Precise Determination of Rho-Meson Families Parameters Differences

Precise determination of rho-meson families parameters diﬀerences from both electromagnetic and weak processes

E. Bartoˇs, S. Dubniˇcka, A.-Z. Dubniˇckov´a, H. Hayashii

Institute of Physics SAS, Bratislava, Slovakia Depart. of Theoretical Physiscs, Comenius University, Bratislava, Slovakia Nara Women’s University, Nara, Japan

September 23th 2015

International School of Nuclear Physics, 37th Course, Erice, Italy

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 1 / 30 Outlook

1 Introduction

2 Current status

3 U&A Models of π Electromagnetic form factor Weak form factor

4 Results and conclusions

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 2 / 30 Main idea of work

Show that ρ meson family parameters really differ and find ways how to evaluate the differences in their values. Prepare complex U&A model of electromagnetic and weak pion form factors. + − + − − − 0 Analyse the data for e e → π π and τ → π π ντ processes. Determinate the differences in mass and widths for neutral and charge rho mesons.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 3 / 30 Main idea of work

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 3 / 30 Vector mesons

+ 0 − spin S = 1, isospin I = 1 three projections I3 ↔ ρ , ρ , ρ

particle quark content K∗0 ds K∗+ us ρ− ud ω uu√+dd 2 ρ0 uu√−dd 2 φ ss ρ+ ud K∗− us  + + 0  ρ → π π ∗0  K ds JP = 1− ρ0 → π+π−   ρ− → π−π0

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 4 / 30 Pseudoscalar mesons

+ 0 − spin S = 0, isospin I = 1 three projections I3 ↔ π , π , π

particle quark content K0 ds K+ us π− ud η uu+d√d−2ss 6 π0 uu√−dd 2 η0 uu+√dd+ss 6 π+ ud − P − K us J = 0 K0 ds

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 5 / 30 Masses ρ0, ρ± for ρ(770)

9 2012: PDG average

8 No. of values

7 2005: Schael

6 2003: Aloisio

5 2002: Achasov

4 1999: Abele

3 1969: Reynolds

2 1968: Foster

1 1968: Pisut

-12 -10 -8 -6 -4 -2 0 2 4 6

∆ m = mρ0 − mρ± [MeV]

Figure: Mass diﬀerence of ρ0 and ρ± mesons for ground state ρ(770).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 6 / 30 Masses ρ0, ρ± for ρ(770)

mρ0 − mρ± [MeV] Processes Literature 2.4 ± 2.1 π±p → ρN [Pisut and Roos, 1968] −5 ± 5 pp → ρπ [Foster et al., 1968] −4 ± 4 π−p → ρN [Reynolds et al., 1969] 1.6 ± 0.6 ± 1.7 pp → π+π−π0 [Abele et al., 1999] 1.3 ± 1.1 ± 2.0 e+e− → π+π−π0 [Achasov et al., 2002] 0.4 ± 0.7 ± 0.6 e+e− → π+π−π0 [Aloisio et al., 2003] − − 0 −2.4 ± 0.8 τ → π π ντ [Schael et al., 2005] −0.7 ± 0.8 PDG weighted average

Table: Mass diﬀerence of ρ0 and ρ± mesons for the state ρ(770).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 7 / 30 Decay widths for ρ(770)

Γρ0 − Γρ± [MeV] Processes Literature 3.6 ± 1.8 ± 1.7 e+e− → π+π−π0 [Aloisio et al., 2003] − − 0 −0.2 ± 1.0 τ → π π ντ [Schael et al., 2005] 0.3 ± 1.3 PDG average

Γρ+ − Γρ− [MeV] 1.8 ± 2.0 ± 0.5 e+e− → π+π−π0 [Aloisio et al., 2003]

Table: Diﬀerence of decay widths of ρ0 and ρ± mesons for the state ρ(770).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 8 / 30 Extraction of ρ data

strong interaction processes π±p → ρN → ππN : π+p → π+π0p, π−p → π+π−n [ρ0], π−p → π−π0n [ρ−] electron-proton annihilation into 3π: e+e− → π+π−π0

Resonance peak as Breit-Wigner formulae, with diﬀerent parametrizations Γm – model dependence – e. g., [Schael et al., 2005]

h 1+δBWω(783)(s) i BWρ(770)(s) 1+δ + βBWρ(1450)(s) + γBWρ(1700)(s) F I=1,0 = π 1 + β + γ m (1 + d · Γ /m ) GS ρ ρ √ ρ Breit-Wigner propagators: BWρ (s) = 2 mρ − s + f (s) − i sΓρ(s)

