PoS(Hadron 2013)031 http://pos.sissa.it/ diquark motions in charmed qq reaction at J-PARC. Systematic ) ∗− D , − π ( p † ∗ [email protected] measurements of the excitation energy spectrumout by and means decays of of the charmed missing baryons mass technique. can be carried Speaker. This article is based on works of the P50 collaboration and discussions with A. Hosaka and his co-workers. baryons appears in the level structure,a production spectroscopic rates, and study decay of branching charmed ratios. baryons We propose via the Charmed baryons with a charm quark provide aparticularly unique diquark opportunity correlations, to in investigate quark baryons. dynamics, Because ainteractions charm with quark the is charm heavy quark and is spin-dependent weaker, charmedthe other baryons two are light-quarks. characterized by We demonstrate the that motions the of nature of light- ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

RCNP, Osaka-U E-mail: Hiroyuki Noumi Spectroscopic study of charmed baryons at J-PARC XV International Conference on Hadron Spectroscopy 4-8/11/2013 Nara, Japan PoS(Hadron 2013)031 Q m and q ]. In light m 6 state, is not , , X, Y, Z, and − 5 + Hiroyuki Noumi , Θ 4 , 3 ]. -mode one is given 9 λ (1405)1/2 Λ reaction, where systematic ) ∗− D , , and/or − + π ( p (1440)1/2 ∗ 2 -mode excitation energy to ρ mode) and a collective motion of them to the heavy quark ρ . This kind of level splitting at orbital excited states occurs when in the case of a harmonic oscillator potential, where 1 ) Q m + q m 2 ( / Q quarks are renormalized due to the strong interaction, as "dressed" quarks, while ]. Therefore, baryons with a charm quark provide unique opportunities to study m 8 s quarks act as constituent quarks. The CQM rather well describes the properties of 3 , b 7 √ = , and λ and d ], have been reported. These states are not yet understood very well. ω c , 2 / u , If a quark in a light baryon is replaced by a heavier quark, orbital excited states split into a Above-mentioned situation indicates rich structure of hadrons. We need to investigate the It is a fundamental question in hadron physics how hadrons form. The principle to describe ρ 1 mode), as illustrated in Fig. [ ω b λ as baryons, where flavor SU(3) symmetry seems to workcorrelated rather each well, other 3 diquark at pairs an are equal expecteda to weight. quark be Extraction in of diquark a correlation lightare may baryon separated not is be from easy. replaced that When by ofquarks a a is heavy heavy proportional quark, quark. to onebecome the expects Since much inverse that stronger. magnitude of In motions of this the of respect, the diquarkwith quark light spin-spin correlation mass, quarks a is interaction expected a heavy between to correlation be quark. singledtwo between out light in light Lattice quarks a quarks with QCD baryon a may calculations spin-singlet,static demonstrate color quark[ anti-triplet strong configuration spatial in a correlations baryon between with introducing a measurements of the level structure, productiona rates, wide and mass range branching can ratios be of carried charmed out baryons by in means of a missing mass technique [ relative motion in the light( quarks ( a confinement potential is given. A ratio of diquark correlation. The nature ofproduction the rates, diquark and correlation decay is branching expected ratios,propose to as a appear described spectroscopic in in study level the of structure, following charmed sections. baryons via We therefore the 2. Level Structure interaction between quarks in hadronsbaryon, further. namely diquark In correlation, particular, has roles yetof of to diquarks quark-quark be correlation in understood, although in many existence a hadronic or processes even evidence has been discussed for a long time [ correspond to constituent quarkcalled masses isotope of shift. light The and levels heavy further quarks, split respectively. due to This the is spin-dependent the interactions. so- In particular, the dynamics of quarksdifficult is to known reproduce as