The Structure of Hadrons

Transcription

1 1 The Structure of Hadrons Paul Hoyer University of Helsinki CP 3 Inauguration 24 November 2009

2 What are Hadrons? Strongly interacting elementary particles 2 Hadrons are extended objects and can be classified as states of a quark + antiquark ( mesons) or three quarks ( baryons). q q qqq E.g., the proton = uud is a hadron Hadron radii are ca. 1 fm = m

3 Discovery of hadrons... 3 using cosmic rays using particle accelerators Lepton

4 ... and discovery of quarks 4 Particles of the Standard Model

5 All quarks u,d,s,c,b,t are equal under the strong interaction 5 But quarks have unequal masses: q q m u m t Hadrons may be formed with any combination of q = u,d,s,c,b,t 2.5 MeV 171 GeV qqq??? Proton

6 Quantum Chromodynamics 6 QCD, the quantum field theory describing quark and gluon interactions, is similar to QED, the theory of electrons and photons α s (M Z )= g2 4π = ± Quark-Gluon coupling Cf. α = e 2 /4π 1/ (46) Electron-Photon coupling We can calculate atomic (Hydrogen) energy levels with a precision of more than 10 digits: Why not apply the QED methods to QCD? Well, it does not work: Quarks and gluons are confined in hadrons, there is no ionization threshold like for atomic electrons and photons.

7 Deep Inelastic Scattering (DIS) 7 Today s accelerators allow to study e + p collisions with momentum transfers q >> mp c : The electron collides with a pointlike quark in the proton The struck quark flies out of the proton They hadronize into a spray (jet) of hadrons (mostly pions) e + p e + anything

8 The parton picture of the proton 8 To interpret the DIS data we must consider that relativistic interactions in the (free) proton can create quarks and gluons: p uud! The proton state is expressed as as a superposition of Fock states, containing any number of quarks and gluons (partons) p uud gluon q q Partonic picture of the proton The wave function of each Fock state specifies the momentum distributions of all partons i in a proton which has large momentum, where xi is the fractional longitudinal momentum carried by the parton k i is the relative transverse momentum carried by the parton The DIS (e + p e + anything) cross section measures the probability distribution for a quark or gluon to carry momentum fraction x

9 Partons have broad momentum distributions 9 Non-relativistic uud state e e q γ* p

10 Origin of the proton mass 10 The u, d quarks in the proton have small masses 2m u + m d m p 10 MeV 938 MeV 1% 99% of the proton mass is due to interactions! 1% is due to Higgs. Ultra-relativistic state Compare this with positronium (e + e ), the lightest QED atom: 2m e % Binding energy is tiny wrt mc 2 m pos Nonrelativistic state The compatibility of the non-relativistic p = uud quark model description of the proton with its ultra-relativistic parton model picture remains a mystery. Both are supported by data: =?? p uud gluon q q

11 Perspective: The divisibility of matter 11 Since ancient times we have wondered whether matter can be divided into smaller parts ad infinitum, or whether there is a smallest constituent. Democritus, ~ 400 BC Vaisheshika school Common sense suggest that these are the two possible alternatives. However, physics requires us to refine our intuition. Quantum mechanics shows that atoms (or molecules) are the identical smallest constituents of a given substance yet they can be taken apart into electrons, protons and neutrons. Hadron physics gives a new twist to this age-old puzzle: Quarks can be removed from the proton, but cannot be isolated. Relativity the creation of matter from energy is the new feature which makes this possible. We are fortunate to be here to address and hopefully develop an understanding of this essentially novel phenomenon!

12 Why is the proton so hard to understand? 12 Hadrons are the only truly relativistic bound states found in Nature. Our intuition of relativistic field theory phenomena is undeveloped. Feynman s Challenge for QED (1961) In his report to the 12th Solvay Congress (Brussels, 1961) on The Present Status of Quantum Electrodynamics (QED), Feynman called for more insight and physical intuition in QED calculations. It seems that very little physical intuition has yet been developed in this subject. In nearly every case we are reduced to computing exactly a coefficient of some specific term. We have no way to get a general idea of the result to be expected. To make my view clearer, consider, for example, the anomalous electron moment, (g 2)/2 = α/2π 0.328α 2 /π 2. We have no physical picture by which we can easily see that the correction is roughly α/2π, in fact, we do not even know why the sign is positive (other than by computing it)

13 Proton Form Factors 13 It was only recently appreciated that elastic scattering (e p e p) measures the transverse shape of the proton. Using Lorentz and gauge invariance, the scattering amplitude is expressed in terms of the Dirac F1 and Pauli F2 form factors, which depend on Q 2 = q 2 p q/2 N e γ* q F1, F2 e p+q/2 N e p e p amplitude A µ λλ A µ λλ = p q, λ J µ (0) p 1 2q, λ [ =ū(p q, λ ) F 1 (Q 2 )γ µ + F 2 (Q 2 ) i 2m σµν q ν ] u(p 1 2q, λ)

14 e p e p is like electron microscopy 14 When the target is static (mq, mn >> Q), the 3-dim. Fourier transform of the form factors gives the spatial distribution of electric and magnetic charge. p e γ quarks e p+q However, this electron microscopy interpretation is not correct for relativistic quark constituents and with quark and nucleon recoil (!)

