By Kaon-Induced Reactions on a Proton Target

PHYSICAL REVIEW D 99, 014045 (2019)

Production of the Λcð2940Þ by kaon-induced reactions on a proton target

† Yin Huang,1 Jun He,2,* Ju-Jun Xie,3 and Li-Sheng Geng1, 1School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China 2Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210097, People’s Republic of China 3Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

(Received 24 October 2016; revised manuscript received 30 November 2018; published 31 January 2019)

We investigate the possibility to study the charmed baryon Λcð2940Þ by kaon-induced reactions on a 0 P proton target. Assuming that the Λcð2940Þ is a pD molecular state with spin parities J ¼ 1=2 ,an effective Lagrangian approach is adopted to calculate the cross section and the D0p invariant mass spectrum − − ¯ of the K p → Ds Λcð2940Þ reaction. The Kp initial state interaction mediated by Pomeron and Reggeon exchanges is also included, which reduces the production of the Λcð2940Þ. Besides, we also consider the DN final state interaction using he chiral unitary approach. We found that the total cross section of the K−p → − 0 Λcð2940ÞDs reaction is about 10 μb. By considering the subsequential decay Λcð2940Þ → D p with − − 0 contributions from the Λcð2286Þ and the Σcð2455Þ as background, the K p → Ds D p reaction is studied. It is found that the Λcð2940Þ is produced mainly at forward angles. The Λcð2940Þ signal is predicted to be 0 − − 0 significant in the D p invariant mass spectrum of the K p → Ds D p reaction. The results suggest that it is promising to study the Λcð2940Þ with high-energy kaon beams on a proton target.

DOI: 10.1103/PhysRevD.99.014045

I. INTRODUCTION and the obtained decay behavior of Λcð2940Þ is consistent with the experimental data [3]. Later, a study of the strong In recent years, many charmed baryons have been and radiative decays of the Λ ð2940Þ was performed by observed. The charmed baryon Λ ð2940Þ was first observed c c Dong and his collaborators [4,5]. Their results indicate that by the BABAR Collaboration in the D0p invariant mass Λ ð2940Þ D0p spectrum [1]. Later, the Belle collaboration also reported the the c can be viewed as a molecular state with spin-parity JP ¼ 1=2þ. In Ref. [6], a dynamical study of the observation of the Λcð2940Þ in the Σcð2455Þπ invariant D0p interaction in the one-boson-exchange model found mass spectrum [2]. The mass and width of the Λcð2940Þ P state reported by the above collaborations [1,2] are con- two bound state solutions with quantum numbers IðJ Þ¼ þ − sistent with each other, i.e., 0ð1=2 Þ and 0ð3=2 Þ, which correspond to an isoscalar S-wave and an isoscalar P-wave D0p molecular state, BABAR∶ M ¼ 2939.8 1.3 1.0 MeV; respectively. In addition to the interpretation of the Λ ð2940Þ as a pD0 molecular state, the possibility to Γ ¼ 17.5 5.2 5.9 MeV; c assign it as a conventional charmed baryon was also ∶ ¼ 2938 0 1 3þ2.0 Belle M . . −4.0 MeV; discussed in many approaches, such as the potential model 3 þ8þ27 [7], the chiral perturbation theory [8], the P0 model [9], the Γ ¼ 13−5−7 MeV: relativistic quark-diquark model [10], the chiral quark model [11], the Faddeev method [12], and the mass load Since the mass of the Λcð2940Þ is just a few MeV below the D0p threshold, it was proposed that this state is an flux tube model [13]. Λ ð2940Þ S-wave D0p molecular state with a spin parity JP ¼ 1=2−, The present knowledge about the c was obtained from the eþe− collision [1,2]. Thus, it will be helpful to understand the nature of the Λ ð2940Þ if we can observe it *corresponding author; c [email protected] in other production processes. In Refs. [14,15], a proposal † Λ ð2940Þ ¯ [email protected] was made to study the c in the pp annihilation which can be performed in the future PANDA detector at Published by the American Physical Society under the terms of FAIR. The production of the Λcð2940Þ via a pion-induced the Creative Commons Attribution 4.0 International license. reaction on a nucleon target was discussed in Ref. [16]. Further distribution of this work must maintain attribution to Λ ð2940Þ the author(s) and the published article’s title, journal citation, A study of the c with electromagnetic probes in the 3 − and DOI. Funded by SCOAP . γn → Λcð2940ÞD reaction was also proposed [17].

