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## Icssnp.mephi.ru

**Line shape of **ψ(3770)

**in**
**N.N. Achasov and G.N. Shestakov**
**Laboratory of Theoretical Physics**
**Sobolev Institute for Mathematics**
**Novosibirsk, Russia**
**MEPHI, November 12–16, 2012, Moscow – p. 1/24**
**Abstract**
**1. Parameters of the **ψ(3770)

**resonance should be extracted**
**from the processing of data on the **e+e− → D ¯

D

**reactions by**
**using models that satisfy the elastic unitarity requirement.**
**2. As the first working candidate, a model with the mixing**
ψ(3770)

**and **ψ(2S)

**resonances is proposed.**
**3. Selection of theoretical models can be toughened by**
**comparing their predictions with the data on the shape of the**

ψ(3770)

**peak in the non-**D ¯

D

**channels **e+e− → γχc0

**,**
J/ψη

**, **φη,

**etc.**
**MEPHI, November 12–16, 2012, Moscow – p. 2/24**
**1. Introduction: **ψ(3770)

**in **e+e− → D ¯

**Current data. Interference patterns**
**2. The **D

**meson electromagnetic form factor **F 0

**Unitarity requirement**
**Description of the data on **e+e− → D ¯

**A simplest model for **F 0

D

**with the mixing **ψ(3770)

**and **ψ(2S)

**resonances**
**3. The **ψ(3770)

**shapes in non-**D ¯

D

**decay channels**
**4. A comment on ambiguity of resonance parameters**
**5. Conclusion**
**MEPHI, November 12–16, 2012, Moscow – p. 3/24**
ψ(3770)

**= **ψ

**. Current data**
mψ

**= 3773 MeV, **Γtot

D

**= 27.2 MeV, **Γψ e+e−

**= 0.262 keV.**
**The resonance **ψ

**was investigated in **e+e− → D ¯

D

**by MARK-I**
**(1977), DELCO (1978), and MARK-II (1980), and after 24 years, by**
**BES (2004-2010), CLEO (2006-2010), BABAR (2007, 2009), Belle**
**(2008) and KEDR (2010-2012).**
**New super-high-statistics era.**
**New data are expected from BESIII and CLEO-c heaving millions**
D

**events. In this regard, we believe it is timely**
**to discuss some dangers which are hidden in the commonly used**
**schemes for the description of the **ψ

**peak.**
**MEPHI, November 12–16, 2012, Moscow – p. 4/24**
**Current data on **e+e− → D ¯

D

**, interference patterns**
D)

**has the following features: (1) the right-side of the **ψ

**peak turns**
**out to be more steep than its left-side, (2) there is a deep dip near 3.81 GeV. These**
**features are hard to describe with the help of a single **ψ

**resonance contribution.**
**MEPHI, November 12–16, 2012, Moscow – p. 5/24**
**Fits to 87 points with a single **ψ

**resonance contribution**
χ2

**values are very bad.**
**MEPHI, November 12–16, 2012, Moscow – p. 6/24**
ψ

**interferes with background**
**In order to qualitatively improve the data description in the **ψ

**resonance region, in particular, to explain a dip near 3.81 GeV, it is**
**necessary to take into account the interference between the**
**resonant and nonresonant **D ¯

D

**production.**
**Note that, in this way, there unexpectedly arose the problem**
**with the ambiguity of the interfering **ψ

**resonance parameters**

determination [KEDR(2010-2012), PDG(2012)]. However, the
**parametrizations used for the **e+e− → D ¯

D

**reaction amplitude**
**have no clear dynamical justification.**
**MEPHI, November 12–16, 2012, Moscow – p. 7/24**
**The **D

**meson electromagnetic form factor **F 0

**In the process **e+e− → D ¯

D

**we investigate the **D

**meson electromagnetic form**
**factor, the phase of which in the elastic region (between the **D ¯

**thresholds: **2mD ≈ 3.739

**GeV and **mD + mD∗ ≈ 3.872

**GeV) is completely**

fixed by the unitarity condition. Here we consider the isoscalar form factor F 0

D

**is a real function of energy and **δ0

1

**is the phase of the **P

**-wave **D ¯

**scattering amplitude **T 0

1

**in the channel with isospin **I

**= 0,**
δbg

**is the elastic background phase and **δres

**is the phase of the resonance**

amplitude Tres

**.**
**MEPHI, November 12–16, 2012, Moscow – p. 8/24**
**The **D

**meson electromagnetic form factor **F 0

**A similar representation of the **e+e− → D ¯

D

**reaction amplitude used**
**for the data description guarantees the unitarity requirement on the model level.**
**The sum of the **e+e− → D0 ¯

D0

**and **e+e− → D+D−

**reaction cross**
**sections is expressed in terms of **F 0

D

**in the following way**
**where **ν(s) = [p3(s) + p3 (s)]/

**To understand how the form factor **F 0

D

**and strong amplitude **T 0

1

**can be con-**
**structed satisfying the unitarity requirement, the easiest way to use, as a guide,**
**the field-theory model shown in the next slide.**
**MEPHI, November 12–16, 2012, Moscow – p. 9/24**
**Unitarity construction of **T 0

