Fortschritte der Physik / Progress of Physics: Band 29, Heft 6 [Reprint 2022 ed.] 9783112655948

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HEFT 6 • 1981 • BAND 29

A K A D E M I E - V E R L A G

31728

EVP 10.- M

•

B E R L I N

ISSN 0015 -8208

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Zeitschrift „Fortschritte der P h y s i k " Herausgeber: Prof. Dr. Frank Kaschluhn, Prof. Dr. Artur Lüsche, Prof. D r . Rudolf Ritsch], Prof. Dr. Robert Rompe, im Auftrag der Physikalischen Gesellschaft der Deutschen Demokratischen Republik. Verlag: Akademie-Verlag, D D R - 1080 Berlin, Leipziger Straße 3 - 4 ; Fernruf: 2236221 und 2236229; Telex-Nr.: 114420; B a n k : Staatsbank der D D R , Berlin, Konto-Nr.: 6836-26-20712. Chefredakteur: Dr. Lutz Rothkirch. Anschrift der Redaktion: Sektion Physik der Humboldt-Universität zu Berlin, D D R • 1040 Berlin, Hessische Straße 2. Veröffentlicht unter der Lizenznummer 1324 des Presseamtes beim Vorsitzenden des Ministerrates der Deutseben Demokratischen Republik. Gesamtherstellung: V E B Druckhaus „Maxim Gorki", D D R - 7400 Altenburg, Carl-von-Ossietzky-Straße 30/31. Erscheinungsweise: Die Zeitschrift „Fortschritte der Physik" erscheint monatlich. Die 12 Hefte eines Jahres bilden einen B a n d . Bezugspreis je Band 180,— M zuzüglich Versandspesen (Preis für die D D R : 120,— M). Preis je H e f t 15,— M (Preis f ü r die D D R : 10,—M). Bestellnummer dieses Heftes: 1027/29/6. © 1981 b y Akademie-Verlag Berlin. Printed in the German Democratio Republic. A N (EDV) 57618

ISSN 0 0 1 5 - 8 2 0 8 Fortschritte der Physik 29, 2 6 1 - 3 0 2 (1981)

Quantum Chromodynamics and Parity-Violating Nucleon-Nucleon-Pion Coupling H R V O J E GALIÖ*)

Stanford, Linear Accelerator Center, Stanford, CA 94305, BBANKO

Max-Planck-Institut

USA

GUBBEINA*'**)

für Physik und Astrophysik, München,

Federal Republic of Germany,

D U B R A V K O TADIÖ

Zavodza teorijskufiziku, Prirodoslovno-matematicki fakultet and Rudjer Boskovic University of Zagreb, Zagreb, Croatia, Yugoslavia

Institute,

Abstract Parity-violating (PV) nucleon-nucleon-pion (NNTT) coupling is studied in order to extract information about nonleptonic weak processes in general. The connection between the PV NNir amplitude and PV nonleptonic hyperon decays is explored in detail. An outline of the historical background is given. It is shown how the PV NNTT amplitude is to be calculated starting from the Weinberg-Salam model for weak interactions. The effective weak Hamiltonian for PV nonleptonic processes is derived in detail, introducing quantum chromodynamics and flavor-symmetry breaking. The role of the so-called penguin terms is clarified. The PV NNTT amplitude is calculated using current algebra, chiral invariance, and quark models (e.g. the MIT bag model) for the description of baryons. It is emphasized that certain techniques used in the description of nonleptonic decays can undergo an independent test via the study of PV NNTT amplitudes. These amplitudes can be experimentally explored in experiments on nuclear parity violation. A discussion of nuclear calculations and experiments is also included.

Contents 1. Historical Introduction

262

2. Theory of Weak Interactions and Quantum Chromodynamics 2.1. History 2.2. The WS-GIM Model and QCD

264 264 266

*) On leave of absence from the Rudjer Boskovic Institute, Zagreb, Croatia, Yugoslavia. * * ) Alexander von Humboldt fellow. 1

Zeitschrift „Fortschritte der Physik", Bd. 29, Heft 6

262

H r v o j e Galic, B r a n k o Guberina, Dubravko Tadic

3. QCD Corrections and the Effective Weak Hamiltonian 3.1. I V B Exchange 3.2. Renormalization 3.3. The Effective Weak Hamiltonian

269 269 270 277

4. Calculation of Parity-Violating NNtt Coupling

281'