2470-0010=2019=99(1)=014045(7) 014045-1 Published by the American Physical Society HUANG, HE, XIE, and GENG PHYS. REV. D 99, 014045 (2019)

High-energy kaon beams are available at OKA@U-70 [18] and SPS@CERN [19], which provide another alter- native to study charmed baryons. The kaon beam at J-PARC can also be upgraded to the energy region required in charmed baryon productions [20]. It is interesting to make a theoretical prediction about charmed baryon productions with kaon beams. With charged kaon beams, Λþ the Λcð2940Þ can be produced with a proton target, e.g., the FIG. 1. Feynman diagram for the mechanism of the c − − production in the K−p → D−Λþ reaction. We also show the K p → Ds Λcð2940Þ reaction. In such a reaction, the s s c channel is usually suppressed seriously because of the very definition of the kinematics (p1, p2, p3, and q) used in the large total energy [16,21,22]. The u-channel contribution is calculation. usually suppressed also and is more important at backward Λ ð2940Þ angles while the c is produced at forward angles mechanism of the Λc production. The Λc is produced by through the t channel [23]. Moreover, compared with the the exchange of a D meson. As discussed in the Intro- pion-induced Λcð2940Þ production, an additional ss¯ quark duction, other production mechanisms will be suppressed pair creation is needed in the kaon-induced production, so heavily and not considered in this work. the u channel will be further suppressed. Hence, the To observe the Λc in experiments, the subsequential − → −Λ ð2940Þ 0 K p Ds c reaction should be dominant with decay to D p shown in Fig. 2 will also be considered. The 0 þ þ the Born term through the t-channel D exchange, which Λcð2286Þ and Σcð2455Þ can also be produced from the makes the background very small. K− and proton interaction by exchanging a D meson and 0 þ In the kaon-induced process considered in the current decay to D p. Therefore, in this work, the Λcð2286Þ and ¯ þ work, the effect from the KN initial state interaction (ISI) Σcð2455Þ will be taken as the background of the Λc should be taken into account in order to make a more production. reliable prediction. Fortunately, there is plenty of experimental information about the K−p interaction in the A. Lagrangians energy region relevant to the Λcð2940Þ production [24–27]. The existing experimental data show that the cross section To compute the amplitudes of the diagrams shown in of the K−p scattering is of the order of 10 millibarns in the Figs. 1 and 2, we need the effective Lagrangian densities energy range relevant here, that is, 1000 times larger than for the relevant interaction vertices. The spin parity of the Λ the theoretical predictions about the Λcð2940Þ production c state was still not determined in experiments. The in Refs. [14,16,17], which are of the order of microbarns. theoretical studies suggested that possible assignments of P þ − Besides, recent theoretical studies also suggested that the spin parity of the Λc are J ¼ 1=2 and 1=2 [3–5,15].In interaction of a D meson with a nucleon is of the same this work, we will consider these two possibilities. For the order of magnitude as that of the KN interaction, i.e., tens ΛcpD and ΛcpD couplings, we take the Lagrangian of millibarns [28,29]. Hence, the DN final state interaction densities as used in Ref. [15], (FSI) should be considered in the subsequential decay of ¯ 0 the produced Λ ð2940Þ. L ¼ Λ γ þ ð Þ c ΛcpD igΛcpD c 5pD H:c:; 1 In this work, we will study the Λcð2940Þ production in the kaon-induced reaction in an effective Lagrangian ¯ μ 0 LΛ ¼ gΛ Λ γ pDμ þ H:c:; ð2Þ approach with the ISI and FSI effects taken into account. cpD cpD c

