Three-body Final State Interaction in η→3π

Guo, Peng; Danilkin, Igor V.; Schott, Diane; Fernández-Ramírez, C.; Mathieu, V.; Szczepaniak, Adam P.

doi:10.1103/PhysRevD.92.054016

Title: Three-body Final State Interaction in η→3π

Journal Article · Fri Sep 11 00:00:00 EDT 2015 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI: https://doi.org/10.1103/PhysRevD.92.054016 · OSTI ID:1223489

Guo, Peng ^[1]; Danilkin, Igor V. ^[2]; Schott, Diane ^[3]; Fernández-Ramírez, C. ^[2]; Mathieu, V. ^[4]; Szczepaniak, Adam P. ^[1]

Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); George Washington Univ., Washington, DC (United States)
Indiana Univ., Bloomington, IN (United States)

We present an unitary dispersive model for the $$\eta \to 3 \pi$$ decay process based upon the Khuri-Treiman equations which are solved by means of the Pasquier inversion method. The description of the hadronic final-state interactions for the $$\eta \to 3\pi$$ decay is essential to reproduce the available data and to understand the existing discrepancies between Dalitz plot parameters from experiment and chiral perturbation theory. Our approach incorporates substraction constants that are fixed by fitting the recent high-statistics WASA-at-COSY data for $$\eta \to \pi^+ \pi^- \pi^0$$. Based on the parameters obtained we predict the slope parameter for the neutral channel to be $$\alpha=-0.022\pm 0.004$$. Through matching to next-to-leading order chiral perturbation theory we estimate the quark mass double ratio to be $$Q=21.4 \pm 0.4$$.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Contributing Organization:: Joint Physics Analysis Center

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1223489

Report Number(s):: JLAB-THY--15-2041; DOE/OR/23177--3343; arXiv:1505.01715

Journal Information:: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Journal Issue: 5 Vol. 92; ISSN PRVDAQ; ISSN 1550-7998

