Amplitude Analysis in Hadron Spectroscopy César Fernández-Ramírez JPAC/Jefferson Lab
Joint Physics Analysis Center G. Fox E. Passemar A. Jackura A.P . Szczepaniak M. Döring V. Mathieu L.-Y. Dai D. Schott P . Guo R. Workman JPAC M. Shi I.V. Danilkin C. Fernández-Ramírez V. Mokeev M.R. Pennington ICN-UNAM Seminar, March 18, 2015 � 2
Why is QCD special? � A single theory is responsible for phenomena at distance scales of the order of 10 -15 m as well as of the order 10 4 m. � It builds from objects (quarks and gluons) that do not exist in a common sense. >90% mass comes from interactions! � Predicts existence of exotic matter, e.g. made from radiation (glueballs,hybrids) or novel plasmas. � A possible template for physics beyond the Standard Model � It is challenging! ICN-UNAM Seminar, March 18, 2015
This talk is about hadrons 1909/1911 Rutherford/Geiger/Marsden discover the nucleus 1919 Rutherford discovers the proton 1932 Chadwick discovers the neutron ρ : Anderson (1960) K - -> π + π - π - ρ : Erwin (1961) φ : Connolly. Pevsner (1962) η : Pevsner (1961) π : Powell (1947) ω : Álvarez (1961) ICN-UNAM Seminar, March 18, 2015
“Bare (free)” particles of QCD: quarks and gluons e.g. as seen in high energy collisions analogous to 8 (color) x 6 (flavor) copies of QED: quark → electron gluon → photon (but non-abelian) ICN-UNAM Seminar, March 18, 2015
e QCD ~ 10 e QED quarks bound in hadrons the nature of physical quarks and gluons “free” quarks remains a mystery inverse distance between quarks ICN-UNAM Seminar, March 18, 2015
Quark models K* + K* 0 ω 1 • Click to add text ρ - ρ + ρ 0 ω 8 K* - K* 0 physical quarks appear to move in a kind of “mean, gluonic field” ICN-UNAM Seminar, March 18, 2015
Plausible model? H QCD = H c.h.o. + non-linear “physical quarks” → quasi particles in gluon mean field finite energy, localized solutions: solitons (monopoles, vortices , ...) gluon mean field The QCD vacuum is not empty. Rather it contains quantum fluctuations in the gluon field at all scales. (Image: University of “physical gluons” → Adelaide) mean field AND quasi particles ICN-UNAM Seminar, March 18, 2015
Confinement in QCD Adiabatic potential Absence of isolated quarks Properties of confinement: • Linearly rising potential • Regge trajectories • String behavior r 0 = 0.5 fm ICN-UNAM Seminar, March 18, 2015
Spectroscopy of Hadrons can • Click to add text teach us about “workings” of QCD 1. Hadrons with gluon excitations (confinement) 2. Hadron molecules (residual forces) ICN-UNAM Seminar, March 18, 2015
• Click to add text ICN-UNAM Seminar, March 18, 2015
Lattice meson spectrum [Dudek 2011] • Click to add text ICN-UNAM Seminar, March 18, 2015
Lattice meson spectrum [Dudek 2011] • Click to add text ICN-UNAM Seminar, March 18, 2015
Lattice meson spectrum [Dudek 2011] • Click to add text ICN-UNAM Seminar, March 18, 2015
Lattice meson spectrum [Dudek 2011] • Click to add text ICN-UNAM Seminar, March 18, 2015
Lattice meson spectrum [Dudek 2011] • Click to add text ICN-UNAM Seminar, March 18, 2015
• Strong, theoretical evidence (lattice) for gluon field excitations in hadron spectrum • Phenomenologically, gluons behave as axial vector, quasiparticles J PC =1 +- • Lowest multiplet of “hybrid mesons” has J PC = 0 -+ , 1 -+ , 2 -+ , 1 -- states • What about other non-quark model possibilities? • Can these be detected and distinguished? ICN-UNAM Seminar, March 18, 2015
New opportunities High statistics new beam-target combinations polarization measurements ICN-UNAM Seminar, March 18, 2015
What kind of experiments? 2 → 2, 3 processes π , K γ π , K π η , ω , ϕ π π , K π π , K γ p p p p π , K π , K N, Δ , Σ , Λ p p γ γ , π , K π , K ϕ γ , π , K N, Δ , Σ , Λ π , K p p p p ICN-UNAM Seminar, March 18, 2015
Evolution in statistics π - p → π - π + π - p BNL (E852) ca 1995 CERN ca. 1970 • Click to add text O(10 2 /10MeV ) O(10 3 /10MeV ) E852 (Full sample) COMPASS 2010 O(10 6 /10MeV ) O(10 5 /10MeV ) ICN-UNAM Seminar, March 18, 2015
Resonance paradigm: Δ (1232) In 1952, Fermi and collaborators π + p → π + p measured the cross section peak in intensity and found it steeply raising. (cross section) mass ~ 30% above proton ∆ ++ width Γ lifetime ~ 4.5 x 10 -24 s width ~ lifetime -1 = 150 MeV ICN-UNAM Seminar, March 18, 2015
