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Chiral Symmetry in Nuclei Wn B T Adv Ysics and Mo Dern Eld-Theory-Based Particle Ph Eptic Migh Ting

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Chiral Symmetry in Nuclei Wn B T Adv Ysics and Mo Dern Eld-Theory-Based Particle Ph Eptic Migh Ting View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Chiral Symmetry in Nuclei J. L. FRIAR Theoretical Division Los Alamos National Laboratory Los Alamos, NM 87545 USA Abstract The impact of chiral symmetry on nuclear physics is discussed in the con- text of recent advances in the few-nucleon systems and of dimensional p ower counting. The tractability of few-nucleon calculations, illustrated byvery re- cent solutions for A =26, is shown to follow from p ower counting based on chiral Lagrangians. The latter predicts the suppression of N -b o dy forces, as originally shown byWeinb erg. Isospin violation in the nuclear force is similarly analyzed using the results of van Kolck, and this is shown to b e consistent with results from the Nijmegen phase-shift analysis. Conventional ! mixing mo d- els with constant mixing strength are not consistent with naivepower counting, which supp orts smaller recent estimates. Meson-exchange currents calculated in chiral p erturbation theory are in go o d agreement with exp eriment. 1 Intro duction My talk will try to merge two rather di erent areas of physics: classical (conventional) nuclear physics and mo dern eld-theory-based particle physics. This is not an easy task. A skeptic mightsay that if you wanted to invent a system with little apparent dynamical basis, great complexityofinternal structure (spin and isospin), and almost pathological computational diculty,you would call it a nucleus! This view was purp osefully overstated, but has elements of truth nevertheless. Nuclear dynamics was mostly phenomenological for decades. The dominance of the tensor force and the one- pion-exchange p otential (OPEP) means that spin and isospin play an essential role at leading order and intuition based on simple central forces do esn't often apply. This internal structure makes computational problems exceptionally challenging, which has inhibited our ability to solve(numerically) the Schrodinger equation. The net result was that in order to learn ab out strong-interaction dynamics in a nucleus we had to b e able to calculate, and we couldn't do the latter with much accuracy. NUCL-TH-9503028 Recent computational advances[1 ] in treating few-nucleon systems mayhave broken this log jam. In spite of all the diculties wehave nally b egun to realize the p otential inherent in studying few-nucleon systems. This area of physics on 1 which I will fo cus is in my opinion the biggest success story in nuclear physics in the past decade. Beginning ab out ten years ago, wehave made sp ectacular progress in solving (numerically) most of the seminal problems that were discussed decades ago as crucial to the success of the eld. New terminology was coined, with \exact" or \complete" denoting calculations of observables with errors of less than 1% (in spite of the computational hardships). Problems are now b eing solved that were considered far out of our reach ten years ago. This work is b eginning to yield dynamical information, which will undoubtedly pay dividends in the future. In order to illustrate how things havechanged, almost everything that wehave calculated \works", with those few disagreements with exp eriment b eing closely examined and debated and providing considerable hop e for more progress. My purview is chiral symmetry (CS) in nuclear physics. Others much more knowledgeable than I am have talked ab out the particle physics asp ects, including the fashionable and successful Chiral Perturbation Theory (PT). I hop e to b e able to convince you that this symmetry has a dominant in uence in nuclear physics. Without the symmetry,nuclear physics would b e intractable. Indeed, we can and will turn this argument around: the tractabilityofnuclear physics provides a strong signature for the e ect of CS in nuclei. Chiral p erturbation theory could turn out to b e the biggest advance in nuclear physics in decades, or of very limited use. There is a huge amount of information contained in our eld on the b ehavior of the strong interactions, and wehave a great opp ortunity for unifying all of hadronic physics. The theoretical approach used in nuclear physics unfortunately lacks (in part) the well- de ned metho dology of particle physics, and the challenge will b e to try to change this. I can summarize the talk by stating that CS and dimensional p ower counting have an opinion ab out: (1) the sizes of various comp onents of the nuclear force (b oth isospin-conserving and isospin-violating); (2) the relative size of three-nucleon forces(3Nf ); (3) the relative size of four-nucleon forces(4Nf ), ... ; (4) the relative size of relativistic corrections in (light) nuclei; (5) the relative size of nucleon (impulse approximation) and meson-exchange currents in nuclear electromagnetic and weak interactions. 