# ${{\boldsymbol f}_{{0}}{(500)}}$ T-MATRIX POLE $\sqrt {\boldsymbol s }$ INSPIRE search

Note that $\Gamma \approx{}$2 Im($\sqrt {{\mathrm {s_{{\mathrm {pole}}}}} }$).
VALUE (MeV) DOCUMENT ID TECN  COMMENT
$\bf{ (400 - 550)−{\mit i}(200 - 350)}$ OUR ESTIMATE
• • • We do not use the following data for averages, fits, limits, etc. • • •
$(512 \pm15)−{\mit i}(188 \pm12)$ 1
 2017
BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}$3 ${{\mathit \pi}}$
$(440 \pm10)−{\mit i}(238 \pm10)$ 2
 2012
RVUE Compilation
$(445 \pm25)−{\mit i}(278 {}^{+22}_{-18})$ 3, 4
 2011
RVUE Compilation
$(457 {}^{+14}_{-13})−{\mit i}(279 {}^{+11}_{-7})$ 5, 3
 2011
RVUE Compilation
$(442 {}^{+5}_{-8})−{\mit i}(274 {}^{+6}_{-5})$ 6
 2011
RVUE Compilation
$(452 \pm13)−{\mit i}(259 \pm16)$ 7
 2010
RVUE Compilation
$(448 \pm43)−{\mit i}(266 \pm43)$ 8
 2010
RVUE Compilation
$(455 \pm6 {}^{+31}_{-13})−{\mit i}(278 \pm6 {}^{+34}_{-43})$ 9
 2008
RVUE Compilation
$(463 \pm6 {}^{+31}_{-17})−{\mit i}(259 \pm6 {}^{+33}_{-34})$ 10
 2008
RVUE Compilation
$(552 {}^{+84}_{-106})−{\mit i}(232 {}^{+81}_{-72})$ 11
 2007 A
BES2 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
$(466 \pm18)−{\mit i}(223 \pm28)$ 12
 2007
CLEO ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$
$(472 \pm30)−{\mit i}(271 \pm30)$ 13
 2007 A
RVUE Compilation
$(484 \pm17)−{\mit i}(255 \pm10)$
 2007
RVUE Compilation
$(430)−{\mit i}(325)$ 14
 2006
RVUE Compilation
$(441 {}^{+16}_{-8})−{\mit i}(272 {}^{+9}_{-12.5})$ 15
 2006
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
$(470 \pm50)−{\mit i}(285 \pm25)$ 16
 2005
RVUE
$(541 \pm39)−{\mit i}(252 \pm42)$ 17
 2004 A
BES2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$(528 \pm32)−{\mit i}(207 \pm23)$ 18
 2004
RVUE Compilation
$(440 \pm8)−{\mit i}(212 \pm15)$ 19
 2004 A
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
$(533 \pm25)−{\mit i}(249 \pm25)$ 20
 2003
RVUE
$517−{\mit i}\text{ 240}$
 2001
RVUE ${{\mathit \pi}^{0}}$ ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$(470 \pm30)−{\mit i}(295 \pm20)$ 15
 2001
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
$(535 {}^{+48}_{-36})−{\mit i}(155 {}^{+76}_{-53})$ 21
 2001
${{\mathit \Upsilon}{(3S)}}$ $\rightarrow$ ${{\mathit \Upsilon}}{{\mathit \pi}}{{\mathit \pi}}$
$610 \pm14−{\mit i}\text{ 620 }\pm26$ 22
 2001
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$(540 {}^{+36}_{-29})−{\mit i}(193 {}^{+32}_{-40})$
 2000 B
${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$445−{\mit i}\text{ 235}$
 1999
RVUE ${{\mathit \pi}}$ scalar form factor
$(523 \pm12)−{\mit i}(259 \pm7)$
 1999
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \sigma}}{{\mathit \sigma}}$
$442−{\mit i} \text{ 227}$
 1999
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$469−{\mit i}\text{ 203}$
 1999 B
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$445−{\mit i}\text{ 221}$
 1999 C
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \eta}}{{\mathit \eta}}$
$(1530 {}^{+90}_{-250})−{\mit i}(560 \pm40)$
 1998 B
RVUE Compilation
$420−{\mit i} \text{ 212}$
 1998
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$440−{\mit i}\text{ 245}$ 23
 1997
RVUE Compilation
$(602 \pm26)−{\mit i}(196 \pm27)$ 24
 1997
${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
$(537 \pm20)−{\mit i}(250 \pm17)$ 25
 1997 B
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , 4${{\mathit \pi}}$
$470−{\mit i}\text{ 250}$ 26, 27
 1996
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit \eta}}{{\mathit \pi}}$
$387−{\mit i}\text{ 305}$ 28, 27
 1995
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$420−{\mit i}\text{ 370}$ 29
 1994
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
$(506 \pm10)−{\mit i}(247 \pm3)$
 1994
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$370−{\mit i}\text{ 356}$ 30
 1994 B
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$408−{\mit i}\text{ 342}$ 30, 27
 1993
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$470−{\mit i}\text{ 208}$ 31
 1986
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \eta}}{{\mathit \eta}}$ , ...
