NNovel ideas about emergent vacua
F. W. Bopp ∗ Department Physik, Universität Siegen, D–57068 Siegen, Germany
Arguments for special emergent vacua which generate fermion and weak boson masses are out-lined. Limitations and consequences of the concept are discussed. If confirmed the Australian dipolewould give strong support to such a picture. Preliminary support from recent DZero and CDF datais discussed and predictions for LHC are presented.
I. GENERAL INTRODUCTION
The hierarchy problem in particle physics is used as aguidance to find theories beyond standard model [1]. Theargumentation in some way wrongly presumes a separa-tion of particle physics and cosmology. Without such aseparation there is no need to directly connect masses toPlanck scale physics as a manageable scale is availablefrom the cosmological constant more or less correspond-ing to the neutrino mass scale. As in Planck scale basedmodels the spread in the fermion mass scales will have tobe explained. This is considerably easier in a two scalemodel in which combinations of the GUT scale and darkenergy scale can appear.This argument seems just to change the context ascosmology contains a worse scale problem [2]: It is widelyassumed that the cosmological constant corresponds tothe vacuum energy density caused by a condensate [3, 4].The properties of the condensate have then somehow toreflect a Grand Unification Theory (GUT) scale of theinteractions when it presumably was formed (i.e. about GeV), whereas the flatness of the universe requiresa non-vanishing but tiny cosmological constant (of about meV) [5].The size of this gap rises a serious question. It isnot excluded that a dynamical solution of a type envi-sioned for the hierarchy problem of particle physics [6, 7]will eventually be found to be applicable. The oppositeopinion seems more plausible. It considers it impossibleto create such scales factors in a direct dynamical way:A Lagrangian with GUT scale mass terms cannot con-tain minima in its effective potential involving such tinyscales. Of course, condensates do contain compensatingenergy terms, but without a new scale true field theoreti-cal minima have to stay close to the GUT or Planck scaleor they have to vanish.Besides this plausibility argument there is a formalproblem with the conventional view. The term hierar-chy problem is properly used if from a single availablescale derived scales have to be obtained which are non-vanishing but many orders of magnitude away. The dis-cussed cosmological problem is not a hierarchy problem.Other scales like the age of the universe are availablewhich can bridge the scale gap. ∗ Electronic address: [email protected]
The observed tiny non-vanishing cosmological constantcan just means that given the age of the universe the trueminimal vanishing vacuum state is not reached [58]. Ourphysical vacuum is then defined as an effective groundstate. The spontaneous symmetry breaking has to bereplaced by an evolving process yielding an unfinishedvacuum structure. Its tiny mass density indicates thatthe present condensate has to be quite close to a finalone. As vacuum-like state the condensate has to largelydecouple from the visible world.What could be the history of such a physical vacuumstate? It is formed at a condensate- (e.g. technicolor)force mass scale, which is assumed to more or less coin-cide which the GUT scale taken to be somehow directlyconnect to the Planck mass. In a chaotic initial phasebound composite states are formed with considerable sta-tistical fluctuations. As the mass scale and the potentialscale are of the same order these states can sometimesbe more or less massless on a GUT scale. Their initialGUT scale geometric extend is not fixed dynamically bya mass scale. They or configurations of them can re-duce their remaining energy by geometrically extending.In this evolving process they more and more decouplefrom the localized hotter incoherent rest. This decou-pling works only in one way. At their scale they can,of course, radiate off energy eventually absorbed by themuch hotter rest. Cooling down eventually a quantumvacuum is formed in a quantum mechanical condensa-tion [59]. Its properties have to be constant, perhapsalmost over GLyr distances [14]. The assumption is thatit reaches coherence over a large, say galactic, scale. Asexplained below a