Signatures of the anomalous $Z\gamma$ and ZZ production at the lepton and hadron Colliders

F.M. Renard; G.J. Gounaris; J. Layssac

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Signatures of the anomalous $Z\gamma$ and ZZ production at the lepton and hadron Colliders

G.J. Gounaris, J. Layssac, F.M. Renard

High Energy Physics - Phenomenology · Submitted 19 Oct 1999 · 21 references

Pith's verdict: The factor-i fix to the ZγV vertices is a real service to the field; the sensitivity tables are illustrations, and the h3 = −f5 relation is not checkable here because the loop derivation sits in an unpublished companion.

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CitationF.M. Renard, G.J. Gounaris, J. Layssac. "Signatures of the anomalous $Z\gamma$ and ZZ production at the lepton and hadron Colliders." arXiv:hep-ph/9910395 (1999). https://pith.science/paper/GI7KURSA

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The thing worth your time here is small and concrete: the standard 1987 parametrization of the ZγV neutral triple-gauge vertices is missing a factor of i, which makes the associated effective Lagrangian antihermitian and flips the sign of the interference between CP-conserving NP amplitudes and the SM. Gounaris, Layssac and Renard flag the change explicitly against [2], and the amplitudes in their Eqs. (7)–(9) are consistent with it — the CP-violating couplings carry the i, the CP-conserving ones are real, matching their own CP assignments. Anyone who has extracted a linear-regime limit with the old convention should check their sign. That is the load-bearing contribution and it holds up on reading. The rest is a survey: ZZ and Zγ at LEP2, a 500 GeV LC, Tevatron and LHC, with the standard observation that CP-conserving couplings interfere and CP-violating ones only add quadratically. The suggestion to bin in invariant mass rather than lean on multiplicative form factors is sensible and, I think, the right methodological instinct. The soft spot is the toy model. The abstract's headline — specific relations among the neutral couplings [abstract:s4] — reduces in practice to h3 = −f5 plus h4 = 0, and the one-loop triangle computation is cited to [17], listed as 'preprint in preparation.' We get final formulas only. The authors themselves note that a degenerate heavy family drives everything to zero, so the relation is spectrum-dependent by their own account; a reader cannot tell how robust it is to the mZ²/MF² expansion or to the anomaly bookkeeping. That is a missing-support issue, not an error, but it means the relation should be quoted as a model expectation, not a result. On the reader's weakest-assumption note: the luminosity and background inputs are indeed asserted, but the paper calls them illustrations and says outright that a careful background study remains to be done, so I would not weight that heavily. The 'two significant figures' complaint is also off — the LC numbers are one significant figure. Verdict: worth a referee, mainly for the vertex correction and the amplitude conventions.

Referee report

Significance

The paper is a useful reference for the neutral triple-gauge sector, which has received less attention than the charged one. The factor-i correction, if correct, is a genuine service: it affects the sign of linear interference terms in a body of existing Zγ analyses, and the authors are right to flag it even while noting that most current limits are quadratic-dominated. The compilation of expected sensitivities across four colliders, and the emphasis on longitudinal polarization at the LC and on binned invariant-mass analyses at hadron colliders, are practically useful. The heavy-fermion relation hZ3 = -fγ5 is a genuinely falsifiable prediction and the paper's most valuable original element, but it is also the element least supported within the manuscript.

Major objections (3)