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 9 / 30 Data sources

Clearest determination of ρ0 and ρ± masses and widths from processes: + − + − − − 0 e e → π π and τ → π π ντ

[Jegerlehner and Szafron, 2011] conﬁrmed compatibility of both sources Had,LO in calculations of αµ —

− − 0 τ → π π ντ – precise measurement of spectral function v−(s) through diﬀerential decay rate 1 dΓ ∼ v (s) → |F −(s)|2 (observables) Γ ds − π

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 10 / 30 Cross section & spectral functions

− + − Relation of spectral function v1,X − of τ decay to e e annihilation (optical theorem, CVC – conserved vector current hypothesis)

2 ( − I=1 4πα X hadronic system in vector state σ + − 0 = v − , e e →X s 1,X X 0 isovector ﬁnal state

+ − − For π π spectral function v0(s) and v−(s)(τ decay) exists relation:

4π2α2 σ(e+e− → π+π−) = v (s), s 0 β3(s) β3 (s) v (s) = v I=1(s), v (s) = 0 |F 0(s)|2 ↔ v (s) = − |F −(s)|2, − 0 0 12π π − 12π π

+ − − 0 0,− βj – pion velocity in π π /π π systems, |Fπ (s)| – pion form factors

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 11 / 30 U&A EM FF model: main properties

EM h p2|Jµ (0)|p1 i = eFπ(t)(p1 + p2), t < 0 Deﬁnition Fπ(t): EM h p1p2|Jµ (0)|0 i = eFπ(t)(p1 − p2), t > 0

nq−1 −1 Fπ(t) ∼ t ∼ t – asymptotic behavior, as in QCD t→∞ 2 −1 Fπ(t) ∼ −16πfπ αs (t)t , fπ = 92.4 ± 0.2 MeV t→−∞ Fπ(0) = 1 – normalization in t = 0 1 + − EM EM + − ? 2i h π π |Jµ (0)|0 i h 0|Jµ (0)|π π i = P + − + EM h π π |T |n i h n|Jµ (0)|0 i – unitarity condition. With reality n ? ? condition (Fπ(t)) = Fπ(t ) leads to elastic unitarity condition for form factor: 1 ? Im Fπ(t) = (A1(t)) Fπ(t) + σ(t) 1 A1(t) – P wave isovector elastic ππ scattering amplitude, σ(t) – higher c.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 12 / 30 U&A EM FF model: main properties

Fπ(t) – analytic func. in complex t-plane, properties: 2 cut on positive real axis from the lowest branching point 4mπ → ∞ cut on the ﬁrst unphysical Riemann sheet for −∞ < t < 0 Nonlinear transformation: 4 Riemann surfaces → 1 complex t-plane t = tin i IV. t = 4(t − t ) ±∞ t = t − in 0 , and inverse W (t) 0 [1/W − W ]2 II. 1 0 1 − I. particle w.: Wv → Wv = W (t) 0 2 t=(mv −iΓv /2) 2 2 i threshold positions: t0 < mv < tin < mv 0 III. − ∗ 1 t = t0 → Wv0 = −Wv0, Wv 00 = ∗ Wv0

10 parameters: tin, mρ,Γρ, mρ0 ,Γρ0 , mρ00 ,Γρ00 , fρππ/fρ, WZ , WP

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 13 / 30 Overview of U&A model

1 The experimental fact of creation of unstable vector meson resonances in the e+ e− annihilation processes into hadrons. 2 Analytic properties of EM FF on the 1st (physical) sheet of Riemann surface → just the contributions of continua are taken into account. 3 Asymptotic behaviour of EM FF followed from the quark model of 1−nq hadrons: F (t) ∼ t , nq – constituent quarks.

asymptotic resonance term z }| { z }| { 1 − W 2 2 (W − W )(W − W ) n f o F E,I=1(t)= Z N P X(... ) ρππ π 2 (W − W )(W − W ) i f 1 − WN N Z P i ρ

f 0 f 00 parameters ρ ππ and ρ ππ can be expressed by fρππ fρ0 fρ00 fρ

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 14 / 30 Our model

Cross section relations: 2 3 2 + − + − πα βπ E,I=1 2 1/2 σ(e e → π π ) = F (s) , βπ = (1 − 4m /t) , 3s π π 2 3 2 2 + − + − πα βπ E,I=1 iΦ mω σ(e e → π π ) = Fπ (s)+ Re 2 , 3s mω − s − imωΓω