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

Neutral decays of the ?-meson Alde, D.; Binon, F.; Bricman, C. Zeitschrift f�r Physik C Particles and Fields, Vol. 25, Issue 3 https://doi.org/10.1007/BF01547921	journal	September 1984
Final-state interactions among three particles Aitchison, I. J. R. Il Nuovo Cimento, Vol. 35, Issue 2 https://doi.org/10.1007/BF02735329	journal	January 1965
Rescattering effects in η → 3π decays Schneider, Sebastian P.; Kubis, Bastian; Ditsche, Christoph Journal of High Energy Physics, Vol. 2011, Issue 2 https://doi.org/10.1007/JHEP02(2011)028	journal	February 2011
Chiral perturbation theory to one loop Gasser, J.; Leutwyler, H. Annals of Physics, Vol. 158, Issue 1 https://doi.org/10.1016/0003-4916(84)90242-2	journal	November 1984
Current algebra and the decay η → 3 π Sutherland, D. G. Physics Letters, Vol. 23, Issue 6 https://doi.org/10.1016/0031-9163(66)90477-X	journal	November 1966
Dispersive analysis of the decay η → 3π Anisovich, A. V.; Leutwyler, H. Physics Letters B, Vol. 375, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00192-X	journal	May 1996
Current algebra and η → 3π Bell, J. S.; Sutherland, D. G. Nuclear Physics B, Vol. 4, Issue 3 https://doi.org/10.1016/0550-3213(68)90316-7	journal	January 1968
η-X mixing, η→3π and chiral lagrangians Osborn, H.; Wallace, D. J. Nuclear Physics B, Vol. 20, Issue 1 https://doi.org/10.1016/0550-3213(70)90194-X	journal	June 1970
η → 3π to one loop Gasser, J.; Leutwyler, H. Nuclear Physics B, Vol. 250, Issue 1-4 https://doi.org/10.1016/0550-3213(85)90494-8	journal	January 1985
The low energy ππ amplitude to one and two loops Knecht, M.; Moussallam, B.; Sterna, J. Nuclear Physics B, Vol. 457, Issue 3 https://doi.org/10.1016/0550-3213(95)00515-3	journal	December 1995
Final state interactions and Khuri-Treiman equations in,ν → 3π decays Kambor, J.; Wiesendanger, C.; Wyler, D. Nuclear Physics B, Vol. 465, Issue 1-2 https://doi.org/10.1016/0550-3213(95)00676-1	journal	April 1996
Roy equation analysis of ππ scattering Ananthanarayan, B.; Colangelo, G.; Gasser, J. Physics Reports, Vol. 353, Issue 4 https://doi.org/10.1016/S0370-1573(01)00009-6	journal	November 2001
Momentum dependence of the decay η→π+π−π0 Abele, A.; Adomeit, J.; Amsler, C. Physics Letters B, Vol. 417, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)01376-2	journal	January 1998
Decay dynamics of the process η→3π0 Abele, A.; Adomeit, J.; Amsler, C. Physics Letters B, Vol. 417, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)01377-4	journal	January 1998
QCD isospin breaking in meson masses, decay constants and quark mass ratios Amoros, G.; Bijnens, J.; Talavera, P. Nuclear Physics B, Vol. 602, Issue 1-2 https://doi.org/10.1016/S0550-3213(01)00121-3	journal	May 2001
Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian Gasparyan, A.; Lutz, M. F. M. Nuclear Physics A, Vol. 848, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2010.08.006	journal	December 2010
Measurement of the KL→e+e−e+e− decay rate Lai, A.; Marras, D.; Bevan, A. Physics Letters B, Vol. 615, Issue 1-2 https://doi.org/10.1016/j.physletb.2005.03.078	journal	May 2005
Measurement of the η→3π0 Dalitz plot distribution with the WASA detector at COSY Adolph, C.; Angelstein, M.; Bashkanov, M. Physics Letters B, Vol. 677, Issue 1-2 https://doi.org/10.1016/j.physletb.2009.03.063	journal	June 2009
Measurement of the η→3π0 slope parameter α with the KLOE detector Ambrosino, F.; Antonelli, A.; Antonelli, M. Physics Letters B, Vol. 694, Issue 1 https://doi.org/10.1016/j.physletb.2010.09.022	journal	October 2010
Odd and even partial waves of η π − and η ′ π − in π − p → η ( ′ ) π − p at 191 GeV / c Adolph, C.; Akhunzyanov, R.; Alexeev, M. G. Physics Letters B, Vol. 740 https://doi.org/10.1016/j.physletb.2014.11.058	journal	January 2015
Measurement of the ω → π + π − π 0 Dalitz plot distribution Kubis, B.; Leupold, S.; Adlarson, P. Physics Letters B, Vol. 770 https://doi.org/10.1016/j.physletb.2017.03.050	journal	July 2017
η→3π at two loops in Chiral Perturbation Theory Bijnens, Johan; Ghorbani, Karim Journal of High Energy Physics, Vol. 2007, Issue 11 https://doi.org/10.1088/1126-6708/2007/11/030	journal	November 2007
Determination of η → π ⁺ π ⁻ π ⁰ Dalitz plot slopes and asymmetries with the KLOE detector collaboration, The KLOE; Ambrosino, F.; Antonelli, A. Journal of High Energy Physics, Vol. 2008, Issue 05 https://doi.org/10.1088/1126-6708/2008/05/006	journal	May 2008
