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Page 1: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Photoproduction of pseudoscalar mesonsin isobar and Regge formalism

HASPECT meeting, Krakow, May 30 – June 1, 2016

Petr Bydzovsky, Nuclear Physics Institute, Rez, Czech Republic

Outline:

Introduction – description of electro- and photoproduction

Isobar model – coments on formalism, reaction mechanism

in π, η, K photoproduction

Regge and Regge-plus-resonance models

Results for kaon photoproduction

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 1 / 23

Page 2: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Description of the electromagnetic production

electroproduction of pseudoscalar mesons (M = π, η, K) on nucleons (N)

e + N −→ e′ +M+ B

electromagnetic interaction is well known and the coupling constant

is small: α = e2

.= 1

137 1 → a one-photon approximation is justified

the leptonic and hadronic parts are separated in opa

Mfi = u(p′e, λ′)(−ieγµ) u(pe, λ)

−gµνq2J ν(pN, σ, q, ε, pB, σ

′, pM)(−ie)

the transition current J ν describes photoproduction by virtual photons

γ(v) + N −→ M+ B

with q2 < 0, a longitudinal polarization

photoproduction (q2=0) is not the limit case (q2→ 0) of electroproduction

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 2 / 23

Page 3: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

kinematics in the laboratory frame: Ee, E′e, θe, θM, ΦM

the unpolarized cross section: ∝ 14 m2

e

∑λλ′σσ′ |Mfi |2 = 1

4e4

q4 Lsµν W νµ

d5σ

dE′e dΩ′e dΩM= Γ

[dσT

dΩM+ ε

dσL

dΩM+ ε

dσTT

dΩMcos 2ΦM+

√2ε(1+ε)

dσTL

dΩMcos ΦM

]

virtual-photon flux: Γ(pe, p′e, θe) polarization: ε =

(1 + 2 q2

−q2 tan2 θe

2

)−1

dσx

dΩM(Q2, s, t), Q2 = −q2, s = (q + pN)2, t = (q− pM)2

laboratory frame (~pN = 0):

Φ

θeθ

p

p'γ

q

p

pB

Scattering (Leptonic) Plane

Reaction (Hadronic) Plane

z

xy

e

e

M

M

M

^

^

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 3 / 23

Page 4: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Photoproduction by real photons (q2=0)

γ + N −→ M+ B in the resonance region√

s < 2.6 GeV.

Which degrees of freedom are relevant: quarks and gluons ↔ hadrons?

non perturbative regime of QCD → effective description via baryons andmesons completed with form factors (short-distance physics)

effective hadronic Lagrangian in lowest order → tree-level approximation

many opened channels, e.g. π (≈ 1.07 GeV), η (≈ 1.49 GeV), K (≈ 1.61 GeV)

→ coupling of the channels via final-state meson-baryon interactions (FSI)

multi-channel ↔ single-channel analysis ?

unitary (coupled-channel) approach – in some cases FSI is not well known

γ + p −→ π0 + p −→ K+ + Λ

−→ η + p −→ K+ + Λ

−→ K+ + Λ −→ K+ + Λ

→ the single-channel approach – FSI included in effective parameters

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 4 / 23

Page 5: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Isobar model – phenomenological description in resonance region

single-channel approach

I violation of unitarity – can be partially restored by means of energydependent widths of nucleon resonances in the propagator

I effective coupling constants (FSI)

effective hadronic Lagrangian: L = Lo + Lint

I baryon, meson and photon fieldsI possible resonances in the intermediate states – “missing resonances”I couplings of the fields in Lint

I short-distance physics (frozen degrees of freedom) → form factorsI gauge invariance: PV coupling, hadron form factors → a contact termI tree-level approximation → s-, t-, and u-channel Feynman diagramsI free parameters determined in a data analysis

reaction mechanism – invariant amplitude: Mfi =Mbgr +Mres

I Mbgr : non resonant contributions: Born, t- and u-channel diagramsI Mres : resonant contributions: N∗ and ∆ s-channel diagrams