How do we catch resonances? • Is every bump a resonance? • Is every resonance a bump? – The answer to both questions is NO • Examples – σ meson in ππ scattering has a broad structure – Threshold effects can appear as resonances ICN-UNAM Seminar, March 18, 2015
Actually, what is a resonance? • A resonance is a pole of the scattering amplitude in the unphysical Riemann sheets ICN-UNAM Seminar, March 18, 2015
• 12 GeV upgrade at JLab: CLAS, GlueX, etc. – Aim: ✑ Complete understanding of the hadron spectrum ✑ discover new resonances e.g, gluonic excitations (states where glue builds their J PC ) – Tools: Amplitude analysis of data E To find new resonances not bump-hunting, but search for poles must build in S-Matrix constraints + state-of-the-art knowledge of reaction dynamics resonance pole Dispersive analytic continuation ICN-UNAM Seminar, March 18, 2015
• 12 GeV upgrade at JLab: CLAS, GlueX, etc. – Aim: ✑ Complete understanding of the hadron spectrum ✑ discover new resonances e.g, gluonic excitations (states where glue builds their J PC ) – Tools: Amplitude analysis of data To find new resonances not bump-hunting, but search for poles must build in S-Matrix constraints + state-of-the-art knowledge Hadron spectrum, exotics of reaction dynamics Experimental Data ChPT + Analyticity + Unitarity FFs, resonance CLAS, GlueX, JEF, Dispersion Relations parameters: M R , COMPASS, BESS, Regge Theory, Models Γ Ρ , couplings LHCb, PANDA,… ICN-UNAM Seminar, March 18, 2015
Scattering theory • S matrix S = I + 2 i ρ T • S is unitary (probability conservation) S † S = I Disc T = Im T = T † ρ T • T is an analytical function (causality) • T has branch cuts at thresholds (several Riemann sheets) • T has no poles in the first Riemann sheet ICN-UNAM Seminar, March 18, 2015
Dispersion theory • Cauchy Theorem Im{ ν } I Riemann 1 t ( ⇥ 0 ) Z sheet ⇥ 0 − ⇥ − i � d ⇥ 0 t ( ⇥ + i � ) = 2 ⇤ i C ν +i ε • Amplitude has no complex poles in the 1st Riemann Re{ ν } sheet and has two branch cuts • We can reconstruct the full amplitude in the whole complex plane ICN-UNAM Seminar, March 18, 2015
Example: Breit-Wigner amplitude M A I ( s ) = M 2 − s − iMq I ( s ) ICN-UNAM Seminar, March 18, 2015
Example: Breit-Wigner amplitude M A I ( s ) = M 2 − s − iMq I ( s ) ICN-UNAM Seminar, March 18, 2015
Riemann sheets � { s } • The amount of I t I � ( s ) Riemann sheets � { s } s 1 s 2 depends on the 0 t III s p ( s ) � III number of open s 0 p t II � ( s ) II channels: 2 N t I � ( s ) I ICN-UNAM Seminar, March 18, 2015
Amplitude analysis: ππ scattering Peláez et al. F ( s, t = t 0 ) Im ( s ) I • Click to add text s 0 = 4 m 2 I=0 Re ( s ) ρ (770) I II σ (500) 1. Parametrize the data 2. Check constrains (unitarity) 3. Continuation to extract the pole I=1 4. Interpretation (hybrid, glueball, tetraquark, ...) ICN-UNAM Seminar, March 18, 2015
γ p → K + K - p Amplitude depends on 5 Mandelstam variables: • One is fixed: s • Two are measured: s K+K- and s K-p • Two are integrated out: t γ K+ and t pp’ K + t γ K + γ s K + K − fixed s K − s K − p p 0 p t pp 0 ICN-UNAM Seminar, March 18, 2015
Interesting channels GlueX (Hall D@JLab) invariant mass range 2-3 GeV Glueballs? X ππ , K ¯ ρ , ρ 3 , φ , φ 3 , f 0 , f 2 , f 0 K X = 2 , a 0 , a 2 πη , πη 0 X = a 0 , a 2 , π 1 Hybrid? ICN-UNAM Seminar, March 18, 2015
K + K - Dalitz plot Phi mesons W = 5 GeV 22 Double Regge 20 18 16 14 K − p 12 M 2 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 M 2 + K − K Disclaimer: not actual data Hyperons (actual data from g12 CLAS@JLab under analysis) ICN-UNAM Seminar, March 18, 2015
K + K - Dalitz plot W = 5 GeV Meson 22 Double Regge 20 18 16 14 K − p 12 M 2 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 M 2 + K − K Hyperon ICN-UNAM Seminar, March 18, 2015
Things we expect/hope to study • Exotics – new physics that will help us understand the role of the gluon and confinement • Strangeonia ( s ¯ s ) – this spectrum is not well studied and looks pretty empty. Also information on gluons and virtual quarks • Hyperons – Strange content of hadrons, impact in hypernuclei physic and strangeness in neutron stars ICN-UNAM Seminar, March 18, 2015
Models • Dual model (B5) – Generalization of the Veneziano model – In the double-Regge limit: Shi et al., PRD91, 034007 (2015) • Deck model – More elaborated – Resonance region: K-matrix, coupled channels – High energy: Regge – Connection through dispersion theory ICN-UNAM Seminar, March 18, 2015
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