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

✦ 2003 @ ✦ Confirmation:

The X(3872) State

B+ → X(3872)K+ → J/!"+"−K+

MX = (3871.20±0.39)MeV

! < 2.3MeV

Favored quantum numbers J : CQM predictions for charmonium states 1⁺⁺ Strong isospin violation:

X(3872) in the Quark model

2−+ 1++

(3 pion distrib. BaBar, but incompatible w/

• ther properties)

23P1(3990) 33P1(4290)

Barnes & Godfrey PRD69 (2004)

!(X→J/"#+#−#0) !(X→J/"#+#−) = 1.0±0.4±0.3 (angular distribution 2 pions + γ J/ψ)

Not a c-cbar state!

PC

Favored quantum numbers J : CQM predictions for charmonium states 1⁺⁺ Strong isospin violation:

X(3872) in the Quark model

2−+ 1++

(3 pion distrib. BaBar, but incompatible w/

• ther properties)

23P1(3990) 33P1(4290)

Barnes & Godfrey PRD69 (2004)

!(X→J/"#+#−#0) !(X→J/"#+#−) = 1.0±0.4±0.3 (angular distribution 2 pions + γ J/ψ)

Not a c-cbar state!

Large phase space Gamermann, Oset (2009) PC

X(3872) quark structure

M(D∗0D0) = (3871.81±0.36)MeV

Close & Page (2004) Swanson(2006) Maiani et al (2005)

Molecule with small biding energy Tetraquark Four-quark states:

Problems with the molecular picture

Radiative decays: 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

B(X→!(2S)") B(X→!")

= 3.4±1.4

!(X→"(2S)#) !(X→"#)

∼ 4×10−3

Swanson (2004)

• C. Bignamini et al (2009)

Evidences of a charmonium component.

✦ 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.

Objectives:

QCD Sum Rules

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

Constrains on the parameters M and s₀

s₀ - continuum threshold

!(Q2) → !(M2)

QCD Sum Rules

M - Borel Mass

Improving the matching: Borel transform

1) Pole > Continuum; 2) OPE Convergence; 3) Stability of the Borel Mass M

X(3872) in QCD Sum Rules

MX = (3.92±0.13)GeV MX = (3.87±0.07)GeV

Tetraquark

R.D. Matheus, S. Narison,

• M. Nielsen and J.-M. Richard,

PRD75 (2007)

Molecule

S.H. Lee, M. Nielsen and U. Wiedner, arXiv:0803.1168

Navarra, Nielsen, PLB639 (02) 272 Narison, Navarra, Nielsen, PRD 83 (2011) 016004

Widths:

The mixed 2q+4q current

Jq

µ(x) = sin(!)j(4q) µ

(x)+cos(!)j(2q)

µ

(x)

Charmonium 1⁺⁺:

j(2q)(x) =

1 6 √ 2q ¯

q(¯ ca(x)!µ!5ca(x))

j(4q)

µ

(x) =

1 √ 2

• ( ¯

qa(x)!5ca(x))(¯ cb(x)!µqb(x)) −(¯ qa(x)!µca(x)))¯ cb(x)!5ub(x))

• D(0)D*(0) molecule (q=u,d):

Sugiyama et al PRD (2007)

The mass of the mixed state

mX = (3.77±0.18)GeV 2.6GeV2 ≤ M2 ≤ 3.0GeV2

5◦ ≤ ! ≤ 13◦

Matheus, Navarra, Nielsen & CMZ, PRD 80 (2009) 056002

Narrow width approximation:

Decays of the X(3872)

X → J/!V → J/!F , F = "+"−("+"−"0) → V = #,$

d! ds (X → J/"f) = BV→F 8#m2

X

!V mV # p(s) (s−m2

V )2+(mV !V )2 |M |2

gX!V

➔ QCDSR for the vertex X J/!V

!(X→J/"#+#−#0) !(X→J/"#+#−) = 0.118

gX"$

gX"%

2

X

p, α(p) p, µ(p) q, ν(q)

V J/ψ

iM = ψ(p)V(q)|X(p) = gXψV εαβδγ pα β(p) ∗

δ(p) ∗ γ(q) gXψV

p = p + q

Narrow width approximation:

Decays of the X(3872)

X → J/!V → J/!F , F = "+"−("+"−"0) → V = #,$

d! ds (X → J/"f) = BV→F 8#m2

X

!V mV # p(s) (s−m2

V )2+(mV !V )2 |M |2

X

p, α(p) p, µ(p) q, ν(q)

V J/ψ

iM = ψ(p)V(q)|X(p) = gXψV εαβδγ pα β(p) ∗

δ(p) ∗ γ(q) gXψV

p = p + q

Narrow width approximation:

Decays of the X(3872)

X → J/!V → J/!F , F = "+"−("+"−"0) → V = #,$

d! ds (X → J/"f) = BV→F 8#m2

X

!V mV # p(s) (s−m2

V )2+(mV !V )2 |M |2

!(X→J/"#+#−#0) !(X→J/"#+#−) = 1.0± 0.4± 0.3

X

p, α(p) p, µ(p) q, ν(q)

V J/ψ

iM = ψ(p)V(q)|X(p) = gXψV εαβδγ pα β(p) ∗

δ(p) ∗ γ(q) gXψV

p = p + q

Sum Rules for the vertex

✦ Three-point function: ✦ Currents: ✦ Sum Rule: ✦

X J/!V

Mixed State

OPE:

(cc) + (D∗0 ¯ D0 − ¯ D∗0D0)+ (D∗+ ¯ D− − ¯ D∗−D+)

!(X→J/"#+#−#0) !(X→J/"#+#−) = 1.0±0.4±0.3

[ ]

Result for the width

gX!" = gX!"(−m2

") = 5.4±2.4

!

