near-threshold behavior of the cross sections of γp φp and ...€¦ · near-threshold behavior of...

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Near-threshold behavior ofthe cross sections of γp→ φp and γd→ φpn:

A resonance interpretation

JLAB and Indiana University

January 18, 2013

Alvin Stanza Kiswandhi1

In collaboration with:Shin Nan Yang1, Yu Bing Dong2, and Ju-Jun Xie1

1 Center for Theoretical Sciences and Department of Physics,National Taiwan University, Taipei 10617, Taiwan

2 Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049, China


Motivation

• Presence of a local peak near threshold at Eγ ∼ 2.0 GeVin the differential cross-section (DCS) of γp → φp atforward angle by Mibe and Chang, et al. [PRL 95182001 (2005)] from the LEPS Collaboration.−→ Observed also by JLAB: Tedeschi et al. and B. Deydissertation.

• Conventional model of Pomeron plus π and η ex-changes usually can only give rise to a monotonically-increasing behavior.

• We would like to see whether this local peak can be explainedas a resonance.

• In order to check this assumption, we apply the results on γp→φp to γd→ φpn to see if we can describe the latter.

1


Reaction model for γp→ φp

• Here are the tree-level diagrams calculated in our model inan effective Lagrangian approach.

p

(b) (c) (d)(a)

γ φ

p pp

φ

p

γ

Pomeron

γ

p

φ

N*

φγ

pp N*

π,η

N ∗ is the postulated resonance.

– pi is the 4-momentum of the proton in the initial state,

– k is the 4-momentum of the photon in the initial state,

– pf is the 4-momentum of the proton in the final state,

– q is the 4-momentum of the φ in the final state.

2


Pomeron exchange

We follow the work of Donnachie, Landshoff, and Nacht-mann

iM = iuf(pf)ε∗µφ Mµνui(pi)ε

νγ

Mµν = M(s, t)Γµν

M(s, t) = CPF1(t)F2(t)1

s

(s− sth

4

)αP (t)

exp [−iπαP (t)/2]

• Γµν is chosen to maintain gauge invariance.

• The strength factor CP = 3.65 is chosen to fit the totalcross sections data at high energy.

• The threshold factor sth = 1.3 GeV2 is chosen to match theforward differential cross sections data at around Eγ = 6GeV.

3


π and η exchanges

• For t-channel exchange involving π and η, we use

LγφM =egγφM

mφ

εµναβ∂µφν∂αAβϕM

LMNN =gMNN

2MN

ψγµγ5ψ∂µϕM

with M = (π, η).

• We choose gπNN = 13.26, gηNN = 1.12, gγφπ = −0.14, andgγφη = −0.71.

• Form factor at each vertex in the t-channel diagram is

FMNN(t) = FγφM(t) =Λ2

M −m2M

Λ2M − t

• The value ΛM = 1.2 GeV is taken for both M = (π, η).

4


Resonances

• Only spin 1/2 or 3/2 because the resonance is close to thethreshold.

• Lagrangian densities that couple spin-1/2 and 3/2 particlesto γN or φN channels are

L1/2±

φNN∗ = g(1)φNN∗ψNΓ±γµψN∗φµ + g

(2)φNN∗ψNΓ±σµνG

µνψN∗,

L3/2±

φNN∗ = ig(1)φNN∗ψNΓ± (∂µψν

N∗) Gµν + g(2)φNN∗ψNΓ±γ5 (∂µψν

N∗)Gµν

+ ig(3)φNN∗ψNΓ±γ5γα (∂αψν

N∗ − ∂νψαN∗) (∂µGµν) ,

where Gµν = ∂µφν − ∂νφµ and Gµν = 12εµναβG

αβ. The operatorΓ± are given by Γ+ = 1 and Γ− = γ5, depending on the parityof the resonance N ∗.

• For the γNN ∗ vertices, simply change gφNN∗ → egγNN∗ andφµ → Aµ.

5


• Current conservation fixes g(1)γNN∗ → 0 for JP = 1/2± and

the term proportional to g(3)γNN∗ vanishes in the case of real

photon.

• The effect of the width is taken into account in a Breit-Wigner form by replacing the usual denominator p2−M 2

N∗ →p2 −M 2

N∗ + iMN∗ΓN∗.

• The form factor for the vertices used in the s- and u-channel diagrams is

FN∗(p2) =Λ4

Λ4 + (p2 −M 2N∗)2

with Λ = 1.2 GeV for all resonances.

6


Fitting to γp→ φp experimental data

• We include only one resonance at a time.

• We fit only masses, widths, and coupling constants of theresonances to the experimental data, while other parametersare fixed during fitting.