4.1. Sum Rules 4.2. Quark Models

281 285

5. Confrontation with Experiments Appendix A (QCD) Appendix B (Nuclear Physics)

291 293 298

References

299

1. Historical Introduction Parity-violation (PV) in nuclear physics was discussed almost immediately after the discovery of parity nonconservation in weak interactions [1, 2, 3]. Nonconservation of parity in weak interactions results in P V nucleon-nucleon (NN) potentials, so all "nuclear states become mixtures consisting mainly of the state they are usually assigned together with small percentages of states possessing the opposite parity" 1 ). P V NN potentials

are usually approximated by one-boson-exchange (OBE) contributions. As shown in Fig. 1, the OBE-contribution diagram has one weak P V vertex. In this paper we discuss calculations of such a weak P V nucleon-nucleon-pion (NNtc) vertex. One-pion exchange (OPE) is not the only contribution to the P V nuclear potential 2 ). However, the PV NNtt vertex is rather sensitive to the model of the weakinteraction Hamiltonian. I t was suggested relatively early that P V O P E could serve as a test to distinguish between weak Hamiltonians with and without neutral currents [/#]. O P E leads to that part of the P V potential which has the longest range and thus should be least sensitive to the difficulties associated with nuclear physics calculations. This makes O P E suitable for testing the weak Hamiltonian itself. The PV NN7t vertex is proportional to the baryonpion P V amplitudes, i.e., A(n_°), n p + 7i" (1.1)

A{p++), p^n

+ ir+

and thus can be related to the observable hyperon decays by relatively simple devices, such as current algebra (CA) and SU(3) symmetry [15, 19, 20]. I t seemed at one time ) The quotation taken from Ref. [1]. ) There are other one-, two-, etc., particle exchanges, e.g., g, In. We refer the reader to review papers [4—17]. J

2

Quantum Chromodynamics

263

that the dynamics associated with OPE could be handled with some confidence and that the only real unknown was the form of the weak Hamiltonian itself [7, 8, 9, 21, 22], This form could then be successfully determined from experimental data. However, this scheme has become less certain in view of recent theoretical investigations [23—28]. They have been prompted by new developments in the theory of nonleptonic hyperon decays [29—36]. In view of this new knowledge, it is no longer simple and straightforward to relate the A(n_°) or Aifp^*) amplitudes to nonleptonic hyperon decays. If the quark structure of hadrons [37—39] is taken into account, the simple sum rules of the old days [7—9, 18—21] do not seem realistic any longer. If strong interactions are mediated by quantum chromodynamics (QCD), their influence should replace the "bare" weak Hamiltonian by an effective weak Hamiltonian [27, 28, 32—34, 39]. By measuring PV OPE in nuclear physics, one can thus test this effective weak Hamiltonian. Conclusions depend on the dynamics of quarks and/or other constituents of hadrons, which was used to determine the ^4(n_°) (^4(p++)) amplitudes. The quark constituents of hadrons carry various "flavors" such as isospin, hypercharge, charm, etc. These quarks are usually grouped into the fundamental representation of the flavor symmetry (FS) of the SU(n) type, n being the number of distinct quarks. The interplay between QCD and FS, which we present in detail later on, determines the effective weak Hamiltonian for a particular model of unified field theory. It has been concluded that the masses of the various quarks 3 ) are not equal [40, 41], This leads to flavor symmetry breaking (FSB), which again influences the structure of the effective weak Hamiltonian. A particular effect of FSB is the appearance of four-quark operators which mix bilinear combinations of left- and right-handed helicities. These operators are particularly important in the strangeness-changing (AS1 = 1) sector of the weak interaction. Their contributions, known as penguin-operator matrix elements, were considered to be an important ingredient for the understanding of nonleptonic weak decays [33, 35]. Such theoretical considerations are based on a particular evaluation of penguin-operator matrix elements 4 ) between hadron states. The operators of a similar type appear in the strangeness conserving sector = 0), with which we are concerned in this paper. They are strongly present even without FSB. The significance of their contributions was realized only a few years ago when three papers dealing with penguin contributions to PV NNTU amplitudes appeared almost simultaneously [26, 27, 28]. Such contributions were calculated using approaches completely analogous to the investigations dealing with nonleptonic weak decays [33, 34, 35]. In the = 0 sector, such operators are present even in the QCD-unrenormalized Hamiltonian. The QCD renormalization enhances their contributions. In the AS = 0 sector this picture is only modified by FSB 5 ). It turns out that the penguin contribution is the most dominant contribution to the PV NN~ amplitude, thus changing entirely our understanding of this field. PV pion exchange is thus particularly suitable for testing the dynamical assumptions used to evaluate penguin matrix elements. The main aim of this paper is to discuss all these theoretical complexities in detail, with an effort to make them comprehensible even to those who are not specialists in particle physics. Our intention is to elucidate what profit particle physics in general, and the theory of weak interactions in particular, can gain from nuclear physics experiments. Figure 2 shows a scheme for calculating the .4(n_0) amplitude and/or nonleptonic hyperon-decay amplitudes. The main ring in the figure receives inputs connected with

3

) The notation u, d, s, c, t, b, etc., is used to denote up-, down-, strange, charm, top, and bottom quarks. 4 ) For details see Sees. 3.3. and 4.2. of this paper. 5 ) In the AS = 1 sector, the appearance of penguin terms is entirely due to FSB.

1*

264

H R V O J E GALI.