• X → J/"#+#−#0

= (9.3±6.9) MeV

5◦ ≤ ! ≤ 13◦; " = 20◦

Radiative decay

M (X(p) → !(q)J/"(p)) = e#$%&'#(

X(p)#µ "(p)#& ! (q) q'

m2

X

(Agµ%g($p·q+Bgµ%p$q( +Cg($p%qµ)

Matrix element describing the radiative decay :

X J/ψ γ c c q q c

Nielsen, CMZ, PRD 82 (2010)116002

Radiative decay

M (X(p) → !(q)J/"(p)) = e#$%&'#(

X(p)#µ "(p)#& ! (q) q'

m2

X

(Agµ%g($p·q+Bgµ%p$q( +Cg($p%qµ)

Matrix element describing the radiative decay :

X J/ψ γ c c q q c

Nielsen, CMZ, PRD 82 (2010)116002

A, B, C: Three couplings to be determined by the Sum Rules for the vertex X J/ψ γ

Radiative decay

M (X(p) → !(q)J/"(p)) = e#$%&'#(

X(p)#µ "(p)#& ! (q) q'

m2

X

(Agµ%g($p·q+Bgµ%p$q( +Cg($p%qµ)

Matrix element describing the radiative decay :

X J/ψ γ c c q q c

Nielsen, CMZ, PRD 82 (2010)116002

✦ Three-point function: ✦ Phenomenological input:

Radiative decay

!µ"#(p, p,q) =

R d4x d4y eip·xeiq·y0|T[j$

µ (x)j% "(y)j†

X (0)]|0

QCD SUM RULES FOR THE VERTEX X J/ψ γ:

!(p)|j"

#(q)|X(p) = i$" #(q)M (X(p) → "(q)J/!(p))

Jq

µ(x) = sin!j(4q) µ

(x)+cos!j(2q)

µ

(x)

jX

µ (x) = cos!Ju µ(x)+sin!Jd µ(x)

j!

µ = ¯

ca"µca j"

# = 2 3 ¯

u"#u− 1

3 ¯

d"#d + 2

3 ¯

c"#c

QCDSR Results:

A = A(Q2 = 0) = 18.65±0.94; A+B = (A+B)(Q2 = 0) = −0.24±0.11; C = C(Q2 = 0) = −0.843±0.008.

5◦ ≤ ! ≤ 13◦; " = 20◦

The couplings

(Same angles)

A(Q2) = A1e−A2Q2

QCDSR Results: The decay width

!(X → J/" #) = $ 3 p∗5 m4

X

• (A+B)2 + m2

X

m2

"

(A+C)2

• ,

p∗ = (m2

X −m2 ")/(2mX)

!(X→J/" #) !(X→J/" $+$−) = 0.19±0.13

!(X→J/" #) !(X→J/" $+$−) Exp. = 0.14±0.05

QCDSR Results: The decay width

!(X → J/" #) = $ 3 p∗5 m4

X

• (A+B)2 + m2

X

m2

"

(A+C)2

• ,

p∗ = (m2

X −m2 ")/(2mX)

!(X→J/" #) !(X→J/" $+$−) = 0.19±0.13

!(X→J/" #) !(X→J/" $+$−) Exp. = 0.14±0.05

QCDSR Results: The decay width

!(X → J/" #) = $ 3 p∗5 m4

X

• (A+B)2 + m2

X

m2

"

(A+C)2

• ,

p∗ = (m2

X −m2 ")/(2mX)

!(X→J/" #) !(X→J/" $+$−) = 0.19±0.13

!(X→J/" #) !(X→J/" $+$−) Exp. = 0.14±0.05

K B b c D* D c s u W

Production in B decays

Contributions from interactions with de charmonium and molecule components of the X(3872) mixed current

CMZ, Matheus, Nielsen, arXiv:1105.1343

Production in B decays

Effective theory of B meson weak decays + factorization hypothesis gives the matrix element:

B K X p q p’ O2

Production in B decays

Effective theory of B meson weak decays + factorization hypothesis gives the matrix element:

B K X p q p’ O2

Production in B decays

Effective theory of B meson weak decays + factorization hypothesis gives the matrix element:

B K X p q p’ O2

Production in B decays

Effective theory of B meson weak decays + factorization hypothesis gives the matrix element:

B K X p q p’ O2

Production in B decays

Effective theory of B meson weak decays + factorization hypothesis gives the matrix element:

B K X p q p’ O2

To be determined by QCDSR

Two point correlator

Three point correlator

Currents Phenomenological side:

Form factor

f

20 25 30 35 40 M 2 GeV2 2.0 2.5 3.0 3.5 4.0 Q 2 GeV2 0.10 0.15 0.20

• 1

2 3 4 0.155 0.16 0.165 0.17 0.175 Q 2 GeV2 f Q 2

Branching ratio

Using the results of the two sum rules

Conclusions

✦ QCD Sum Rules calculations for the X(3872)

as a mixed state of molecule and charmonium

✦ Mass, decay widths and production calculated

are compatible using the mixing angles

(cc) + (D∗0 ¯ D0 − ¯ D∗0D0)+ (D∗+ ¯ D− − ¯ D∗−D+)

5◦ ≤ ! ≤ 13◦; " = 20◦

Thank you!