[PPT] - Amplitude Analysis in Hadron Spectroscopy Csar Fernndez-Ramrez PowerPoint Presentation

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Amplitude Analysis in Hadron Spectroscopy

César Fernández-Ramírez JPAC/Jefferson Lab

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ICN-UNAM Seminar, March 18, 2015

A.P . Szczepaniak

C. Fernández-Ramírez

I.V. Danilkin

M. Shi

M.R. Pennington

V. Mokeev

P . Guo

V. Mathieu
G. Fox
A. Jackura
E. Passemar
R. Workman
M. Döring
D. Schott

L.-Y. Dai

JPAC

Joint Physics Analysis Center

2

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ICN-UNAM Seminar, March 18, 2015

Why is QCD special?

Predicts existence of exotic matter, e.g. made from radiation (glueballs,hybrids) or novel plasmas. It builds from objects (quarks and gluons) that do not exist in a common

sense. >90% mass comes from

interactions! A single theory is responsible for phenomena at distance scales of the

rder of 10-15m as well as of the
rder 104m.

It is challenging! A possible template for physics beyond the Standard Model

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ICN-UNAM Seminar, March 18, 2015

This talk is about hadrons

1919 Rutherford discovers the proton

1932 Chadwick discovers the neutron 1909/1911 Rutherford/Geiger/Marsden discover the nucleus K-->π+ π- π- π: Powell (1947) η: Pevsner (1961) ω: Álvarez (1961) φ: Connolly. Pevsner (1962) ρ: Erwin (1961) ρ: Anderson (1960)

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ICN-UNAM Seminar, March 18, 2015

“Bare (free)” particles of QCD: quarks and gluons

analogous to 8 (color) x 6 (flavor) copies of QED: quark → electron gluon → photon (but non-abelian)

e.g. as seen in high energy collisions

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ICN-UNAM Seminar, March 18, 2015

the nature of physical quarks and gluons remains a mystery

eQCD ~ 10 eQED “free” quarks quarks bound in hadrons inverse distance between quarks

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ICN-UNAM Seminar, March 18, 2015

Quark models

Click to add text

physical quarks appear to move in a kind of “mean, gluonic field”

ω1 ω8

K*0 K*+ K*- ρ- K*0 ρ+ ρ0

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ICN-UNAM Seminar, March 18, 2015

The QCD vacuum is not

empty. Rather

it contains quantum fluctuations in the gluon field at all scales. (Image: University of Adelaide)

HQCD = Hc.h.o. + non-linear

“physical gluons” → mean field AND quasi particles “physical quarks” → quasi particles in gluon mean field finite energy, localized solutions: solitons (monopoles, vortices , ...) gluon mean field

Plausible model?

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ICN-UNAM Seminar, March 18, 2015

Confinement in QCD

Properties of confinement:

Linearly rising potential
Regge trajectories
String behavior

r0 = 0.5 fm Adiabatic potential

Absence of isolated quarks

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ICN-UNAM Seminar, March 18, 2015

Click to add text

Spectroscopy of Hadrons can teach us about “workings” of QCD

2. Hadron molecules

(residual forces)

1. Hadrons with gluon

excitations (confinement)

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ICN-UNAM Seminar, March 18, 2015

Click to add text

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ICN-UNAM Seminar, March 18, 2015

Lattice meson spectrum

Click to add text

[Dudek 2011]

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ICN-UNAM Seminar, March 18, 2015

Lattice meson spectrum

Click to add text

[Dudek 2011]

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ICN-UNAM Seminar, March 18, 2015

Lattice meson spectrum

Click to add text

[Dudek 2011]

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ICN-UNAM Seminar, March 18, 2015

Lattice meson spectrum

Click to add text

[Dudek 2011]

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ICN-UNAM Seminar, March 18, 2015

Lattice meson spectrum

Click to add text

[Dudek 2011]

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ICN-UNAM Seminar, March 18, 2015

Strong, theoretical evidence (lattice) for gluon field

excitations in hadron spectrum

Phenomenologically, gluons behave as axial vector,

quasiparticles JPC=1+-

Lowest multiplet of “hybrid mesons” has JPC = 0-+, 1-+, 2-+,

1-- states

What about other non-quark model possibilities?
Can these be detected and distinguished?

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ICN-UNAM Seminar, March 18, 2015

High statistics new beam-target combinations polarization measurements

New opportunities

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ICN-UNAM Seminar, March 18, 2015

What kind of experiments?