• Experimental data to fit

– Differential cross sections (DCS) at forward angle

– DCS as a function of t at eight incoming photon energybins

– Nine spin-density matrix elements (SDME) at threeincoming photon energy bins

7


Results for γp→ φp

• Both JP = 1/2± resonances cannot fit the data.

• DCS at forward angle and as a function of t aremarkedly improved by the inclusion of the JP = 3/2± reso-nances.

• In general, SDME are also improved by both JP = 3/2±

resonances.

• Decay angular distributions, not used in the fitting proce-dure, can also be explained well.

• We study the effect of the resonance to the DCS of γp→ ωp.−→ The resonance seems to have a considerable amount ofstrangeness content.

8


DCS of γp→ φp at forward angle

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7Eγ (GeV)

0

0.5

1

1.5

2

2.5

3

dσ/d

t (µb

GeV

-2)

Black→JP = 3/2− Red→ JP = 3/2+

Total → full, Nonresonant → dotted, Resonant → dashed

9


DCS of γp→ φp as a function of t

-0.5 -0.25

0.2

0.4

0.6

0.8

1

dσ/d

t (µb

/GeV

2 )

-0.5 -0.25 -0.5 -0.25 -0.5 -0.25

t + |t|min

(GeV2)

-0.5 -0.25 -0.5 -0.25 -0.5 -0.25 -0.5 -0.25 0

1.62 GeV 1.72 GeV 2.12 GeV1.82 GeV 1.92 GeV 2.02 GeV 2.22 GeV 2.32 GeV

Black→JP = 3/2− Red→ JP = 3/2+

Total → full, Nonresonant → dotted, Resonant → dashed

10


SDME of γp→ φp as a function of t

-0.1

0

0.1

0.2

0.3

0.4

1.77 < Eγ < 1.97 GeV

-0.2-0.1

00.10.20.3

0 0.05 0.1 0.15-0.5

-0.25

00.250.5

0.75

0 0.05 0.1 0.15

|t - tmax

| (GeV2)

0 0.05 0.1 0.15 0.2

ρ0

00ρ0

10 ρ0

1-1

ρ1

11ρ1

00 ρ1

10

ρ1

1-1Im ρ2

10Im ρ2

1-1

11



-0.1

0

0.1

0.2

0.3

0.4

1.97 < Eγ < 2.17 GeV

-0.4

-0.2

0

0.2

0 0.05 0.1 0.15-0.5

-0.25

00.250.5

0.75

0 0.05 0.1 0.15

|t - tmax

| (GeV2)

0 0.05 0.1 0.15 0.2

ρ0

00 ρ0

10 ρ0

1-1

ρ1

11ρ1

00 ρ1

10

ρ1

1-1 Im ρ2

10 Im ρ2

1-1

12



-0.1

0

0.1

0.2

0.3

0.4

2.17 < Eγ < 2.37 GeV

-0.4

-0.2

0

0.2

0 0.05 0.1 0.15-0.5

-0.25

00.250.5

0.75

0 0.05 0.1 0.15

|t - tmax

| (GeV2)

0 0.05 0.1 0.15 0.2

ρ0

00ρ0

10 ρ0

1-1

ρ1

11 ρ1

00ρ1

10

ρ1

1-1 Im ρ2

10 Im ρ2

1-1

13


Decay angular distributions at two energy bins[Eγ = 2.07 GeV (upper) and Eγ = 2.27 GeV (lower)]

Not fitted

0

0.2

0.4

0.6

0.8

1W

-1 -0.5 0 0.5 1cosΘ

0

0.2

0.4

0.6

0.8

W

0.5

1

1.5

2

2πW

0 90 180 270 360Φ - Ψ

0

0.5

1

1.5

2

2πW

(a) (b)

14


Decay angular distributions at two energy bins[Eγ = 2.07 GeV (upper) and Eγ = 2.27 GeV (lower)]

Not fitted

0.5

0.75

1

1.25

1.5

2πW

0 90 180 270 360Φ

0.5

0.75

1

1.25

2πW

90 180 270 360Φ + Ψ

90 180 270 360Ψ

(c)

