Electromagnetic KY production from the proton in a Regge-plus-resonance approach

0.16 MB·English

by  T. Corthals

EPJ manuscript No.
(will be inserted by the editor)
Electromagnetic KY production from the proton
in a Regge-plus-resonance approach
T. Corthals1, T. Van Cauteren1, J. Ryckebusch1, and D.G. Ireland2
7
0 1 Department of Subatomic and Radiation Physics, Ghent University,Proeftuinstraat 86, B-9000 Gent, Belgium
0 2 University of Glasgow, Glasgow G12 8QQ, United Kingdom
2

n Received: date/ Revised version: date
a
J Abstract A Regge-plus-resonance (RPR) description of the p(γ,K)Y and p(e,e′K)Y processes (Y =

9 Λ,Σ0,+) is presented. The proposed reaction amplitude consists of Regge-trajectory exchanges in the
1 t channel, supplemented with a limited selection of s-channel resonance diagrams. The RPR framework

containsaconsiderablysmallernumberoffreeparametersthanatypicaleffective-Lagrangianmodel.Nev-
1
ertheless,itprovidesanacceptableoveralldescriptionofthephoto-andelectroproductionobservablesover
v
anextensivephotonenergyrange.Itisshownthattheelectroproduction responsefunctionsandpolariza-
7
tion observables are particularly useful for fine-tuningboth thebackground and resonance parameters.
5
0
1 PACS. 11.10.Ef LagrangianandHamiltonianapproach12.40.NnReggetheory,duality,absorptive/optical
0 models 13.60.Le Meson production 14.20.Gk Baryon resonances with S=0
7
0
/ 1 Introduction invarianceissuesplaguingtraditionaleffective-Lagrangian
h
models [19].
t
- Recent measurements performed at the JLab, SPring-8,
In this work, the RPR prescription from Refs. [20,21]
l
c ELSA and GRAAL facilities have resulted in an exten- is appliedto the electroproductionprocessesp(e,e′K+)Λ,
u sive set of precise p(γ,K)Y [1–7] and p(e,e′K)Y [8–10] Σ0.Itwillbedemonstratedthattheelectroproductionre-
n data in the few-GeV regime. These experimental achieve-
sponsefunctionsareparticularlyusefulforfine-tuningcer-
:
v ments have motivated renewed efforts by various theoret- tainmodel choiceswhich the photoproductiondata failed
Xi ical groups. A great deal of attention has been directed to determine unambiguously.
towards the development of tree-level isobar models, in
r which the scattering amplitude is constructed from a se-
a
lection of lowest-orderFeynmandiagrams [11–16],as well
as to coupled-channels approaches [17–19]. While the lat- 2 Constructing the RPR amplitude
ter successfully address a number of issues, the multitude
of parameters involved constitutes a complicating factor.
2.1 Background contributions
It is therefore our opinion that ambiguities related to, for
example,formfactors,gauge-invariancerestoration,orpa-
rameterizationof the background,can be addressedmore Regge theory rests upon the proposition that, at ener-
efficiently at the level of the individual channels. gies where individual resonances can no longer be distin-
In Refs. [20,21], a tree-level effective-field model was guished, the reaction dynamics are governed by the ex-
developed for KY (Y = Λ,Σ0,+) photoproduction from change of entire Regge trajectories rather than of single
the proton. It differs from traditional isobar models in its particles. This high-energy approachapplies in particular
description of the background contribution to the ampli- totheforwardorbackwardangularranges,corresponding
tude, which involves the exchange of a number of kaonic to t- or u-channel exchanges, respectively. This work fo-
Reggetrajectoriesinthetchannel,anapproachpioneered cuses on the forward-angle kinematical region which, for
by Guidal and Vanderhaeghen [22]. To this Regge back- electromagnetic KY production, implies the exchange of
ground, we added a number of resonant contributions. kaonic trajectories in the t channel.