[§2, Eqs. (11)-(15); §4] The abstract's headline prediction [abstract:s4] — specific relations among the neutral couplings — is carried entirely by Eqs. (11)-(15), and in particular by hZ3 = -fγ5 in Eq. (15). These are quoted from ref. [17], which is listed as 'preprint in preparation'. A reader cannot check whether the relation survives the full triangle-diagram structure, the mZ^2/MF^2 expansion, or the anomaly-cancellation bookkeeping; the paper's own discussion of the degenerate-family case, where all couplings vanish, shows the relation is spectrum-dependent. Since this is the paper's most testable claim, either sketch the leading terms of the triangle computation in an appendix (the mZ^2/MF^2 expansion and the cancellation argument are enough) or state the precise hypothesis under which Eq. (15) holds — a single heavy fermion, or one doublet much lighter than the rest of the family — in the abstract itself, not only in the body.
[§2, Eqs. (1)-(2); §4, paragraph 2] The claim that ref. [2] omitted a factor i, making the effective Lagrangian antihermitian and reversing the interference pattern of the CP-conserving and CP-violating amplitudes with the SM, is asserted rather than demonstrated. The corrected amplitudes in Eqs. (7)-(9) are internally consistent — the CP-violating couplings f4, h1, h2 carry the i and the CP-conserving f5, h3, h4 do not — but a reader cannot verify the claim about [2] without a side-by-side comparison with the explicit vertex expression there. A short appendix reproducing the [2] expression and exhibiting the sign flip in one amplitude (for instance the CP-conserving term of Eq. (8)) would settle the point. The further statement in §4 that existing limits are largely unaffected because they are quadratic-dominated should be quantified for at least one published case, e.g. the LEP Zγ limits of [20], by showing the shift in the extracted coupling when the sign of the interference term is flipped.
[§3, 'Form factors' and 'Application to ZZ and Zγ production at hadron colliders'; Figs. 8-9] The paper argues, correctly in my view, that multiplicative form factors are in tension with the effective-Lagrangian expansion and proposes instead binned invariant-mass analyses. It then nevertheless presents the Tevatron and LHC sensitivities using form factors with Λ_FF = 0.75 TeV and 3 TeV respectively. The tension is acknowledged, but its quantitative cost is not: the reader is not told how much the quoted hadron-collider reach in Figs. 8-9 moves if Λ_FF is varied over a plausible range, nor is even one bin of the proposed invariant-mass analysis shown. Since the hadron-collider part is half of what the abstract advertises [abstract:s1], at least one worked bin — with a stated mass window, angular cut and event count — would make the proposal concrete and allow the comparison across colliders that the paper advocates.

Minor objections (6)

[Figs. 2-9] The captions state only the process and the collider. They should also state the coupling values shown, the c.m. energy, and the angular or pT cuts, so that the curves can be read without hunting through the text.
[Eqs. (B.2) and (B.4)] Eq. (B.2) restricts the ZZ angular integral to 0 ≤ cosϑ* ≤ 1 to account for the identity of the two Z bosons; Eq. (B.4) should state explicitly that A_LR is defined over the same restricted range.
[§2, Eqs. (7)-(9)] The symbol gZλ is defined in Eq. (A.4) but used in Eqs. (7)-(9), which precede Appendix A; a forward reference at first use would help the reader.
[§3, LEP2 sensitivities] The one-sigma sensitivities (e.g. 2×10^-3 for fγ4, 4×10^-5 for hγ4) are quoted to two significant figures from inputs — 150 pb^-1, a factor-2 selection loss, 1% accuracy, 'no appreciable background' — that are order-of-magnitude estimates anchored to a conference report [19]. Rounding to one significant figure, or labelling them explicitly as order-of-magnitude, would better represent what has been computed.
[§2, toy model] The statement that heavy scalar particles cannot generate these neutral self-couplings deserves a one-line justification or a reference, since it is used to motivate the fermion toy model.
[References and typography] 'similarely' appears in the line after Eq. (3); 'thy∗1 = β∗1 cos ϑ∗' in Appendix B should read tanh y*1; 'anf' appears in ref. [18]; 'Acciari' should be 'Acciarri' in ref. [20]; and 'SLAC-329(1928)' in ref. [21] should presumably be 1989.

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The paper

The paper claims

The standard parametrization of the neutral triple-gauge vertices (ZZZ, ZZ$gamma$, Z$gamma$$gamma$) is missing a factor of $i$, and putting it back makes the effective Lagrangian hermitian and reverses which new-physics terms interfere with