15


JP = 3/2+ JP = 3/2−

MN∗(GeV) 2.08 ± 0.04 2.08 ± 0.04ΓN∗(GeV) 0.501 ± 0.117 0.570 ± 0.159

eg(1)γNN∗g

(1)φNN∗ 0.003 ± 0.009 −0.205 ± 0.083

eg(1)γNN∗g

(2)φNN∗ −0.084 ± 0.057 −0.025 ± 0.017

eg(1)γNN∗g

(3)φNN∗ 0.025 ± 0.076 −0.033 ± 0.017

eg(2)γNN∗g

(1)φNN∗ 0.002 ± 0.006 −0.266 ± 0.127

eg(2)γNN∗g

(2)φNN∗ −0.048 ± 0.047 −0.033 ± 0.032

eg(2)γNN∗g

(3)φNN∗ 0.014 ± 0.040 −0.043 ± 0.032

χ2/N 0.891 0.821

• The ratio A1/2/A3/2 = 1.05 for the JP = 3/2− resonance.−→ Similarity to D13(2120) is interesting to note.(PDG lists A1/2/A3/2 = 0.83)

• The ratio A1/2/A3/2 = 0.89 for the JP = 3/2+ resonance.

16


Predictions for single polarization observables

for γp→ φp

0 45 90 135 180

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0 45 90 135 180θ (degree)

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 45 90 135 180

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Σx

Ty

Py’

Asymmetries of the polarized beam Σx, polarized targetTy, and recoil polarization Py′

17


Predictions for double polarization observables

for γp→ φp

-0.15

-0.1

-0.05

0

0.05

0.1

Cyx

(BT

)

-0.05

0

0.05

0.1

0.15

0.2

Cyz

(BT

)

0 45 90 135 180θ (degree)

-0.75

-0.5

-0.25

0

0.25

0.5

Czx

(BT

)

0 45 90 135 180θ (degree)

-0.5

-0.25

0

0.25

0.5

0.75

1

Czz

(BT

)

Beam-target (BT) asymmetries CBTyx , CBT

yz , CBTzx , and CBT

zz ,with the photon beam and the nucleon target polarized

18


Reaction model for γd→ φpn

pp

pd

p1

pn

p2

p1

p2

pp pn

pd

1p’

k

γ

d

p

n

p

φ

q

np

q

p n

γ

dk

φ

p+ + pn interchange

• Fermi motion of the proton and neutron inside the deuteronis included using deuteron wave function calculated byMachleidt in PRC 63 024001 (2001).

• Final-state interactions (FSI) of pn is included usingGWU-SAID phase-shift data on pn scattering.

19


• The same model for the amplitude of γp→ φp.

• A JP = 3/2− resonance is also present in the γn → φnamplitude

– For φnn∗ vertex, φp and φn cases are the same sinceφ is an I = 0 particle.

– For γnn∗ vertex, we assume that the resonance wouldhave the same properties as a CQM state with thesame JP and similar value of A1/2/A3/2 for the γpdecay−→N 3

2−(2095)[D13]5 in Capstick’s work in PRD 46, 2864

(1992), the only one with positive value of A1/2/A3/2for γp in the energy region.

• JP = 3/2+ resonance has not been calculated yet.

20


Results for γd→ φpn

• Notice that no fitting is performed to the LEPS data onDCS [PLB 684 6-10 (2010)] and SDME [PRC 82 015205 (2010)]of γd→ φpn from Chang et al..

• We found a very good agreement with the LEPS experi-mental data on both observables.

• Notice that LEPS DCS data given with error bars are ac-tually processed to remove the effect of Fermi motion.

• Our reconstructed data, given in grey bands, reinstatethe removed Fermi motion.−→ We actually discussed this reconstruction with Changfrom the LEPS Collaboration.

• Both resonance and pn FSI effects are found to be large.−→ Without them, the DCS data cannot be described.

21


DCS of γd→ φpnNot fitted

Blue → no resonance, no pn FSI; Red → resonance, no pn FSI;Black → resonance, pn FSI; Grey bands → reconstructed data

22


DCS of γd→ φpnNot fitted

23


SDME of γd→ φpn as a function of tNot fitted

0

0.1

0.2Blue: No FSI, No resonance; Red: Resonance, No FSI; Black: Resonance, FSI

-0.2

0

0.2

Spin

-den

sity

mat

rix

elem

ents

0 0.05 0.1 0.15

-0.5

0

0.5

0.05 0.1 0.15

|t - tmax

| (GeV2)

0.05 0.1 0.15

ρ0

00 ρ0

10 ρ0

1-1

ρ1

11ρ1

00 ρ1

10

ρ1

1-1 Im ρ2

10

Im ρ2

1-1

1.77 < Eγ < 1.97 GeV

24



0

0.1

0.2

0.3

-0.4

-0.2

0

0.2

Spin

-den

sity

mat

rix

elem

ents

0 0.05 0.1 0.15

-0.5

0

0.5

0.05 0.1 0.15

|t - tmax

| (GeV2)