R and Φ are the ρ–ω interference amplitude and phase. In [Dubnickova et al., 1993] found relation for form factors

√ W E,I=1 Fπ (s) = 2Fπ

⇒ combined analysis of τ − decay to e+ e− annihilation data

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 15 / 30 Comparison of results

Belle 10 ALEPH CLEO 10 G&S Fit ρ ρ ρ ( (770) + (1450) + (1700)) 1 2 | π

|F -1 10 1

-2 10

10-1

-3 10 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 3.5 0 2 2 2 (Mππ ) (GeV/c )

Figure: The ﬁts of Belle results by G&S and U&A models.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 16 / 30 Comparison of results

45 45 Belle (a) 40 ALEPH 40 CLEO 35 G&S Fit 35

30 30 2 |

π 25 25 |F 20 20

15 15

10 10 5 5

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 2 2 2 (Mππ ) (GeV/c )

Figure: The ﬁts of Belle results by G&S and U&A models.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 17 / 30 Comparison of results

12 Belle (b) 7 ALEPH CLEO 10 6 G&S Fit

8 5 2 | π

|F 6 4

3 4

2 2 1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 2 2 2 (Mππ ) (GeV/c )

Figure: The ﬁts of Belle results by G&S and U&A models.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 18 / 30 Results

ρ0 (e+ e− data) ρ± (τ − data) ∆ (ρ0-ρ±) Parameter [MeV] [MeV] [MeV]

mρ(770) 758.23 ± 0.46 761.60 ± 0.95 − 3.37 ± 1.06 mρ(1450) 1342.31 ± 46.62 1373.83 ± 11.37 −31.53 ± 47.99 mρ(1700) 1718.50 ± 65.44 1766.80 ± 52.36 −48.30 ± 83.81 Γρ(770) 144.56 ± 0.80 139.90 ± 0.46 4.66 ± 0.85 Γρ(1450) 492.17 ± 138.38 340.87 ± 23.84 151.30 ± 140.42 Γρ(1700) 489.58 ± 16.95 414.71 ± 119.48 74.87 ± 120.67

Table: The results for the masses and decay widths of ρ0 and ρ± mesons.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 19 / 30 Masses ρ0, ρ± for the state ρ(770)

9 2012: PDG average

8 Our result No. of values

7 2005: Schael

6 2003: Aloisio

5 2002: Achasov

4 1999: Abele

3 1969: Reynolds

2 1968: Foster

1 1968: Pisut

-12 -10 -8 -6 -4 -2 0 2 4 6

∆ m = mρ0 − mρ± [MeV]

Figure: Mass diﬀerence of ρ0 and ρ± mesons for the state ρ(770).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 20 / 30 Decay widths for ρ(770)

Γρ0 − Γρ± [MeV] Processes Literature 3.6 ± 1.8 ± 1.7 e+e− → π+π−π0 [Aloisio et al., 2003] − − 0 −0.2 ± 1.0 τ → π π ντ [Schael et al., 2005] 4.7 ± 0.9 e+e−; τ − Our result

Table: Diﬀerence of decay widths of ρ0 and ρ± mesons for the state ρ(770).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 21 / 30 Results

ρ0 (e+ e− data) ρ± (τ − data) ∆ (ρ0-ρ±) Parameter [MeV] [MeV] [MeV]

mρ(770) 758.23 ± 0.46 < 761.60 ± 0.95 − 3.37 ± 1.06 mρ(1450) 1342.31 ± 46.62 < 1373.83 ± 11.37 −31.53 ± 47.99 mρ(1700) 1718.50 ± 65.44 < 1766.80 ± 52.36 −48.30 ± 83.81 Γρ(770) 144.56 ± 0.80 > 139.90 ± 0.46 4.66 ± 0.85 Γρ(1450) 492.17 ± 138.4 > 340.87 ± 23.84 151.30 ± 140.42 Γρ(1700) 489.58 ± 16.95 > 414.71 ± 119.48 74.87 ± 120.67

Table: The results for the masses and decay widths of ρ0 and ρ± mesons.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 22 / 30 Results

Parameter e+ e− data τ − data Belle-10 Belle-11

mρ(770) 0.758 0.761 0.775 0.775 mρ(1450) 1.342 1.374 1.446 1.428 mρ(1700) 1.719 1.767 1.728 1.694 Γρ(770) 0.145 0.140 0.148 0.149 Γρ(1450) 0.492 0.341 0.434 0.413 Γρ(1700) 0.490 0.415 0.164 0.135

Table: The results for the masses and decay widths of ρ mesons compared with Belle results [Fujikawa et al., 2008].