lower limit of this coherency scale canbe obtained from weak interactions. Eventually if theuniverse would continue to expand it will of course reacha vanishing energy density [60].The advantage of this picture is that it requires no newscale. States without scale are known from condensedmatter physics and they are called “gap-less” [11]. With-out such an extra scale the evolution of the dark energyin a comoving cell (cid:15) vac . has to be a linear decrease like: ∂(cid:15) vac . /∂ ( (cid:15) vac . t ) = − κ(cid:15) vac . where κ is a dimensionless decay constant and t the time.The absence of the usual exponential decrease has theconsequence that the age of the universe is no longerpractically decoupling and irrelevant.The expansion of the universe is not linear in time andin the above equation the time t has presumably to be a r X i v : . [ h e p - ph ] A p r replaced by the dynamical relevant expansion parameter a to obtain a less rough estimate. It yields (cid:15) vac. ∝ a .Phenomenologically the expansion constant is taken to be a ∼ √ t initially and a ∼ t / later on [5]. The “hierarchyratio” of grand unification scale and present vacuum scale (cid:15) GUT (cid:15) vacuum ( t ) = 10 can be obtained from the age of universe t = 5 · M GUT with a ∝ t . . . to be (cid:15) GUT (cid:15) vacuum ( t ) = 2 . · resp . . · . To the accuracy considered the problematic hierarchy ra-tio is explained.For the emergent vacuum reached in this way a richand complicated structure is natural. Heavier massesmight involve combined scales. As suggested by Zel-dovich, Bjorken and others [16, 17] combinations of suit-able powers of both scales:
H M ∼ Λ might explain needed intermediate mass values. TheHubble constant H is here related to the condensatemass density and Λ QCD is the QCD mass scale. In chiralperturbation theory the mass of the pion-like GUT-scalebound state can be estimated as [39] : M = B condensate scale · (fermion mass scale) == (3m eV · G eV ) = 170G eV All observed masses lie between the dark energy scaleand this Goldstone state scale.The above hierarchy argument is not new [13, 18].Of course, the argumentation presented is rather vague.However, without the constraint that the physical vac-uum is at an actual minimum there is too much free-dom and it seems futile to try to obtain a more defi-nite description. A realistic ab initio description is pre-sumably impossible. Actually this lack is quite typicalfor most condensed matter in solid state physics wherethe term Emergent Phenomena was coined for such ob-jects [19, 20] [61].Sometimes ‘emergent vacuum’ is used synonym withthe ’consecutively broken vacuum’ of the standardmodel [23]. Here we take a narrower definition sometimescalled strong emergence [19, 24] which includes basic un-predictability. The established complexity of the knownpart of the vacuum legitimates this assumption. It hastwo immediate consequences:i) It is extremely ugly from a model building pointof view and actually leads to a murky situation:
The vacuum is largely unpredictable but predictions are necessary for the way science proceeds . In thisway strong emergency is a physical basis of Smolin’swall [25] possibly severely limiting the knowledgeobtainable.To proceed beyond this barrier is at least difficult. Quim-bay and Morales [45] assume an equilibrium and use thezero temperature limit of a thermal field theory. Volovikand Klinkhamer [12, 13] try to rely on analogies to solidstate physics. Bjorken argues [17] that the situation issomewhat analogous to the time around 1960 where onhad to turn to effective theories to parameterize the data.Here we will not attempt to contribute to this difficultproblem.The rich structure of the (strong) emergent vacuumhas a second consequence:ii) The standard model contains many aspects withbroken symmetries, asymmetric situations and par-tially valid conservation laws. In emergent vacuumpicture many of these observations might not betruly fundamental and just reflect asymmetries ofthe accidental vacuum structure. This takes awaythe fundament of many theoretical considerations.Textbooks have to be worded more carefully.The second consequence of the emergent vacuum willbe expanded here. Physics was often based on estheticconcepts. In this spirit we postulate: “Fundamentalphysics should be as simple as achievable.”