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 5 / 23

Page 6: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Dominant resonances in pion and eta photoproduction

0.2 0.3 0.4 0.5 0.6 0.7 0.8Eγ [GeV]

0

5

10

15

20

25

30

dσ /

dΩ [

µb/s

r]

Born termsBorn + ∆(M1)

γ + n --> π- + p

θ = 90o

Mbgr – Born terms: exchanges ofn in s channel, p in u channel,and π− in t channel

Mres is dominated by ∆(1232) 32

+

with a branching ratio to Nπ ≈ 100%

γN −→ ∆ −→ πN

0.7 0.8 0.9 1 1.1 1.2Eγ [GeV]

0

0.4

0.8

1.2

1.6

dσ /

dΩ [

µb/s

r]

Born termsBorn + S11(1535)

γ + p --> η + p

θ = 90o

Mbgr – Born terms: exchanges ofp in s and u channels;– other contributions: ρ, ω in t channel

Mres : N∗(1535) 12

−(42% to Nη)

other states, e.g.: N∗(1710) 12

+(10-30%)

N∗(1650) 12

−(5-15%), N∗(1720) 3

2

+(4%)

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 6 / 23

Page 7: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

No dominant resonance in kaon photoproduction

many N∗ with a reasonable branching ratio to K Λ can contribute

Mres in the Kaon-MAID model: S11(1650) (3–11%), P11(1710) (5–25%),P13(1720) (1–15%), D13(1895) (missing resonance – not seen in π and η channels)

Born terms (p, Λ, Σ0, and K+) suppressed by the hadron form factors

Mres in the BS1 model: S11(1535), S11(1650), F15(1680), P13(1720),F15(1860), D13(1875), P13(1900), F15(2000)Mbgr : Born terms, K∗(892), K1(1270), Λ(1520), Σ(1660), Σ(1750),Λ(1800), Λ(1890), Σ(1940);

1.2 1.6 2 2.4Eγ [GeV]

0

0.05

0.1

0.15

0.2

dσ /

dΩ [

µb/s

r]

SAPHIRCLASKaon-MAIDBorn + K* + K1

γ + p --> K+ + Λ

θ = 90o

1,2 1,6 2 2,4Eγ [GeV]

0

0,05

0,1

0,15

0,2

dσ /

dΩ [

µb/s

r]

full BS1 modelbackground

γ + p --> K+ + Λ

θ = 90o

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 7 / 23

Page 8: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Consistent description of higher-spin resonances

contributions of resonances with spin> 12 important: ∆(1232), N∗(1720),..

the Rarita Schwinger propagator for spin 3/2

Sµν(p) =/p + m

p2 −m2P3/2µν −

2

3m2(/p + m)P1/2

22,µν +1√3m

(P1/212,µν + P1/2

21,µν)

allows nonphysical contributions of the lower spin components

the nonphysical contributions can be removed by a suitable form of Lint

[V. Pascalutsa, P.R.D 58 (1998) 096002; T. Vrancx et al, P.R.C 84 (2011) 045201]

invariance of Lint under local U(1) gauge transformation of the R.-S. field

⇒ transverse interaction vertexes:

V Sµ pµ = V EM

µ pµ = 0

⇒ removes all nonphysical contributions:

V Sµ P

1/2,µνij V EM

ν = 0N B

MγS

µν(p)

VEMµ V

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 8 / 23

Page 9: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

the gauge-invariant coupling results in high momentum-power dependence;it is good: regularizes the resonance contributionbut it has also a drawback: too big growth of the cross section⇒ strong form factors (multidipole, Gauss) are introduced

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 9 / 23

Page 10: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Using symmetries to constrain models

SU(3)f symmetry can be used to determin (constrain) some couplingconstants: SU(3)-invariant Lagrangian for baryon and meson octets

L(BBM) = ga Sp([BB]M) + gs Sp(BBM)

[BB] and BB is antisymmetric and symmetric part, respectively.

