Studies of the X(3872) as a mixed molecule-charmonium state in QCD - PowerPoint PPT Presentation

Studies of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules Carina M. Zanetti Universidade de São Paulo, Brazil XIV Hadron Spectroscopy 13-17/06/2011 - München, Germany

The X(3872) State ✦ 2003 @ B + → X ( 3872 ) K + → J / !" + " − K + ✦ Confirmation: M X = ( 3871 . 20 ± 0 . 39 ) MeV ! < 2 . 3MeV

X(3872) in the Quark model Favored quantum 1 ++ (angular distribution 2 pions + γ J / ψ ) PC numbers J : (3 pion distrib. BaBar, but incompatible w/ 2 − + other properties) CQM predictions for 2 3 P 1 ( 3990 ) 3 3 P 1 ( 4290 ) charmonium states 1 ⁺⁺ Barnes & Godfrey PRD69 (2004) Strong isospin violation: ! ( X → J / "# + # − # 0 ) ! ( X → J / "# + # − ) = 1 . 0 ± 0 . 4 ± 0 . 3 Not a c-cbar state!

X(3872) in the Quark model Favored quantum 1 ++ (angular distribution 2 pions + γ J / ψ ) PC numbers J : (3 pion distrib. BaBar, but incompatible w/ 2 − + other properties) CQM predictions for 2 3 P 1 ( 3990 ) 3 3 P 1 ( 4290 ) charmonium states 1 ⁺⁺ Barnes & Godfrey PRD69 (2004) Strong isospin violation: ! ( X → J / "# + # − # 0 ) ! ( X → J / "# + # − ) = 1 . 0 ± 0 . 4 ± 0 . 3 Large phase space Gamermann, Oset (2009) Not a c-cbar state!

X(3872) quark structure Four-quark states: M ( D ∗ 0 D 0 ) = ( 3871 . 81 ± 0 . 36 ) MeV Close & Page (2004) Molecule with small biding energy Swanson(2006) Tetraquark Maiani et al (2005)

Problems with the molecular picture B ( X → ! ( 2 S ) " ) = 3 . 4 ± 1 . 4 B ( X → !" ) Radiative decays: Swanson (2004) ! ( X → " ( 2 S ) # ) ∼ 4 × 10 − 3 ! ( X → "# ) Production cross section of a bound DD* state with biding energy as small as 0.25 MeV is much smaller than the cross section obtained from the CDF data C. Bignamini et al (2009) Evidences of a charmonium component.

Objectives: ✦ Study the X(3872) as a mixed molecule- charmonium state in QCD Sum Rules ✦ Extraction of observables: mass, decay widths and production in B decays.

QCD Sum Rules Fundamental assumption: Principal of duality Equivalence of quark and hadron description Phenomenological side: Theoretical side (OPE): Determination of Masses, couplings, form factors

QCD Sum Rules s ₀ - continuum threshold Improving the matching: ! ( Q 2 ) → ! ( M 2 ) Borel transform M - Borel Mass 1 ) Pole > Continuum; Constrains on the 2 ) OPE Convergence; parameters M and s ₀ 3 ) Stability of the Borel Mass M

X(3872) in QCD Sum Rules R.D. Matheus, S. Narison, Tetraquark M X = ( 3 . 92 ± 0 . 13 ) GeV M. Nielsen and J.-M. Richard, PRD75 (2007) S.H. Lee, M. Nielsen and U. Wiedner, Molecule M X = ( 3 . 87 ± 0 . 07 ) GeV arXiv:0803.1168 Widths: Navarra, Nielsen, PLB639 (02) 272 Narison, Navarra, Nielsen, PRD 83 (2011) 016004

The mixed 2q+4q current µ ( x ) = sin ( ! ) j ( 4 q ) ( x )+ cos ( ! ) j ( 2 q ) J q Sugiyama et ( x ) µ µ al PRD (2007) D(0)D*(0) molecule (q=u,d): � � j ( 4 q ) 1 ( x ) = ( ¯ q a ( x ) ! 5 c a ( x ))( ¯ c b ( x ) ! µ q b ( x )) − ( ¯ q a ( x ) ! µ c a ( x ))) ¯ c b ( x ) ! 5 u b ( x )) µ √ 2 Charmonium 1 ⁺⁺ : 1 j ( 2 q ) ( x ) = 2 � q ¯ q � ( ¯ c a ( x ) ! µ ! 5 c a ( x )) √ 6

