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

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

  • 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