The invariant mass spectrum for the subsequential decay of P þ − − − 0 for the case J ¼ 1=2 , and the Λcð2940Þ in the K p → Ds Λcð2940Þ → Ds ðD pÞ reaction will be investigated as well. This paper is organized as follows. In Sec. II, we will present the theoretical formalism. In Sec. III, the numerical result of the kaon-induced Λcð2940Þ (we abbreviate it as Λc hereafter) production on a proton target will be given. In − − 0 Sec. IV, the invariant mass spectrum of the K p → Ds D p reaction will be presented, followed by discussions and conclusions in the last section.

II. THEORETICAL FORMALISM − 0 FIG. 2. Feynman diagram for the K p → DsD p reaction. We In Fig. 1, we illustrate the Feynman diagram for the also show the definition of the kinematics (p1, p2, p3, p4, and p5) − − t-channel K p → Ds Λc interaction, which is the dominant used in the calculation.

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¯ 0 L ¼ Λ þ ð Þ B. ISI and FSI ΛcpD gΛcpD cpD H:c:; 3 Following Ref. [36] the initial state interaction for the μ 0 − − L ¼ − Λ¯ γ γ þ ð Þ K p → K p reaction at high energies will be taken into ΛcpD gΛcpD c 5 pDμ H:c:; 4 account. The amplitude T K−p→K−p is written in terms of the for the case JP ¼ 1=2−. The coupling constants in the Pomeron and Reggeon exchanges [36] above Lagrangians were determined in Refs. [4,5] in a T − − ¼ þ þ þ þ ð Þ ¼ −0 54 ¼ K p→K p AP Af2 Aa2 Aω Aρ: 12 hadronic molecular picture with gΛcpD . , gΛcpD − 6 64 P ¼ 1 2 ¼ −0 97 ¼ 3 75 pffiffiffi . for J = and fΛcpD . , fΛcpD . for P þ When the center-of-mass energy s is large, the elastic J ¼ 1=2 − . K p scattering amplitude is a sum of the following terms, For the Λ pD, Λ pD, KD D, Σ ND, and Σ ND c c s c c vertices, we adopt the commonly employed Lagrangian α ð Þ−1 i s i t B ð Þ¼η KN KN ð Þ densities as follows [15,30,31], Ai s; t isCi exp t ; 13 s0 2 ¯ 0 LΛ ¼ igΛ Λ γ5pD þ H:c:; ð5Þ cpD cpD c where i ¼ P for Pomeron and f2, a2, ω, and ρ Reggeons. 2 The energy scale s0 ¼ 1 GeV . The coupling constants μ 0 L ¼ Λ¯ γ þ ð Þ KN Λ pD gΛ pD c pDμ H:c:; 6 Ci , the parameters of the Regge linear trajectories c c α ð Þ¼α ð0Þþα0 η [ i t i it], the signature factors( i), and the μ ¯ ¯ Bi used in Ref. [36] provide a rather good description L ¼ ig D ½D ∂μK − ð∂μD ÞKþH:c:; ð7Þ KN KDsD KDsD s s of the experimental data. The parameters determined in ¯ Ref. [36] are listed in Table I. LΣ ¼ − Σ γ5τ Σ þ ð Þ cND ig cNDN · cD H:c:; 8 The final state DN interaction can be described by the