Withthis postulate it is then possible to come to a num-ber of interesting consistency checks and testable con-sequences. The basic ignorance of the vacuum keepssuch predictions on a qualitative level. Formulated inBjorken’s historic context today might be a time wheresimple minded, Zweig-rule type phenomenological argu-ments [26] are needed to sort things out.Section 2 will discusses general implications. Aspectsconnected with fermion and boson masses follow in Sec-tions 3 and 4. Section 5 turns to indications from Fermi-lab and predictions for LHC.
II. GENERAL CONSEQUENCES OFEMERGENT VACUA
One immediate outcome of this argument is the follow-ing cosmological argument. Here no novelty is claimedand on the considered conceptual level it is contained p.e.in dark fluid models [29]. In our context it is importantas it invalidates an argument for unneeded new particles.As the present vacuum is not at a unique point it has tobe influenceable by gravity [62]. The distinction betweencompressed dark energy and dark matter is blurred . Fol-lowing the simplicity postulate we assume that a suit-able compressibility can eliminate the need of dark mat-ter altogether and lead to an effective MoND descrip-tio n [27, 28, 31]. The changed power dependence pre-dicted from the MoND theory for galactic distances canbe obtained if the extra compression-mass density of thecondensate drops off in the relevant region accordingly.There is no fine tuning: All mass densities are more orless on the same order of magnitude. Lorentz-invarianceis no problem as the resulting effective theory does nottouch fundamental laws. We will see later how an al-most massless condensate mimics an effective relativisticinvariance in the world outside of the condensate. Theoffset between the centers of baryonic and dark mattercomponent seen after galaxy collisions [32] was said tocontradict MoND theory. Here it constitutes no prob-lem as it takes cosmic times to rearrange the dark energyeffects.Another important simple outcome is the not uniquevacuum can act as a reservoir . It can have several con-sequences. We begin with the most drastic one, whichwould eliminate one of the most ugly aspects in physicstext books.It is unsatisfactory and potentially problematic to at-tribute the matter-antimatter asymmetry to the initialcondition of the universe. It is also widely agreed [33]that no suitable, sufficiently strong asymmetry generat-ing process could be identified. The emergent vacuum of-fers a simple way to abolish the asymmetry: the vacuumcan just contain the matching antimatter. The vacuummust be charge-less and spin-less, but nothing forbids itto contain a non-vanishing antifermionic density [63].Such a antifermionic density could be important forthe stability of the vacuum. Most known physical con-densates are fermionic. As these extremely extended an-tifermionic states are practically massless their Fermi re-pulsion will dominate. They provide an anti-gravitatingcontribution in the cosmological expansion [64] possiblyreplacing inflatons. Such a so called ’self-sustained’ vac-uum was postulated by Volovik [13]. He assumes a fillingwith superfluid He − A like atoms. Keeping the GUTscale condensation force generic, the condensate can bepartially characterized by its color and flavor structure.We here assume that there is no lepton asymmetry thata hadronic antifermionic structure suffices. There are ofcourse many possible contributions. In the following weconsider spin- and charge-less Cooper pairs of antineu-tron like states.We follow Bjorken who argues that the various compo-nents of the vacuum should not be considered as separateobjects [17]. Our picture is that the antibaryonic con-densate, whose density is regulated by Fermi repulsion,is accompanied by a somewhat less tidily bound mesoniccloud largely responsible for the fermion masses. Bothare then seed to the known gluonic component mimick-ing the spontaneous chiral symmetry breaking. Are thereproblems with such a picture?For such a vacuum structure there is a firm limit onthe dielectric constant (cid:15) (vacuum) (cid:15) − ≈ θ C < from the unobserved vacuum Cherenkov radiation [38]. However, the