Parameters: gs − ga =√

2 gπNN (well known) and α ≡ gs

gs−ga

from SU(6) α =35

or experimental value: 0.644± 0.009.

⇒ gKΛN = − 1√3

gπNN (3− α), gKΣN = −gπNN (1− 2α), ...

If we take 20% breaking of the SU(3) symmetry → constraints

−4.4 ≤ gKΛN√4π≤ −3 0.8 ≤ gKΣN√

4π≤ 1.3

crossing symmetry: description of processes in crossed channels,

e.g. Γ(K−p −→ γ Λ) in K+Λ photoproduction: s ↔ u

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 10 / 23

Page 11: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Isobar models

MAID – the interactive Web page of Mainz University(www.kph.kph.uni-mainz.de/MAID/)

I models for photo- and electroproduction on NI pion: unitary isobar modelI eta: isobar model – Breit-Wigner forms for N∗ contributions;

effective Lagrangian approach for the non resonant part of amplitudeI kaon: isobar model (Kaon-MAID) – effective Lagrangian approach;

hadron form factors; no hyperon exchanges in the u channel

other isobar models

I eta photoproduction: Benmerrouche at al (95)– an effective Lagrangian; Born terms and N∗(1/2,3/2), ρ, and ωexchanges; hadron form factors

I kaon production: Adelseck-Saghai (90), Williams-Ji-Cotanch (92),Saclay-Lyon (96), Gent isobar (01), Maxwell (07), Skoupil-B. (16)

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 11 / 23

Page 12: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Regge theory for γ + N −→ M+ B

high-energy approach – economically takes into account “infinite” numberof exchanges of high-spin and large-mass particles in the t (u) channel

the main idea: the angular momentum → a complex continuous variable

Regge trajectory – a family of hadrons with the same internal quantumnumbers, except the spin → a linear dependence between the spin and m2

α(t) = α0 + α1t, for t = m2, α(t) equals the particle spin

0 1 2 3 4 5

t [GeV2]

0

1

2

3

4

5

α(t)

ρ(770)ω(782)

a2(1320)

b1(1235)

π

π2(1670)

ρ3(1690)

a4(2040)

ρ5(2350)

f2(1270)

π, ρ, ω trajectories f4(2050)

ω3(1670)

0 1 2 3 4 5 6 7

t [GeV2]

0

1

2

3

4

5

6

α(t)

K*(892)

K*2(1430)

K*3(1780)

K*4(2045)

K*5(2380)

K1(1270)

K+

K2(1770)

K3(2320)

K4(2500)

K and K*

trajectories

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 12 / 23

Page 13: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Regge theory

two signatures (ζ = ±1) – a mathematical requirement due to convergenceof a contour integral ⇒ two amplitudes, propagators, trajectories

assumption of strong degeneracy: trajectories for even and odd spinscoincide and residua of both signatures are equal, β+(s, t) = β−(s, t)

validity is seen in the data: dσ/dt should be a smooth function of energy

if dσ/dt reveals dips ⇒ the assumption is not valid

the Regge propagator for degenerate trajectories

PRegge(s, t) =(s/s0)α(t)

sinπ α(t)

π α′

Γ(1 + α(t))

1

e−iπα(t)

undetermined relative phase makes constant or rotating phase→ have to be fixed in a data analysis

in the lowest mass pole, t → m20, PRegge(s, t) −→ 1

t−m20

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 13 / 23

Page 14: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Regge theory

the amplitude M = PRegge(s, t) β(s, t)

determination of the residue β(s, t): near the lowest pole, t → m20

PRegge(s, t)× β(s, t) −→ β(s, t)

t −m20

⇐⇒ t−channel Feynman diagram

the “first materialisation” of the trajectory

a formal approach – “reggeisation”: the Feynman propagatorin the t-channel exchange is substituted with the Regge propagator