**and **F 0

**The graphical representation of the strong **D ¯

D

**scattering amplitude **T 0

**the **D

**meson electromagnetic form factor **F 0

**MEPHI, November 12–16, 2012, Moscow – p. 10/24**
**The model for **F 0

**with the mixing **ψ

**and **ψ(2S)

**resonances**
**It is clear that the main sources of the background in the **ψ

**region are the tails from the **J/ψ

**, **ψ(2S)

**, **ψ(4040)

**, **ψ(4160)

**and other resonances. It is easy to incorporate the right number of**
**resonances in our scheme.**
**Here we present the simplest variant of the model taking into**
**account the background contribution from the nearest neighbor**
**resonance **ψ(2S)

**and also discuss how it can be checked.**
**In the considered model the **ψ

**and **ψ(2S)

**resonances mix**
**via transitions **ψ

D → ψ(2S)

**.**
**MEPHI, November 12–16, 2012, Moscow – p. 11/24**
**The model for **F 0

**with the mixing **ψ

**and **ψ(2S)

**resonances**
− ψ(2S)

**mixing amplitude caused by **ψ → D ¯

D → ψ(2S)

**transitions**
**via the real **D ¯

D

**intermediate states has the form**
**MEPHI, November 12–16, 2012, Moscow – p. 12/24**
**The model for **F 0

**with the mixing **ψ

**and **ψ(2S)

**resonances**
mψ

**, **gψ D ¯

D

**, **gψ γ

**, and **gψ(2S)D ¯

D

**are determined by fitting;**
mψ(2S)

**and **gψ γ

**are fixed by the PDG data.**
**Note that **F 0

D

**in the considered model is proportional to the**
**first-degree polynomial in **s

**with real coefficients (see **RD ¯

**above ). Hence the dip observed in **σ(e+e− → D ¯

D)

**near 3.81**
**GeV can be explained by the **F 0

D (s)

**zero, caused by compensation**
**between the **ψ

**and **ψ(2S)

**contributions.**
**MEPHI, November 12–16, 2012, Moscow – p. 13/24**
**The simplest variant of the **ψ − ψ(2S)

**mixing model for **F 0

**The solid curve is the fit to the data. The dashed and dot-dashed curves show the**
ψ

**and **ψ(2S)

**contributions, respectively. Bare parameters: **mψ

**= 3.794 GeV,**
D

**= 56.8 MeV, **Γψ e+e−

**= 0.062 keV, **g2

/4π

**= 32.2.**
**MEPHI, November 12–16, 2012, Moscow – p. 14/24**
**The simplest variant of the **ψ − ψ(2S)

**mixing model for **T 0

**From the fitting of the **e+e− → D ¯

D

**data we all know, at the**
**model level, about the **I

**= 0 **P

**wave **D ¯

D

**elastic scattering**
**amplitude **T 0

**MEPHI, November 12–16, 2012, Moscow – p. 15/24**
**Cross section and phase for **D ¯

D

**elastic scattering in the **P

**wave**
**(a) The cross section **σ(D0 ¯

D0)

**= **3π| sin δ0(s)

**and (b) the**
**phase **δ0(s)

**for the simplest variant of the **ψ

− ψ(2S)

**mixing model.**
**Unfortunately, these predictions are not possible to verify. However, there are many**
**other reactions which can be measured experimentally.**
**MEPHI, November 12–16, 2012, Moscow – p. 16/24**
**The **ψ

**shapes in non-**D ¯

D

**decay channels**
**The solid curves show predictions of the model with the mixing **ψ

**and **ψ(2S)

**resonances for the **ψ

**peak shapes in the **e+e− → γχc0

**, **e+e− → J/ψη

**, and**
e+e− → φη

**cross sections; the dashed and dotted curves show the contributions**

from ψ

**and **ψ(2S)

**production amplitudes proportional to **gψ ab

**and **gψ(2S)ab

**,**
**respectively (**ab = γχc0

**, **J/ψη

**, **φη

**). The points with errors are the CLEO data.**
**MEPHI, November 12–16, 2012, Moscow – p. 17/24**
**The **ψ

**shapes in non-**D ¯

D

**decay channels**
**The above examples tell us that the mass spectra in the **ψ

**region in the non-**D ¯

D

**channels can be very diverse. Therefore we**
**should expect that the future data on such spectra, together with**
**the high-statistics data on **D ¯

D

**channels, will impose severe**
**restrictions on the constructed dynamical models.**
**MEPHI, November 12–16, 2012, Moscow – p. 18/24**
**A comment on ambiguity of resonance parameters**
**Here we illustrate the root of the ambiguity of the interfering resonances**
**parameters determination by using a simplest example. Consider the “usual”**
h