$(750 \pm50)−{\mit i}(450 \pm50)$ 32
 1979
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$(660 \pm100)−{\mit i}(320 \pm70)$
 1973
HBC ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$
$650−{\mit i}\text{ 370}$ 33
 1972
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
1  S-matrix pole; 8595 events.
2  Applying the chiral unitary approach at NLO to the ${{\mathit K}_{{e4}}}$ data of BATLEY 2010 and ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit N}}$ data of HYAMS 1973 , GRAYER 1974 , and PROTOPOPESCU 1973 .
3  Uses the ${{\mathit K}_{{e4}}}$ data of BATLEY 2010C and the ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit N}}$ data of HYAMS 1973 , GRAYER 1974 , and PROTOPOPESCU 1973 .
4  Analytic continuation using Roy equations.
5  Analytic continuation using GKPY equations.
6  Using Roy equations.
7  Average of three variants of the analytic K-matrix model. Uses the ${{\mathit K}_{{e4}}}$ data of BATLEY 2008A and the ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit N}}$ data of HYAMS 1973 and GRAYER 1974 .
8  Average of the analyses of three data sets in the K-matrix model. Uses the data of BATLEY 2008A, HYAMS 1973 , and GRAYER 1974 , partially of COHEN 1980 or ETKIN 1982B.
9  From the ${{\mathit K}_{{e4}}}$ data of BATLEY 2008A and ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit N}}$ data of HYAMS 1973 .
10  From the ${{\mathit K}_{{e4}}}$ data of BATLEY 2008A and ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit N}}$ data of PROTOPOPESCU 1973 , GRAYER 1974 , and ESTABROOKS 1974 .
11  From a mean of three different ${{\mathit f}_{{0}}{(500)}}$ parametrizations. Uses 40k events.
12  From an isobar model using 2.6k events.
13  Reanalysis of ABLIKIM 2004A, PISLAK 2001 , and HYAMS 1973 data.
14  Using the N/D method.
15  From the solution of the Roy equation (ROY 1971 ) for the isoscalar S-wave and using a phase-shift analysis of HYAMS 1973 and PROTOPOPESCU 1973 data.
16  Reanalysis of the data from PROTOPOPESCU 1973 , ESTABROOKS 1974 , GRAYER 1974 , ROSSELET 1977 , PISLAK 2003 , and AKHMETSHIN 2004 .
17  From a mean of six different analyses and ${{\mathit f}_{{0}}{(500)}}$ parameterizations.
18  Using data on ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \pi}}{{\mathit \pi}}$ from BAI 2000E and on ${{\mathit \Upsilon}{(nS)}}$ $\rightarrow$ ${{\mathit \Upsilon}{(mS)}}{{\mathit \pi}}{{\mathit \pi}}$ from BUTLER 1994B and ALEXANDER 1998 .
19  Reanalysis of data from PROTOPOPESCU 1973 , ESTABROOKS 1974 , GRAYER 1974 , and COHEN 1980 in the unitarized ChPT model.
20  From a combined analysis of HYAMS 1973 , AUGUSTIN 1989 , AITALA 2001B, and PISLAK 2001 .
21  A similar analysis (KOMADA 2001 ) finds ($580$ ${}^{+79}_{-30})−{\mit i}(190$ ${}^{+107}_{-49}$) MeV.
22  Coupled channel reanalysis of BATON 1970 , BENSINGER 1971 , BAILLON 1972 , HYAMS 1973 , HYAMS 1975 , ROSSELET 1977 , COHEN 1980 , and ETKIN 1982B using the uniformizing variable.