Such a “Regge-plus-resonance” (RPR) strategy has the An efficient way to model trajectory exchanges in-
advantagethatthebackgroundcontributioninvolvesonly volves embedding the Regge formalism into a tree-level
afewparameters,whichcanbelargelyconstrainedagainst effective-field model [22]. The amplitude for t-channel ex-
thehigh-energydata.Furthermore,theuseofReggeprop- change of a linear kaon trajectory
agators eliminates the need to introduce strong form fac-
tors in the background terms, thus avoiding the gauge- α (t)=α +α′ (t−m2 ), (1)
X X,0 X X
2 T. Corthals et al.: Electromagnetic KY production from theproton in a Regge-plus-resonance approach
with m the mass and α the spin of the trajectory’s 2.2 Resonance contributions
X X,0
lightestmember(or“firstmaterialization”)X,canbeob-
tainedfromthestandardFeynmanamplitudebyreplacing Although Regge phenomenology is a high-energy tool by
the Feynman propagatorwith a Regge one: construction,theexperimentalmesonproductioncrosssec-
tions are observed to exhibit Regge behavior for photon
1 energies as low as 4 GeV. Even in the resonance region,
−−→ PX [s,α (t)]. (2)
t−m2 Regge X theorderofmagnitudeoftheforward-anglepionandkaon
X
electromagneticproductionobservablesisremarkablywell
The Regge amplitude can then be written as reproduced in the Regge model [22].
It is evident, though, that a pure background ampli-
MX (s,t)=PX [s,α (t)] × β (s,t), (3) tude cannot be expected to account for all aspects of the
Regge Regge X X
reaction dynamics. At low energies, the cross sections re-
with β (s,t) the residue of the original Feynman ampli- flect the presence of individual resonances. These are in-
X
tude,tobecalculatedfromtheinteractionLagrangiansat corporatedintotheRPRframeworkbysupplementingthe
the γ(∗)KX and pXY vertices. reggeizedbackgroundwithanumberofresonants-channel
In our treatment of K+Λ and K+Σ0 photoproduc- diagrams. For the latter, standard Feynman propagators
∗ are assumed, in which the resonances’ finite lifetimes are
tion[20,21],weidentifiedtheK(494)andK (892)trajec-
taken into account through the substitution
tories as the dominant contributions to the high-energy
amplitudes. The corresponding propagators assume the
s−m2 −→ s−m2 +im Γ (7)
following form [23]: R R R R
in the propagator denominators, with m and Γ the
R R
s αK(t) 1 mass and width of the propagating state (R=N∗,∆∗).
PK(494)(s,t)=
Regge (cid:18)s (cid:19) sin πα (t) Further, the condition is imposed that the resonance
0 K
amplitudes vanish at large values of ω . This is accom-
πα′ (cid:0) (cid:1)1 lab
× Γ 1+αKK(t) (cid:26)e−iπαK(t)(cid:27) , (4) aptlisthheedKbyYiRncvluerdtiincgesa: GaussianhadronicformfactorF(s)
(cid:0) (cid:1)
(s−m2)2
F(s)=exp − R , (8)
PK∗(892)(s,t)= s αK∗(t)−1 1 (cid:26) Λ4res (cid:27)
Regge (cid:18)s0(cid:19) sin παK∗(t) A single cutoff mass Λres is assumed for all resonances.
× Γ πααK′K∗(∗t) (cid:26)e(cid:0)−iπα1K∗(t)(cid:1)(cid:27) , (5) frAreelsoeonngpaanwrcaeimt-hreetgteihroenwdrheasetonan.aoOnpuctreimmciozoiutnipvglaitntihgosen,fmΛororeadssesliusamguiansiegndsataGstahuaes-
(cid:0) (cid:1) sian shape is explained in Ref. [20].
withtrajectoryequationsgivenbyαK(t)=0.70(t−m2K), Theleadingdiagramscontributingtothereactionam-
αK∗(t)=1+0.85(t−m2K∗)[20].Foreachofthese propa- plitudeareassumedidenticalforthephoto-andelectroin-
gators, a constant (1) or rotating (e−iπα(t)) phase can be ducedprocesses,as arethe variousmodel parameters.In-
selected. steadof employing the standardphenomenologicaldipole
It is argued in Ref. [22] that, for the sake of current parameterization,wecalculateallelectromagneticN∗ and
conservation,theamplitudeforthecharged-kaonchannels ∆∗ form factors in the context of the Lorentz-covariant
shouldinclude the electric (∼eNγµNAµ) contributionto constituent-quark model (CQM) developed by the Bonn
the s-channel Born term: group [24].