Pion-Pion Scattering and K ± → 3 π Decay Khuri, N. N.; Treiman, S. B. Physical Review, Vol. 119, Issue 3 https://doi.org/10.1103/PhysRev.119.1115	journal	August 1960
Khuri-Treiman Representation and Perturbation Theory Bronzan, John B.; Kacser, Claude Physical Review, Vol. 132, Issue 6 https://doi.org/10.1103/PhysRev.132.2703	journal	December 1963
Analytic Structure of Partial-Wave Amplitudes for Production and Decay Processes Kacser, C. Physical Review, Vol. 132, Issue 6 https://doi.org/10.1103/PhysRev.132.2712	journal	December 1963
Dispersion Theory Model of Three-Body Production and Decay Processes Aitchison, I. J. R. Physical Review, Vol. 137, Issue 4B https://doi.org/10.1103/PhysRev.137.B1070	journal	February 1965
Three-Body Unitarity and Khuri-Treiman Amplitudes Aitchison, I. J. R.; Pasquier, R. Physical Review, Vol. 152, Issue 4 https://doi.org/10.1103/PhysRev.152.1274	journal	December 1966
Phenomenological Model of Strong and Weak Interactions in Chiral U ( 3 ) ⊗ U ( 3 ) Cronin, Jeremiah A. Physical Review, Vol. 161, Issue 5 https://doi.org/10.1103/PhysRev.161.1483	journal	September 1967
Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes Pasquier, R.; Pasquier, J. Y. Physical Review, Vol. 170, Issue 5 https://doi.org/10.1103/PhysRev.170.1294	journal	June 1968
Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes. II Pasquier, R.; Pasquier, J. Y. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2482	journal	January 1969
Measurement of the slope parameter for the η → 3 π 0 decay in the pp → pp η reaction Bashkanov, M.; Bogoslawsky, D.; Calén, H. Physical Review C, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevC.76.048201	journal	October 2007
Measurement of the slope parameter α for the η → 3 π 0 decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C) Prakhov, S.; Nefkens, B. M. K.; Aguar-Bartolomé, P. Physical Review C, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevC.79.035204	journal	March 2009
Measurement of the η → π + π − π 0 Dalitz plot distribution Adlarson, P.; Augustyniak, W.; Bardan, W. Physical Review C, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevC.90.045207	journal	October 2014
Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson Aitchison, I. J. R.; Brehm, J. J. Physical Review D, Vol. 17, Issue 11 https://doi.org/10.1103/PhysRevD.17.3072	journal	June 1978
Experimental Determination of the Dalitz-Plot Distribution of the Decays η → π + π − π 0 and η → π + π − γ , and the Branching Ratio η → π + π − γ η → π + π − π 0 Gormley, M.; Hyman, E.; Lee, W. Physical Review D, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevD.2.501	journal	August 1970
What π − π scattering tells us about chiral perturbation theory Stern, J.; Sazdjian, H.; Fuchs, N. H. Physical Review D, Vol. 47, Issue 9 https://doi.org/10.1103/PhysRevD.47.3814	journal	May 1993
Study of Dalitz-Plot Distributions of the Decays η → π + π − π 0 and η → π + π − γ Layter, J. G.; Appel, J. A.; Kotlewski, A. Physical Review D, Vol. 7, Issue 9 https://doi.org/10.1103/PhysRevD.7.2565	journal	May 1973
Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV García-Martín, R.; Kamiński, R.; Peláez, J. R. Physical Review D, Vol. 83, Issue 7 https://doi.org/10.1103/PhysRevD.83.074004	journal	April 2011
Analytical dispersive construction of η → 3 π amplitude: First order in isospin breaking Kampf, Karol; Knecht, Marc; Novotný, Jiří Physical Review D, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevD.84.114015	journal	December 2011
Review of Particle Physics Beringer, J.; Arguin, J. -F.; Barnett, R. M. Physical Review D, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevD.86.010001	journal	July 2012
Leading isospin breaking effects on the lattice de Divitiis, G. M.; Frezzotti, R.; Lubicz, V. Physical Review D, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevD.87.114505	journal	June 2013
Dispersive analysis of ω / ϕ → 3 π , π γ * Danilkin, I. V.; Fernández-Ramírez, C.; Guo, P. Physical Review D, Vol. 91, Issue 9 https://doi.org/10.1103/PhysRevD.91.094029	journal	May 2015
Measurement of the matrix elements for the decays η → π + π − π 0 and η / η ′ → π 0 π 0 π 0 Ablikim, M.; Achasov, M. N.; Ai, X. C. Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.012014	journal	July 2015