23  Using the inverse amplitude method and data of ESTABROOKS 1973 , GRAYER 1974 , and PROTOPOPESCU 1973 .
24  Reanalysis of data from HYAMS 1973 , GRAYER 1974 , SRINIVASAN 1975 , and ROSSELET 1977 using the interfering amplitude method.
25  Average and spread of 4 variants (up'' and down'') of KAMINSKI 1997B 3-channel model.
26  Uses data from BEIER 1972B, OCHS 1973 , HYAMS 1973 , GRAYER 1974 , ROSSELET 1977 , CASON 1983 , ASTON 1988 , and ARMSTRONG 1991B. Coupled channel analysis with flavor symmetry and all light two-pseudoscalars systems.
27  Demonstrates explicitly that ${{\mathit f}_{{0}}{(500)}}$ and ${{\mathit f}_{{0}}{(1370)}}$ are two different poles.
28  Analysis of data from FALVARD 1988 .
29  Analysis of data from OCHS 1973 , ESTABROOKS 1975 , ROSSELET 1977 , and MUKHIN 1980 .
30  Analysis of data from OCHS 1973 , GRAYER 1974 , and ROSSELET 1977 .
31  Coupled-channel analysis using data from PROTOPOPESCU 1973 , HYAMS 1973 , HYAMS 1975 , GRAYER 1974 , ESTABROOKS 1974 , ESTABROOKS 1975 , FROGGATT 1977 , CORDEN 1979 , BISWAS 1981 .
32  Analysis of data from APEL 1972C, GRAYER 1974 , CASON 1976 , PAWLICKI 1977 . Includes spread and errors of 4 solutions.
33  Analysis of data from BATON 1970 , BENSINGER 1971 , COLTON 1971 , BAILLON 1972 ,PROTOPOPESCU 1973 , and WALKER 1967 .
References:
 ABLIKIM 2017
PRL 118 012001 Amplitude Analysis of the Decays ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
PR D86 034003 Size of the ${{\mathit \sigma}}$ Meson and Its Nature
 GARCIA-MARTIN 2011
PRL 107 072001 Precise Determination of the ${{\mathit f}_{{0}}{(600)}}$ and ${{\mathit f}_{{0}}{(980)}}$ Pole Parameters from a Dispersive Data Analysis
 MOUSSALLAM 2011
EPJ C71 1814 Couplings of Light $\mathit I = 0$ Scalar Mesons to Simple Operators in the Complex Plane
 MENNESSIER 2010
PL B688 59 The ${{\mathit \sigma}}$ and ${{\mathit f}_{{0}}{(980)}}$ from ${{\mathit K}_{{e4}}}$⊕${{\mathit \pi}}{{\mathit \pi}}$ Scatterings Data
 CAPRINI 2008
PR D77 114019 Finding the $\sigma$ Pole by Analytic Extrapolation of ${{\mathit \pi}}{{\mathit \pi}}$ Scattering Data
 ABLIKIM 2007A
PL B645 19 Production of ${{\mathit \sigma}}$ in ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
 BONVICINI 2007
PR D76 012001 Dalitz Plot Analysis of the ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ Decay
 BUGG 2007A
JP G34 151 The Mass of the $\sigma$ Pole
 GARCIA-MARTIN 2007
PR D76 074034 Experimental Status of the ${{\mathit \pi}}{{\mathit \pi}}$ Isoscalar ${\mathit S}{\mathrm wave}$ at Low Energy: ${{\mathit f}_{{0}}{(600)}}$ Pole and Scattering Length
 ANISOVICH 2006
IJMP A21 3615 Scalar Mesons and Low-Mass Sigma: Does the $\sigma$ Reveal the Confinement Singularity?