The reading

The paper's central move is a correction, not a discovery claim: the widely used 1987 parametrization of the vertices where two on-shell neutral gauge bosons meet an off-shell Z or photon omits a factor of $i$. Without it the associated effective Lagrangian is antihermitian, and the practical consequence is that CP-conserving new-physics amplitudes were being treated as the ones that add incoherently while CP-violating ones were treated as the ones that interfere. Restoring the factor swaps those roles, so every limit extracted in the regime where interference dominates carries the wrong sign. Beyond the bookkeeping, the authors rederive the Standard Model and new-physics helicity amplitudes for $fbar f o ZZ$ and $fbar f o Zgamma$ with all conventions fixed, then project how strongly each of the ten neutral couplings could be pinned down at LEP2, at a 500 GeV linear collider, at the Tevatron and at the LHC. A heavy-fermion loop model is used as a guide to what pattern of couplings is plausible: only $f_5$ and $h_3$ are generated at one loop, and they satisfy $h^Z_3 = -f^gamma_5$, a relation that is independent of the heavy fermion's couplings.

What carries the argument

The load-bearing object is the corrected vertex function: $Gamma^{alpha beta mu}_{ZZV}$ carrying the two CP-odd couplings $f^V_4, f^V_5$ and $Gamma^{alpha beta mu}_{Zgamma V}$ carrying $h^V_1$ through $h^V_4$, with the inserted factor of $i$ in the second. Translated through the equations of motion into contact $fbar f ZZ$ and $fbar f Zgamma$ interactions, these vertices generate the new-physics helicity amplitudes that are added to the Standard Model fermion-exchange amplitudes. The amplitude-level statement that CP-conserving couplings give real terms and CP-violating ones purely imaginary terms is what converts a sign convention into an experimentally visible interference pattern in angular distributions and in the left-right polarization asymmetry.

Extended reading notes

Core claim

The paper argues that the general $V_1V_2V_3$ vertex for two on-shell neutral bosons and one off-shell $Z$ or photon requires an extra factor of $i$ in the $Zgamma V$ sector relative to the standard reference form, so that the effective Lagrangian generating the $ZZZ$, $ZZgamma$ and $Zgammagamma$ vertices is hermitian. The authors state that with the old convention the interference pattern of CP-conserving and CP-violating new-physics amplitudes with the Standard Model was reversed, and that while existing experimental limits are barely affected because they are dominated by the quadratic term, increasing accuracy would eventually produce non-intuitive results. On that corrected basis they give the new-physics helicity amplitudes for $fbar f o ZZ$ and $fbar f o Zgamma$, note that CP-conserving couplings give real amplitudes that interfere linearly with the Standard Model while CP-violating ones give imaginary amplitudes that enter only quadratically, and collect one-standard-deviation sensitivity estimates for each coupling at LEP2, a 500 GeV linear collider, the Tevatron and the LHC. The heavy-fermion toy model supplies the testable prediction $h^Z_3 = -f^gamma_5$ together with the vanishing of $h^Z_4$ and $h^gamma_4$.

Load-bearing premise

The sensitivity numbers quoted for each coupling rest on assumed rather than derived experimental inputs: a LEP2 luminosity of 150 inverse picobarns with a factor-two selection loss, a linear-collider sample of 100 inverse femtobarns with one percent accuracy, and a claim of negligible background for $Zgamma$ at large angles.

Editorial extensions

If this is right

Any fit to $Zgamma$ production data that assumed the old convention and sat in the interference-dominated regime should be re-examined for a sign flip in the extracted CP-conserving couplings.
At a 500 GeV linear collider with polarized beams, the left-right asymmetry $A_{LR}$ departs from its Standard Model values of about 0.28 for $ZZ$ and 0.14 for $Zgamma$ in a way that differs sharply between photon-type and Z-type couplings, giving a handle for separating them.
If the heavy-fermion loop picture is right, measuring $h^Z_3$ and $f^gamma_5$ should return equal magnitudes and opposite signs, while $h^Z_4$ and $h^gamma_4$ should come out consistent with zero.
Because no neutral triple-gauge vertex arises from dimension-six operators in the linear representation, observing any of these couplings would point either to enhanced higher-dimensional operators or to a nearby new-physics scale.
Sensitivity to the dimension-eight couplings $h^V_2$ and $h^V_4$ grows faster with energy than to the dimension-six ones, so they should be bounded more tightly at the same collider.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The sign correction is the kind of error that is invisible until interference terms matter, which suggests the same convention should be checked in the charged triple-gauge literature where interference is already large.
The proposal to quote limits in narrow bins of subprocess invariant mass, rather than with multiplicative form factors, would make collider comparisons meaningful but also would require each experiment to publish a correlated set of limits rather than a single number.
If $h^Z_3 = -f^gamma_5$ holds, a global fit imposing it halves the number of free parameters in the CP-conserving sector, which would tighten the remaining bounds more than the naive gain from one fewer parameter.
The one-loop estimate of order $10^{-3}$ for these couplings at a few-hundred-GeV fermion mass implies that observability at LEP2 or the Tevatron needs an enhancement factor of order $10^2$, so a null result there constrains strongly interacting new-physics sectors more than weakly coupled ones.

