Strong interactions C. Forss´en Introduction Strong Interactions and Nuclear Forces Properties of the NN force Advanced Subatomic Physics (FUF025) Yukawa theory Meson theory QCD Christian Forss´en Fundamental Physics, Chalmers, Sweden e-mail: [email protected] March 2, 2009 C. Forss´en Strong interactions Outline Strong interactions C. Forss´en Introduction 1 Introduction Properties of the NN force Yukawa 2 Properties of the (low-energy) nucleon-nucleon force theory Meson theory QCD 3 The Yukawa theory of nuclear forces Meson theory of the nucleon-nucleon force 4 Quantum Chromodynamics C. Forss´en Strong interactions Outline Strong interactions C. Forss´en Introduction 1 Introduction Properties of the NN force Yukawa 2 Properties of the (low-energy) nucleon-nucleon force theory Meson theory QCD 3 The Yukawa theory of nuclear forces Meson theory of the nucleon-nucleon force 4 Quantum Chromodynamics C. Forss´en Strong interactions Introduction Strong interactions One of the basic problems in nuclear physics is determining the C. Forss´en nature of the interactions between the nucleons, which is crucial for understanding the properties of nuclei. Introduction Properties of According to our present understanding, the nuclear force is due the NN force to residual strong interactions between the color-charge neutral Yukawa hadrons. A direct derivation of the nuclear force from QCD, the theory Meson theory underlying theory of strong interactions, is not yet possible due QCD to its non-perturbative nature at low energy. The standard way to describe the nuclear force is based on the meson-exchange picture, which goes back to the seminal work by Yukawa. His idea as well as experimental discovery of π- and heavier mesons (ρ, ω, . .) stimulated the development of boson-exchange models of the nuclear force, which still provide a basis for many modern, highly sophisticated phenomenological nucleon-nucleon (NN) potentials. C. Forss´en Strong interactions The standard model Strong interactions C. Forss´en Electroweak theory Introduction Gauge invariance (see Chapter 12) of non-Abelian Properties of the NN force (non-commuting) vector fields, and Spontaneous Symmetry Yukawa theory breaking leads to the unification of the electromagnetic and Meson theory weak interactions into the electroweak theory (see Chapter 13). QCD Quantum chromodynamics At high energies (momentum transfer) the theory of strong interactions can be described in a similar fashion. This theory is known as Quantum Chromodynamics (QCD). C. Forss´en Strong interactions QCD versus QED Strong interactions C. Forss´en QED QCD Introduction Fundamental particles Leptons Quarks Properties of the NN force Gauge quanta Photon Gluons Yukawa Interaction source Electric charge Color charge theory e2 Meson theory Coupling constant α = αS ~c QCD Asymptotic freedom (perturbative) at large momenta [small distances] Quark confinement (“infrared slavery”) at small momenta [large distances] C. Forss´en Strong interactions QCD versus QED Strong interactions C. Forss´en QED QCD Introduction Fundamental particles Leptons Quarks Properties of the NN force Gauge quanta Neutral Photon Charged Gluons Yukawa Interaction source Electric charge Color charge theory e2 Meson theory Coupling constant α = αS ~c QCD Asymptotic freedom (perturbative) at large momenta [small distances] Quark confinement (“infrared slavery”) at small momenta [large distances] C. Forss´en Strong interactions QCD versus QED Strong interactions C. Forss´en QED QCD Introduction Fundamental particles Leptons Quarks Properties of Gauge quanta Neutral Photon Charged Gluons the NN force Interaction source Electric charge Color charge Yukawa e2 theory Coupling constant α = c αS Meson theory ~ QCD Asymptotic freedom (perturbative) at large momenta [small distances] Quark confinement (“infrared slavery”) at small momenta [large distances] C. Forss´en Strong interactions Outline Strong interactions C. Forss´en Introduction 1 Introduction Properties of the NN force Yukawa 2 Properties of the (low-energy) nucleon-nucleon force theory Meson theory QCD 3 The Yukawa theory of nuclear forces Meson theory of the nucleon-nucleon force 4 Quantum Chromodynamics C. Forss´en Strong interactions Effective degrees of freedom Strong interactions C. Forss´en The nucleon-nucleon (NN) force Introduction Properties of QCD is commonly accepted as the theory of the strong the NN force interaction. Therefore, the NN interaction should be Yukawa theory completely determined by the underlying quark-quark dynamics. Meson theory QCD Non-perturbative Since the quarks are bound inside the nucleons, the NN force is an effective interaction. However, due to the non-perturbative character of low-energy QCD, one is still far from a quantitative understanding of this effective NN interaction. C. Forss´en Strong interactions General properties Strong interactions Attraction C. Forss´en Nuclei are self-bound. The force is predominantly attractive. Introduction Properties of Range and Strength the NN force 2 3 4 Yukawa E.g., comparison of the binding energies