Physics 795 Nuclear Theory at OSU

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1 Physics 795 Nuclear Theory at OSU Department of Physics Ohio State University October, 2006

2 Nuclear Theory Group Bunny Clark Ulrich Heinz Sabine Jeschonnek Yuri Kovchegov Robert Perry

3 Current Students/Postdocs and Openings Furnstahl, Jeschonnek, Perry (NSF + SCIDAC funding) Sunethra Ramanan, Renormalization Group Methods for Nuclear Interactions (finishing Winter, 2007) one or two GRA openings Postdoc: Scott Bogner Heinz (DOE funding) Anthony Kuhlman: azimuthal pion HBT, U+U collisions Evan Frodermann: photon emission, photon HBT Huichao Song: (viscous) hydrodynamic simulations Yezhe Pei: application of hydrodynamic code Postdoc: Magdalena Djordjevic Kovchegov (DOE/OJI funding) new student just starting Postdocs: Javier Albacete, Heribert Weigert

4 Recently Graduated Students Anirban Bhattacharyya (Ph.D 2005, Furnstahl) Density functional theory (DFT) using effective field theory (EFT) Postdoc at Oak Ridge National Lab Rick Mohr (Ph.D 2003, Perry) Quantum mechanical three-body problem with short-range interactions Systems Engineer, Ohio Supercomputing Center Peter Kolb (Ph.D 2002, Heinz) Early thermalization and hydrodynamic expansion in nuclear collisions at RHIC Postdoc, SUNY/Stony Brook = software engineer, Germany

5 What is modern Nuclear Theory? There are 4 known fundamental interactions in nature: STRONG ELECTRIC WEAK GRAVITY

6 STRONG ELECTRIC WEAK GRAVITY Standard Model of Particle Physics (20 th century) 21 st Century NUCLEAR PHYSICS PARTICLE PHYSICS (+ beyond standard model)

7 Quantum Chromodynamics (QCD) QED vs. QCD photon gluon electric charge color charge electric, magnetic fields chromoelectric, chromomagnetic

8 Quantum Chromodynamics (QCD) QED vs. QCD photon gluon electric charge color charge electric, magnetic fields chromoelectric, chromomagnetic e γ e + q q q + q q q e e q g q g q g q e γ e γ e e e + e g q q + + q q g g g +

9 Bridging the islands of nuclear physics RHIC CEBAF quarks gluons few nucleons RIA heavy nuclei vacuum quark-gluon plasma QCD nucleon QCD few-body systems free NN force many-body systems effective NN force

10 Exploring the QCD Phase Diagram early universe temperature T [MeV] atomic nuclei neutron stars baryonic chemical potential µ B [GeV]

11 Exploring the QCD Phase Diagram early universe quark-gluon plasma temperature T [MeV] deconfinement chiral restoration 50 hadron gas atomic nuclei neutron stars baryonic chemical potential µ B [GeV]

12 Exploring the QCD Phase Diagram early universe LHC RHIC quark-gluon plasma temperature T [MeV] SPS thermal freeze-out hadron gas chemical freeze-out AGS SIS atomic nuclei deconfinement chiral restoration neutron stars baryonic chemical potential µ B [GeV]

13 Heavy Ion Collisions Quarks and gluons are confined inside hadrons. In heavy ion collisions people are trying to create a new state of matter called Quark Gluon Plasma: : a soup of de confined quarks and gluons. This state of matter has not been around since the Big Bang! Heavy Ion Collision experiments are running at RHIC Collider at Brookhaven. In the recent past they were performed at SPS at CERN and in the near future they will start at LHC also at CERN.

14 Space time picture of the Collision 1. First particles are produced: Initial Conditions 4. Particles interact with each other and thermalize forming a hot and dense medium Quark Gluon plasma. 9. Plasma cools, undergoes a confining phase transition and becomes a gas of hadrons. 13. The system falls apart: freeze out.

15 Ulrich Heinz Research Interests: Heavy Ion collisions. Hydrodynamic evolution of the system of quarks and gluons produced in heavy ion collisions, HBT determination of the size of the system, elliptic flow. Thermal field theories, QCD equation of state.

16 Yuri Kovchegov's research: High energy interactions of hadrons and nuclei. Dense partonic wave functions of high energy protons and nuclei (Color Glass Condensate) as probed in deep inelastic scattering experiments (DIS). Heavy Ion Collisions: particle production and thermalization of the system leading to creation of Quark Gluon Plasma.

