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Abstract Cosmology and the Neutron

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Abstract Cosmology and the Neutron 103 COSMOLOGY AND THE NEUTRON ELECTRIC DIPOLE MOMENT John Ellis CERN - Geneva ABSTRACT There is a contribution to the neutron electric dipole moment d from the CP violating e vacuum parameter of QCD. Diagrams analogous to thosg responsible for the baryon number of the universe also contribute to e, providing an order of magnitude lower bound on dn in terms of the baryon-to-photon ratio n8!ny · GUTs sufficiently complicated to explain the observed nBlny predict that dn should be close to the present experimental upper limit. The comparison between dn and n8!ny gives us information about entropy generation after the epoch of baryon generation in the very early Universe . 104 1. - INTRODUCTION l) 2) Much experimental effort , has been devoted to the search for an electric dipole moment of the neutron, d which violates CP . Detection of a n ' non-zero d would add much to our knowledge of CP violation , confined hitherto n 2) to the K0-R0 system 3l and the present experimental limit 10-25 d 6 x e cm ( l) n < - l) is already a strong constraint on different models of this phenomenon . Theo­ retical analysis of d has proceeded along two lines , the first being calcula­ n tion of perturbation theory diagrams in GP-violating weak interaction models . More recently it has been realized 4 l that non-perturbative effects in QCD will violate CP if a hitherto unremarked parameter e is non-zero. While it is QCD not renormalized by the strong interactions alone , e is in general renorma­ QCD lized by the non-strong interactions , even if its bare value is zero . Mary Gaillard , Demetre Nanopoulos , Serge Rudaz and I have recently em­ phasized that there are contributions to e from Higgs exchange diagrams 5l QCD in GUTs , which are closely analogous to those responsible for the baryon number H of the Universe produced in the decays of very heavy iggs particles &) These contributions to e give us an order of magnitude lower bound on d of QCD n (2) -lO If we take from astrophysics a lower bound on n /n of 2xlO then we 7l 8 y find that -28 (3) d > 5 l0 e-cm n "' x to be compared with the upper bound (1) . In this talk I will review our work S),B), starting with a reminder of the meaning of e its relation to Higgs couplings and its renormalization QCD ' g). Then we will see how n8/n is believed to be generated in GP-violating decays of Higgs bosons via dia rams similar to some contributing to e " In fact , 6l � QCD in many models e and hence d is mueh larger than the lower bound QCD n 5 l,S) 2) (2) or (3) . Finally we will see how the experimental upper limit on d n 105 already gives us useful information on the amount of entropy that could have been generated subsequent to the creation of a baryon-antibaryon asymmetry. The bound lO ) (1) already poses problems for the scenario of symmetry breaking by radiative corrections in the Weinberg-Salam model , and constrains S) deviations from the usual Robertson-Walker-Friedmann (RWF ) big bang cosmology with some implications ll) for models of galaxy formation 2. - THE QCD 6 PARAMETER 12 ) In perturbation theory , QCD automatically conserves CP However , there is a possible term 4l in the QCD Lagrangian ';[ QCD (4) a where is the gluon field strength tensor and G µv is its dual . The e G v QCD term (4)� is a total derivative and hence does not show up in perturbation theory , but it is non-zero for non-perturbative field configurations such as instantons 4l. It conserves charge conjugation C because it is the product of two gauge field v strengths , but it violates parity because the dual tensor µ contains an p aa antisymmetric E vpo 'symbol. Therefore the 6 term (4) violates CP . µ QCD However, it is not directly related to the CP violation seen 3 l in the K0-K0 system since there it occurs in an effective interaction with l�sl = 2, whereas the interaction ( ) clearly conserves strangeness . It will , however , con­ 4 tribute to the neutron electric dipole moment d in an amount estimated 1 as n ' 3) d (5) n e-cm from both MIT baggery and chiral perturbation theory techniques . Using the most 2 recent ) upper limit on d we infer that (1) n ( 6) - !This upper bound on e means that the 0(10 3 ) CP violation in the QCD K0-R0 system cannot be due to a combination of e and a CP conserving !