PoS(ICHEP2016)704 http://pos.sissa.it/ , have been predicted . Moreover we have also calculated the masses of ) 2 ( ∗ b P Department of physics, Jogamaya Devi College, Kolkata, India. ∗ , ) 1 ( ∗ b P , ) 2 ( ∗ s P , ) 1 [email protected] ( ∗ s exotic for the charm and the bottom families constituting a heavy . Speaker. The masses of crypto exotic heavy pentaquarksconsisting have of been a probed considering and a a di-hadronicder state Waals’ type . of molecular The interaction interaction and betweenA we the have spin estimated the interaction is binding has assumed energies of to alsoP the be been states. Van considered. Masses of the crypto heavy pentaquarks such as ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 38th International Conference on High Energy3-10 Physics August 2016 Chicago, USA Ballari Chakrabarti Exploring the Masses of Exotic Heavy Pentaquarks E-mail: PoS(ICHEP2016)704 , 1 = − has ) = and C (2.2) (2.5) (2.3) (2.4) (2.1) ) ) K ( p r GeV − , 1 K 67 4380 . − ( Ψ 3 ∗ c ]for possible / P represents the 7 is the effective J GeV ) = C 7 BE s . Ballari Chakrabarti . → 1 ], Monemzadeh et E B 4 0 b ( 4 − r Λ ( , ) = 0 b 1 , Bicudo [ n GeV 2. Input values are − Λ ) ( ¯ / s r is the interaction potential , ]] 2 12 1 ) ) 977 β r r . − GeV 2 ( 12 5 ] for cryptoexotic pentaquarks − r cudd C , V 97 8 . ) is the radius of the di-hadronic − )( 4 GeV = ) = ¯ > 0 s 0 6 25 r ∆ . r ) β ( ( SD 2 ], Gignoux et al [ r 2 ) = 12 , θ E , / 3 r 2 ) = − cuud ], ( 1 / 2 12 p + 75 ( r 3 D . − ( 2 Ψ ) ( 10 2 r | C r BE ( ) 12 − , , r E e ) 12 GeV 1 r 1 − + 9 ( , − . represents the spin dependent term. The binding 12 representing the individual radii of the hadrons 0 2 mol 5 r 3 V r . k 1 | 2 is the wave function of the dihadronic state and is ( M 1 ) SD r 2 − ) [( GeV E / 12 + ) = 2 9 0 r 12 1 r ( Σ F r 63 and ( . 2 ( ) = π M [ 315 Ψ r 1 1 12 Ψ , r 64 = r 1 < mol ( , − k 0 = ) = = V Tot 2 r ϒ r 2 25 ( | M . ]. The works of Lipkin [ BE ) r GeV 2 + 2 E , 12 ] which is expressed as 1 82 r r 9 1 = . ( − 3 ]. The radii considered are = Ψ BE | ] recently. The intermediate states have been identified as 0 10 E 1 r ) = GeV o is the usual step function. Employing the additive rule for the radii of 0 . B 65 [ . ) ( 5 r 0 12 ] in the context of the exotic doublets , represent the masses of the constituent hadrons respectively, r 6 1 = ) = 2 is the relevant hypergeometric function and − − Φ 2 M 0 mol ( F r r k 2 ( GeV , ] is the residual strength of the strong interaction molecular coupling and θ 8 and 1 is the radius parameter of the di-hadronic and 0 , . . New impetus has been put forward to the study of the properties and dynamics of the − 11 1 4 ) [ 12 mol > M r k β The existence of charmonium states with the decay of In the present work exotic heavy pentaquarks have been described as di-hadronic ) = ], Diakonov [ GeV s 4450 5 ( MeV Re D 77 ∗ . c ( taken as Van der Waals’ type [ where 50 r constituting the molecule, we(2.4), have which executed yields the binding energy using equations (2.2),(2.3) and if energy can be expressed as where corresponding to the linearmolecule, type of background potential. 4 constituent hadrons i.e. binding energy of the di-hadronic system and color screening of the confinedassumed . to be in the context of the statistical model as [ consisting of a meson and aThe baryon mass held formula together for by the Van low-lying der di-hadronic Waals’ type molecule of is molecular taken interaction. as Exploring the Masses of Exotic Heavy Pentaquarks 1. Introduction been reported by LHCb [ P al [ crypto heptaquark hadrons with exoticwith flavors, hidden Kopeliovich beauty et are al noteworthy. [ 2. Methodology where multiquark states by Jaffe et al [ PoS(ICHEP2016)704 ϒ is 2 | (2.6) ) 0 ( Ψ | as - 2 for heavier . + ) 2 Ballari Chakrabarti / 3 ( ∗ b have been assumed to P + ) 6.351 [3] 5.752 [5] Others Mass (GeV) 2.303 [8] 2.373 [8] 10.743 [8] 10.813 [8] 2.650 [6] 2.710 [3] 2.870[3] 3.135[3] 2.427[5] 6.050 [3] 6.210 [3] 2 and / 3 + ( ) ∗ s 2 P 005 / . 1 0 ( 2 ∗ b ] is available but that is not confirmed | and ± ) P 0 + 13 ( 59 for light hadrons and 0 [ ) . have also been calculated and have been 003 2 0 c . 