A Model of Leptons Weinberg, Steven Physical Review Letters, Vol. 19, Issue 21 https://doi.org/10.1103/PhysRevLett.19.1264	journal	November 1967
Unitarity Condition Below Physical Thresholds in the Normal and Anomalous Cases Mandelstam, S. Physical Review Letters, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevLett.4.84	journal	January 1960
Determination of the Quadratic Slope Parameter in η → 3 π 0 Decay Tippens, W. B.; Prakhov, S.; Allgower, C. E. Physical Review Letters, Vol. 87, Issue 19 https://doi.org/10.1103/PhysRevLett.87.192001	journal	October 2001
Dynamics of η→3π0 decay Achasov, M. N.; Beloborodov, K. I.; Berdyugin, A. V. Journal of Experimental and Theoretical Physics Letters, Vol. 73, Issue 9 https://doi.org/10.1134/1.1385655	journal	May 2001
Determination of the Dalitz plot parameter $ \alpha$ for the decay $ \eta$ → 3 $ \pi^{0}_{}$ with the Crystal Ball at MAMI-B Unverzagt, M.; Aguar-Bartolomé, P.; Ahrens, J. The European Physical Journal A, Vol. 39, Issue 2 https://doi.org/10.1140/epja/i2008-10710-7	journal	January 2009
Electromagnetic corrections in η→3π decays Ditsche, Christoph; Kubis, Bastian; Meißner, Ulf-G. The European Physical Journal C, Vol. 60, Issue 1 https://doi.org/10.1140/epjc/s10052-009-0863-z	journal	February 2009
Review of lattice results concerning low-energy particle physics Colangelo, G.; Dürr, S.; Jüttner, A. The European Physical Journal C, Vol. 71, Issue 7 https://doi.org/10.1140/epjc/s10052-011-1695-1	journal	July 2011
Dispersive analysis of ω→3π and ϕ→3π decays Niecknig, Franz; Kubis, Bastian; Schneider, Sebastian P. The European Physical Journal C, Vol. 72, Issue 5 https://doi.org/10.1140/epjc/s10052-012-2014-1	journal	May 2012
Review of lattice results concerning low-energy particle physics Aoki, S.; Aoki, Y.; Bernard, C. The European Physical Journal C, Vol. 74, Issue 9 https://doi.org/10.1140/epjc/s10052-014-2890-7	journal	September 2014
Analyticity of $$\eta \pi $$ η π isospin-violating form factors and the $$\tau \rightarrow \eta \pi \nu $$ τ → η π ν second-class decay Descotes-Genon, S.; Moussallam, B. The European Physical Journal C, Vol. 74, Issue 7 https://doi.org/10.1140/epjc/s10052-014-2946-8	journal	July 2014
A new analysis of $\pi K$ scattering from Roy and Steiner type equations Büttiker, P.; Descotes-Genon, S.; Moussallam, B. The European Physical Journal C, Vol. 33, Issue 3 https://doi.org/10.1140/epjc/s2004-01591-1	journal	March 2004
Present and Future of Hadron Spectroscopy at Jefferson lab Battaglieri, M. International Journal of Modern Physics E, Vol. 19, Issue 05n06 https://doi.org/10.1142/S0218301310015291	journal	June 2010
Measurement of the ω → π+π−π0 Dalitz plot distribution Adlarson, P.; Augustyniak, W.; Bardan, W. RWTH Aachen University https://doi.org/10.18154/rwth-2017-06784	text	January 2017
Review of Particle Physics Beringer, J.; Arguin, J.; Barnett, R. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/phppubdb-24149	text	January 2012
Review of lattice results concerning low-energy particle physics Aoki, S.; Aoki, Y.; Becirevic, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01038	text	January 2016
Review of lattice results concerning low-energy particle physics Aoki, S.; Aoki, Y.; Bečirević, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01363	text	January 2017
Review of Particle Physics Tanabashi, M.; Hagiwara, K.; Hikasa, K. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03100	text	January 2018
Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian Gasparyan, A.; Lutz, M. F. M. arXiv https://doi.org/10.48550/arxiv.1003.3426	text	January 2010
What $π-π$ Scattering Tells Us About Chiral Perturbation Theory Stern, J.; Sazdjian, H.; Fuchs, N. H. arXiv https://doi.org/10.48550/arxiv.hep-ph/9301244	text	January 1993
Review of Particle Physics Group, Particle Data; Amsler, C.; Doser, M. Elsevier https://doi.org/10.5167/uzh-11249	text	January 2008
Study of the Dalitz Plot of the $\eta \rightarrow \pi ^+ \pi ^- \pi ^0$ Decay with the KLOE Detector Caldeira Balkeståhl, L. Acta Physica Polonica B, Vol. 46, Issue 1 https://doi.org/10.5506/APhysPolB.46.31	journal	January 2015
Review of lattice results concerning low-energy particle physics Wenger, Urs; Colangelo, Gilberto EDP Sciences https://doi.org/10.7892/boris.60235	text	January 2014