(3.7)

I t s decomposition is as follows: •Hch

=

Of

{c2Qf7(2) +

s2

Ql*U) "I" s2 Qia) + (°2

^S2) $27(0)

+ (2c2 - ««)Q%0) + Q?*0) + ««G», + (2c2 - s2) 0 ,

(3.35)

280

HRVOJE GALIC, BRANKO GUBERINA, DUBRAVKO TADIC

so that (3.33) transforms into

H™{n = mc-,x)=\£ \ ¿-(Ar),{

9) — \ 2J —, —, g)Tt + \ fi mc I

}pv cc pair})

pieces with the

.

Here T ; is a multiplicatively renormalizable combination of operators R„ i.e.,

Ti = ESiiRi, i

Ti-^Z^Ti.

(3.38)

Here ¿¡ ) =

y=" [* + VC) [4J4(A_°) + 24(3_~)].

(4.5)

The parameter f, being the ratio of the reduced matrix element of the two nonequivalent octet tsnsors can not be determined by symmetry (or CA) arguments alone. Additional dynamical analysis is needed and thus, in the WS model, one is naturally led to the usage of quark models for hadrons. We shall outline this in the next section. In this section we give some additional extensions and applications of sum-rule techniques, because, in a certain sense, they are also useful for recent applications based on quark models. The CA and/or SU(3) symmetry which lead to the Lee-Sugawara sum rule and to the sume rule (4.2) do not lead to satisfactory simultaneous fits of s-wave and p-wave hyperon-decay amplitudes. Such approaches actually work for off-mass-shell pions (i.e., the pion momenta q 0 or q2 = 0 instead of q2 = mj-) because they assume that all octet baryon masses are equal. However, it is $t7(3)-(fIavor)-symmetry breaking which is responsible for nonleptonic decays in the first place. In order to compensate for this discrepancy, one attempts some sort of analytical continuation, or better, interpolation from off-mass-shell to on-mass-shell decay amplitudes 25 ). This was made by either considering final-state interactions [37] or introducing vector-meson or ) Applications to some special models with colored currents [80, 82] are now of historical interest. 2 6 ) The same problem remains and has to be tackled in approaches based on quark models.

24

283

Quantum Chromodynamics

= CAT + PT

BL(Bf)

B,(B0

B,(BJ

BL(B,)

PT (baryon) Fig. 4. Current-algebra (CAT) and/or SI7(3)-symmetry contributions and poleterm (PT) contributions to the PV NNit amplitude. Either vector-meson pole terms or baryon (decuplet) pole terms have been included in the calculations:

baryon pole terms vanishing in the q 0 limit [29, 30], In the latter case, as illustrated graphically in Fig. 4, the final result contains the standard CA term (CAT) plus a pole term (PT). An appropriate combination of the CAT and a vector-meson pole term is ¿(nj>) = « f (F + D) + /? (l + U |/i2 \ < p / ^ a 1.06 X 10"' + 0.64 X 10" 9 .

(Mp -

Mn)

'V

(4.6)

The parameters F, D, C, 4(n_°) amplitude was just the opposite. First, a paper on H w e t t [33] prompted several elaborate calculations of 4(n_°) [26, 27, 28]. Subsequent encouraging analyses [34, 35, 91-93] of AS = 1 transitions indicated that the earlier found results for 4(n_°) can be reasonably accurate. I t turns out that for AS = 0, $f7(4)-flavor-symmetry breaking is negligible, but that the techniques used in the dynamical calculations of AS = 1 decays lead to surprising results. We shall explain them later in detail. 31 32

) Compare with (4.11). ) For AS = 1, the worst disagreement between theory and experiment is by a factor 1.8.

288

H R V O J E GALI (uy"u + dy"d) |n) -

(y,

y,ys)}.

(4.20)

I n (4.20) we have kept only the terms which are of further interest for our considerations. A suitable Fierz transformation leaves us with the leading factorial contribution 2i (Vn | R3 |n) ^ — (p| ud |n)

=

0,

(A. 11)

with y and yB defined by Eq. (2). Using Athe short-distance .expansion (1), one obtains the equation E i

r0t™

+ CfV&rofi*)

-

(ny + 2pygh -

yA -

yB) C^To^A

= 0

for each m, which specifies the local operator 0i(m)(jli...,,m(0)) with m Lorentz indices. Using Eq. (8), one finally obtains the R G E for the Wilson coefficients C^ m ) (x): + YA + YB) dti -

yfi] C/«>(®) = 0.

(A.12)

Now we discuss briefly the solution of Eq. (12) for the simple case of multiplicatively renormalizable operators. Eq. (12) then becomes 3

3

d(i

8g

CNI—*,

=

0.

( A . 13)

295

Quantum Chromodynamios

The solution of this equation is written as

HQ'ln') (A. 14)

in terms of an effective coupling constant g (t), t = 1/2 Irt Q2l/n2, with g(t) satisfying % = P(S),

9(t = 0) =

(A. 15)

g.

In the asymptotically free region, one can make the following expansions : Cn( 1, g(t)) =

•

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H R V O J E GALIC, BRANKÖ GUBERINA, DUBBAVKO TADIÖ

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