LHCb pentaquarks in a constituent quark model Pablo G. Ortega ,D.R. - PowerPoint PPT Presentation

LHCb pentaquarks in a constituent quark model Pablo G. Ortega ,D.R. Entem, F. Fern´ andez

Outline Motivation 1 The model 2 Results 3 Conclusions 4

Outline Motivation 1 The model 2 Results 3 Conclusions 4 0 / 28 Motivation

Quark model 1 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

Discoveries at B -factories Exotic Mesons: X (3872), D s 0 (2317), Z c (3900), Z b (10600),. . . Exotic baryons: Λ c (2940), P c (4380), P c (4450),. . . Signals of exotic structures? Possibility to study the coupling with higher Fock spaces. Some of them may be naive q ¯ q or qqq structures. Others are more elusive: X (3872) ֌ 2 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

X (3872) state Quantum numbers compatible with J PC = 1 ++ Width : Γ < 1 . 2 (90% C.L.) Mass : M X = 3871 . 63 ± 0 . 19 MeV / c 2 ֌ Close to D 0 ¯ D ∗ 0 threshold: δ m = − 0 . 9 ± 0 . 34 MeV. � 1 . 0 ± 0 . 4 ± 0 . 3 (Belle) R 1 = B ( X → J /ψπ + π − π 0 ) = , B ( X → J /ψπ + π − ) 0 . 8 ± 0 . 3 (BaBar) � 0 . 33 ± 0 . 12 (BaBar) B ( X → J /ψγ ) R 2 = B ( X → J /ψπ + π − ) = , 0 . 14 ± 0 . 05 (Belle) R 3 = B ( X → ψ (2 S ) γ ) B ( X → J /ψγ ) ≤ 2 . 1 ( at 90% C . L . ) (Belle) . Experimental data suggest a weakly-bound D 0 D ∗ 0 molecule coupled to 2 P c ¯ c states. 3 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

Λ c (2940) + baryon Discovered in D 0 p and Σ c (2455) 0 , ++ π ± channels Mass: 2939 . 8 ± 1 . 3 ± 1 . 0 MeV / c 2 Width: 17 . 5 ± 5 . 2 ± 5 . 9 MeV (BaBar) Mass: 2938 . 0 ± 1 . 3 +2 . 0 Width: 13 +8 +27 − 5 − 7 MeV (Belle) − 4 . 0 MeV / c 2 D ∗ 0 p molecule in S -wave? ֌ Quantum numbers: 2 S +1 L J J P − 1 2 S 1 4 D 1 2 2 2 + 1 2 P 1 4 P 1 2 2 2 − 3 4 S 3 2 D 3 4 D 3 2 2 2 2 + 3 2 P 3 4 P 3 4 F 3 2 2 2 2 J P = 3 − ֌ Similar to X (3872) state 2 4 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

LHCb Pentaquarks: P c (4380) and P c (4450) R. Aaij et al, Phys. Rev. Lett. 115 , 072001 (2015). Discovered in 2015 in Λ 0 b → J /ψ K − p decay. ∓ , 5 ± ) Preferred quantum numbers: ( 3 2 2 − , 3 − ) But other combinations such as ( 3 2 2 not excluded ( L. Roca, arxiv:1602.06791 ) Masses close to D Σ ∗ c and D ∗ Σ c channel thresholds. M P c (4380) = 4380 ± 8 ± 29 MeV , M P c (4450) = 4449 . 8 ± 1 . 7 ± 2 . 5 MeV , Γ P c (4380) = 205 ± 18 ± 86 MeV , Γ P c (4450) = 39 ± 5 ± 19 MeV . 5 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

LHCb Resonances: X (4140) , X (4274) , X (4500) , X (4700) 6 / 28 Motivation Multiquarks, molecules and baryon and meson spectra

Outline Motivation 1 The model 2 Results 3 Conclusions 4 6 / 28 The model

Ingredients of constituent quark model The model includes: Spontaneous breaking of chiral symmetry ֌ Constituent mass and Pseudo-Goldstone bosons. C. D. Roberts, arxiv:1109.6325v1 [nucl-th] QCD perturbative effects ֌ Gluon exchange. Confinement ֌ Screened potential. 7 / 28 The model Constituent quark model