15 Transverse charge density of the proton 15 Taking a 2-dimensional Fourier transform of the e p e p form factors (in the plane transverse to the collision axis) gives charge densities: ρ 0 (b) = 0 ρ x (b) =ρ 0 (b) + sin(φ b ) dq 2π QJ 0(bQ)F 1 (Q 2 ) where J0 and J1 are Bessel functions. 0 dq 2π Q 2 For longitudinally polarized protons 2m J 1(bQ)F 2 (Q 2 ) For protons polarized polarized along x-axis

16 Using measured form factors, find the 16 by + ρ0(b) quark transverse charge densities in a neutron ρ T bx ρx(b) ρ 0 by + data : Bradford, Bodek, Budd, Arrington (2006) bx densities : Miller (2007); Carlson, Vdh (2007) M. Vanderhaeghen, ECT* May 2008

17 The anomalous magenetic moment of the electron 17 Conversely, the form factors may be expressed in terms of the densities. In particular, F 2 (0) = πm 0 db b 2 ( ρ φ b=π/2 x ) (b) ρ φ b=3π/2 x (b) Since F2(Q 2 =0) is the anomalous magnetic moment, intuition about the density distribution of the electron allows to address Feynman s challenge. PH and Kurki (2009)

18 Current of classical spinning particle 18 ρx(b) is the matrix element of j + = j 0 + j 3 ρ x (b) d 2 q e iq b 1 (2π) 2 2P + P +, 1 2 q,sx =+ 1 2 j+ (0) P +, 1 2 q,sx =+ 1 2 x + =0 ( Classical picture of a spinning particle: p γ ŷ ẑ j z > 0 Burkardt j 0 (y>0) = j 0 (y<0) j z < 0 j 3 (y>0) = j 3 (y<0) > 0 ) 0 in (3.1). ρ φ b=π/2 x (b) ρ φ b=3π/2 x (b) > 0 e F2(0) > 0 Similar arguments apply to single spin asymmetries

19 Hadron physics thrives on experimental information PANDA detector (GSI, Darmstadt) p p, p A Jefferson Lab (VA, USA) ep, ea Large Hadron Collider (CERN, Geneva) pp, pa, AA 19

20 ... and on theoretical insights 20 L QCD = ψ(i/ g /A m)ψ 1 4 F µν F µν Perturbative calculations at short distance Lattice calculations at long distance p 1 p 3 p 2 p 4 π +.K + KS γ γ Chiral expansions at low energy

21 Summary 21 Hadrons are the only truly relativistic bound states found in Nature Quarks and gluons are confined in hadrons Chiral symmetry is spontaneously broken (Nobel prize 2008) Phenomenology: The explanation of measurements in terms of theory Quark and parton models qualitatively explain many observations The quest is to achieve a precise understanding of the data based on QCD Hadrons are studied both at dedicated and other acclerator facilities The variety of beams, targets, energies and polarizations is important. Experiment + theory builds intuition, which is required for creating appropriate approaches to the novel, relativistic world of hadrons. Feynman on QED: (1961) We have been computing terms like a blind man exploring a new room, but soon we must develop some concept of this room as a whole, and to have some idea of what is contained in it.

22 22 Backup slides

23 Hint from experiments: The Constituent Quark Model 23 Hadrons can be classified as qq or qqq bound states, using non-relativistic n, L, S quantum numbers, as for QED atoms

24 24 Charmonium the Positronium of QCD Binding energy [mev] Mass [MeV] 4100 (4040) Ionisationsenergie 3 1 S S D D2 3 3 D1 2 1 S 2 3 S 2 1 P 2 3 P P D2 2 3 P ev ~ 600 mev c(3590) (3770) (3686) 3 D 1 h c (3525) 3 P 2 (~ 3940) 3 P 1 (~ 3880) 3 P 0 (~ 3800) 2(3556) 1(3510) 0(3415) 1 D 2 DD 3 D 3 (~ 3800) 3 D S S ev e nm e c(2980) (3097) C 1 fm C 2900

25 25 Light-Front Wavefunctions x i P +, x i P + k i ni x i = 1 ni k i = 0 Fixed τ = t + z/c F.T. < 0 ψ(y 1 )ψ(y 2 )ψ(y 3 ) p > τi =0 P +, P P + = P 0 + P z Ψ n (x i, k i, λ i ) Invariant under boosts! Independent of P! Jyv!skyl!, Finland March 24, 2007 Novel QCD Phenomena 5 Stan Brodsky, SLAC

26 Do hadrons and nuclei Lorentz contract? 26? p = 0 p >> m... and if so, does this refer to wave functions at equal LF time x + = t + z = 0 or equal ordinary time t = 0?

27 Lorentz contraction at equal ordinary time? 27 In analogy to classical relativity, the equal time w.f. Ψ 0 (x) might Lorentz contract in a moving frame. Observers measure endpoints at equal times in their respective frames. Ψ 0 (x) p >> m But: Time-ordered Feynman diagrams are not individually boost invariant Fock state content is frame dependent Decay angles are not boost invariant: More than just contraction is involved: p = 0 p >> m

28 Does the Hydrogen atom Lorentz contract? 28 Calculate the t = 0 Positronium wave function at lowest order, for arbitrary CM momentum p. Matti Järvinen, Phys. Rev. D71, (2005) Find that both the e + e and e + e γ Fock components contribute for p 0, giving (non-trivially) E(p) = (2m e c 2 E b ) 2 + p 2 c 2 where Eb is the binding energy in the rest frame. Find that the e + e γ Fock amplitude does not simply contract.

29 Angular distribution of the photon in positronium e+ e 29 f(cos θ c )/γβ 2 Plot of the angular distribution of the photon in the e + e γ Fock state of positronium for various β = p /E. The photon goes only forward in the infinite momentum frame, β 1 cos(θ c )