2→ 2, 3 processes

p p p p p p p p p p γ, π, K γ, π, K π, K π, K π, K π, K π, K π, K γ γ π π π π, K π, K η, ω, ϕ ϕ N, Δ, Σ, Λ N, Δ, Σ, Λ γ

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ICN-UNAM Seminar, March 18, 2015

Evolution in statistics

Click to add text

π- p → π-π+π- p

CERN ca. 1970

BNL (E852) ca 1995

E852 (Full sample) COMPASS 2010 O(102 /10MeV ) O(103 /10MeV ) O(105 /10MeV ) O(106 /10MeV )

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ICN-UNAM Seminar, March 18, 2015

Resonance paradigm: Δ(1232)

In 1952, Fermi and collaborators measured the cross section and found it steeply raising.

π+p → π+p

peak in intensity (cross section) width Γ mass ~ 30% above proton lifetime ~ 4.5 x 10-24 s width ~ lifetime-1 = 150 MeV

∆++

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ICN-UNAM Seminar, March 18, 2015

How do we catch resonances?

Is every bump a resonance?
Is every resonance a bump?

– The answer to both questions is NO

Examples

– σ meson in ππ scattering has a broad structure – Threshold effects can appear as resonances

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ICN-UNAM Seminar, March 18, 2015

Actually, what is a resonance?

A resonance is a pole of the scattering

amplitude in the unphysical Riemann sheets

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ICN-UNAM Seminar, March 18, 2015

12 GeV upgrade at JLab: CLAS, GlueX, etc.

– Aim: ✑ Complete understanding of the hadron spectrum ✑ discover new resonances e.g, gluonic excitations (states  where glue builds their JPC)   – Tools: Amplitude analysis of data  To find new resonances not bump-hunting, but search for poles  must build in S-Matrix constraints   + state-of-the-art knowledge  

f reaction dynamics

resonance pole

E

Dispersive analytic continuation

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ICN-UNAM Seminar, March 18, 2015

12 GeV upgrade at JLab: CLAS, GlueX, etc.

– Aim: ✑ Complete understanding of the hadron spectrum ✑ discover new resonances e.g, gluonic excitations (states  where glue builds their JPC)   – Tools: Amplitude analysis of data  To find new resonances not bump-hunting, but search for poles  must build in S-Matrix constraints   + state-of-the-art knowledge  

f reaction dynamics

ChPT + Analyticity + Unitarity Dispersion Relations Regge Theory, Models Experimental Data

CLAS, GlueX, JEF, COMPASS, BESS,   LHCb, PANDA,…

FFs, resonance   parameters: MR,   ΓΡ, couplings

Hadron spectrum, exotics

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ICN-UNAM Seminar, March 18, 2015

Scattering theory

S matrix
S is unitary (probability conservation)
T is an analytical function (causality)
T has branch cuts at thresholds (several

Riemann sheets)

T has no poles in the first Riemann sheet

S†S = I S = I + 2iρT Disc T = Im T = T †ρT

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ICN-UNAM Seminar, March 18, 2015

Dispersion theory

Cauchy Theorem
Amplitude has no complex

poles in the 1st Riemann sheet and has two branch cuts

We can reconstruct the full

amplitude in the whole complex plane

t(⇥ + i) = 1 2⇤i Z

C

t(⇥0) ⇥0 − ⇥ − id⇥0

ν+iε Re{ν} Im{ν} I Riemann sheet

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ICN-UNAM Seminar, March 18, 2015

AI(s) = M M 2 − s − iMqI(s)

Example: Breit-Wigner amplitude

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ICN-UNAM Seminar, March 18, 2015

AI(s) = M M 2 − s − iMqI(s)

Example: Breit-Wigner amplitude

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ICN-UNAM Seminar, March 18, 2015

II III I

sp s0

p

I

tI

(s)

tII

(s)

tIII

(s)

tI

(s)

{s} {s} s1 s2

Riemann sheets

The amount of

Riemann sheets depends on the number of open channels: 2N

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ICN-UNAM Seminar, March 18, 2015

Amplitude analysis: ππ scattering

Click to add text

Peláez et al.

I=0 I=1

1. Parametrize the data
2. Check constrains (unitarity)
3. Continuation to extract the pole
4. Interpretation (hybrid, glueball,

tetraquark, ...)