Constituent quark model Nucleon-Nucleon interaction: D. R. Entem, F. Fern´ andez, A. Valcarce, PRC62 , 034002 (2000). A. Valcarce, A. Faessler, F. Fern´ andez, PLB345 , 367 (1995). F. Fern´ andez, A. Valcarce, U. Straub, A. Faessler, JPG19 , 2013 (1993). Baryon spectra: A. Valcarce, H. Garcilazo, and J. Vijande, PRC72 , 025206 (2005). H. Garcilazo, A. Valcarce, F. Fern´ andez, PRC64 , 058201 (2001). Meson spectrum: J. Vijande, F. Fern´ andez y A. Valcarce, JPG31 , 481 (2005). J. Segovia, A. M. Yasser, D. R. Entem, F. Fern´ andez, PRD78 , 114033 (2008). J. Segovia, P. G. Ortega, D. R. Entem, F. Fern´ andez, PRD90 , 074027 (2016). 8 / 28 The model Constituent quark model

Solving the two body problem Meson wave function ֌ Gaussian Expansion Method: (2 η n ) l +3 / 2 p l e − p 2 p ) = � n max p ) φ nl ( p ) , with φ nl ( p ) = ( − i ) l N nl ψ lm ( � n =1 C nl Y lm (ˆ 4 η n GEM free parameters: { n max , r 1 , a } Rayleigh-Ritz variational principle: n ′ l + � n o chnl � V αα ′ nn ′ c α ′ � � n max ( T α nn ′ − EN α nn ′ ) c α = 0 n ′ l n ′ =1 α ′ Baryon wave functions ֌ Gaussian with scaled range. Resonating Group Method: Interaction at quark level ֌ Interaction between clusters Direct and exchange potentials: q 1 q 1 q 1 q 1 q 2 ¯ q 2 ¯ q 2 ¯ q 2 ¯ q 3 q 3 q 3 q 3 q 4 q 4 q 4 q 4 ¯ ¯ ¯ ¯ 9 / 28 The model Solving the two body problem

3 P 0 interaction Pair creation hamiltonian: A � d 3 x ¯ H = g ψ ( x ) ψ ( x ) q ¯ q B Non relativistic reduction: √ � C =1 , I =0 , S =1 , J =0 d 3 pd 3 p ′ δ (3) ( p + p ′ ) � � p − p ′ � 2 γ ′ � � b † µ ( p ) d † ν ( p ′ ) T = − 3 Y 1 µ 2 with γ ′ = 2 5 / 2 π 1 / 2 γ and γ = g 2 m Running of the 3 P 0 strength γ γ 0 γ ( µ ) = log( µ/µγ ) γ 0 = 0 . 81 ± 0 . 02 µγ = 49 . 84 ± 2 . 58 MeV Solid line is the fit Shaded area → 90% C.L. 3 P 0 Model 10 / 28 The model

Coupling between q ¯ q and q ¯ q − q ¯ q sectors Effect of q ¯ q on meson-meson states ֌ Molecular states Mixed states: | Ψ � = � α c α | ψ � + � β χ β ( P ) | φ M 1 φ M 2 β � Solving the coupling with the q ¯ q meson spectrum ֌ Schr¨ odinger-type equation: � � � � H M 1 M 2 ( P ′ , P ) + V eff β ′ β ( E ; P ′ , P ) χ β ( P ) P 2 dP = E χ β ′ ( P ′ ) β ′ β β with V eff β ′ β ( E ; P ′ , P ): q ¯ q A ′ A B ′ B 11 / 28 The model Coupled channel formalism

Coupling formalism with T matrix Resonances → Poles of the Scattering Matrix: α = 1 − 2 π i √ µ α µ α ′ k α k α ′ T α ′ S α ′ α ( E + i 0; k α ′ , k α ) T matrix obtained with Lippmann-Schwinger: T β ′ β ( E ; P ′ , P ) = V β ′ β dP ′′ P ′′ 2 V β ′ β ′′ E − E β ′′ ( P ′′ ) T β ′′ β ( E ; P ′′ , P ) ( P ′ , P ) + � ( P ′ , P ′′ ) 1 � T β ′′ T With V β ′ β ( P ′ , P ) = V β ′ β ( P ′ , P ) + V β ′ β eff ( P ′ , P ) T q ¯ q A ′ A where h β ′ α ( P ′ ) h αβ ( P ) V β ′ β B ′ eff ( P ′ , P ) = � B α E − M α The complete T matrix factorizes like V T : T β ′ β ( E ; P ′ , P ) = T β ′ β α,α ′ φ β ′ α ′ ( E ; P ′ )∆ α ′ α ( E ) − 1 ¯ ( E ; P ′ , P ) + � φ αβ ( E ; P ) V 12 / 28 The model Coupled channel formalism