gauge invariance: the π± and K+ t-channel exchanges are not gaugeinvariant, Mµ

t qµ 6= 0 but together with the s- or u-channel exchangesthe invariance is restored: (Mµ

t +Mµs(u)) qµ = 0

⇒ the s- or u-channel proton exchange have to be added

β(s, t)

t −m20

⇐⇒ (Mµt (meson) +Mµ

s(u)(proton) ) εµ

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 14 / 23

Page 15: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Regge-plus-resonance model – hybrid Regge-isobar approach

for kaon photoproduction [L.De Cruz et al, Phys.Rev.C86 (2012) 015212]

Invariant amplitude:

M =Mbgr (Regge) +Mres(isobar)

the background part – exchanges of degenerate K+ and K∗ trajectories

Mbgr = (MKFeyn +Mp,elec

Feyn ) (t −m2K )× PK

Regge +MK∗

Feyn (t −m2K∗)× PK∗

Regge

Regge propagators with the rotating phase; materialisation of K+ and K∗

⇒ only 3 parameters of Mbgr fixed by high-energy data (W>2.6 GeV)

Mres : s-channel Feynman diagrams for N∗ with multidipole hadron f. f.

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 15 / 23

Page 16: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Regge and Regge-plus-resonance models

StrangeCalc – the interactive Web page of Gent University(http://rprmodel.ugent.be/calc/)

I models for photo- and electroproduction on NI pionsI kaons: RPR-2007, RPR-2011

Gent Regge model for kaon photoproduction – Regge2011;fit to CLAS data above the resonance region (W> 2.5 GeV)

Guidal et al (97) – Regge model for pion and kaon photoproduction;pion: π and ρ trajectories for charged-pion production,

ρ, ω and b1(1235) trajectories for neutral-pion productionkaon: Regge97 model, K+ and K∗ trajectories,

SU(3)f symmetry for gKΛN and gKΣN ;fit to SLAC high-energy data

Wen-Tai Chiang and Shin Nan Yang (03) – Regge modelfor eta and eta’ photoproduction – ρ and ω trajectories

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 16 / 23

Page 17: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Results for kaon photoproduction – isobar and Regge models

0

0,1

0,2

0,3

0,4

0,5

CLAS 2010CLAS 2005

0

0,1

0,2

0,3

0,4

dσ /

dΩ [

µb/s

r] Saclay-LyonKaon-MAIDBS1RPR fit

0 30 60 90 120 150 180θ

K

c.m. [deg]

0

0,1

0,2

0,3

0,4

W = 1.805 GeV

W = 2.005 GeV

W = 2.205 GeV

angular dependence of the cross section in p(γ, Κ+)Λ

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 17 / 23

Page 18: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

0

0,1

0,2

0,3

0,4

0,5

LEPS (0.85)

Saclay-LyonKaon-MAIDBS1RPR fit

1,6 1,8 2 2,2 2,4W [GeV]

0

0,1

0,2

dσ /

dΩ [

µb/s

r]

CLAS 2010CLAS 2005Adelseck-Saghai

1,6 1,8 2 2,2 2,4

cos θK

c.m. = 0.8 cos θ

K

c.m. = 0.5

cos θK

c.m. = 0.2

cos θK

c.m. = -0.4

energy dependence of the cross section in p(γ, K+)Λ

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 18 / 23

Page 19: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Very small kaon angles

lack of very-forward kaon-angle data (CLAS: −0.9 < cos θK < 0.9)

models are not well determined below θK ≈ 30

this region is crucial for the calculations of hypernucelus-production crosssections (in DWIA, contributions from larger kaon angles are suppressedby nucleus-hypernucleus transition form factors)

0 30 60 90 120 150 180

θK

c.m. [deg]

0

0,1

0,2

0,3

0,4

0,5

0,6

dσ /

[µb/

sr]