F(s, t = t0) s0 = 4m2 Im(s) Re(s)

ρ(770) σ(500)

II I I

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ICN-UNAM Seminar, March 18, 2015

γp → K+K-p

Amplitude depends on 5 Mandelstam variables:

One is fixed: s
Two are measured: sK+K- and sK-p
Two are integrated out: tγK+ and tpp’

p γ K+ K− tγK+ tpp0 p0

sK+K−

sK−p

fixed s

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ICN-UNAM Seminar, March 18, 2015

Interesting channels

ππ, K ¯ K X = ρ, ρ3, φ, φ3, f0, f2, f 0

2, a0, a2

πη, πη0 X = a0, a2, π1

X

GlueX (Hall D@JLab) invariant mass range 2-3 GeV Hybrid? Glueballs?

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ICN-UNAM Seminar, March 18, 2015

K+K- Dalitz plot

2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 20 22

M2

K

+K −

M2

K−p

Hyperons Double Regge

W = 5 GeV

Phi mesons

Disclaimer: not actual data (actual data from g12 CLAS@JLab under analysis)

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ICN-UNAM Seminar, March 18, 2015

K+K- Dalitz plot

2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 20 22

M2

K

+K −

M2

K−p

W = 5 GeV

Hyperon

Meson

Double Regge

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ICN-UNAM Seminar, March 18, 2015

Things we expect/hope to study

Exotics

– new physics that will help us understand the role of the gluon and confinement

Strangeonia

– this spectrum is not well studied and looks pretty

empty. Also information on gluons and virtual quarks
Hyperons

– Strange content of hadrons, impact in hypernuclei physic and strangeness in neutron stars

(s¯ s)

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ICN-UNAM Seminar, March 18, 2015

Models

Dual model (B5)

– Generalization of the Veneziano model – In the double-Regge limit:

Shi et al., PRD91, 034007 (2015)

Deck model

– More elaborated – Resonance region: K-matrix, coupled channels – High energy: Regge – Connection through dispersion theory

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ICN-UNAM Seminar, March 18, 2015

Veneziano model (B4)

Advantages

–Analyticity –Incorporates Regge-resonance duality –Right behavior at high energy –Generalization to N legs

Caveats:

–Unitarity is violated –Resonance details get lost –Only for high energy –Spinless particles (spin factor)

B4(s, t) = Γ(−α(s)Γ(−α(t)) Γ(−α(s) − α(t) =

∞

X

n=0

βn(t) n − α(s) =

∞

X

n=0

βn(s) n − α(t)

lim

s→∞ B4(s, t) = [−α(s)]α(t) Γ(−α(t))

B4(s, t) = Z 1 dx x−α(s)−1(1 − x)−α(t)−1

1 2 4 3 2 1 2 3 4 1 1 3 4 2 3 1

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ICN-UNAM Seminar, March 18, 2015

B5 for γp→K+K-p

A B 1 2 3 A1 12 23 B3 AB

B5(sAB, sA1, s12, s23, sB3) = Z 1 dt Z 1 dx x−α12−1t−α23−1(1 − t)−αA1−1(1 − x)−αB3−1(1 − xt)−αAB+α12+α23

A lot more complicated to compute
We consider the double-Regge limit

sAB, s12, s23 → ∞; s12s23 sAB = fixed; tA1 sAB , tB3 sAB → 0

A + B → ¯ 1 + ¯ 2 + ¯ 3 γ + p → K+ + K− + p

P1 γ P2 K+ K− ρ/ω, f2/a2 K∗, K∗

2

P2 K+ P1 γ K− ρ/ω, f2/a2 K∗, K∗

2

P1 K+ P2 γ K− ρ/ω, f2/a2 K∗, K∗

2

P2 γ P1 K+ K− ρ/ω, f2/a2 K∗, K∗

2

γ P1 P2 K− K+ γ P1 K− K+ P2 γ P1 P2 K+ K− γ P1 K+ P2 K− γ P1 K− P2 K+ γ P1 K+ K− P2 K+ P1 γ K− K− P1 γ P2 K+ P2 P1 γ K− K+ P2 1 2 3 4 5 6 7 8 10 11 K+ P1 γ K− P2 K− P1 γ K+ P2 9 P2 P1 γ K+ K− 12

⇒

Shi et al., PRD91, 034007 (2015)

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ICN-UNAM Seminar, March 18, 2015