chiral unitary approach of Ref. [29]. We choose two μ πΣ L ¼ ¯ γ τ Σ þ ð Þ channels, Dp and c, to reproduce the position of the ΣcND gΣcND N μ · cD H:c:: 9 Λcð2595Þ resonance in isospin zero. Then, the amplitude T 0 → 0 can be obtained. We note that the other channels The coupling constants gΛ ¼ −13.98 and gΛ ¼ D p D p cpD cpD – ηΛ Ξ Ξ0 Λ −5 20 considered in Refs. [37 39], such as c, K c,K c,Ds , . are determined from the SU(4) invariant 0 and η Λc, play a negligible role in dynamically generating Lagrangians [5] in terms of gπNN ¼ 13.45 and gρNN ¼ the Λcð2595Þ state, and therefore are not considered here. 6.0. The coupling constants gΣ ¼ 2.69 and gΣ ¼ cND cND In the chiral unitary approach, the scattering amplitude in 3.0 [5]. The coupling constant g ¼ 5.0 can also be KDsD the Dp and πΣ coupled channels is given by determined using the SU(4) symmetry [30,32,33]. c − When evaluating the scattering amplitude of the K p → T ¼½1 − −1 ð Þ − VG V; 14 Ds Λc reaction, we need to include form factors because hadrons are not pointlike particles. We adopt here a where V is the chiral potential, and G is a diagonal matrix, common scheme used in many previous works [14,16], whose elements are loop functions of DN or πΣc, defined as 2 2 2 Λ − M ð Þ¼ D D ð Þ Z FD qD ;Mex 2 2 ; 10 4 Λ − q d q 1 2M D D G ¼ i i ; ð Þ ð2πÞ4 2 − 2 þ ϵ ð − Þ2 − 2 þ ϵ 15 q mi i p q Mi i for t-channel D meson exchange, and the form factor employed in Ref. [34], where m and M are the masses of the π or D (i ¼ 2) mesons and the baryons Σc or N (i ¼ 1), respectively. In the Λ4 above equation, p is the total incident momentum of the F ðq2 ;M Þ¼ B ; ð Þ B B B Λ4 þð 2 − 2 Þ2 11 B qB MB TABLE I. Parameters of Pomeron and Reggeon exchanges þ þ for the exchanged baryon, Λc, Λcð2286Þ or Σcð2455Þ . determined from elastic and total cross sections in Ref. [36]. Here the qð Þ and Mð Þ are the four momentum and the D ;B D ;B i η α ðtÞ CKN(mb) BKNðGeV−2Þ mass of the exchanged D meson (baryon), respectively. i i i i 1 081þð0 25 −2Þ In this work, we choose Λ ¼ Λ ¼ 3 GeV to minimize Pi . . GeV t 11.82 2.5 D B −0 861þ 0 548þð0 93 −2Þ the number of free parameters. This value is chosen in f2 . i . . GeV t 15.67 2.0 ρ −1.162−i 0.548þð0.93 GeV−2Þt 2.05 2.0 accordance with Refs. [15,35], and was employed in −2 ω −1.162−i 0.548þð0.93 GeV Þt 7.055 2.0 Refs. [14,16]. A variation of the cutoff will be made to −2 a2 −0.861þi 0.548þð0.93 GeV Þt 1.585 2.0 show the sensitivity of the results on the cutoff.