The mass of the mixed state 5 ◦ ≤ ! ≤ 13 ◦ 2 . 6GeV 2 ≤ M 2 ≤ 3 . 0GeV 2 m X = ( 3 . 77 ± 0 . 18 ) GeV Matheus, Navarra, Nielsen & CMZ, PRD 80 (2009) 056002

Decays of the X(3872) F = " + " − ( " + " − " 0 ) → V = # , $ X → J / ! V → J / ! F , V q, � ν ( q ) i M = � ψ ( p � ) V ( q ) | X ( p ) � = g X ψ V ε αβδγ p α � β ( p ) � ∗ δ ( p � ) � ∗ g XψV X γ ( q ) p = p � + q p, � α ( p ) J/ψ p � , � µ ( p � ) Narrow width approximation: p ( s ) ds ( X → J / " f ) = B V → F ! V m V d ! V ) 2 +( m V ! V ) 2 | M | 2 8 # m 2 ( s − m 2 # X � 2 ! ( X → J / "# + # − # 0 ) � g X "$ ! ( X → J / "# + # − ) = 0 . 118 g X "% g X ! V ➔ QCDSR for the vertex X J / ! V

Decays of the X(3872) F = " + " − ( " + " − " 0 ) → V = # , $ X → J / ! V → J / ! F , V q, � ν ( q ) i M = � ψ ( p � ) V ( q ) | X ( p ) � = g X ψ V ε αβδγ p α � β ( p ) � ∗ δ ( p � ) � ∗ g XψV X γ ( q ) p = p � + q p, � α ( p ) J/ψ p � , � µ ( p � ) Narrow width approximation: p ( s ) ds ( X → J / " f ) = B V → F ! V m V d ! V ) 2 +( m V ! V ) 2 | M | 2 8 # m 2 ( s − m 2 # X

Decays of the X(3872) F = " + " − ( " + " − " 0 ) → V = # , $ X → J / ! V → J / ! F , V q, � ν ( q ) i M = � ψ ( p � ) V ( q ) | X ( p ) � = g X ψ V ε αβδγ p α � β ( p ) � ∗ δ ( p � ) � ∗ g XψV X γ ( q ) p = p � + q p, � α ( p ) J/ψ p � , � µ ( p � ) Narrow width approximation: p ( s ) ds ( X → J / " f ) = B V → F ! V m V d ! V ) 2 +( m V ! V ) 2 | M | 2 8 # m 2 ( s − m 2 # X ! ( X → J / "# + # − # 0 ) ! ( X → J / "# + # − ) = 1 . 0 ± 0 . 4 ± 0 . 3

Sum Rules for the vertex X J / ! V ✦ Three-point function: ✦ Currents: ✦ Sum Rule: ✦

Mixed State [ ] ( cc ) + ( D ∗ 0 ¯ D ∗ 0 D 0 )+ ( D ∗ + ¯ D 0 − ¯ D − − ¯ D ∗− D + ) OPE: ! ( X → J / "# + # − # 0 ) ! ( X → J / "# + # − ) = 1 . 0 ± 0 . 4 ± 0 . 3

Result for the width g X !" = g X !" ( − m 2 " ) = 5 . 4 ± 2 . 4 X → J / "# + # − # 0 � � = ( 9 . 3 ± 6 . 9 ) MeV ! 5 ◦ ≤ ! ≤ 13 ◦ ; " = 20 ◦

Radiative decay J / ψ c c c X q γ q Matrix element describing the radiative decay : ! ( q ) q ' X ( p ) # µ " ( p � ) # & M ( X ( p ) → ! ( q ) J / " ( p � )) = e # $%&' # ( ( Ag µ % g ($ p · q + Bg µ % p $ q ( + Cg ($ p % q µ ) m 2 X Nielsen, CMZ, PRD 82 (2010)116002

Radiative decay J / ψ c c c X q γ q Matrix element describing the radiative decay : ! ( q ) q ' X ( p ) # µ " ( p � ) # & M ( X ( p ) → ! ( q ) J / " ( p � )) = e # $%&' # ( ( Ag µ % g ($ p · q + Bg µ % p $ q ( + Cg ($ p % q µ ) m 2 X Nielsen, CMZ, PRD 82 (2010)116002