0 Ψ | / 0 + b Θ 2 1 = Ξ ( S ± . ∗ s , s 1 P α 0 0 state and S 099 Ξ 2 are the spins of the hadrons involved. 2 . Φ , s — — Expt. Mass (GeV) — — — — 3 [13] — — — — — — 2 M 1 α S + − b 8 M N ∆ , 9 and 0 c = 1 N S , SD + bs E Masses of cryptoexotic heavy pentaquarks Θ state and , 6.043 6.067 6.127 6.366 6.128 10.639 10.881 2.656 2.670 2.752 2.905 2.751 Mass (GeV) 2.110 2.381 Φ ++ cs 0 Θ s Table 1: − 0 0 , 0 B D 0 s s + ¯ ¯ ¯ ϒ Φ B B B ϒ D D D Φ B D + b + + + + + + + + + + + + Θ + + + + , p p p p p p p p n Σ ∆ n Σ Approach ∆ 0 c has been estimated subsequently. Θ state respectively. Based on this formulation several cryptoexotic heavy pentaquark + + + + ) ) ) ) ) ) ) ) ) ) ) ) ) ϒ ¯ ) ¯ SD ¯ ¯ ¯ b c ¯ ¯ s b ¯ 2 2 2 2 s b s c ¯ ¯ b c E / / / / − 1 3 1 3 ] ∆ ( ( ( ( + bs ++ cs + b 0 c + 0 0 c + b b c ∗ ∗ ∗ ∗ s s b b uudb uudd uuds uuss uuss uudc uudb uudd uuds uuds 12 Θ ( ( N ( Ξ ( Ξ ( Θ ( Θ ( Θ ( N ( P P ( P P We have investigated several cryptoexotic pentaquark systems as hadronic composites of a The spin hyperfine interaction can be expressed as, is the strong interaction constant, s the di-hadronic wave function atsector the [ origin. With have configuration as proton- state and masses such as meson and a baryon. Our resultsexperiments wherever are available. in Experimental good mass agreement of with the other theoretical works as well as displayed in the Table I along with the comparison with others. 3. Conclusion α Exploring the Masses of Exotic Heavy Pentaquarks PoS(ICHEP2016)704 39 (2015) (2006) , 6 80 B 588 (1987) 484. , B195 Ballari Chakrabarti Pramana J. Phys. , J. Mod. Phys. (1987) 323. Ind. J. Phys. (2009) 025103. , , 79 , [hep-ph/1003.2157]. Phys. Lett. , (2003) 232003; M. Karlinar et B 193 (2003) 249. 91 B 575 Phys. Scr. , Phys. Lett. , ]. We want to explore the properties of (1991) 168. as di-hadronic states 15 ) Phys. Lett. Phys. Rev. Lett. , 200 p resonances consistent with pentaquark states in , Ψ 4450 / ( 3 ∗ c as 4168 MeV and 4491 MeV describing these as ) and P Phys. Rep. ) , 4450 (2015) 072001. ( ∗ c Search for a strongly decaying neutral charmed pentaquark Phys. 4380 P ( 115 ∗ c Observations of J and Evidence for a narrow anti-charmed baryon state Phys. Lett. ) Effect of the confined gluons in quark-quark interaction Calculating masses of pentaquarks composed of and 4380 Simple estimates of the masses of pentaquarks with hidden beauty or On some properties of di-hadronic states ( di-hadronic states respectively [ ∗ c Possibility of stable multiquark baryons P Diquarks and exotic spectroscopy Ψ Phys. Rev. Lett. Bound states of Low-lying di-hadronic states in relativistic harmonic model The masses of P / , p J Prediction of new charmed and bottom exotic pentaquarks New possibilities for exotic hadrons anticharmed baryons − (2005) 229. + , [hep-ph/1510.05958]. K Exotic pentaquarks, crypto-heptaquarks and linear three hadronic molecules ∆ Ψ / J B 622 and ]. We hope that this ambiguity could be understood in near future experiments. In this → A -triquark model for the KN pentaquark Ψ 0 b 14 / [hep-ph/1601.00642]. strangeness [hep-ph/0410097]. (1992) 47. 387. (2004) 17. Lett. 2070. Λ al., Author is thankful to University Grants Commission, New Delhi for financial assistance. J + [3] H. J. Lipkin, [4] C. Gignoux et al., [6] D. Diakonov, [1] R. Aaij et al. (LHCb Collab.), [2] R. L. Jaffe et al., [5] M. Monemzadeh et al., [7] P. Bicudo, [8] V. Kopeliovich et al., [9] P. C. Vinodkumar et al., p References other exotic pentaquark families .be Although looked the for production at rates are LHC,inspire probably Fermilab, the very future B-factories, low, experiments. RHIC these can etc. The predictions made in this4. work Acknowledgement may Exploring the Masses of Exotic Heavy Pentaquarks later [ context it may be pertinent toof state that recently in our reported previous work we have already estimated the masses [10] B. Chakrabarti et al., [11] A. K. Rai et al., [12] W. Lucha et al., [13] A. Aktas et al. (H1 Collab.), [14] J. M. Link et al. (FOCUS Collab.) [15] R. Ghosh et al.,