014045-3 HUANG, HE, XIE, and GENG PHYS. REV. D 99, 014045 (2019) external meson-baryon system. The loop function G can be (a) (b) regularized with dimensional regularization in terms of a subtraction constant, 2M m2 M2 − m2 þ s M2 G ¼ i a ðμÞþlog i þ i i log i i ð4πÞ2 i μ2 2s m2 pffiffiffi i Q ð sÞ pffiffiffi pffiffiffi þ ipffiffiffi ½logðs − ðM2 − m2Þþ2 sQ ð sÞÞ s i i i pffiffiffi pffiffiffi þ logðs þðM2 − m2Þþ2 sQ ð sÞÞ i i pffiffiffi i pffiffiffi − logð−s þðM2 − m2Þþ2 sQ ð sÞÞ i i i pffiffiffi pffiffiffi 2 2 − logð−s − ðM − m Þþ2 sQið sÞÞ ; ð16Þ − − i i FIG. 3. Total cross section σ for the K p → Ds Λc reaction as a p þ function of the beam momentum pK− for the J ¼ 1=2 case − where s ¼ E2 with E being the energy of the system in the (left) and the 1=2 case (right). center of mass frame, Q is the on shell momentum of the i Z particles in a certain channel, μ is the regularization scale, 1=2 i 2 2 M ¼ ⃗T − − ð Þ and a ðμÞ is the subtraction constant. With μ ¼ 1000 MeV, 2 d kt K p→K p s; kt i ISI 16π s aiðμÞ¼−2.02, and the potential V in Ref. [29], a rather M1=2 ð− − þ Þ ð Þ narrow state around 2596 MeV is dynamically generated, × B p2 kt q ; 19 which indicates that the Λcð2595Þ might be a DN bound state. The obtained scattering amplitude T 0 → 0 will be − − D p D p where kt is the momentum transfer in the K p → K p used to calculate the FSI in the subsequantial decay of the reaction. Λ − − c in the following section. In Fig. 3, the total cross section of the K p → Ds Λc reaction is shown as a function of the beam momentum. Because III. KAON-INDUCED Λc PRODUCTION ON the cutoff can not be well determined, the results obtained PROTON TARGET with several cutoffs other than 3 GeV are also presented. − The results show that the total cross section increases First, we calculate the total cross section of the K p → − sharply near the D Λ threshold. At higher energies, the Λ D reaction. The corresponding unpolarized differential s c c s cross section increases continuously but relatively slowly cross section reads compared with that near threshold. With the increase of the X dσ M MΛ jp⃗3 j 1 cutoff, the total cross section increases, and generally ¼ p c cm jM1=2 j2 ð Þ ; 17 speaking, the total cross section for 1=2þ is smaller than d cos θ 16πs jp⃗1cmj 2 sc;s2 that for 1=2−. At a beam momentum about 15 GeV the 2 10 μ where s ¼ðp1 þ p2Þ , θ is the scattering angle of the cross section is of the order of b, which is quite large − for an experimentally observation of the Λ at current and outgoing Ds meson relative to the beam direction, p⃗1cm and c − − future facilities. p⃗3cm are the K and Ds three momenta in the center of mass frame, Mp and MΛc are the masses of the proton and Λc, respectively. − Taking the ISI of the K p system into account, the full (a) (b) − amplitude for the process K p → ΛcDs is a sum of the Born and ISI amplitudes. With the Lagrangians given in the − previous section, the Born amplitude of the K ðp1Þpðp2Þ → ΛcðqÞDsðp3Þ reaction can be obtained as,

1=2 μ μν M ¼ ¯ð ÞΓ ð Þ ð Þ B gΛcpD u q; sc u p2;s2 GD qD ν ν 2 2 ð þ Þ ð Þ ð Þ × gKDsD p1 p3 FD qD ;MD ; 18 μ μ μ where Γ ¼ðγ ; −γ5γ Þ, and u¯ðq; scÞ and uðp2;s2Þ are the Dirac spinors with sc (q) and s2 (p2) being the spins (the four-momenta) of the outgoing Λc and the initial proton, respectively. FIG. 4. Total cross section σ with or without ISI for the K−p → − Following the strategy of Ref. [36], the ISI amplitude can Ds Λc reaction as a function of the beam momentum pK− for the be written as Jp ¼ 1=2þ case (left) and the 1=2− case (right).