Cited By (15)

Theoretical analysis of the γγ ^(*) → π ⁰ η process Deineka, Oleksandra; Danilkin, Igor; Vanderhaeghen, Marc EPJ Web of Conferences, Vol. 199 https://doi.org/10.1051/epjconf/201919902005	journal	January 2019
One spatial dimensional finite volume three-body interaction for a short-range potential Guo, Peng Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/physrevd.95.054508	journal	March 2017
Theoretical analysis of the γ γ → π 0 η process Danilkin, Igor; Deineka, Oleksandra; Vanderhaeghen, Marc Physical Review D, Vol. 96, Issue 11 https://doi.org/10.1103/physrevd.96.114018	journal	December 2017
Numerical approach for finite volume three-body interaction Guo, Peng; Gasparian, Vladimir Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/physrevd.97.014504	journal	January 2018
Amplitude analysis of the anomalous decay η ′ → π + π − γ Dai, Ling-Yun; Kang, Xian-Wei; Meißner, Ulf-G. Physical Review D, Vol. 97, Issue 3 https://doi.org/10.1103/physrevd.97.036012	journal	February 2018
Variational approach to N -body interactions in finite volume Guo, Peng; Döring, Michael; Szczepaniak, Adam P. Physical Review D, Vol. 98, Issue 9 https://doi.org/10.1103/physrevd.98.094502	journal	November 2018
Multiple-particle interaction in ( 1 + 1 )-dimensional lattice model Guo, Peng; Morris, Tyler Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/physrevd.99.014501	journal	January 2019
η → 3 π : Study of the Dalitz Plot and Extraction of the Quark Mass Ratio Q Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich Physical Review Letters, Vol. 118, Issue 2 https://doi.org/10.1103/physrevlett.118.022001	journal	January 2017
Three-body unitarity with isobars revisited Mai, M.; Hu, B.; Döring, M. The European Physical Journal A, Vol. 53, Issue 9 https://doi.org/10.1140/epja/i2017-12368-4	journal	September 2017
Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P. The European Physical Journal C, Vol. 77, Issue 7 https://doi.org/10.1140/epjc/s10052-017-5024-1	journal	July 2017
What is the right formalism to search for resonances? Mikhasenko, M.; Pilloni, A.; Nys, J. The European Physical Journal C, Vol. 78, Issue 3 https://doi.org/10.1140/epjc/s10052-018-5670-y	journal	March 2018
Khuri–Treiman equations for $$\pi \pi $$ π π scattering Albaladejo, M.; Sherrill, N.; Fernández-Ramírez, C. The European Physical Journal C, Vol. 78, Issue 7 https://doi.org/10.1140/epjc/s10052-018-6045-0	journal	July 2018
Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich The European Physical Journal C, Vol. 78, Issue 11 https://doi.org/10.1140/epjc/s10052-018-6377-9	journal	November 2018
Solving integral equations in $$\eta \rightarrow 3\pi $$ η → 3 π Gasser, Jürg; Rusetsky, Akaki The European Physical Journal C, Vol. 78, Issue 11 https://doi.org/10.1140/epjc/s10052-018-6378-8	journal	November 2018
Variational approach to $N$-body interactions in finite volume Guo, Peng; Döring, Michael; Szczepaniak, Adam P. arXiv https://doi.org/10.48550/arxiv.1810.01261	text	January 2018

Similar Records

A preliminary analysis of {eta}'{yields}{eta}{pi}{pi} in chiral theories

Journal Article · Thu Aug 05 00:00:00 EDT 2010 · AIP Conference Proceedings · OSTI ID:21426483

Escribano, R

Status of the analysis of the pp{yields}pp({eta} {yields}3{pi}{sup 0}) reaction

Journal Article · Tue Nov 06 23:00:00 EST 2007 · AIP Conference Proceedings · OSTI ID:21039249

Vlasov, Peter

Studies of the {eta}{yields}{pi}{sup +}{pi}{sup -}e{sup +}e{sup -} decay channel

Journal Article · Tue Nov 06 23:00:00 EST 2007 · AIP Conference Proceedings · OSTI ID:21039254

Janusz, Michal

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Title: Three-body Final State Interaction in η→3π

Citation Formats

References (66)

Cited By (15)

Similar Records

Related Subjects