�SI = 2 QCD interaction .J 106 l) For comparison , the best upper limit on d by an American group is n -24 d � xlo e-cm, and they are now starting an extensive series of experiments n 3 to improve this by as many as three orders of magnitude , A major problem of theo­ (6). retical physics is to determine why e is so small QCD In pure QCD , e is an arbitrary parameter which is not renormalized QCD by the strong interactions but has no natural reason to be small or zero . When one takes into account the non-strong interactions e is in general renorma­ ) QCD lized 9 . The most obvious contribution to renormalization of ' which seems eQCD to give the correct order of magnitude in general, arises from the renormalization of the quark matrix which is necessary at each order of perturbation theory in the non-strong interactions . If we define an effective quark mass parameter m(q) from the inverse quark propagator : ) <( - rn(q) (7 then it gets renormalized in each order of perturbation theory by diagrams shown Ren generically in Fig. la . The renormalized mass matrix m should then be restored to real and diagonal form at each order in perturbation theory. This entails phase rotations on the left- and right-handed quark fields which feed through via the QCD U(l) anomaly into a renormalization of e by an amount QCD en arg det rnR (8) The leading contribution to comes from one particle irreducible diagrams o8QCD F1 making a transition between left- and right-handed quarks : Ren rn "' = arg det - 1 F QCD "' Im Tr(m ) (9) lie o 1 where m is the zeroth order quark mass matrix . Since the effective mass para­ �en (7) meter m is a function of the momentum scale q , so also will be o8 QCD ' The observation (or non-observation) of d constrains the effective value of n renormalized at a momentum scale of order 1 GeV or so. Presumably there is an eventual theory of everything (TOE ) which fixes e at some enormous scale 1 QCD q � O (lo 9) GeV . Between this enormous scale and the scale of the neutron e QCD is renormalized by all the non-strong interactions , and we can distinguish 5 ) the following contributions : 107 (10) 1 We denote by o the renormalization due to GUTs at energy scales �10 5 GeV , 8GUT and by o the renormalization due to conventional six-quark Kobayashi-Maskawa 8KM 1 (KM) weak interactions at momentum scales <10 5 GeV. These latter effects have been estimated 9 ) as (11) -31 -3 resulting in a contribution to d of order l0 to lo 2 e-cm. This contri­ n bution to d is in fact dwarfed by the direct contribution to d from pertur- n n . 9) 14) bation theory in the strong and weak interactions which has been estimated ' as m2 2 �d c s S s (12) n sin 1 2 3 in the standard KM model . We see that the standard KM weak interaction contribu­ tions to d are very small. n As yet we do not know how to estimate e but we can calculate TOE ' o This is derived from the quark mass matrix, which is in turn given by a 8GUT' Higgs vacuum expectation value multiplied by a Higgs coupling matrix H as il­ 1 lustrated in Fig. 1 : F = v H . For convenience we will work directly with the 1 1 coupling matrix of this so-called m -Higgs . We will see that in general a GUT sufficiently complicated to explain the observed n /n will yield a oe B y GUT >> oe In the absence of a TOE we will assume that there is no conspiratorial >> KM' cancellation between 8 and o8 so that in order of magnitude TOE GUT (13) and we will now go on to consider the relation of to in some detail . 3 . - THE COSMIC CONNECTION ) In his talk at this meeting, Demetre Nanopoulos 6 has already described to you the mechanisms offered by GUTs for generating a baryon-antibaryon asymmetry in the very early Universe . It seems most likely that the net baryon number ori­ ginates from the C- and CP- violating decays of some very heavy particles , typically 14 15 gauge bosons , Higgs bosons or fermions with masses 0(10 to 10 ) GeV. Figure 2 ) - shows how 15 a net baryon asymmetry of order 10 9 can be built up at high tempe- ratures if one postulates heavy particles X with a suitable B- , C- and CP-viola- ting asymmetry in their decays . Superheavy fermions are not present in the simplest ) GUTs , though they are commonplace in larger ones 6 Most quantitative analyses of baryon number generation have focused on the decays of gauge and/or Higgs bosons , and we shall concentrate on them here. Their contributions to in simple 1 ) models have been calculated 6 numerically to be (1 01 ev ) 160 for gauge bosons 10-1' I £G [ -1·3 ( nB/ny) :\: J (14) for Higgs bosons f"0.5 X 10-l•I EH The factor in square parentheses for gauge bosons in (14 ) represents the suppres­ sion effects of 2-2 interactions which tend to dilute the asymmetry generated by gauge boson decays and inverse decays .
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