Double-Regge Limit: Van Hove Plots

50 100 150 200 250 300 350 w

6
4
2

2 4 @GeVD^2 s12 s23 tA1 tB3

R23 R12 D123

4
2

2 4

4
2

2 4 Eg=5.5 GeV ppL=0 pK+ L=0 pK- L=0 +

+
+
+
+
+
R23

D123 R12

2-dimensional plot of the longitudinal momenta

q = q p2

K+L + p2 K−L + p2 pL

pK+L = p 2/3q sin ω pK−L = p 2/3q sin(2π/3 + ω) ppL = p 2/3q sin(4π/3 + ω)

In the DRL we want t to be small and s large

fixed transverse momentum

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ICN-UNAM Seminar, March 18, 2015

Double-Regge Limit: Synthetic Data

)

2

) (GeV

K

+

(K

2

Mass

1 2 3 4 5 6

)

2

P) (GeV

(K

2

Mass

2 3 4 5 6 7 8 9

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Data )

2

) (GeV

K

+

(K

2

Mass

1 2 3 4 5 6

)

2

P) (GeV

(K

2

Mass

2 3 4 5 6 7 8 9

500 1000 1500 2000 2500 3000

Data

Events )

2

) (GeV

K

+

(K

2

Mass

1 2 3 4 5 6

)

2

P) (GeV

(K

2

Mass

2 3 4 5 6 7 8 9

200 400 600 800 1000 1200

Data )

2

) (GeV

K

+

(K

2

Mass

1 1.5 2 2.5 3 3.5 4 4.5 5

)

2

P) (GeV

(K

2

Mass

2 2.5 3 3.5 4 4.5 5 5.5 6

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Data

1. We generate an uniform distribution (phase space)
2. We cut the large transverse momenta
3. We perform the Van Hove selection
4. We incorporate spin

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ICN-UNAM Seminar, March 18, 2015

Deck Model: one step at a time

X

Reggeon

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ICN-UNAM Seminar, March 18, 2015

KN scattering

High energy region Resonance region

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ICN-UNAM Seminar, March 18, 2015

KN in resonance region: Hyperons

Partial-wave analysis
Coupled channels
Unitarity
Analyticity
Right threshold behavior (angular momentum barrier)
Resonances are incorporated “by-hand” through

Breit-Wigner amplitudes

tI(s, cos θ) = X

f I

(s)P (cos θ)

¯ KN → ¯ KN, πΣ, πΛ

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ICN-UNAM Seminar, March 18, 2015

Single channel

S = I + 2i ρ(s)T(s) ρ(s) = q q2` 1 + q2` T(s) = K(s) 1 − iρa(s)K(s) K(s) = MΓ M 2 − s iρa(s) = s − sth π Z 1

sth

ds0 s − s0 ρ(s0) s0 − sth

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ICN-UNAM Seminar, March 18, 2015

Coupled channels: 2 amplitudes

(K)kj = x1

k x1 j K1 + x2 k(s) x2 j(s) K2

(T)kj = c11 x1

k x1 j + c12 x1 k x2 j + c21 x2 k xa j (s) + c22 x2 k x2 j

c11 = T1(s)/C(s) c22 = T2(s)/C(s) c12 = c21 = i " nC X

k=1

x1

k x2 k[ρa(s)]k

# (s)T1(s)T2(s)/C(s) T1(s) = M1 M 2

1 − s − i PnC k=1[ρa(s)]kM1[x1 k]2

C(s) = 1 + " nC X

k=1

x1

k x2 k[ρa(s)]k

#2 T1(s)T2(s)

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ICN-UNAM Seminar, March 18, 2015

KN in resonance region

Fit single-energy partial waves from Kent State University analysis of:

~8000 exp. data for
~4500 exp. data for
~5000 exp. data for

¯ KN → ¯ KN

¯ KN → πΣ ¯ KN → πΛ

0.3
0.2
0.1

0.1 0.2 0.3 Re S01 0.4 0.5 0.6 0.7 0.8 0.9 1 Im S01

0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25 Re P01

0.1

0.1 0.2 0.3 0.4 0.5 0.6 Im P01

0.1
0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Re P03

0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Im P03

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 2 2.5 3 3.5 4 4.5 5 s (GeV2) Re D03

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 2 2.5 3 3.5 4 4.5 5 s (GeV2) Im D03

Model can be readjusted once we extend to the two kaon photoproduction process, getting more insight on hyperons

Preliminary

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ICN-UNAM Seminar, March 18, 2015