Coupling elements From T β ′ β ( E ; P ′ , P ) = T β ′ β α,α ′ φ β ′ α ′ ( E ; P ′ )∆ α ′ α ( E ) − 1 ¯ φ αβ ( E ; P ) : ( E ; P ′ , P ) + � V Modified vertex: | AB > β | AB > β ′ | AB > β � T β ′ β ( E ; P , q ) h αβ ( q ) | q ¯ q > α | q ¯ q > α φ αβ ′ ( E ; P ) = h αβ ′ ( P ) − � q 2 dq , V β q 2 / 2 µ − E − � h αβ ′ ( q ) T β ′ β ( q , P , E ) q 2 dq φ αβ ( E ; P ) = h αβ ( P ) − � ¯ V β ′ q 2 / 2 µ − E � ( E − M α ) δ α ′ α + G α ′ α ( E ) � ∆ α ′ α ( E ) = Complete propagator: Exact mass-shift of the | AB > β | AB > β | AB > β ′ state: | q ¯ q > α | q ¯ q > α ′ | q ¯ q > α | q ¯ q > α ′ − dqq 2 φ αβ ( q , E ) h βα ′ ( q ) G α ′ α ( E ) = � � β q 2 / 2 µ − E 13 / 28 The model Coupled channel formalism

Outline Motivation 1 The model 2 Results 3 Conclusions 4 13 / 28 Results

Results for the X (3872) coupled calculation D 0 D ∗ 0 and D ± D ∗∓ molecular states are included c (2 3 P 1 ) meson state ֌ Theoretical bare Coupled to c ¯ mass= 3947 . 4 MeV Inclusion of J /ψρ y J /ψω channels, needed for describing the strong decays ֌ Rearrangement diagrams Small contribution to the mass The value of γ is fine-tuned to obtain the X (3872) experimental mass c (2 3 P 1 ) D 0 D ∗ 0 D ± D ∗∓ γ E bind c ¯ J /ψρ J /ψω 0 . 231 − 0 . 60 12 . 40 79 . 24 7 . 46 0 . 49 0 . 40 0 . 226 − 0 . 25 8 . 00 86 . 61 4 . 58 0 . 53 0 . 29 X (3872) 14 / 28 Results

X (3872) Decay results Results for strong decays Experimental results: � 1 . 0 ± 0 . 4 ± 0 . 3 R 1 = B ( X → J /ψπ + π − π 0 ) = B ( X → J /ψπ + π − ) 0 . 8 ± 0 . 3 Theoretical results: E bind (MeV) Γ π + π − J /ψ ( KeV ) Γ π + π − π 0 J /ψ ( KeV ) R 1 − 0 . 60 27 . 61 14 . 40 0 . 52 − 0 . 25 24 . 18 10 . 64 0 . 44 X (3872) 15 / 28 Results

X (3872) Decay results Results for radiative decays Experimental results: � 0 . 33 ± 0 . 12 B ( X → J /ψγ ) R 2 = B ( X → J /ψπ + π − ) = 0 . 14 ± 0 . 05 Theoretical results: Γ VMD Γ ANN R M Γ c ¯ c R c ¯ c E bind (MeV) R 2 2 2 J /ψγ J /ψγ J /ψγ 2 . 5 10 − 3 − 0 . 60 0 . 014 0 . 056 8 . 15 0 . 29 0 . 30 2 . 3 10 − 3 − 0 . 25 0 . 011 0 . 045 5 . 25 0 . 22 0 . 22 Table : Decays in KeV. Molecular component ֌ Vector Meson Dominance (VMD) mechanism and Annihilation (ANN). R M 2 is the ratio including only contributions from the molecular component, R c ¯ c only contributions from the c ¯ c component and R 2 is the complete result. 2 X (3872) 15 / 28 Results