Radiative decay J / ψ c c c X q γ q Matrix element describing the radiative decay : ! ( q ) q ' X ( p ) # µ " ( p � ) # & M ( X ( p ) → ! ( q ) J / " ( p � )) = e # $%&' # ( ( Ag µ % g ($ p · q + Bg µ % p $ q ( + Cg ($ p % q µ ) m 2 X A, B, C: Three couplings to be determined by the Sum Rules for the vertex X J/ ψ γ Nielsen, CMZ, PRD 82 (2010)116002

Radiative decay QCD SUM RULES FOR THE VERTEX X J/ ψ γ : ✦ Three-point function: R d 4 x d 4 y e ip � · x e iq · y � 0 | T [ j $ µ ( x ) j % " ( y ) j † ! µ "# ( p , p � , q ) = X ( 0 )] | 0 � j ! µ = ¯ c a " µ c a j X µ ( x ) = cos ! J u µ ( x )+ sin ! J d µ ( x ) µ ( x ) = sin ! j ( 4 q ) ( x )+ cos ! j ( 2 q ) J q j " 3 ¯ ( x ) # = 2 u " # u − 1 d " # d + 2 3 ¯ 3 ¯ c " # c µ µ ✦ Phenomenological input: � ! ( p � ) | j " # ( q ) | X ( p ) � = i $ " # ( q ) M ( X ( p ) → " ( q ) J / ! ( p � ))

QCDSR Results: The couplings A ( Q 2 ) = A 1 e − A 2 Q 2 A ( Q 2 = 0 ) = 18 . 65 ± 0 . 94; A = ( A + B )( Q 2 = 0 ) = − 0 . 24 ± 0 . 11; A + B = C ( Q 2 = 0 ) = − 0 . 843 ± 0 . 008 . C = 5 ◦ ≤ ! ≤ 13 ◦ ; " = 20 ◦ (Same angles)

QCDSR Results: The decay width p ∗ 5 ( A + B ) 2 + m 2 � � $ X ( A + C ) 2 ! ( X → J / " # ) = , m 4 m 2 3 " X ( m 2 X − m 2 p ∗ = " ) / ( 2 m X ) ! ( X → J / " # ) ! ( X → J / " $ + $ − ) = 0 . 19 ± 0 . 13 ! ( X → J / " # ) ! ( X → J / " $ + $ − ) Exp . = 0 . 14 ± 0 . 05

QCDSR Results: The decay width p ∗ 5 ( A + B ) 2 + m 2 � � $ X ( A + C ) 2 ! ( X → J / " # ) = , m 4 m 2 3 " X ( m 2 X − m 2 p ∗ = " ) / ( 2 m X ) ! ( X → J / " # ) ! ( X → J / " $ + $ − ) = 0 . 19 ± 0 . 13 ! ( X → J / " # ) ! ( X → J / " $ + $ − ) Exp . = 0 . 14 ± 0 . 05

QCDSR Results: The decay width p ∗ 5 ( A + B ) 2 + m 2 � � $ X ( A + C ) 2 ! ( X → J / " # ) = , m 4 m 2 3 " X ( m 2 X − m 2 p ∗ = " ) / ( 2 m X ) ! ( X → J / " # ) ! ( X → J / " $ + $ − ) = 0 . 19 ± 0 . 13 ! ( X → J / " # ) ! ( X → J / " $ + $ − ) Exp . = 0 . 14 ± 0 . 05

Production in B decays Contributions from interactions with de charmonium and molecule components of the X(3872) mixed current c D * b c W D B s u K CMZ, Matheus, Nielsen, arXiv:1105.1343

Production in B decays Effective theory of B meson weak decays + factorization hypothesis gives the matrix element: X q B p O 2 p’ K

Production in B decays Effective theory of B meson weak decays + factorization hypothesis gives the matrix element: X q B p O 2 p’ K

Production in B decays Effective theory of B meson weak decays + factorization hypothesis gives the matrix element: X q B p O 2 p’ K

Production in B decays Effective theory of B meson weak decays + factorization hypothesis gives the matrix element: X q B p O 2 p’ K

Production in B decays Effective theory of B meson weak decays + factorization hypothesis gives the matrix element: X q To be determined by B p O 2 p’ K QCDSR

Two point correlator