2 Nuclear Physics Overview Any discussion of the role of chiral symmetry in nuclear physics must b egin with a brief discussion of three topics that will tell us hownuclear theorists do business and p ossibly how this should change: what we do, whywe do it, and what we need to 2 do. For the purp oses of this talk when I say\nuclear physics", I mean \low-energy few-nucleon physics", unless stated otherwise. Restricting myself to the traditional < domain of nuclear physics ( a few hundreds of MeV) frames the problem suciently for my allotted time. Potentials used in the context of the Schrodinger equation (or a generaliza- tion) are central to the organization of nuclear calculations. Dynamics, assumptions, and prejudices are contained in this quantity. The reason why p otentials are used is twofold and simple: (1) nuclei are self-b ound con gurations of nucleons, and binding cannot b e achieved in ( nite-order) p erturbation theory; (2) when twonucleons inter- act and propagate b etween interactions there is an infrared singularity that enhances successive iterations, and this is treated exactly by the Schrodinger equation[2]. Thus our scheme is extremely ecient and reduces the complexity of calculating an ampli- tude to that of de ning a p otential. Although the underlying dynamics of nuclei and elementary particles is shared, the two are rather di erent in their scales. Simply stated, nuclei are large, squishy, and soft, while particles are small, sti , and hard. These are words used to state that 1 3 the radii of nuclei follow R ' 1:2A fm, while particles are smaller than 1 fm. The excitation energies of nuclei are typically tens of MeV or less, while particles require hundreds of MeV, and nuclear internal momenta are on average fairly small, while in particles they can b e high. We can estimate the latter, p , using the uncertainty principle in the He isotop es[3 ]. Equating pR h and R 1.5-2.0 fm, we obtain pc 100-150 MeV. For mnemonic purp oses only , one can equate this to the pion mass: 2 pc m c . This is clearly inappropriate in the chiral limit, m ! 0. Note that this value is ab out half of the Fermi momentum,hk c = 260 MeV, whichcharacterizes F nuclear matter. Momentum comp onents larger than this can play a signi cant role in some cases and the estimate should not b e taken to o literally. Given this scale for momenta there are other scales that can b e constructed. Nucleons with mass M are heavy and slowmoving. The average kinetic energy of a 2 p 2 2 3 3 nucleon is roughly or m =M 20 MeV, which is fairly accurate for H, H, He, M 4 and He. Because nuclei are weakly b ound systems, p otential and kinetic energies are comparable in magnitude. Semirelativistic calculations[4] for these nuclei (using p 2 2 p + m m) nd corrections of 5% to the kinetic energy, which are typically balanced bychanges in the p otential. The dominantphysics is nonrelativistic. Given these scales we can easily estimate what happ ens when twonucleons prop- M 2 agate b etween interactions. The Green's function, G,schematically is 1=(p =M ) 2 m and b ecomes very large for small p.Itisworth rememb ering that p otentials (unlike amplitudes) are not uniquely de ned[2]. Rather, p otentials are (nonunique) subam- 3 plitudes, and this leads to the \o -shell" problem of nuclear physics. Although it 1 is p ossible to set criteria for how one de nes V , the fact that G is small means that rather small changes in V can b e comp ensated by the infrared singularityin G, leading to an alternative (de nition of ) V , whichmay di er substantially. 120.0 100.0 80.0 60.0 40.0 Percentage of Total 20.0 Kinetic Energy 0.0 Potential Energy Correlation Function -20.0 0.0 1.0 2.0 3.0 4.0 x (fm) Figure 1: Percentages of accrual of kinetic energy (solid line), p otential energy (short dashed line), and probability (long dashed line) within an interparticle separation, x, for any pair of nucleons in the triton. The biggest conceptual problem in nuclear physics calculations (in my opinion) is the lackofa well-de ned regularization scheme. The successive iteration of two p otentials (or the sequential exchange of two mesons) is given by a lo op integral, which is almost always divergent. In order to regularize this divergence nuclear p otentials are cut o at short distances (large momenta), which leads to short-range repulsion and renders the calculations nite. These cuto s are typically for momenta 1 GeV, are assumed to derive from meson clouds around the nucleons (i.e., form factors), and are treated as parameters.
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