M (γ(∗)p→K+Λ,Σ0)=MK+(494)+
Regge Regge 3 Results for p(e, e′K+)Y
MK∗+(892)+Mp,elec×PK+(494)×(t−m2 ). (6)
Regge Feyn Regge K+
In Refs. [20,21],the RPR prescription was applied to the
Eq. (6) applies to electro- as well as photoproduction. It variousγp→KY reactionchannels.Anumberofvariants
turns out that the measured Q2 behaviour of the σL/σT of the RPR model were found to provide a comparably
ratiocanonlybereproducedprovidedthatthesameform good description of the Λ, Σ0 and Σ+ photoproduction
factorisusedattheγ∗ppandγ∗K+K+ vertices[22].The observables.TheirpropertiesarelistedinTable1.Inciden-
unknown coupling constants and trajectory phases con- tally, the parameters of the K+Λ variants from Ref. [20]
tained in MRegge are determined from the high-energy havebeenslightlyreadjustedinorderto describethe new
p(γ,K+)Y data. singly-polarizedGRAAL data [5].
Amonopoleelectromagneticformfactorisassumedfor The background contribution to the RPR amplitude
theK+(494)andK∗+(892)trajectories,withcutoffvalues involves three parameters: one for the K(494) trajectory
chosen so as to optimally match the high-Q2 behavior of (g ) and two for the K∗(892)one (Gv and Gt , cor-
KYp K∗ K∗
the Λ and Σ0 electroproduction data: ΛK+ = ΛK∗+ = responding to the vector and tensor couplings). In ad-
1300 MeV. dition, for each trajectory propagator, either a constant
T. Corthals et al.: Electromagnetic KY production from theproton in a Regge-plus-resonance approach 3
KRP+RΛ2 rpBohata.cKske,,grGrootKtu.∗Kn<d∗ 0 D13(1⋆–900) P11(1⋆–900) 32χ..272 sm (b/sr)L 00..46 K+L CCCMEooorrAhnnr eei[n2llllg 811 ][99877]47 [[2390]] 000.1..125 K+SR0PR 4¢
RPR 3 rot.K, cst.K∗ – ⋆ 3.1 e + T 0.2 0.05
RPR 4 rpohta.Kse,,GcstKt.∗K>∗ 0 ⋆– ⋆– 33..12 s 0.030 1 2 3 4 0.010 1 2 3 4
RKP+RΣ40′ rpohta.Kse,,GcstKt.∗K<∗ 0 ⋆– –– 32..10 m (b/sr)L 00..12 RPR 2 FFBuuGllll ,,c iionnncctllr.. ibDPu11t13i((o11n990000)) 00.0.0755 RPR 4¢ FBuGll caomnptrliibtuudtieon
phase, GtK∗ <0 s 0.025
0 0
Table 1. RPR variants providing the best description of the 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
0.6 0.2
p(γ,K+)Λandp(γ,K+)Σ0data.Allmodelsincludetheknown
AS1p1a(r1t65fr0o)m, Pt1h1e(s1e7,1e0a)c,hPK13+(1Λ72v0a)riaanntdaPss1u3m(1e9s00e)ithNer∗astmatisess-. b/sr) 0.4 00.1.15
ing D13(1900) or P11(1900) resonance. A good description of m (T 0.2 0.05
theK+Σ0 channelcouldbeachievedwithouttheintroduction s
0 0
of any missing resonances. The K+Σ0 amplitude further con- 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
tains the D33(1700), S31(1900), P31(1910) and P33(1920) ∆∗ Q2 (GeV2) Q2 (GeV2)
states. The last column mentions χ2 in comparison with the Figure 1. Q2 evolutionoftheunseparatedandseparated dif-
low- and high-energy data from Refs. [1–6,25–27]. ferential cross sections for the K+Λ (left) and K+Σ0 (right)
finalstates.ThedataforσT+ǫσLweretakenatW ≈2.15GeV
and θK∗ ≈ 0, and those for σL and σT at W ≈ 1.84 GeV and
θ∗ ≈ 8 deg. For the K+Λ channel, results of the two RPR-2
(const.) or rotating (rot.) phase may be assumed. As can K
variants from Table 1 are displayed, whereas for the K+Σ0
be appreciated from Table 1, in the K+Λ channel two ′
channel, the prediction of the RPR-4 model from Table 1 is
∗ ∗
combinations (rot. K, rot. K /rot. K, const. K ) lead to
shown.ThedottedcurvescorrespondtotheReggebackground.