**amplitude**
**At fixed **M

**and **Γ

**, there are two solutions for parameters **Ax

**, **ϕx

**, and **Cx

**:**
**(I) **Ax

**= **A

**, **ϕx

**= **ϕ

**, **Cx

**= **C

**and (II) **Ax

**=**
A2 − 2AC sin ϕ + C2Γ2

**,**
tan ϕx

**= **− tan ϕ + CΓ/(A cos ϕ)

**, **Cx

**= **C

**, which yield the same cross**

section as a function of energy, σ(E)

**= **|F (E)|2

**, and differ in the magnitude and**

phase of the resonance contribution. For example, at M

**= 3.77 GeV, **Γ

**= 0.03 GeV,**
A

**= 0.045 nb**1/2

**GeV, **ϕ

**= 0, and **B

**= 1.5 nb**1/2

**, solution (II) gives **Ax

**=**
ϕx

**= **π/4

**.**
**MEPHI, November 12–16, 2012, Moscow – p. 19/24**
**A comment on ambiguity of resonance parameters**
**For each energy, the two solutions also give the different overall phase of the**
**amplitude **F (E)

**, **δ = δres + δbg

**. For the above numerical example, **δbg

**for**
**solutions (I) and (II) is shown by the dashed and solid curves, respectively; the**
**phase **δres

**is shown by the dotted curve.**
**MEPHI, November 12–16, 2012, Moscow – p. 20/24**
**A comment on ambiguity of resonance parameters**
**The origin of the rapid change of the phase **δbg

**(which is**
**additional to **δres

**) requires a special dynamical explanation (for**

example, the presence of extra intermediate states), for which we
**do not see at present any reasons. **∗

**————————–**

∗

**If **h

**and **¯h

**interact with each other only in the resonance way, then to resolve**

ambiguity one must take into account the resonance final state interaction of
**hadrons produced via the amplitude **Bx

**and put the phase **ϕx

**= 0 in the elastic**
**region according to the unitarity requirement.**
**MEPHI, November 12–16, 2012, Moscow – p. 21/24**
**Conclusion**
**1. We tried to show that the shape of the **ψ

**resonance keep**
**important information about the production mechanism and**
**interference with background.**
**2. We considered the models satisfying the unitarity requirement**
**and obtained good descriptions of the current data on the**

e+e− → D ¯

D

**reaction cross section, in particular, in the**
**model with the mixing **ψ

**and **ψ(2S)

**resonances.**
**(See arXiv:1208.4240 for details.)**
**3. The parametrization suggested in this model for the **D

**meson**
**electromagnetic form factor in the **ψ

**resonance region can be**

used in the processing of new series data on the reactions

e+e− → D ¯

**4. We also extracted from experiment**
≈ 13 − 30

**.**
**MEPHI, November 12–16, 2012, Moscow – p. 22/24**
**Conclusion**
**5. New high-statistics data on the reactions **e+e− → D ¯

**should help reveal the complex mechanism of the **ψ

**production.**
**6. As we shown the measurements of mass spectra in the **ψ

**region in the non-**D ¯

D

**channels, such as **e+e− → γχc0

**,**
J/ψη

**, **φη

**, etc., will promote comprehensive study of the **ψ

**resonance physics and effective selection of theoretical**
**7. Additional information about the **ψ

**in the **D ¯

D

**mass spectra**
**can be extracted, for example, from weak decays **B → ψ K

**and photoproduction reactions at high energies **γA → ψ A

**.**
**MEPHI, November 12–16, 2012, Moscow – p. 23/24**
**Appendix: another description of the data on **e+e− → D ¯

**The model with the mixing **ψ

**and **ψ(2S)

**resonances and residual backgrounds.**
**The dashed, dot-dashed, and dotted curves show the **ψ

**, **ψ(2S)

**, and residual**
**background contributions, respectively (see arXiv:1208.4240 for details).**
**MEPHI, November 12–16, 2012, Moscow – p. 24/24**
Source: http://www.icssnp.mephi.ru/content/file/symposium/2/SQ_15_Achasov_MIPHI.pdf

Türk Kardiyol Dern Arﬂ - Arch Turk Soc Cardiol 2007;35(5):295-298Sol ventrikül yerleﬂimli kist hidatik: Olgu sunumuEmin Alio¤lu, M.D., U¤ur Önsel Türk, M.D., ‹stemihan Tengiz, M.D., Ertu¤rul Ercan, M.D. Department of Cardiology, Central Hospital, ‹zmirCardiac hydatid disease is uncommon, occurring inKardiyak hidatik hastal›¤› nadirdir ve ekinokokkosizli0.2% to 2% of patie

See www.DynamicMedical.com for the latest version as DynaMed is updated daily You are viewing a DynaMed summary. Use of DynaMed indicates acceptance of DynaMed Terms of Use. Limitations of DynaMed are contained in the DynaMed Terms of Use. To search within this summary, click Expand All, and then Edit - Find (Ctrl-F) in your browser. Meniere's disease Updated 2008 Aug 11 11:29 AM: review