 CAPRINI 2006
PRL 96 132001 Mass and Width of the Lowest Resonance in QCD
 ZHOU 2005
JHEP 0502 043 The Pole Structure of the Unitary, Crossing Symmetric Low Energy ${{\mathit \pi}}{{\mathit \pi}}$ Scattering Amplitudes
 ABLIKIM 2004A
PL B598 149 The $\sigma$ Pole in ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
 GALLEGOS 2004
PR D69 074033 ${{\mathit \pi}}{{\mathit \pi}}$ Invariant Mass Spectrum in ${{\mathit V}^{\,'}}$ $\rightarrow$ ${{\mathit V}}{{\mathit \pi}}{{\mathit \pi}}$ and the ${{\mathit f}_{{0}}{(600)}}$ Pole
 PELAEZ 2004A
MPL A19 2879 Light Scalars as Tetraquarks or Two-meson States from Large ${{\mathit N}_{{c}}}$ and Unitarized Chiral Perturbation Theory
 BUGG 2003
PL B572 1 Comments on the $\sigma$ and $\kappa$
 BLACK 2001
PR D64 014031 Unitarized Pseudoscalar Meson Scattering Amplitudes in Three Flavor Linear Sigma Models
 COLANGELO 2001
NP B603 125 ${{\mathit \pi}}{{\mathit \pi}}$ Scattering
 ISHIDA 2001
PL B518 47 The ${{\mathit \sigma}}$ Meson Production in Excited ${{\mathit \Upsilon}}$ Decay Processes: Constraint from Chiral Symmetry
 SUROVTSEV 2001
PR D63 054024 Existence of the ${{\mathit \sigma}}$ Meson below 1 GeV and ${{\mathit f}_{{0}}{(1500)}}$ Glueball
 ISHIDA 2000B
PTP 104 203 Effect of Light ${{\mathit \sigma}}$ Meson Production in ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ at Rest
 HANNAH 1999
PR D60 017502 Pion Scalar Formfactor and the ${{\mathit \sigma}}$ Meson
 KAMINSKI 1999
EPJ C9 141 Scalar Mesons and Multichannel Amplitudes
 OLLER 1999
PR D60 099906 (erratum) Meson-Meson Interaction in a Nonperturbative Chiral Approach
 OLLER 1999C
PR D60 074023 N/D Description of Two Meson Amplitudes and Chiral Symmetry
 OLLER 1999B
NP A652 407 (erratum) Chiral Symmetry Amplitudes in the S-wave Isoscalar and Isovector Channels and the ${{\mathit \sigma}}$, ${{\mathit f}_{{0}}{(980)}}$, ${{\mathit a}_{{0}}{(980)}}$ Scalar Mesons
 ANISOVICH 1998B
SPU 41 419 The Lightest Scalar Glueball
 LOCHER 1998
EPJ C4 317 Structure of ${{\mathit f}_{{0}}{(980)}}$ from a Coupled Channel Analysis of S-wave ${{\mathit \pi}}{{\mathit \pi}}$ Scattering
PR D56 3057 Inverse Amplitude Method in Chiral Perturbation Theory
 ISHIDA 1997
PTP 98 1005 Further Analysis on sigma Particle Properties
 KAMINSKI 1997B
PL B413 130 Three Channel Model of Meson-Meson Scattering and Scalar Meson Spectroscopy
 TORNQVIST 1996
PRL 76 1575 Resurrection of the ${{\mathit \sigma}}$ Meson
 JANSSEN 1995
PR D52 2690 On the Structure of the Scalar Mesons ${{\mathit f}_{{0}}{(975)}}$ and ${{\mathit a}_{{0}}{(980)}}$
 ACHASOV 1994
PR D49 5779 Phenomenological $\sigma$ Models
 KAMINSKI 1994
PR D50 3145 Relativistic Effects in the Scalar Meson Dynamics
 ZOU 1994B
PR D50 591 Remarks on $\mathit I = 0$ $\mathit J{}^{PC} = 0{}^{++}$ States: $\sigma /\epsilon$ and ${{\mathit f}_{{0}}{(975)}}$
 ZOU 1993
PR D48 3948 Is ${{\mathit f}_{{0}}{(975)}}$ a Narrow Resonance?
 VANBEVEREN 1986
ZPHY C30 615 A Low Lying Scalar Meson Nonet in a Unitarized Meson Model
 ESTABROOKS 1979
PR D19 2678 Where and What are the Scalar Mesons?
 PROTOPOPESCU 1973
PR D7 1279 ${{\mathit \pi}}{{\mathit \pi}}$ Partial Wave Analysis from Reactions ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \Delta}^{++}}$ and ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \Delta}^{++}}$ at 7.1 ${\mathrm {GeV/}}\mathit c$
 BASDEVANT 1972
PL 41B 178 ${{\mathit \pi}}{{\mathit \pi}}$ Phenomenology Below 1100 MeV