Original abstract

The possible form of New Physics (NP) interactions affecting the ZZZ, $ZZ \gamma$ and $Z\gamma \gamma$ vertices, is critically examined. Their signatures and the possibilities to study them, through ZZ and $Z\gamma$ production, at the e^-e^+ Colliders LEP and LC and at the hadronic Colliders Tevatron and LHC, are investigated. Experimental limits obtained or expected on each coupling are collected. A simple theoretical model based on virtual effects due to some heavy fermions is used for acquiring some guidance on the plausible forms of these NP vertices. In such a case specific relations among the various neutral couplings are predicted, which can be experimentally tested and possibly used to constrain the form of the responsible NP structure.

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The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; show every role.

The possible form of New Physics (NP) interactions affecting the ZZZ, $ZZ \gamma$ and $Z\gamma \gamma$ vertices, is critically examined. Their signatures and the possibilities to study them, through ZZ and $Z\gamma$ production, at the e^-e^+ Colliders LEP and LC and at the hadronic Colliders Tevatron and LHC, are investigated. Experimental limits obtained or expected on each coupling are collected. A simple theoretical model based on virtual effects due to some heavy fermions is used for acquiring some guidance on the plausible forms of these NP vertices. In such a case specific relations among the various neutral couplings are predicted, which can be experimentally tested and possibly used to constrain the form of the responsible NP structure.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The possible form of New Physics (NP) interactions affecting the ZZZ, $ZZ \gamma$ and $Z\gamma \gamma$ vertices, is critically examined.	contribution 0.84	0.61	0.07	hedged possibility 0.58
s1	Their signatures and the possibilities to study them, through ZZ and $Z\gamma$ production, at the e^-e^+ Colliders LEP and LC and at the hadronic Colliders Tevatron and LHC, are investigated.	contribution 0.96	0.70	0.06	asserted 0.75
s2	Experimental limits obtained or expected on each coupling are collected.	contribution 0.58	0.23	0.09	asserted 0.94
s3	A simple theoretical model based on virtual effects due to some heavy fermions is used for acquiring some guidance on the plausible forms of these NP vertices.	method 0.99	0.77	0.04	asserted 0.95
s4	In such a case specific relations among the various neutral couplings are predicted, which can be experimentally tested and possibly used to constrain the form of the responsible NP structure.	interpretation 0.47	0.55	0.29	asserted 0.66

What kind of paper the classifier reports this is: review 0.88 · evidence from literature 0.64.

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sources read

arXiv listing abstract v5

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Feynman rule for the general V1V2V3 vertex. 18

**Figure 2.** Standard and anomalous contributions to the unpolarized

**Figure 3.** Standard and anomalous contributions to the unpolarized

**Figure 4.** Standard and anomalous contributions to unpolarized

**Figure 5.** Standard and anomalous contributions to unpolarized

**Figure 6.** Standard and anomalous contributions to Left-Right asy

**Figure 7.** Standard and anomalous contributions to Left-Right asy

**Figure 8.** Standard and anomalous contributions to the

**Figure 9.** Standard and anomalous contributions to the

Figures reproduced from arXiv:hep-ph/9910395 by the authors.