17 DGLAP Equation: an Example of Renormalization Group (RG) Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 72 As we go to smaller and smaller distances we see more particles: The number of particles we resolve at smaller distances is proportional to the number of particles we resolved at larger distances: ln Q 2 xg x, Q2 = S K DGLAP xg x, Q2

18 Nonlinear Equation At very high energy parton recombination becomes important. Partons not only split into more partons, but also recombine. Recombination reduces the number of partons in the wave function. N x, k 2 ln 1/ x = Number of parton pairs ~ N 2 s K BFKL N x, k 2 s [ N x, k 2 ] 2 Yu. K. 99 (large N C QCD) I. Balitsky 96 (effective lagrangian)

19 BK Equation at Work First partons are produced overlapping each other, all of them about the same size. When some critical density is reached no more partons of given size can fit in the wave function. The proton starts producing smaller partons to fit them in. The story repeats itself for smaller partons. The picture is similar to Fermi statistics.this way some critical density is never exceeded. Proton Color Glass Condensate

20 From Quark-Gluon to Hadronic DOF s [Jeschonnek] RHIC CEBAF quarks gluons few nucleons RIA heavy nuclei vacuum quark-gluon plasma QCD nucleon QCD few-body systems free NN force many-body systems effective NN force

21 Sabine Jeschonnek Location (F W): Lima Location (R): M2047 Lots of Interaction with Experimentalists at Jefferson Lab, Newport News, VA Main Interest: transition from quark gluon to hadronic degrees of freedom, studied with electron scattering

22 Electron Scattering from light Nuclei Main focus: (e,e p) on the deuteron Things to learn: reaction mechanism (Color Transparency, ), short range structure of light nuclei (correlations, ), the deuteron as a lab for neutron form factor measurements

23 Quark Hadron Duality: Theoretical Modeling of Duality: why? where? how accurate?

24 How to Describe Nuclei from QCD? [Furnstahl/Perry] RHIC CEBAF quarks gluons few nucleons RIA heavy nuclei vacuum quark-gluon plasma QCD nucleon QCD few-body systems free NN force many-body systems effective NN force

25 SciDAC: Building a Universal Nuclear Energy Density Functional Nuclear DFT DME Nuclear Matter PT+ V low k NN N RG Chiral EFT NN N LEC s Lattice QCD Density Functional Theory A>100 Coupled Cluster, Shell Model A<100 Exact methods A 12 GFMC, NCSM Chiral EFT interactions (low-energy theory of QCD) QCD Lagrangian Low-mom. interactions Lattice QCD

26 Nuclear and Cold Atom Many-Body Problems Lennard-Jones and nucleon-nucleon potentials O -O potential (mev) n-n potential (MeV) n-n system O -O system n-n distance (fm) O 2-O 2 distance (nm) Are there universal features of such many-body systems? How can we deal with hard cores in many-body systems?

27 The Many-Body Schrödinger Wave Function [adapted from Joe Carlson] How to represent the wave function for an A-body nucleus? Consider 8 Be (Z = 4 protons, N = 4 neutrons) Ψ = σ,τ χ σ χ τ φ(r) where R are the 3A spatial coordinates χ σ = 1 2 A (2 A terms) = 256 for A = 8 χ τ = n 1 n 2 p A ( A! N!Z! terms) = 70 for 8 Be

28 The Many-Body Schrödinger Wave Function [adapted from Joe Carlson] How to represent the wave function for an A-body nucleus? Consider 8 Be (Z = 4 protons, N = 4 neutrons) Ψ = σ,τ χ σ χ τ φ(r) where R are the 3A spatial coordinates χ σ = 1 2 A (2 A terms) = 256 for A = 8 χ τ = n 1 n 2 p A ( A! N!Z! terms) = 70 for 8 Be So for 8 Be there are 17,920 complex functions in 3A 3 = 21 dimensions!

29 The Many-Body Schrödinger Wave Function [adapted from Joe Carlson] How to represent the wave function for an A-body nucleus? Consider 8 Be (Z = 4 protons, N = 4 neutrons) Ψ = σ,τ χ σ χ τ φ(r) where R are the 3A spatial coordinates χ σ = 1 2 A (2 A terms) = 256 for A = 8 χ τ = n 1 n 2 p A ( A! N!Z! terms) = 70 for 8 Be So for 8 Be there are 17,920 complex functions in 3A 3 = 21 dimensions! Suppose you represent this for a nucleus of size 10 fm with a mesh spacing of 0.5 fm. You would need grid points!