considered vacuum state is not excluded.Its density is well known. As we see later the mesonicand the antibaryonic densities in such a vacuum have tobe of the same order of magnitude. The antibaryonicdensity equals the baryon density outside of the vacuumwhich is: n baryon = ρ c · Ω baryon /m neutron == 0 . · m − = 1 . · − ( MeV¯ hc ) The spin-less GUT scale bound states in the consid-ered vacuum have no initial dipol moments. A factor ( 10 MeV / ¯hc) − has to be added to obtain the dielec-tric constant. The result is well below the limit.The simplicity postulate presumably requires grandunification. In a framework in which fermions representa SU [5] , SO [10] or a similar gauge group, proton decaylike processes could present a problem for the antibary-onic vacuum. Depending on the details of the symmetrybreaking and on evolution of temperature and fermionmasses processes like ¯ d right ¯ d right → d left ν could occur without the protection of large mass scaledifferences possibly destroying the condensate.Presumably one can find a symmetry breaking andevolution path which avoids the problem. A more dras-tic solution is the following: In the emergent-vacuumframework left- and right-handed GUT partners do nothave to correspond to the mass partners [65]. Most de-cay channels of the antineutron-like states are then ex-cluded. Two remaining channels involve a charged lep-ton and a strange quark. It can be prevented by zeroesin the corresponding lepton-quark Cabibbo-Kobayashi-Maskawa matrix. The evolution of the vacuum couldnaturally select such a stable vacuum configuration. Itwould also explain the observed stability of the proton.It is non-trivial to obtain a sufficiently uniform vac-uum state. By themselves the vacuum states are ex-tremely extended. Initial statistical fluctuation could beaugmented by magnetic effects in a rapidly expandinguniverse [36] separating different U (1) -charges at leasedfor a time relevant for condensation. Known condensa-tion often involves replication processes which select cer-tain species and allow to amplify initial asymmetries overmany decades. Once an asymmetry between vacuum andvisible world is established annihilation processes withinthe vacuum radiating into the visible world should pu-rify its antimatter nature. The GUT scale condensationis thought to precedes at least part of an inflationary pe-riod. In this way a relatively small area can be magnifiedto extend over essentially our complete horizon [37].There is, however, no reason that the tiny region weoriginate in happens to have a constant (i.e. extremal)fermoinic density. In section 4 we will discuss how ahigher antifermionic density increases the vector bosonmass. So we expect a temporal and spatial variation ofmasses. As long as all masses vary in the same way itwill be hard to observe.The fine structure constant is not fundamental [14, 48].This holds in any framework with a non-fundamental vac-uum structure. The fine structure constant is determinedby /e = 1 /g +1 /g (cid:48) at the vector boson mass scale andrelates the fine structure constant to the in this contextfundamental U (1) and SU (2) couplings. As the renor-malization scale dependence of the left hand and righthand side is different the fine structure constant will de-pend on point where the relation can be applied, i.e. onthe non-fundamental Z mass. The fine structure con-stant deceases with increasing M Z .As the fine structure constant enters different opticalspectral lines with distinct powers astronomical measure-ments in far away galaxies are possible with high preci-sion. There is evidence for a spatial dependence of theform: ∆ α/α ∼ B cos(Θ) + m where B = 1 . ± . · − GLyr − , where m = − . ± . · − and where Θ is an angle to a specified siderealdirection [14]. If confirmed this means that the expectedspatial variation has a GLyr scale. Naturally the an-tifermionic density and the vector-boson mass was higherin the past explaining the observed reduction in the finestructure constant at o . The same sign in the variationof the fine structure constant with time was indicated bythe LNE-SYRTE clock assemble preliminary yielding: ∂∂t α/α = − . ± .