hadrons, especially the excitedthe Quantum hadrons, equation from Chromodynamics bare of (QCD). quarks QCD However, and itmodel gluons due by is to (CQM), solving still its quarks non-perturbative arelight nature treated in as low an energy. effective In degree the of constituent freedom quark in hadrons. In the CQM, Spectroscopic study of charmed baryons at J-PARC 1. Introduction clearly explained. Recently, unexpected, narrow states inZ excited hadrons, such as heavy hadrons, such as classification basedof on ground spin/flavor state symmetry, baryons, mass and relations, somany magnetic on. undiscovered moments states However, the predicted situation by isproblem. CQM, different which The in is excited mass known states. order as of There the are resonances, so-called missing i.e. resonance the N PoS(Hadron 2013)031 ud and (3.1) (3.2) (3.3) ) λ ), spin ( λ quark in ρ ` ` u or ρ is a kinematic Hiroyuki Noumi ` K -(a). Here, a 2 . Schematic level structure s χ , . The level structure reflects a ) ∗ 1 , 2 D )] m r ( i − ϕ , characterizes the level structure. An- 2 [ j r q ( m eff , i / q B ) e m p 1 ) / 2 r j | ˙ ( − I σ f ∗ B · K ϕ | i 3 [ m 3 C σ 2 of 1/2 (1/6) for the good (bad) diquark configuration. r γ j / , | i d γ B ∼ ∑ p ∫ | R 2 ( ∼ π √ ss k ∗ V 0 D ∼ k exchange model at a forward scattering angle in order to estimate ), and colors (antisymmetric) are determined. Here, I ∗ Σ ∼ D quark to form an excited charmed baryon. Let us consider that a K c , or Λ ), isospin ( s χ Schematic picture of quark correlations in a baryon. In a baryon with light quarks, the correlations stands for a kind of spectroscopic factor to pick up good or bad diquark configuration in the is the overlap integral of the initial and final states. , or γ I λ represent antisymmetric (symmetric) orbital and spin configurations of light quarks, respec- χ ) We consider the t-channel , λ ( ρ is a spin dependent coefficient, which is the products of the Clebush-Gordan coefficients based ρ χ χ diquark in a baryon acts as a spectator in the reaction. Then, the production rate is expressed as: tisymmetrizing a fermion system, configurations of orbital angular momentum ( the proton is converted to a on the quark-diquark spin configurations in the initial and final baryon states. Then, the production rates for the excited charmed baryons, as shown in Fig. where 3. Production rate the spin-spin interaction, denoted as ( tively. A symmetric configuration for 3 quark spins is represented by factor expressed as: Figure 1: are equal weight and thecase orbital that excitation two levels light are quarks degenerated,excited make as states a illustrated split collective in system the into by left two:the introducing hand light a a side. quarks relative heavy relative In orbital quark to the motion in the heavy a between quark. baryon, two The the light levels orbitally quarks further and split due a to collective the motion spin-dependent of interactions. Spectroscopic study of charmed baryons at J-PARC motion of a light-quark pair. target proton. A naive quark model gives the of charmed baryons are illustrated in the right-hand side of Fig. C PoS(Hadron 2013)031 - + c qq λ ud Y ) (3.4) (3.5) ∗− D , − π ( if we ignore p L Hiroyuki Noumi ) A / e f f q ( . The relative strength of stands for the residual I d m , the relative rate increases as exchange reaction is considered at A ∗ D , , can be expressed as, 2 ]. The present model calculation sug- c states due to a large momentum trans- A decreases rapidly. d is the orbital angular momentum of the . This can be called as the momentum I Y 2 11 I A / L m L M 2 2 e f f × q √ greater than c − -(b) [ Y e = 2 L p e f f ) 4 q − A e f f / q p d m M e f f in Fig. q . One finds that the production rate strongly depends on reaction. The t-channel c × ( p + c 5.1 p ∼ Λ ) I GeV/ = ∗− , the absolute value of represents a recoil effect, where for the ground state is proportional to D 20 eff ) , 0.45 GeV. The quantity e f f eff 0 q . In the case of − ( q ∼ = is maximum at q A π I in the reaction, although an absolute cross section is expected to be ( ] I π / p p c 11 e f f .