30 Nuclear Matter in Low-Order Perturbation Theory Standard Argonne v 18 potential Brueckner ladders order-by-order 1st order is Hartree-Fock = unbound! Repulsive core = series diverges E/A [MeV] st order 2nd order pp ladder 3rd order pp ladder Argonne v k f [fm -1 ]

31 Principles of Effective Low-Energy Theories

32 Principles of Effective Low-Energy Theories If system is probed at low energies, fine details not resolved

33 Principles of Effective Low-Energy Theories If system is probed at low energies, fine details not resolved use low-energy variables for low-energy processes short-distance structure can be replaced by something simpler without distorting low-energy observables

34 Wavelength and Resolution

35 Wavelength and Resolution

36 Wavelength and Resolution

37 Wavelength and Resolution

38 Wavelength and Resolution

39 Wavelength and Resolution

40 Wavelength and Resolution

41 Wavelength and Resolution

42 Wavelength and Resolution

43 The Deuteron (Bound np) at High Resolution S1 deuteron probability density 0.15 ψ(r) 2 [fm -3 ] 0.1 Argonne v r [fm] Repulsive core = short-distance suppression = important high-momentum (small λ) components Makes the many-body problem complicated!

44 The Deuteron at Lower Resolutions S1 deuteron probability density ψ(r) 2 [fm -3 ] Argonne v 18 Λ = 4.0 fm -1 Λ = 3.0 fm -1 Λ = 2.0 fm r [fm] Smear out potential: V (r)ψ(r) d 3 r V (r, r )ψ(r ) Low-momentum potential = much simpler wave function!

45 Consequence for Basis Expansions [nucl-th/ ] Error in Deuteron Binding vs. Cutoff N max = 40 hω (Ω optimized at each Λ) (E var - E d ) [MeV] sharp cutoff exponential cutoff (n=4) Λ [fm -1 ]

46 Nuclear Matter with NN Ladders Only st order 2nd order pp ladder 3rd order pp ladder Brueckner ladders order-by-order Repulsive core = series diverges E/A [MeV] 50 0 Argonne v k f [fm -1 ]

47 Nuclear Matter with NN Ladders Only st order 2nd order pp ladder 3rd order pp ladder Brueckner ladders order-by-order Repulsive core = series diverges E/A [MeV] 50 0 Argonne v 18 V low k converges! -50 V low k ( Λ=1.9 fm -1 ) k f [fm -1 ]

48 Nuclear Matter with NN Ladders Only st order 2nd order pp ladder 3rd order pp ladder Brueckner ladders order-by-order Repulsive core = series diverges E/A [MeV] 50 0 Argonne v 18 V low k converges! Add 3-body force V low k ( Λ=1.9 fm -1 ) k f [fm -1 ]

49 Nuclear Matter is Perturbative with Λ 2 fm 1! Construct a chiral EFT to a given order Evolve Λ down with RG (to Λ 2 fm 1 for ordinary nuclei) NN interactions fully, NNN interactions approximately 5 0 Λ = 1.6 fm -1 Λ = 1.9 fm -1 Λ = 2.1 fm -1 Λ = 2.3 fm -1 Λ = 2.1 fm -1 [no V 3N ] 5 0 Λ = 1.6 fm -1 Λ = 1.9 fm -1 Λ = 2.1 fm -1 Λ = 2.3 fm -1 Λ = 2.1 fm -1 [no V 3N ] E/A [MeV] -5 E/A [MeV] -5 Hartree-Fock + " 2nd order" -10 Hartree-Fock k F [fm -1 ] k F [fm -1 ] Use this as input to nuclear density functional theory

50 Bethe and Calculating Nuclear Matter Hans Bethe in review of nuclear matter (1971): The theory must be such that it can deal with any nucleon-nucleon (NN) force, including hard or soft core, tensor forces, and other complications. It ought not to be necessary to tailor the NN force for the sake of making the computation of nuclear matter (or finite nuclei) easier, but the force should be chosen on the basis of NN experiments (and possibly subsidiary experimental evidence, like the binding energy of H 3 ). Thirty+ years of working with a difficult potential!

51 EFT and RG Make Physics Easier Weinberg s Third Law of Progress in Theoretical Physics: You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you ll be sorry!

52 EFT and RG Make Physics Easier Weinberg s Third Law of Progress in Theoretical Physics: You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you ll be sorry! There s an old vaudeville joke about a doctor and patient... Patient: Doctor, doctor, it hurts when I do this! Doctor: Then don t do that.

53 Nuclear Theory Group Bunny Clark Ulrich Heinz Sabine Jeschonnek Yuri Kovchegov Robert Perry