a comparable quality of agreement between the calcula-
Thedata are from [8,28–30].
tions andthe combinedhigh-energyand resonance-region
data. Furthermore, for the latter combination, the avail-
able photoproduction data do not allow one to determine
the sign of GtK∗. With respect to the quantum numbers <W> = 1.69 GeV <W> = 1.84 GeV <W> = 2.03 GeV
of a potential missing N∗(1900) resonance, both P and 1
11 K+L RPR 2
D13 emerged as valid candidates. P'x 0
Withoutreadjustinganyparameter,wehaveconfronted
theRPRvariantsfromTable1withtheelectroproduction -1
1
data.Inthisway,theirpredictivepowercanbeestimated.
A seTlehcetiloenftopfatnheelsreosfulFtsigi.s1codnitsapilnaeydtihneFQig2s.ev1o-3lu.tion of P'z 0 FFBuuGllll ,,c iionnncctllr.. ibDPu11t13i((o11n990000))
the unseparated (σT +ǫσL) and separated (σT and σL) -11
p(e,e′K+)Λ differential cross sections. The RPR variants
3 and 4 (not shown) are incompatible with these data, P'x' 0
as they predict an unrealistically steep decrease of σ as
T -1
a function of Q2. As seen from the figure, both RPR-2 1
variBanectsaudseescthriebuentphoelaslroizpeedoefletchtirsoopbrosedruvcatbiolenwdealtla. donot P'z' 0
allow to discriminate between the RPR-2 amplitudes as- -1
-1 0 1 0 1 0 1
struamnisnfegrraedmpisoslianrgizaDt1io3nofrorPt1h1es−→teatpe→, wee′Kal−→sΛopcoroncseidsse.rFtihge- cosq *K cosq *K cosq *K
tuoreth2ecdoamtpaa[r9e]s. IotuirsccallecaurlatthiaotnsthfoerRPPx′R,-P2z′a,mPpx′′litaunddePinz′-′ aFnidguPrz′e′ f2o.rtThreanKsΛferfirendalpstoalaterizaastaiofnunccotmiopnoonfecnotssθPK∗x′,,foPrz′,WPx≈′′
1.69, 1.84 and 2.03 GeV. Line conventions as in Fig. 1 (left
cluding a D (1900) state produces results far superior
13 panel). Thedata are from [9].
to those of the one assuming a P (1900). Our combined
11
analysis of the photo- and electroproduction data thus
leads to the identification of RPR2 (Table 1) as the pre-
ferred model variant, and of D (1900) as the most likely
13
missing-resonance candidate, in the K+Λ channel. observables, the data are well matched by the computed
For the p(e,e′K+)Σ0 process, only unpolarized data curves. It turns out that σ +ǫσ and σ can be reason-
T L L
are available. In the right panels of Fig. 1, the separated ably well described in a pure background model, whereas
and unseparatedcross sections are comparedwith the re- reproducingtheslopeofσ clearlyrequiressomeresonant
T
′
sults of the RPR-4 variant from Table 1. For all three contributions to the amplitude.
4 T. Corthals et al.: Electromagnetic KY production from theproton in a Regge-plus-resonance approach
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