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 23 / 30 Contribution to muon anomaly

g − 2 α α2 α3 α ≡ µ = α(1) + α(2)QED + α(2)Had +α(2)EW+O µ 2 µ π µ µ π µ π Had,LO −11 Had,LO −11 αµ [e] = 6907.5(47.2) × 10 , αµ [τ] = 6909.6(46.5) × 10

Had,LO −11 αµ [×10 ] 2 2 2 Model 4mπ — 3.24 4mπ — 2.0499 4mπ — 0.8 U&A [e ] 5132.37 ± 3.00 5128.25 ± 2.86 4870.44 ± 2.64 BABAR [e ] 5141 ± 38 – – U&A [τ ] 5358.57 ± 4.87 5139.83 ± 3.25 4867.21 ± 2.45 G-S [τ ] 5235 ± 39 – – BABAR - [Aubert et al., 2009], [Davier et al., 2011]

Table: π π channel hadronic contribution to muon anomaly.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 24 / 30 Conclusions

It was succesfully shown that ρ meson family parameters really diﬀer. We have prepared complex U&A models of electromagnetic and weak pion form factors which allow to analyse the data for + − + − − − 0 e e → π π and τ → π π ντ processes. The diﬀerences in mass and widths for neutral and charge rho mesons were calculated. The precise results (better evaluation of uncertainties) need the new input from the experiment(s).

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 25 / 30 Conclusions

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 25 / 30 Thank you

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 26 / 30 ReferencesI

Abele, A., Adomeit, J., Amsler, C., Anisovich, A., Baker, C., et al. (1999). The rho mass, width and line-shape in p-bar p annihilation at rest into pi+ pi- pi0. Phys.Lett., B469:270–275. Achasov, M., Aulchenko, V., Beloborodov, K., Berdyugin, A., Bogdanchikov, A., et al. (2002). Study of the pi pi mass spectra in the process e+ e- → pi+ pi- pi0 at s**(1/2) = 1020-MeV. Phys.Rev., D65:032002. Aloisio, A. et al. (2003). Study of the decay phi → pi+ pi- pi0 with the KLOE detector. Phys.Lett., B561:55–60.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 27 / 30 ReferencesII

Aubert, B. et al. (2009). Precise measurement of the e+ e- —¿ pi+ pi- (gamma) cross section with the Initial State Radiation method at BABAR. Phys. Rev. Lett., 103:231801. Davier, M., Hoecker, A., Malaescu, B., and Zhang, Z. (2011). Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ). Eur. Phys. J., C71:1515. [Erratum: Eur. Phys. J.C72,1874(2012)]. Dubnickova, A., Dubnicka, S., and Rekalo, M. (1993). − − 0 Conserved vector current hypothesis and the νee → π π process. Czech.J.Phys., 43:1057–1070.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 28 / 30 ReferencesIII

Foster, M., Gavillet, P., Labrosse, G., and Montanet, L. (1968). Production of Three Pions in pbar p Annihilations at Rest. Nucl.Phys., B6:107. Fujikawa, M. et al. (2008). − − 0 High-Statistics Study of the τ → π π ντ Decay. Phys. Rev., D78:072006. Jegerlehner, F. and Szafron, R. (2011). 0 e ρ − γ mixing in the neutral channel pion form factor Fπ and its role in comparing e+e− with τ spectral functions. Eur. Phys. J., C71:1632. Pisut, J. and Roos, M. (1968). The rho meson shape. Nucl.Phys., B6:325–352.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 29 / 30 ReferencesIV

Reynolds, B., Albright, J. R., Bradley, R., Brucker, E., Harms, B., et al. (1969). Single-pion production in pi- p interactions at 2.26 gev/c. Phys.Rev., 184:1424–1442. Schael, S. et al. (2005). Branching ratios and spectral functions of tau decays: Final ALEPH measurements and physics implications. Phys.Rept., 421:191–284.

Bartoˇs (IP SAS, Slovakia) ρ mesons September 23th 2015 30 / 30