References

Works cited (21)

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Forward citations

Cited by 7 Pith papers

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Two longitudinally polarised Z bosons are produced in ZZ events at a rate consistent with the Standard Model, seen at 4.3 standard deviations, and the CP-sensitive angular distribution of the same events constrains CP...
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The U(2)-invariant CP-violation measures of the two-Higgs-doublet model are expressed in terms of neutral Higgs masses and couplings, and ZZZ, ZHH, and Z to VVHH amplitudes are shown to probe them.
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How the literature uses it

32 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 40 sentences without a confident label

Contests it 2 papers

On the other hand, our $_4^$ bound in Eq.[ref] is much weaker than the ATLAS bounds on $(h_4^, h_4^Z)$, by a large factor of $∼32$, because the conventional nTGC form factor formulae are incompatible with the gauge-invariant SMEFT formulation of dimension-8 (including spontaneous electroweak gauge symmetry breaking), as we explain in Appendix [ref] and Table [ref].We emphasize that the existing ATLAS result [ref] used the conventional on-shell nTGC formula of the vertex $ZV^*$ [ref] for analyzing the $νν̅$ channel, which caused a significant underestimate of the sensitivity to $_3^$ by about $60%$.

Probing Neutral Triple Gauge Couplings with $Z^* \gamma\, (\nu \bar \nu \gamma)$ Production at Hadron Colliders · . Probing nTGCs with $Z^*(νν̅)$ Production at Hadron Colliders · contest 0.87
[For the toy model [ref] states that the NTGC scales as $m_Z^2/M_F^2$, which is obviously not the correct scaling for a coupling generated from $d=8$ operators.

Fermionic UV models for neutral triple gauge boson vertices · Introduction · contest 0.90

Uses its method or tool 1 paper

The results are then reinterpreted to constrain aNTGC using an effective vertex function approach [ref] .

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Compares with it 3 papers

We present this comparison in Table [ref], where the third row (red color) depicts the sensitivity reaches on $_4,2^$ obtained by using our nTGV formula [ref], and the last two rows (blue color) show the sensitivity reaches on $h_4,2^V$ that would be obtained by using the (incorrect) conventional nTGV formulas [ref] [ref] .Table [ref] demonstrates that the sensitivity reaches on the conventional nTGC form factors $h_4,2^V$ are erroneously stronger than those for our new formulation [ref] by about a factor of $O(20)$ at the LHC and by about a factor of $O(170)$ at a 100TeV $pp$ collider.

Probing Neutral Triple Gauge Couplings with $Z^* \gamma\, (\nu \bar \nu \gamma)$ Production at Hadron Colliders · . Matching $Z^*V^*$ Form Factors to the SMEFT Operators · 0.83
In doing so, we compare the results for the form factor $h_3^γ(s)$ [ref] with a full (UV) theory example mentioned above, merely as a demonstration of the validity of our procedure.

Chiral Anomaly Cancellation and Neutral Triple Gauge Boson Vertices in the SM EFT · Introduction · 1.00
This is suggested by a comparison with results in Hagiwara:1986vm and [ref] , respectively.] We use the definitions:

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From a phenomenological point of view, there are many cases where dimension-6 operators are absent, but the dimension-8 operators show up [ref] .

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Thus better limits can be obtained for $h_2/4^V$ [ref] .

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Cites it as background 13 papers

The MSSM contribution to the trilinear neutral gauge couplings has been calculated in the references [ref] .

New Physics Contribution to Neutral Trilinear Gauge Boson Couplings · MSSM · 0.80
Keeping these considerations in mind, the issue of sensitivity to linear order of CP-violating anomalous gauge boson couplings, denoted by $λ_1$ ($γZ Z$) and $λ_2$ ($γγZ$) to be defined later, that contribute to the process $e^+e^-→γZ$ with longitudinal beam polarization was considered in Ref. [ref] , and with transverse beam polarization in Ref. [ref] (for earlier discussions in the context of unpolarized beams see Ref. [ref] , and Ref. [ref] for beam polarization effects).

Isolating CP-violating \gamma ZZ coupling in e+e- \to \gamma Z with transverse beam polarizations · Introduction · 0.83
The most general parametrization of nTGCs in $ZZ$ and $Zγ$ production is given by [ref] , cf. also [ref] ,

Constraining CP violating operators in charged and neutral triple gauge couplings · Neutral aTGCs · 0.81

Discussion

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