0.05 0.1 0.15

ρ0

00 ρ0

10ρ0

1-1

ρ1

11

ρ1

00 ρ1

10

ρ1

1-1Im ρ2

10

Im ρ2

1-1

1.97 < Eγ < 2.17 GeV

25



0

0.1

0.2

0.3

-0.2

0

0.2

Spin

-den

sity

mat

rix

elem

ents

0 0.05 0.1 0.15

-0.5

0

0.5

0 0.05 0.1 0.15

|t - tmax

| (GeV2)

0 0.05 0.1

ρ0

00 ρ0

10 ρ0

1-1

ρ1

11

ρ1

00 ρ1

10

ρ1

1-1 Im ρ2

10

Im ρ2

1-1

2.17 < Eγ < 2.37 GeV

26


Summary and conclusions

• Inclusion of a resonance is needed to explain the non-monotonic behavior in the DCS γp→ φp near threshold.

• Resonance with J = 3/2 of either parity is preferred for γp →φp, while JP = 1/2± cannot fit the data.

• We can also explain the experimental data on the DCS andSDME of γd→ φpn very well using JP = 3/2− resonance.−→ Final-state interaction of pn and resonance effectsare found to be large and important to describe the data.

• Similarity between the JP = 3/2− and D13(2120) is inter-esting to note.−→Rather similar value of the ratio of helicity am-plitudes A1/2/A3/2 for γp (Ours = 1.05, PDG = 0.83).

• The resonance seems to have a considerable amount ofstrangeness content.−→ Based on a separate study on its effect on γp→ ωp.

27


Outlooks

• We plan to work out γd→ φd for even more consistent check.

• Coupled-channel analysis for φN , KΣ, and KΛ will alsobe interesting to do.−→ JLAB already has the data.

• More experiments, e.g. measurement of single and doublepolarizations, would be helpful to check our predictions.−→ Asymmetry of the polarized beam Σx would beideal to distinguish the parity since different parities havedifferent signs.

28


THANK YOU!


Pomeron exchange

We follow the work of Donnachie, Landshoff, and Nacht-mann

iM = iuf(pf)ε∗µφ Mµνui(pi)ε

νγ

Mµν = ΓµνM(s, t)

with

Γµν = k/

(gµν −

qµqν

q2

)− γν

(kµ − qµ

k · qq2

)−

(qν − pν

k · qp · k

) (γµ − q/

qµ

q2

); p =

1

2(pf + pi)

where Γµν is chosen to maintain gauge invariance, and

A1


M(s, t) = CPF1(t)F2(t)1

s

(s− sth

4

)αP (t)

exp [−iπαP (t)/2]

in which

F1(t) =4m2

N − 2.8t

(4m2N − t)(1− t/0.7)2

F2(t) =2µ2

0

(1− t/M 2φ)(2µ2

0 +M 2φ − t)

; µ20 = 1.1 GeV2

F1(t) → isoscalar EM form-factor of the nucleonF2(t) → form-factor for the φ-γ-Pomeron couplingPomeron trajectory αP = 1.08 + 0.25t.

• The strength factor CP = 3.65 is chosen to fit the totalcross sections data at high energy.

• The threshold factor sth = 1.3 GeV2 is chosen to match theforward differential cross sections data at around Eγ = 6GeV.

A2


Effects on γp→ ωp

• From the φ − ω mixing, we expect the resonance to also con-tribute to ω photoproduction.

• The coupling constants gφNN∗ and gωNN∗ are related, andin our study we choose to use the so-called “minimal”parametrization,

gφNN∗ = −xOZItan∆θV gωNN∗

where xOZI = 1 is the ordinary φ− ω mixing.

• By using xOZI = 12 for the JP = 3/2− resonance and xOZI = 9for the JP = 3/2+ resonance, we found that we can explainquite well the DCS of ω photoproduction.

• The large value of xOZI indicates that the resonance has aconsiderable amount of strangeness content.

B1


DCS of γp→ ωp as a function of t

0.25 0.3 0.35 0.4

101

0 0.5 1100

101

102

0 0.5 1 1.5 2

100

101

102

0 0.5 1 1.5 2 2.5 310

-1

100

101

dσ

/dt (

µb G

eV-2

)

0 1 2 3 4

|t| (GeV2)

10-1

100

101

0 1 2 3 4 510

-2

10-1

100

101

W = 1.725 GeV W = 1.905 GeV W = 2.105 GeV

W = 2.305 GeV W = 2.505 GeV W = 2.705 GeV

Data from M. Williams, PRC 80, 065209 (2009)

B2

near-threshold behavior of the cross sections of γp φp and ...€¦ · near-threshold behavior of...

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