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${{\mathit f}_{{{0}}}{(500)}}$ T-MATRIX POLE $\sqrt {\mathit s }$

INSPIRE JSON (beta) PDGID:

M014PP

Note that $\Gamma $ = $−$2 Im($\sqrt {s }$).

VALUE (MeV)

DOCUMENT ID

TECN

COMMENT

$\bf{ (400 - 550)−{\mit i}(200 - 350)}$

OUR ESTIMATE (see Fig. 64.3 in the review)

$(458 \pm7 {}^{+4}_{-10})−{\mit i}(245 \pm6 {}^{+7}_{-10})$

DANILKIN

RVUE

Compilation

$(410 \pm20)−{\mit i}(240 \pm15)$

SARANTSEV

RVUE

${{\mathit J / \psi}{(1S)}}$ $\rightarrow$ ${{\mathit \gamma}}$ (${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \eta}}{{\mathit \eta}}$ , ${{\mathit \omega}}{{\mathit \phi}}$)

$(512 \pm15)−{\mit i}(188 \pm12)$

ABLIKIM

BES3

${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}$3 ${{\mathit \pi}}$

$(440 \pm10)−{\mit i}(238 \pm10)$

ALBALADEJO

RVUE

Compilation

$(445 \pm25)−{\mit i}(278 {}^{+22}_{-18})$

⁴ ^{, 5}

GARCIA-MARTIN

RVUE

Compilation

$(457 {}^{+14}_{-13})−{\mit i}(279 {}^{+11}_{-7})$

⁶ ^{, 4}

GARCIA-MARTIN

RVUE

Compilation

$(442 {}^{+5}_{-8})−{\mit i}(274 {}^{+6}_{-5})$

⁷

MOUSSALLAM

RVUE

Compilation

$(452 \pm13)−{\mit i}(259 \pm16)$

⁸

MENNESSIER

RVUE

Compilation

$(448 \pm43)−{\mit i}(266 \pm43)$

⁹

MENNESSIER

RVUE

Compilation

$(455 \pm6 {}^{+31}_{-13})−{\mit i}(278 \pm6 {}^{+34}_{-43})$

¹⁰

CAPRINI

RVUE

Compilation

$(463 \pm6 {}^{+31}_{-17})−{\mit i}(259 \pm6 {}^{+33}_{-34})$

¹¹

CAPRINI

RVUE

Compilation

$(552 {}^{+84}_{-106})−{\mit i}(232 {}^{+81}_{-72})$

¹²

ABLIKIM

BES2

${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$

$(466 \pm18)−{\mit i}(223 \pm28)$

¹³

BONVICINI

CLEO

${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$

$(472 \pm30)−{\mit i}(271 \pm30)$

¹⁴

BUGG

RVUE

Compilation

$(484 \pm17)−{\mit i}(255 \pm10)$

GARCIA-MARTIN

RVUE

Compilation

$(430)−{\mit i}(325)$

¹⁵

ANISOVICH

RVUE

Compilation

$(441 {}^{+16}_{-8})−{\mit i}(272 {}^{+9}_{-12.5})$

¹⁶

CAPRINI

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

$(470 \pm50)−{\mit i}(285 \pm25)$

¹⁷

ZHOU

RVUE

$(541 \pm39)−{\mit i}(252 \pm42)$

¹⁸

ABLIKIM

BES2

${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$

$(528 \pm32)−{\mit i}(207 \pm23)$

¹⁹

GALLEGOS

RVUE

Compilation

$(533 \pm25)−{\mit i}(249 \pm25)$

²⁰

BUGG

RVUE

$517−{\mit i}\text{ 240}$

BLACK

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

$(470 \pm30)−{\mit i}(295 \pm20)$

¹⁶

COLANGELO

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

$(535 {}^{+48}_{-36})−{\mit i}(155 {}^{+76}_{-53})$

²¹

ISHIDA

${{\mathit \Upsilon}{(3S)}}$ $\rightarrow$ ${{\mathit \Upsilon}}{{\mathit \pi}}{{\mathit \pi}}$

$610 \pm14−{\mit i}(310 \pm13)$

²²

SUROVTSEV

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$(540 {}^{+36}_{-29})−{\mit i}(193 {}^{+32}_{-40})$

ISHIDA

${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$

$445−{\mit i}\text{ 235}$

HANNAH

RVUE

${{\mathit \pi}}$ scalar form factor

$(523 \pm12)−{\mit i}(259 \pm7)$

KAMINSKI

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$, ${{\mathit \sigma}}{{\mathit \sigma}}$

$442−{\mit i} \text{ 227}$

OLLER

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$469−{\mit i}\text{ 203}$

OLLER

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$445−{\mit i}\text{ 221}$

OLLER

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$, ${{\mathit \eta}}{{\mathit \eta}}$

$420−{\mit i} \text{ 212}$

LOCHER

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$

$440−{\mit i}\text{ 245}$

²³

DOBADO

RVUE

Compilation

$(602 \pm26)−{\mit i}(196 \pm27)$

²⁴

ISHIDA

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

$(537 \pm20)−{\mit i}(250 \pm17)$

²⁵

KAMINSKI

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}

TORNQVIST

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}

JANSSEN

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$420−{\mit i}\text{ 370}$

²⁹

ACHASOV

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

$(506 \pm10)−{\mit i}(247 \pm3)$

KAMINSKI

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$370−{\mit i}\text{ 356}$

³⁰

ZOU

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$408−{\mit i}\text{ 342}$

³⁰ ^{, 27}

ZOU

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$470−{\mit i}\text{ 208}$

³¹

VANBEVEREN

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

ESTABROOKS

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$(660 \pm100)−{\mit i}(320 \pm70)$

PROTOPOPESCU

HBC

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$

$650−{\mit i}\text{ 370}$

³³

BASDEVANT

RVUE

${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$

¹	Data driven analysis using partial-wave dispersion relations.

²	S-matrix pole; 8595 events.

³	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.

⁴	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.

⁵	Analytic continuation using Roy equations.

⁶	Analytic continuation using GKPY equations.

⁷	Using Roy equations.

⁸	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.

⁹	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.

¹⁰	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.

¹¹	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.

¹²	From a mean of three different ${{\mathit f}_{{{0}}}{(500)}}$ parametrizations. Uses 40k events.

¹³	From an isobar model using 2.6k events.

¹⁴	Reanalysis of ABLIKIM 2004A, PISLAK 2001, and HYAMS 1973 data.

¹⁵	Using the N/D method.

¹⁶	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.

¹⁷	Reanalysis of the data from PROTOPOPESCU 1973, ESTABROOKS 1974, GRAYER 1974, ROSSELET 1977, PISLAK 2003, and AKHMETSHIN 2004.

¹⁸	From a mean of six different analyses and ${{\mathit f}_{{{0}}}{(500)}}$ parameterizations.

¹⁹	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.

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

Except where otherwise noted, content of the 2025 Review of Particle Physics is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT and KEK (Japan), INFN (Italy) and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2025. See LBNL disclaimers.

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