[ q c are the wave functions of the initial and final quark states, respectively. The ) r ( f GeV/ ϕ reaction at 20 + = c and Y π can be taken as 0.4 ) ) p r (a) Diagram of the A ( is the average of the oscillator parameters of the initial and final wave functions. A typical ∗− i ϕ A D , for the excited state to We consider decays of excited charmed baryons. On one hand, a string between the light- We summarize the production rates relative to the ground state estimated in the cases of the − ) π increases. One finds that L ( ( p reaction at gests that the production rate is kept even at the higher spin/isospin structures of baryons. It should be noted that the reaction is expected to favor the 4. Decay matched condition. For larger where much smaller, as described in Section a forward scattering angle. (b) Production rate relative to the ground state estimated in the where value of excited baryon. This expressionI shows some interesting features for fer of greater than 1 GeV/ mode excitations. The production ratesmomentum of will excited provide the states information with on different the isospin spin and and radial orbital wave angular functions of charmed baryons. Figure 2: Spectroscopic study of charmed baryons at J-PARC the small difference of L effective momentum transfer diquark mass. Taking harmonic oscillator wave functions, PoS(Hadron 2013)031 ) ¯ q Q (5.1) (5.2) (5.3) ). On ¯ q q expressed . increases. We Hiroyuki Noumi | et al t | reaction at the J- ) ∗− D , : − ) π t ( stands for the square of the ) and a light meson ( F 0 , s ) , t ) ( Qqq . As a result, the t-dependence of t ( α 2 )) Reaction α 2 diquark in a excited charmed baryon. ) ) ) 0 max s t s 0 ∗− reaction is an experimental issue, which qq s ( s : ( D α + c ( , ∞ )) Λ − 2 -mode excited state. If the excited energy is t − ) -mode excited state. Measurements of decay ( ) ( t → λ π Γ ρ , which can covers a large acceptance of greater . A dispersive beam optics is realized so that ( ∗− α ( s c F p ∗− D − 5 s , ( D 2 2 | − 2 2 1 Γ ]. π g p s ( | 2 1 2 , p 10 | t g 10 MeV, where the charmed baryons can be identified π 2 2 2 1 R g ∼ p ] and the scale parameter 64 | e 2 1 g π 14 ]. The high-momentum beam line is designed to deliver high- ∼ 9 64 ]. In the Regge theory, the differential cross section of a binary ) = t σ ( dt = 13 d ], suggests a small cross section of charmed baryons at a level of F σ 12 dt d -dependence in the limit every second at 20 GeV/ s ) rather than a decay to a heavy baryon ( 7 pair is created in a string. This may favor a decay to a heavy meson ( ¯ q , where the typical angular distribution decreases rapidly as 10 s qqq q ∼ |  t | is the Regge trajectory [ dependence of the Gamma function as t ) t ( α We employ the Regge model to estimate the cross section as it well describes binary (two- Estimation of the cross section of the We propose a spectroscopic study of charmed baryons via the p( threshold energy in the reaction. Thetive above region formula of of the cross section isignore applicable the at the diffrac- nb. body) reactions at high energy [ reaction shows a typical where PARC high-momentum beam line [ independent of their decay final states.detect Owing decay to particles the emitted large from acceptancemeasure observed of decay the branching charmed spectrometer, ratios baryons we as in can and well a spectrometer as can wide spin-parity. be angular More found range, detailed elsewhere description [ and of can the beam line 5.1 Cross section the cross section is expressedthe as differential the cross exponential section function. introducing an Then, exponential V. form Yu. factor Grishina sufficiently high, a than 50 %. Charmed baryons with aspectrum wide with mass range an are expected energy to resolution be observed of in a missing mass 5. Charmed Baryon Spectroscopy via the Spectroscopic study of charmed baryons at J-PARC diquark and a charm quark will be expanded in an and a light baryon ( intensity pions of a pion beam momentummagnetic can spectrometer