M

eV

]

KK

f0(980)

Partial-wave mixing, coupled channels,. . .→ in complex hadronic systems, Luscher method needsto be complemented by techniques from experimental data analysis.

The Λ(1405): Predictions from Unitarized CHPTRaquel Molina, M.D., arXiv:1512.05831

Large experimental efforts, e.g., E. Epple et al., PRC 87 (2013).

0 1e+05 2e+05 3e+05

Mπ

2(MeV

2)

1300

1400

1500

1600

1700

1800

1900

2000

2100

E(M

eV)

Lattice (Adelaide, arXiV:1411.3402)

UCHPT, Level 1

UCHPT, Level 2

Chiral extrapolation breaks down

Coupled channelsπΣ, KN , ηΛ,KΞUnitarized LO χ potentialV in T = V + VGTNo freedom at this order→ full prediction.UCHPT has two poles forthe Λ(1405).→ new data not in conflictwith two-pole structure ofa molecular Λ(1405) (butnot yet a proof thereof).→ needed: StatisticalNLO analysis incombination with moreaccurate data.

The Λ(1405): Predictions from Unitarized CHPTRaquel Molina, M.D., arXiv:1512.05831

Large experimental efforts, e.g., E. Epple et al., PRC 87 (2013).

0 100 000 200 000 300 000

1400

1600

1800

2000

MΠ2HMeV2L

Re

@s p

DHMeV

L

H1369,- 64L

H1443,- 17L Cusp

H1565,-19L H1671,0L

H1700,-22LH1836,0L

H1875,-28L H1998,0L

H2077,0.5L

Coupled channelsπΣ, KN , ηΛ,KΞUnitarized LO χ potentialV in T = V + VGTNo freedom at this order→ full prediction.UCHPT has two poles forthe Λ(1405).→ new data not in conflictwith two-pole structure ofa molecular Λ(1405) (butnot yet a proof thereof).→ needed: StatisticalNLO analysis incombination with moreaccurate data.

The ρ(770) on the latticeRaquel Molina, Bin Hu, M.D.

New lattice data from the GWU LQCD group (A. Alexandru, Dehua Guo)Nf = 2 calculationSU(3) NLO unitarized CHPT (inverse amplitude method)Short circuiting the Luscher equation:

LQCD Eigenvalues → phases → Hadronic fit.Instead: LQCD Eigenvalues → direct fit of LEC’s.

Finite volume corrections, chiral extrapolations and Nf = 2→ Nf = 3extrapolation in one step.Missing LEC’s for Nf = 2→ Nf = 3 extrapolation determined from fit toexperimental data (ππ in I = 0, 2, πK in I = 1/2, 3/2, L = 0, 1).based on [Oller, Oset, Pelaez, PRD 1998]

Alternatively: Resonance CHPT LO calculation in ππ, KK .

The ρ(770) on the lattice – NLO UCHPT resultsRaquel Molina, Bin Hu, M.D., preliminary

Separate fits to eigenlevels at different quark masses

Compared to Luscher-extracted phases

The ρ(770) on the lattice – NLO UCHPT resultsRaquel Molina, Bin Hu, M.D., preliminary

Chiral extrapolation plus Nf = 2→ Nf = 3 extrapolation

The ρ(770) on the lattice – Resonance CHPTRaquel Molina, Bin Hu, M.D., preliminary

Resonance CHPT at LO (NLO corrections under way), in 1 channel (ππ)to fit Nf = 2 LQCD data, and 2 channels (ππ, KK) for extrapolation toNf = 3.

Nf = 2: ρ is now tooheavy, in contrast to NLOUCHPT (!)KK channel againcorrects qualitativelycorrectly— this time inopposite direction.Consistency check:2-channel fit of g, Mρ,MK (yes!) to exp. phases⇒ MK = 498± 185 MeV

World data on lattice simulations of the ρ(770)Nf = 2 simulations [Selected results]

Lattice data [Alexandru/Guo, GWU] Nf=2 extrapolation

+ exp. DataN

f=2 → N

f=3

extrapolation

Data: Lang et al. (Graz)

Data: Bali et al. (Regensburg)

Perspectives

The study of resonances at intermediate energies provides a key to ourunderstanding of Quantum Chromodynamic.

JLab, MAMI, ELSA, . . . provide high-precision photoprodution data. Newdata from FROST and HD-ICE.

The analysis allows to extract the resonance spectrum to test QCDpredictions.

Baryon analysis tools can boost the analysis of lattice and meson data(upcoming GlueX experiment at JLab).

Hadronic methods to analyze Lattice QCD data and extrapolate involume, mass, flavor: Comparison with physical world.

Next level of complexity: Complex hadronic systems (3-body) in the finitevolume of a lattice simulation.

Two-body scatteringScattering in the infinite volume limit

Unitarity of the scattering matrix S : SS† = 1 [S = 1− i p4πE T ].

Im T−1(E) = σ ≡ p8πE

→ Generic (Lippman-Schwinger) equation for unitarizing the T -matrix:

T = V + V G T Im G = −σ

V : (Pseudo)potential, σ: phase space.

G: Green’s function:

G =∫

d3~q(2π)3

f (|~q|)E2 − (ω1 + ω2)2 + iε ,

ω21,2 = m2

1,2 + ~q 2

DiscretizationDiscretized momenta in the finite volume with periodic boundary conditions

Ψ(x) != Ψ(x + ei L) = exp (i L qi) Ψ(x) =⇒ qi = 2πL ni , ni ∈ Z, i = 1, 2, 3

∫d3~q

(2π)3 g(|~q |2)→ 1L3

∑~n

g(|~q|2), ~q = 2πL ~n, ~n ∈ Z3

G → G = 1L3

∑~q

f (|~q|)E2 − (ω1 + ω2)2

1000 1200 1400 1600E [MeV]

0

G, ~ G

below thresh. above threshold

E > m1 + m2: G has poles atfree energies in the box, E = ω1 + ω2

E < m1 + m2: G → G exponentiallywith L (regular summation theorem).Formalism can be mapped to Luscher’s Z`m .

Finite → infinite volume: the Luscher equationWarning: Very crude re-derivation.

Measured eigenvalues of the Hamiltonian (tower of lattice levels E(L))→ Poles of scattering equation T in the finite volume → determines V :

T = (1−V G)−1V → V−1 − G != 0 → V−1 = G

The interaction V determines the T -matrix in the infinite volume limit:

T =(V−1 −G

)−1 =(G −G

)−1

Re-derivation of Luscher’s equation (T determines the phase shift δ):

p cot δ(p) = −8π√

s(G(E)− Re G(E)

)V and dependence on renormalization have disappeared (!)