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As shown in Refs. [15,40,41], the ISI for pp or pp¯ and the amplitudes for the Λcð2286Þ and the Σcð2455Þ can reactions reduces the cross section. In Fig. 4 we compare be obtained analogously. Here we take Γ ¼ 0 MeV for the the cross sections obtained with and without ISI for the Λcð2286Þ and the Σcð2455Þ states because of their small Λ ¼ 3 0 cutoff of . GeV. It shows that the role of the ISI is to decay widths. For the Λc, the width is taken to be Γ ¼ reduce the cross section by approximately 30%. 17 MeV according to BABAR, consistent with the one obtained by Belle [42]. − − 0 − 0 IV. THE K p → Ds D p REACTION Taking the ISI of the K p and FSI of the D N systems − − 0 0 into account, the amplitude of the K p → Ds D p reaction Since the Λc can not be observed directly, the D p can be written as channel of the Λc decay, which is the observation channel Λ of the c at BABAR, should be introduced to give a more M1=2 ð − → − 0 Þ Λ K p Ds D p realistic prediction for the observation of the c in experi- Z Λ 1 2 i ments. Here we consider the subsequential decay of the c ¼ M = ð Þþ 2 ⃗ − − 0 s 2 d kt after being produced in the K p → ΛcDs reaction, i.e., 16π s − − 0 the K p → Ds D p reaction, which is illustrated in Fig. 2. 2 1=2 T − − ð ÞM ð− − þ Þ The contributions from the Λcð2286Þ and the Σcð2455Þ will × K p→K p s; kt 0 p2 kt q be included as background. Being a two-to-three-body ð1 þ 0 T 0 0 Þ ð Þ process, the cross section can be obtained from the × GD p D p→D p : 23 amplitude as, With the formalism and ingredients given above, the − − 0 dσðK p → D D pÞ − s cross section as a function of the beam momentum pK for X the K−p → D−D0p reaction is calculated using a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMp − − 0 2 s ¼ jMðK p → Ds D pÞj 2 ð Þ2 − 2 2 Monte Carlo multiparticle phase space integration program, p1 · p2 MK− Mp si;sf FOWL, and crosschecked with direct integration with 3 3 3 Λ ¼ 3 0 ⃗ ⃗ M d p⃗5 Eq. (20). The theoretical results at a cutoff . GeV d p3 d p4 p δ4ð þ − − − Þ × p1 p2 p3 p4 p5 ; for the beam momentum pK− from near threshold up to 2E3 2E4 E5 16.5 GeV are shown in Fig. 5. The contributions from the ð Þ 20 Λcð2286Þ and the Λcð2455Þ are also presented in the same figure. where M − is the mass of the kaon, and E3, E4, and E5 K As in the Λ production, the total cross section of the Λ stand for the energy of the D−, D− and final proton, c c s for the JP ¼ 1=2− case is much larger than that for the respectively. 1=2þ case. The order of magnitude of the total cross section The amplitude MðK−p → D−D0pÞ can be obtained s is about 1 and 10 μb for positive and negative parities, with the Lagrangians given in Sec. II as, respectively. The background contribution from the 1 2þ = − − 0 Σcð2455Þ to the total cross section is much smaller than M0 ðK p → Ds D pÞ all the other contributions. The contribution from the Λc is gΛ gΛ g ¼ cpD cpD KDsD i 2 2 much larger than all the other contributions if the spin q − M þ iMΛ ΓΛ Λc c c 1 2 2 2 ð Þ ð Þð þ Þ × 2 2 FΛc q ;MΛc FD k ;MD p1μ p3μ k − M 0 D μ μ =kk ¯ð Þγ ð þ Þ γ − ð Þ × u p5;s5 5 =q MΛc 2 u p2;s2 ; MD ð21Þ 1=2− − − 0 M0 ðK p → Ds D pÞ fΛ fΛ g ¼ cpD cpD KDsD 2 2 q − M þ iMΛ ΓΛ Λc c c 1 2 2 2 × FΛ ðq ;MΛ ÞF ðk ;M Þðp1μ þ p3μÞ − − 0 2 2 c c D D FIG. 5. Total cross section σ for the K p → D D p reaction as k − M 0 s D P þ a function of the beam momentum pK− for J ¼ 1=2 (left) and μ − μ =kk JP ¼ 1=2 (right). The dashed, dotted, and dash-dotted curves × u¯ðp5;s5Þð=q þ MΛ Þγ5 γ − uðp2;s2Þ; c 2 Λ Λ ð2286Þ M stand for the contributions from the c, the c , and the D Σ ð2455Þ ð Þ c , respectively. The total contribution is shown by the 22 solid line.