23 (10 year) − . involving a different time period [15].The antimatter vacuum was introduced for reasonsgiven above. It also affects other symmetries. Whetherthe resulting consequences are consistent offers a nontrivial cross check. III. VACUUM AND FERMION MASS MATRIX
How do fermions interact with the vacuum? As saidthe tiny energy scale of the vacuum requires to a hugegeometrical extension and the momenta exchanged withthe vacuum have to be practically zero. Such interac-tions are described with scalar, first order terms of a lowenergy effective theory [39]. Scalar interaction with the(very light) vacuum state does not depend on its Lorentzsystem. There is no contradiction to the observed
Lorentzinvariance in the outside world [40].All masses have to arise from interaction with the vac-uum. Their effective couplings should be rather similar.The mass differences have to originate in distinct den-sities of the components of the vacuum they couple to.The excessive number of mass parameters is unacceptablefor fundamental physics. Here the problem is solved byattributing them to properties of the emergent vacuum. The concept then conforms to Hawking’s postulate [41],stating that ‘the various mass matrices cannot be deter-mined from first principles ’. The postulate doesn’t pre-clude that certain regularities might be identified andeventually explained [42, 43].We denote vacuum-fermions with a subscript ( V ). Therelevant interaction q i + (¯ q i ) V → q j + (¯ q j ) V in the lowestperturbative order is shown in Figure 1. Relying on theFierz transformation it can be shown to contain a scalarexchange. In a theory without elementary scalar particlesthis flavor exchange term is the only such contribution. Figure 1: A process responsible for the fermion mass terms
We assume that such a flavor-dependent contributionstays important if higher orders in the perturbative ex-pansion are included. The matrix elements then dependon the corresponding fermion densities and on the prop-erties of their binding, as interactions with fermions in-volve replacement processes [44, 45]. Multi-quark bary-onic states should be more strongly bound than themesonic states [46] and fermion masses should be domi-nated by the less tidily bound mesonic contribution. Inthis way the required dominance of the mesonic t ¯ t con-tribution is not diluted by the light antiquarks from theantineutrons.The “flavor half-conservation” is a serious problem inthe conventional view. Here the flavor of q i does not haveto equal the flavor of q j . In this way flavor conservationcan be restored and the apparent flavor changes in thevisible world can be attributed to a reservoir effect of thevacuum. As the vacuum has to stay electrically neutralthe mass matrix decomposes in four × matrices whichcan be diagonalized and the CKM matrix can be obtainedin the usual way. If the coherent vacuum state is prop-erly included unitarity relations are not affected. As thematrix elements mainly depend on fermion densities andnot on messenger particles with intermediate mass scalesno significant scale dependence is expected. In this wayflavor changing neutral currents are suppressed on a treelevel. As in the standard model non tree level correctionsfrom weak vector mesons or heavier bosons are tiny.The antifermionic vacuum state is obviously not sym-metric under CP and CP T symmetry. This allows torestore these symmetries for fundamental physics. With-out any assumptions about discrete symmetries it is theneasy to see why
CP T is conserved separately in the out-side world and why CP not.In the low momentum limit the interaction f i +( ¯ f i ) V → f j + ( ¯ f j ) V will equal ¯ f j + ( ¯ f i ) V → ¯ f i + ( ¯ f j ) V by conti-nuity in the exchanged momentum. In consequence theasymmetry of the vacuum cannot be seen and CP T isseparately conserved in the outside world.On the other hand the (¯ q i ) V / ( q i ) V asymmetry in thevacuum will differentiate between q i + (¯ q i ) V → q j + (¯ q j ) V and ¯ q i + ( q i ) V → ¯ q j + ( q j ) V . In consequence CP appearsas not conserved [66]. Figure 2: A process responsible for the vector boson massterms
IV. VACUUM AND VECTOR BOSON MASSES
How do weak vector bosons obtain their masses?Relevant is a Compton scattering process like W µ +( { ¯ q · · · } i ) V → W ν + ( { ¯ q · · · } j ) V shown in Figure 2.In this framework pure gluon and meson condensates(p.e. simple Technicolor [47] models with GUT bind-ing scale) have a problem. In the low momentum limitthe interaction with the B -meson measures the squaredcharges of the vacuum content. As these objects are U (1) B neutral states they cannot contribute to a m B -mass term. The appearance of antibaryonic states in thevacuum provides a U (1) B charge. This has to be con-sidered as an independent success of the antifermionicvacuum concept.Depending on the isospin structure of the bound statesin the vacuum the m W -mass term can obtain contribu-tions from the mesonic and antifermionic component. Itcreates a ( B, W ) mass matrix, which diagonalizes in theusual way. The symmetry of this matrix allows diag-onalization and the electrical neutrality of the vacuumensures m γ = 0 .One obvious question is why the running Weinberg an-gle obtained from the running fundamental charges g (cid:48) and g equals a diagonalization angle of the mass ma-trix. The question is related to the origin of Gell-Mann -Nishijima relation Q = T + Y . Here the diagonalizationangle has to take a value for which the antineutrons ofthe vacuum are neutral at the symmetry breaking scale. V. PREDICTIONS FOR LHC
Can one make predictions for LHC? Three “vacuum”fluctuations in bosonic densities are of course needed forthe third component of the weak vector bosons. Theforces controlling these fluctuations must allow for chargetransfers analogously to pion fields in nuclei. Their con-tribution will lead to an effective scalar interaction withtheir longitudinal part shown in Figure 3 manufacturingthe mass and adding the third component [49].
