A Partial-Wave Analysis of Centrally Produced Two-Pseudoscalar Final States in pp Reactions at COMPASS Alexander Austregesilo for the COMPASS Collaboration ATHOS 2013 May 21-24, 2013 COMPASS Supported by
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Outline Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 2/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook The COMPASS Experiment Multi-Purpose Setup COMPASS Fixed-target experiment @ CERN SPS Two-stage magnetic spectrometer Broad kinematic range E/HCAL Tracking, calorimetry, particle ID SM2 SM1 target + RPD RICH Data Set CEDARs 190 GeV / c proton beam Liquid H 2 target Trigger on recoil proton A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 3/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Central Production × 6 10 Entries COMPASS 2009 → π π - 0.5 p p p + p s f π 2 M(p ) > / 2.0 GeV/c 1.5 0.4 π π - p + p s y f 0.3 r a n i m i l e r 0.2 p 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Feynman x F p p → p fast X p slow Proton beam impinging on liquid hydrogen target Double-Pomeron Exchange as glue-rich environment ⇒ Production of non- q ¯ q -mesons (Glue Balls, Hybrids) at central rapidities A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 4/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Central Production × 6 × 3 10 10 2 0.12 2 Events / 5MeV/c COMPASS 2009 Events / 5MeV/c COMPASS 2009 9 → π π → + - p p p + - p p p p K K p f s f s 0.1 ρ 8 (770) 7 0.08 6 y y r 5 r 0.06 a a f (980) n n 0 m i i m l i 4 i e l r e p p r 0.04 3 f (1270) 2 2 0.02 1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 1.2 1.4 1.6 1.8 2 2.2 2.4 π π - 2 + - 2 Invariant Mass of + System (GeV/c ) Invariant Mass of K K System (GeV/c ) p p → p fast X p slow Proton beam impinging on liquid hydrogen target Double-Pomeron Exchange as glue-rich environment ⇒ Production of non- q ¯ q -mesons (Glue Balls, Hybrids) at central rapidities Decay into two-pseudoscalar final state ( π + π − , π 0 π 0 , K + K − , η η , ..) A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 4/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Two-Body Partial-Wave Analysis in Mass Bins A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 5/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Partial-Wave Analysis X → π + π − Assumption: collision of two 1 ) θ COMPASS 2009 cos( 0.8 → π + π - p p p p space-like exchange particles ( P , R ) f s 0.6 0.4 Decay fully described by 0.2 M ( π + π − ) , cos ( θ ) and φ 0 y r a n m i -0.2 l i e p r -0.4 -0.6 -0.8 -1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 π + π - 2 Invariant Mass of (GeV/c ) φ 3 COMPASS 2009 → π π p p p + - p s f 2 1 0 y r a n i m i l e -1 r p -2 -3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 π π - Invariant Mass of + (GeV/c^2) A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 6/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Partial-Wave Analysis X → π + π − Assumption: collision of two 1 ) θ COMPASS 2009 cos( 0.8 → π + π - p p p p space-like exchange particles ( P , R ) f s 0.6 0.4 Decay fully described by 0.2 M ( π + π − ) , cos ( θ ) and φ 0 y r a n m i -0.2 Fit complex production amplitudes in l i e p r -0.4 mass bins to match spin contributions -0.6 and interference pattern -0.8 -1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 π + π - 2 Invariant Mass of (GeV/c ) φ 3 COMPASS 2009 → π π p p p + - p s f 2 1 0 y r a n i m i l e -1 r p -2 -3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 π π - Invariant Mass of + (GeV/c^2) A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 6/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Construction of Wave-Set Strong Interaction Conserves Parity Linear combination of spherical harmonics as eigenstates of reflectivity ǫ , limiting the spin projection m ≥ 0, waves with opposite ǫ do not interfere m ( θ, φ ) − ǫ ( − 1 ) m Y ℓ Y ǫℓ � Y ℓ � m ( θ, φ ) = c ( m ) − m ( θ, φ ) Naturality Minus-sign was chosen such that reflectivity coincide with exchanged naturality η for reaction with pion beam ’Pomeron beam’ has opposite parity → η = − ǫ For central production, natural transfers ( J P = 0 + , 1 − , 2 + , ...) correspond to ǫ = − 1 and are expected to dominate Techniques of amplitude analysis for two-pseudoscalar systems S.-U. Chung, [Phys. Rev. D 56 (1997), 7299] A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 7/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Partial-Wave Decomposition Expand intensity I ( θ, φ ) in terms of partial-waves for narrow mass bins: 2 � � � � � � T εℓ m Y εℓ I ( θ, φ ) = m ( θ, φ ) � � � � ε � � ℓ m Complex transition amplitudes T εℓ m , no dynamics Explicit incoherent sum over the reflectivities ε Spectroscopic notation: ℓ ǫ m Significant contributions only from ℓ = S , P , D , m ≤ 1 ⇒ Maximum Likelihood Fit in Mass Bins A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 8/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Partial-Wave Decomposition Expand intensity I ( θ, φ ) in terms of partial-waves for narrow mass bins: 2 � � � � � � T εℓ m Y εℓ I ( θ, φ ) = m ( θ, φ ) � � � � ε � � ℓ m Complex transition amplitudes T εℓ m , no dynamics Explicit incoherent sum over the reflectivities ε Spectroscopic notation: ℓ ǫ m Significant contributions only from ℓ = S , P , D , m ≤ 1 ⇒ Maximum Likelihood Fit in Mass Bins Inherent Ambiguities of Two-Pseudoscalar Final State Intensity can also be expressed as a 4 th -order polynomial Complex conjugation of the roots (’Barrelet zeros’) results in the same angular distribution, i.e. the same likelihood A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 8/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Barrelet Zeros 3 ) ) 2 k k COMPASS 2009 COMPASS 2009 Re(u Im(u → π π → π π p p p + - p p p p + - p f s f s 1.5 2 y r y 1 a r n 1 a i n m 0.5 i m i l e i 0 l 0 r e p r p -0.5 -1 -1 -2 -1.5 -3 -2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 π π - 2 π π - 2 Invariant Mass of + System (GeV/c ) Invariant Mass of + System (GeV/c ) Real (left) and imaginary (right) part of polynomial roots Well separated, imaginary parts do not cross the real axis ⇒ Solutions can be uniquely identified, no linking procedure necessary A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 9/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Ambiguities in the π + π − System 8 different solutions can be calculated analytically Differentiation requires additional input (e.g. behaviour at threshold, physics content) A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 10/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Fit to the π 0 π 0 System Identical particles, only even waves allowed Reduces number of ambiguities to 2, choice by S -wave dominance at threshold A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 11/17
Introduction Partial-Wave Analysis in Mass Bins Mass-Dependent Parametrisation Conclusion and Outlook Fit to the ππ Systems Consistent picture of symmetric reaction, measured with different parts of experimental setup ρ (770) signal cannot be described by this model, different production mechanism Interpretation with mass dependent parametrisation under way! A. Austregesilo (aaust@cern.ch) — PWA of Centrally Produced Two-Pseudoscalar System at COMPASS 12/17
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