# Photoproduction of pseudoscalar mesons in isobar jpac/Krakow/HASPECT_ Photoproduction

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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 mechanismin , , 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

Description of the electromagnetic production

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

e + N e +M+ B

electromagnetic interaction is well known and the coupling constant

is small: = e2

2

.= 1137 1 a one-photon approximation is justified

the leptonic and hadronic parts are separated in opa

Mfi = u(pe, )(ie) u(pe, )g

q2J (pN, , q, , pB, , pM)(ie)

the transition current J describes photoproduction by virtual photons

(v) + N M+ Bwith 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

kinematics in the laboratory frame: Ee, Ee, e, M, M

the unpolarized cross section: 14 m2e

|Mfi |2 =

14

e4

q4 Ls W

d5

dEe de dM

=

[dTdM

+ dLdM

+ dTTdM

cos 2M+

2(1+)dTLdM

cos M

]

virtual-photon flux: (pe, pe, e) polarization: =

(1 + 2 q

2

q2 tan2 e

2

)1dxdM

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

laboratory frame (~pN = 0):

e

p

p'

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

Photoproduction by real photons (q2=0)

+ 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. ( 1.07 GeV), ( 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

+ p 0 + p K+ + + p K+ + K+ + K+ +

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

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 + LintI baryon, meson and photon fieldsI possible resonances in the intermediate states missing resonancesI couplings of the fields in LintI 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 +MresI 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

Dominant resonances in pion and eta photoproduction

0.2 0.3 0.4 0.5 0.6 0.7 0.8E [GeV]

0

5

10

15

20

25

30

d /

d [

b/s

r]

Born termsBorn + (M1)

+ n --> - + p

= 90o

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

Mres is dominated by (1232) 32+

with a branching ratio to N 100%N N

0.7 0.8 0.9 1 1.1 1.2E [GeV]

0

0.4

0.8

1.2

1.6

d /

d [

b/s

r]

Born termsBorn + S11(1535)

+ p --> + p

= 90o

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

Mres : N(1535) 12

(42% to N)

other states, e.g.: N(1710) 12+

(10-30%)

N(1650) 12

(5-15%), N(1720) 32+

(4%)

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

No dominant resonance in kaon photoproduction

many N with a reasonable branching ratio to K can contribute

Mres in the Kaon-MAID model: S11(1650) (311%), P11(1710) (525%),P13(1720) (115%), D13(1895) (missing resonance not seen in and channels)Born terms (p, , 0, 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), (1520), (1660), (1750),(1800), (1890), (1940);

1.2 1.6 2 2.4E [GeV]

0

0.05

0.1

0.15

0.2

d /

d [

b/s

r]

SAPHIRCLASKaon-MAIDBorn + K* + K1

+ p --> K+ +

= 90o

1,2 1,6 2 2,4E [GeV]

0

0,05

0,1

0,15

0,2

d /

d [

b/s

r]

full BS1 modelbackground

+ p --> K+ + = 90o

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

Consistent description of higher-spin resonances

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

the Rarita Schwinger propagator for spin 3/2

S(p) =/p + m

p2 m2P3/2

2

3m2(/p + m)P1/222, +

13m

(P1/212, + P1/221,)

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 S p = V EM p

= 0

removes all nonphysical contributions:

V S P1/2,ij V

EM = 0

N B

MS

(p)

VEM V

S

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

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

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({BB}M)

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

Parameters: gs ga =

2 gNN (well known) and gsgsgafrom SU(6) =

35

or experimental value: 0.644 0.009.

gKN = 13 gNN (3 ), gKN = gNN (1 2), ...

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

4.4 gKN4 3 0.8 gKN

4 1.3

crossing symmetry: description of processes in crossed channels,

e.g. (Kp ) in K+ photoproduction: s u

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

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), , and exchanges; 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

Regge theory for + 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

(t) = 0 + 1t, for t = m2, (t) equals the particle spin

0 1 2 3 4 5

t [GeV2]

0

1

2

3

4

5

(t)

(770)(782)

a2(1320)

b1(1235)

2(1670)

3(1690)

a4(2040)

5(2350)

f2(1270)

, , trajectories f4(2050)

3(1670)

0 1 2 3 4 5 6 7

t [GeV2]

0

1

2

3

4

5

6

(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) Photoprodu

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