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25

K

– N→ K – N

Re D15

0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Im D15

0.06
0.04
0.02

0.02 0.04 0.06 0.08 0.1 0.12 0.14

K

– N→ π Σ

0.04
0.02

0.02 0.04 0.06 0.08 0.1 0.12 0.14

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25

K

– N→ π Λ

0.35
0.3
0.25
0.2
0.15
0.1
0.05

0.05

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

2 2.5 3 3.5 4 4.5 5 Im s (GeV2) s (GeV2)

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

2 2.5 3 3.5 4 4.5 5 s (GeV2)

Pole positions

D15

Closest poles to the physical axis
Errors computed through

Bootstrap technique

Preliminary

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ICN-UNAM Seminar, March 18, 2015

Hyperons from KN scattering

0.3
0.25
0.2
0.15
0.1
0.05

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 Im [sp

1/2] (GeV)

Re [sp

1/2] (GeV)

physical axis KN

S01

P01 P03 D03 D05 F05 F07 G07

Preliminary

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ICN-UNAM Seminar, March 18, 2015

KN scattering in high energy region

p

p ¯ K ¯ K

ρ, ω, a, f, P

Reggeon

0.1 0.2 0.3 0.4 0.5 0.6 0.7 10

−2

10 10

2

10

4

10

6

10

8

10

−t (GeV2) dσ/dt (mb/GeV2) K+ p → K+ p

50 GeV x100 70 GeV x102 100 GeV x104 140 GeV x106 175 GeV x108

0.1 0.2 0.3 0.4 0.5 0.6 0.7 10

−2

10 10

2

10

4

10

6

10

8

10

−t (GeV2) dσ/dt (mb/GeV2) K− p → K− p

Preliminary

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ICN-UNAM Seminar, March 18, 2015

Connecting high and low energies

Let’s use πN scattering as a

playground

Dispersion theory (Finite

energy sum rules)

We use high-energy to

constrain low-energy

Construct Im A from 0 to

infinity via FESR

Reconstruct amplitude from

dispersion relations

Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ÊÊÊÊÊÊÊÊÊÊÊ Ê Ê Ê Ê ÊÊÊÊÊÊÊ Ê Ê Ê Ê ÊÊÊÊÊÊÊÊÊÊÊ Ê Ê Ê Ê ÊÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ÊÊÊÊÊÊÊÊÊÊÊÊÊÊ ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê

t=-0.0 GeV2
t=-0.3 GeV2

0.0 0.5 1.0 1.5 2.0 2.5

200
150
100
50

50

Elab mb.GeV2 Re nBH+LHn,tL

- Regge Model
- SAID
New Amplitude

0.0 0.5 1.0 1.5 2.0 2.5 3.0

150
100
50

50 100

n HGeVL mb.GeV Im nB+Hn, t=0L

Re νB(+)(ν, t) = g2

r

2m 2ν2 ν2

m − ν2 + 2ν2

π P Z 1

ν0

Im B(+)(ν0, t) ν02 − ν2 dν0

Preliminary

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ICN-UNAM Seminar, March 18, 2015

Connecting high and low energies

This is as far as I can go... we are working on finalizing

both the high-energy and the low-energy models as well as the the pion-nucleon case

Next steps will be to connect high and low energy in KN,

build the full two kaon photoproduction amplitude and compare to data

For B5 the next step is to compute the single Regge limit

(associated to hyperon excitations)

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ICN-UNAM Seminar, March 18, 2015

Summary

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool
Lattice is making big steps forward

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool
Lattice is making big steps forward
A lot of experimental data are going to come during the next

years: JLAB, COMPASS, LHC, MAMI, ELSA, PANDA, KLOE, BES, J-PARC

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool
Lattice is making big steps forward
A lot of experimental data are going to come during the next

years: JLAB, COMPASS, LHC, MAMI, ELSA, PANDA, KLOE, BES, J-PARC

Amplitude analysis is a critical part of all this effort

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool
Lattice is making big steps forward
A lot of experimental data are going to come during the next

years: JLAB, COMPASS, LHC, MAMI, ELSA, PANDA, KLOE, BES, J-PARC

Amplitude analysis is a critical part of all this effort

✓ No solid amplitude analysis ⇒ No reliable data interpretation

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ICN-UNAM Seminar, March 18, 2015

Summary

Many interesting questions remain open regarding hadrons,

QCD and confinement

Hadron spectroscopy has been and remains as a prime tool
Lattice is making big steps forward
A lot of experimental data are going to come during the next

years: JLAB, COMPASS, LHC, MAMI, ELSA, PANDA, KLOE, BES, J-PARC

Amplitude analysis is a critical part of all this effort