Figure 3: Mixing with the effective scalar
The rich flavor structure of the vacuum allows to ex-cite many different oscillation modes. Such phononic ex-citations H f i ¯ f j directly couple to matching f i ¯ f j pairs. Ofcourse, three boson couplings like W W H f i ¯ f j can also ap-pear. Their masses should correspond within orders ofmagnitude to the weak vector boson masses.Unlike GUT-scale bound objects their masses have tosomehow reflect the tumbled down vacuum scale. Asdescribed above with GUT-scale constituent masses andwith the tumbled down physical condensate mass suchpion-like states could reach the TeV range.It is not difficult to distinguish such phonons from theusual Higgs bosons [50] as they couple to the fermionsin a specific way. In literature they are called “privateHiggs” particles [51], which couple predominantly to onefermion pair.Their respective masses could reflect the constituentsthey are made of. The light lepton and light quarkphonons then have the lowest mass. The signalof a H ν ¯ ν could be that of an invisible Higgs bo-son [52]. The absence of abnormal backward scatteringin e + e − annihilation at LEP could limit the correspond-ing leptonic-“Higgs”-boson to M ( H e + e − ) >
189 GeV [53].Also the large-transverse-momentum jet production atFermilab could limit the mass of light quark H q ¯ q to anenergy above [54].However, the fermionic coupling constants are presum-ably much too tiny. The couplings to weak bosons andfermions are drawn in Figure 4. In the limit of vanishingphonon momenta their couplings correspond to the usualfermion mass terms. For heavier phonons this limit mightbe far away and meaningless. But for light phononstheir couplings should depend on mass of the fermionsinvolved similar to the usual Higgs bosons. Then thereis no chance to observe the light phonons in fermionicchannels. Their couplings to weak bosons is not known.Very light bosons would be rather stable. With massesin the range of weak vector bosons they could appear asquasi fermi-phobic “Higgs” particles.For the very heavy quarks there is no problem withthe coupling. The t ¯ t -phonons will look like a normalHiggs allowing t ¯ t decays and will be hard to distinguish.However, the expected mass range is different and suchphonons are possibly out of reach kinematically.The best bet might be the intermediate range. HereFermilab collaborations presented two canditates.The first candidate is a τ ¯ τ -phonon in a mass rangearound GeV. It is seen as broad { e ± µ ∓ missing p ⊥ }-structure in preliminary D0 data [55]. It is said to be sta-tistically on discovery level. At the moment D0 does nottrust their µ -energy calibration sufficiently to announceit as such. Figure 4: Coupling to phononic excitations
More significant is the . sigma excess at GeVin the dijet mass spectrum of W + jets published byCDF [56]. One of the virtual vector-boson decays W ∗ → W H s ¯ s , W ∗ → W H c ¯ c or Z ∗ → W H c ¯ s could contribute in the observed region [57] in a way comparable to theseen processes W ∗ → W Z or Z ∗ → W W yielding theobserved two jet final state.
Conclusion
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