be is designed measured for scattered with a resolution of 0.1 % at a beam focal plane. A branching ratios provide information on the motion of the the other hand, the situation may be opposite in an affects an experimental design in orderdata to achieve on reasonable the signal reaction sensitivity. are However, available limited.13 An GeV/c, upper reported limit, at 7 nb BNL (68% [ CL) at the incident pion momentum of PoS(Hadron 2013)031 1 − GeV -(b) for 2 reactions 13 reaction at . Λ ) 2 + c 0 ∗ ]. Background Λ = Hiroyuki Noumi ) K 2 , 19 ∗− R − -dependence of the hyperon production D π s , ( Λ − p π calculated based on the ( p + c ]. Here, Λ ) 15 ∗− 1000 events/nb for 100 days of D masses. A signal to background ∼ , and no decay widths for the others hydrogen target. 0 − 2 2 ¯ c D π Simulated missing mass spectrum of ( p reggeons are assumed respectively. The values for the ] are used except for three peaks, labeled and ∗ 0 18 s D and / ∗− s Λ D ]. We expect ) and 0 ∗ 6 ∗ 10 charmed baryons. Figure 4: [ K K , 0 ¯ − D π ( p , where we expect the cross section as large as 10 nb. ]. c 15 [ ] as plotted with s 17 , in the rest frame of 16 pions per second irradiated on a 4 g/cm 7 − and the excited states, respectively. The masses and the decay widths of the π + c Λ or + reactions [ 100 MeV for the broader peak at around 3 GeV/ K shows cross sections of the Cross sections calculated based on shows a simulated missing mass spectrum of charmed baryons. In the simulation, the ∼ Λ is a parameter related to the so-called slope parameter [ ) 3 4 Γ ∗ 2 K ] as plotted with closed squares. The Grishina’s model reproduces the R , ", demonstrated as a case if there are. The cross section of 1 nb is assumed for each. A decay ∗ c − scattering angles assuming t-channel dominance and discarding forward and backward angles Fig. Fig. 17 Λ π , ( ∗− p closed squares. Figure 3: the Regge model witheters. the Grishina’s The param- crossas sections to are reproduce the normalized experimental so data of the 16 the beam momentum of 20 GeV/ the ground state charmed baryons reported by the Particle Data Group [ running time with 10 width of as " of scattered [ are taken into account. Background eventsground are generated level by is using reduced the JAMratio mainly code is [ by further improved reconstructing by applyingD some additional cuts, such as selection of a forward region of 5.2 Expected spectrum cross sections are assumed to be 1 nb and the estimated production rates shown in Fig. where is chosen so as toreactions reproduce in the a differential wide cross range sections of of pion-induced Regge model with the Grishina’s parameters. cross sections are normalized so as to reproduce the experimental data of the data very well. An arrow in the figure indicates the Spectroscopic study of charmed baryons at J-PARC PoS(Hadron 2013)031 ) ∗− D , ]. − 18 π ( p , Hiroyuki Noumi 61 , 172(2012). , Phys. Rev. C . reaction", J-PARC P50 Proposal, , 054013(2000). 1441 , 222002(2006). ) et al 61 97 ∗− D , − π ( , 010001(2012). ; Y. Nara, 86 , 846(1966). 7 ) provide a unique opportunity to investigate quark 36 c , 154(1985). 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Nakano Note on "Developements in Heavy Quarkonium Spectroscopy", Review ofM. Particle Ida Physics and [ R. Kobayashi, Prog. Theor. Phys. M. Anselmino R. L. Jaffe, Phys. Rep. Charmed baryons with a charm quark ( diquark motions in charmed baryons could appear in the level structure, production rates, and [8] [9] [3] [4] [5] [6] [7] [1] [2] [17] [18] [19] [13] [14] [15] [16] [10] [11] [12] reaction at J-PARC. Systematiccharmed measurements baryons of can the be carried excitationhigh-momentum out energy beam by spectrum line means is and of in the decays progress. missing of mass technique. Construction of the References Spectroscopic study of charmed baryons at J-PARC 6. Summary and Outlook dynamics, particularly diquark correlations, inqq baryons. We demonstrated that thedecay nature branching of ratios. light- We propose a spectroscopic study of charmed baryons via the