Brown72BS1BS2E94-107CLASLEPSSAPHIRRPR-2007RPR-1SLARPR-2H2

p(γ, K+)Λ

W = 2.24 GeV

Elab

γ = 2.21 GeV

DWIA 1 1,5 2 2,5 3

Eγlab

[GeV]

0

0,2

0,4

0,6

0,8

1

dσ /

dΩ [

µb/s

r]

BleckmannBrownE94-107SLASLKMH2RPR-1GiessenBS2BS1

θK

c.m. = 6

op(γ, K+)Λ

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 19 / 23

Page 20: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Angular dependence of the hypernucleus cross section

electroproduction of 16NΛ (Elabγ = 2.21 GeV, θlab

e = 6o) as predictedby Kaon-MAID and Saclay-Lyon models → factor 10 different magnitudes

generally a steeply decreasing dependence, the slope depends on the spin (J)

the angular behaviour depends also on the spin structure of the elementaryamplitude at small θK → more detailed information on the amplitude

6 7 8 9 10 11 12 13

θKe

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

nb

/sr2 /G

eV

16O(e,e’K+)16NΛ Ei=3.654 GeV, Ef=1.445 GeV, θe=6

E=0.03 MeV, J=1- state SLA1

KMAID 10x

6 7 8 9 10 11 12 13

θKe

0.0

0.5

1.0

1.5

2.0

2.5

3.0

nb

/sr2 /G

eV

16O(e,e’K+)16NΛ Ei=3.654 GeV, Ef=1.445 GeV, θe=6

J=1+, 2+ states at E approx. 11 MeV

J=2+

J=1+

SLA1

KMAID 10x

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 20 / 23

Page 21: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

The very forward angular dependence above the resonance region

inconsistency of CLAS and SLAC data

0

0.1

0.2

0.3

0.4

/dΩ

b/s

r]

Regge97

RPRRegge2011

0 20 40 60 80θ

K

0

0.1

0.2

0.3

0.4

/dΩ

b/s

r]

0 20 40 60 80θ

K

0 20 40 60 80θ

K

0 20 40 60 80θ

K

CLAS09 CLAS09 CLAS09

SLAC69 SLAC69 SLAC69 SLAC69

Elab

γ = 2.19 GeV E

lab

γ = 2.90 GeV

Elab

γ = 5 GeV E

lab

γ = 8 GeV E

lab

γ = 11 GeV E

lab

γ = 16 GeV

Elab

γ = 3.81 GeV

CLAS09

Elab

γ = 1.74 GeV

W = 2.04 GeV

W = 2.24 GeV

W = 2.52 GeV W = 2.84 GeV

W = 3.20 GeV W = 3.99 GeV W = 4.64 GeV W = 5.56 GeV

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 21 / 23

Page 22: Photoproduction of pseudoscalar mesons in isobar …jpac/Krakow/HASPECT_Bydzovsky.pdf · Photoproduction of pseudoscalar mesons in isobar and Regge formalism ... Introduction {description

Summary

in the resonance region, photoproduction of π, η, and K mesons can besuccessfully described by an effective Lagrangian on tree-level (isobar model);

data above the resonance region reveal a smooth energy dependence andcan be described using the Regge formalism;

a hybrid isobar-Regge model can be used to describe data both in theresonance region and above this region, e.g., up to 16 GeV in p(γ,K)Λ;

predictions of isobar and Regge-plus-resonance models for the cross sectionsin p(γ,K)Λ still significantly differ for small kaon angles due to lack of data;

the ample world data (CLAS, SAPHIR, LEPS,..) on p(γ,K)Λ cover mainlythe region θK > 20 which is not enough to fully determine the angulardependence of the elementary cross section;

new good quality data at very small θK (and Q2) are needed to testthe models which then will provide more reliable predictions of the crosssections in electroproduction of hypernuclei;

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Thank you

P. Bydzovsky (NPI Rez) Photoproduction of pseudoscalar mesons Krakow,May 30 -June 1,2016 23 / 23