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angle and decreases with the increase of the scattering angle. It can be seen more clearly at the differential cross sections as a function of the scattering angle at the invariant (a) (b) 0 ¼ 2 94 – mass MpD . GeV in Fig. 6(c) 6(f). − − 0 In Figs. 6(c) and 6(d), the results for the K p → Ds D p reaction at different kaon momenta pK− are presented. The results show that with the increase of the kaon momentum, the increase of the total cross section shown in Fig. 5 is mainly from the increase of the differential cross section at forward angles. − − 0 We also present the results of the K p → Ds D p reaction through Λc only in Figs. 6(e) and 6(f), which shows the effects of the background on the differential (c) cross sections as a function of the scattering angle is very (d) small. With the increase of the kaon momentum, more Λð2940Þ can be produced at forward angles. The results suggest that it is better to observe the Λc at forward angles especially at high energies.

V. SUMMARY (e) (f) − In this work, we studied the Λc production in the K p → − − − 0 Ds Λc and the K p → Ds D p reactions within the effective Lagrangian approach to investigate the possibility to produce the charmed baryon Λcð2940Þ with kaon beams on 2 σ Ω 0 a proton target. The t-channel D exchange was considered FIG. 6. Second order differential cross section d =d =dMD p − − 0 0 KN¯ for the K p → Ds D p reaction as a function of the pD to be the dominant production mechanism. The initial 0 θ invariant mass MD p (a and b), and the scattering angle cos state interaction(ISI) was included by Pomeron and (c, d, e, and f). The subfigures (a, c, and e) are for JP ¼ 1=2þ Reggeon exchanges [36], which was shown to reduce case, and the subfigures (b,d, and f) are for 1=2þ. The subfigures the cross section by about 30%. In addition, we have also (c and d) are for the cross section with background, and the considered the DN final state interaction (FSI) with the subfigures (e and f) are for the cross section without background. amplitudes provided by the chiral unitary approach [29]. The total cross section of the Λc production was found to − be at the order of 10 μb. After considering the subsequen- parity of the Λc is 1=2 , which makes the observation of the þ tial decay of the Λ in the D0p channel, we found a clear Λc easy. However, if the Λc carries a spin parity of 1=2 , c Λ 0 the total cross section from the Λ is much smaller and signal of the c in the D p invariant mass spectrum of the c − → − 0 comparable with the background contribution especially K p Ds D p reaction. Our study indicates that it is Λ ð2940Þ that from the Λcð2286Þ. feasible to produce the c with kaon beams on a To give more information about the Λc production in the proton target. − − 0 K p → Ds D p reaction, we present the second order 2 σ Ω 0 differential cross section d =d =dMD p as a function ACKNOWLEDGMENTS 0 of the pD invariant mass for pK− ¼ 16 GeV at several typical scattering angles, θ ¼ 0, π=6, π=3, and π=2,in This project is partially supported by the National Figs. 6(a) and 6(b) for positive and negative parities of the Natural Science Foundation of China (Grant Λ, respectively. An obvious peak can be found around the No. 11675228, No. 11522539, No. 11735003, and c No. 11475227), the Major State Basic Research invariant mass M 0 ¼ 2.94 GeV as expected. The differ- D p Development Program in China (No. 2014CB845405). ential cross section is the largest at the extreme forward

014045-6 PRODUCTION OF THE Λcð2940Þ BY KAON- … PHYS. REV. D 99, 014045 (2019)

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