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

INSPIRE   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) $(458 \pm7 {}^{+4}_{-10})−{\mit i}(245 \pm6 {}^{+7}_{-10})$ 1 DANILKIN 2021 RVUE Compilation $(410 \pm20)−{\mit i}(240 \pm15)$ SARANTSEV 2021 RVUE ${{\mathit J / \psi}{(1S)}}$ $\rightarrow$ ${{\mathit \gamma}}$ (${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \eta}}{{\mathit \eta}}$ , ${{\mathit \omega}}{{\mathit \phi}}$) $(512 \pm15)−{\mit i}(188 \pm12)$ 2 ABLIKIM 2017 BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}$3 ${{\mathit \pi}}$ $(440 \pm10)−{\mit i}(238 \pm10)$ 3 ALBALADEJO 2012 RVUE Compilation $(445 \pm25)−{\mit i}(278 {}^{+22}_{-18})$ 4, 5 GARCIA-MARTIN 2011 RVUE Compilation $(457 {}^{+14}_{-13})−{\mit i}(279 {}^{+11}_{-7})$ 6, 4 GARCIA-MARTIN 2011 RVUE Compilation $(442 {}^{+5}_{-8})−{\mit i}(274 {}^{+6}_{-5})$ 7 MOUSSALLAM 2011 RVUE Compilation $(452 \pm13)−{\mit i}(259 \pm16)$ 8 MENNESSIER 2010 RVUE Compilation $(448 \pm43)−{\mit i}(266 \pm43)$ 9 MENNESSIER 2010 RVUE Compilation $(455 \pm6 {}^{+31}_{-13})−{\mit i}(278 \pm6 {}^{+34}_{-43})$ 10 CAPRINI 2008 RVUE Compilation $(463 \pm6 {}^{+31}_{-17})−{\mit i}(259 \pm6 {}^{+33}_{-34})$ 11 CAPRINI 2008 RVUE Compilation $(552 {}^{+84}_{-106})−{\mit i}(232 {}^{+81}_{-72})$ 12 ABLIKIM 2007 A BES2 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$ $(466 \pm18)−{\mit i}(223 \pm28)$ 13 BONVICINI 2007 CLEO ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ $(472 \pm30)−{\mit i}(271 \pm30)$ 14 BUGG 2007 A RVUE Compilation $(484 \pm17)−{\mit i}(255 \pm10)$ GARCIA-MARTIN 2007 RVUE Compilation $(430)−{\mit i}(325)$ 15 ANISOVICH 2006 RVUE Compilation $(441 {}^{+16}_{-8})−{\mit i}(272 {}^{+9}_{-12.5})$ 16 CAPRINI 2006 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $(470 \pm50)−{\mit i}(285 \pm25)$ 17 ZHOU 2005 RVUE $(541 \pm39)−{\mit i}(252 \pm42)$ 18 ABLIKIM 2004 A BES2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $(528 \pm32)−{\mit i}(207 \pm23)$ 19 GALLEGOS 2004 RVUE Compilation $(533 \pm25)−{\mit i}(249 \pm25)$ 20 BUGG 2003 RVUE $517−{\mit i}\text{ 240}$ BLACK 2001 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $(470 \pm30)−{\mit i}(295 \pm20)$ 16 COLANGELO 2001 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $(535 {}^{+48}_{-36})−{\mit i}(155 {}^{+76}_{-53})$ 21 ISHIDA 2001 ${{\mathit \Upsilon}{(3S)}}$ $\rightarrow$ ${{\mathit \Upsilon}}{{\mathit \pi}}{{\mathit \pi}}$ $610 \pm14−{\mit i}(310 \pm13)$ 22 SUROVTSEV 2001 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $(540 {}^{+36}_{-29})−{\mit i}(193 {}^{+32}_{-40})$ ISHIDA 2000 B ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $445−{\mit i}\text{ 235}$ HANNAH 1999 RVUE ${{\mathit \pi}}$ scalar form factor $(523 \pm12)−{\mit i}(259 \pm7)$ KAMINSKI 1999 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$, ${{\mathit \sigma}}{{\mathit \sigma}}$ $442−{\mit i} \text{ 227}$ OLLER 1999 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $469−{\mit i}\text{ 203}$ OLLER 1999 B RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $445−{\mit i}\text{ 221}$ OLLER 1999 C 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 1998 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $440−{\mit i}\text{ 245}$ 23 DOBADO 1997 RVUE Compilation $(602 \pm26)−{\mit i}(196 \pm27)$ 24 ISHIDA 1997 ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $(537 \pm20)−{\mit i}(250 \pm17)$ 25 KAMINSKI 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 TORNQVIST 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 JANSSEN 1995 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $420−{\mit i}\text{ 370}$ 29 ACHASOV 1994 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $(506 \pm10)−{\mit i}(247 \pm3)$ KAMINSKI 1994 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $370−{\mit i}\text{ 356}$ 30 ZOU 1994 B RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $408−{\mit i}\text{ 342}$ 30, 27 ZOU 1993 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $470−{\mit i}\text{ 208}$ 31 VANBEVEREN 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 ESTABROOKS 1979 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $(660 \pm100)−{\mit i}(320 \pm70)$ PROTOPOPESCU 1973 HBC ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$, ${{\mathit K}}{{\overline{\mathit K}}}$ $650−{\mit i}\text{ 370}$ 33 BASDEVANT 1972 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.

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