of H, H, and He theory indicates that the range is of the order of 1 fm. Meson theory QCD Saturation For nuclei with A > 4 the binding energy saturates at around 8 MeV/A. The average distance between nucleons is ∼ 2 fm which should roughly correspond to the range of the attractive part. Both the binding energy and the volume ∝ A. Saturation can be explained by repulsive forces at short distances (hard core) and/or by exchange forces. C. Forss´en Strong interactions Properties derived from studies of the deuteron Strong interactions C. Forss´en Spin dependence: V Introduction σ Properties of the NN force The deuteron spin is J = sp + sn + L. The value of the Yukawa ground-state magnetic moment implies that L = 0. theory Meson theory The ground state is 1+, but there is no 0+ bound state. So QCD 3 1 the S1 partial wave must be more attractive than the S0. This implies that the NN interaction includes a spin-dependent part Vσσ1 · σ2 C. Forss´en Strong interactions Properties derived from studies of the deuteron Strong interactions Tensor interaction (noncentral forces): S12 C. Forss´en The deuteron magnetic moment does not correspond Introduction exactly to the expected s-state value. Properties of the NN force In addition, the deuteron has a small quadrupole Yukawa theory deformation. Since Q ∝ Y20, a non-zero value of < Q > Meson theory implies L > 1/2 (s-states are sperically symmetric). QCD So, in the deuteron case, the dominantly L = 0 ground state must contain an admixture of L = 2. This implies broken rotational symmetry and can be achieved through adding a tensor component to the NN interaction VT S12, where S12 = 3(σ1 · ˆr)(σ2 · ˆr) − σ1 · σ2 C. Forss´en Strong interactions Properties derived from scattering experiments Strong interactions np scattering C. Forss´en momentum transfer: q = pi − pf θ Introduction elastic scattering (pi = pf = p): q = 2p sin 2 Properties of the NN force Yukawa theory Angular distribution Meson theory QCD dσ = |f (q)|2, where in Born approx. dθ m Z iq · r f (q) = − V (r) exp dr. 2π~2 ~ Backscattering implies exchange force C. Forss´en Strong interactions Properties derived from scattering experiments Strong interactions np scattering C. Forss´en momentum transfer: q = pi − pf θ Introduction elastic scattering (pi = pf = p): q = 2p sin 2 Properties of the NN force Yukawa theory Angular distribution Meson theory QCD dσ = |f (q)|2, where in Born approx. dθ m Z iq · r f (q) = − V (r) exp dr. 2π~2 ~ Backscattering implies exchange force C. Forss´en Strong interactions Properties derived from scattering experiments Strong interactions np scattering C. Forss´en momentum transfer: q = pi − pf θ Introduction elastic scattering (pi = pf = p): q = 2p sin 2 Properties of the NN force Yukawa theory Angular distribution Meson theory QCD dσ = |f (q)|2, where in Born approx. dθ m Z iq · r f (q) = − V (r) exp dr. 2π~2 ~ Backscattering implies exchange force C. Forss´en Strong interactions Spin-orbit force !"#$%&#'()*+,"(%&- ./0#$1(20'+3"(%& ! ! Strong interactions Consider scattering of polarized nucleons!"!"" off a spin-zero target. *&,' C. Forss´en (056' Introduction Properties of the NN force !4%*&4-+"(+/("'"# Yukawa theory 7("'"#+9 Meson theory 7("'"#+8 QCD !"#$%&'()*+, -.&()%/#01/&)2#3 4)&,./)#5##### =A 6*2,1/78#0%&,28#9'):1;"##<=>>?@ The observation of a “left-right” asymmetry can be explained by adding a spin-orbit interaction VLS L · S, since it will have opposite signs for nucleons 1 and 2. C. Forss´en Strong interactions Spin-orbit force !"#$%&#'()*+,"(%&- ./0#$1(20'+3"(%& ! ! Strong interactions Consider scattering of polarized nucleons!"!"" off a spin-zero target. *&,' C. Forss´en (056' Introduction Properties of the NN force !4%*&4-+"(+/("'"# Yukawa theory 7("'"#+9 Meson theory 7("'"#+8 QCD !"#$%&'()*+, -.&()%/#01/&)2#3 4)&,./)#5##### =A 6*2,1/78#0%&,28#9'):1;"##<=>>?@ The observation of a “left-right” asymmetry can be explained by adding a spin-orbit interaction VLS L · S, since it will have opposite signs for nucleons 1 and 2. C. Forss´en Strong interactions Charge independence. Strong interactions After correcting for the electromagnetic interaction, the forces C. Forss´en between nucleons (nn, pp, np) in the same state are almost the same. Introduction Properties of the NN force Equality between pp and nn forces is called Charge Yukawa symmetry theory Meson theory Equality between (pp,nn) and np forces is called Charge QCD independence Isospin symmetry Introduce isospin: T = 1/2 for nucleons; Tz = +1/2 (proton), −1/2 (neutron). Isospin symmetry is an invariance under rotations in isospin, i.e. isospin dependence is either 1 or τ1 · τ2 C. Forss´en Strong interactions . to charge dependence Strong interactions Studies of charge dependence in scattering experiments. Reults C. Forss´en 1 for the S0 scattering length (See Sakurai Ch. 7). Introduction Properties of Charge-symmetry breaking (CSB) the NN force Yukawa theory After correcting for the electromagnetic interaction Meson theory a = −17.3(4) fm QCD pp ann = −18.8(5) fm Charge-independence breaking (CIB) apn = −23.74(2) fm C.