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Kinetic Mixing and the Supersymmetric Gauge Hierarchy

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Keith R. Dienes, Christopher Kolda, John March-Russell (Institute for Advanced Study, Princeton)

High Energy Physics - Phenomenology · Submitted 24 Oct 1996 · 24 references

Pith's verdict: The field-theory core is right and durable; the string section is an estimate dressed as a result, and the abstract's 'generic in string models' line outruns what was computed.

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arXiv IDhep-ph/9610479 (version 2)
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CitationChristopher Kolda, John March-Russell (Institute for Advanced Study, Keith R. Dienes, Princeton). "Kinetic Mixing and the Supersymmetric Gauge Hierarchy." arXiv:hep-ph/9610479 (1996). https://pith.science/paper/LH7NBHMT
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The paper

The paper claims

A renormalizable mixing between two U(1) gauge fields can transmit supersymmetry breaking to the visible sector as hypercharge-proportional scalar masses, large enough to undo the gauge hierarchy.

The reading

The paper asks a narrow question with wide consequences: if the sector that breaks supersymmetry contains its own U(1) gauge factor, can that sector talk to the visible world through an operator nobody was watching? The operator is kinetic mixing, the renormalizable term that lets two U(1) field strengths share a kinetic term. Because it is renormalizable, it is not suppressed by any large mass scale, so physics at arbitrarily high energies can leave a permanent, dimensionless residue $|chi|$ in the low-energy theory. The authors show that once the gauge kinetic terms are put in canonical form, the visible scalars pick up hidden charges and, more importantly, the hidden D-term acquires a piece proportional to visible charge; the resulting shift in soft scalar masses is proportional to hypercharge and scales as $|chi| langle D_b angle$. If the hidden D-term is of order the fundamental supersymmetry-breaking scale, this shift drags the weak scale up toward that scale unless $|chi|$ is absurdly small, roughly $10^{-16}$ for supergravity mediation and $10^{-6}$ for gauge mediation. The paper's second half argues that field-theory loops and string threshold corrections naturally produce $|chi|$ well above those bounds, so the mixing cannot be assumed away.

What carries the argument

The load-bearing object is the supersymmetric kinetic mixing operator $frac{1}{32}int d^2 heta,{W_a W_a + W_b W_b - 2|chi| W_a W_b}$ (Eq. 2.2), together with the field shift that diagonalizes it. That shift is what converts a term written purely in field strengths into a coupling between visible matter and hidden D-terms, and hence into a soft mass. The parameter that carries the phenomenology is $eta = |chi| langle D_b angle / M_Z^2$: it is the single number that says whether kinetic mixing is a catastrophe, a measurable correction, or noise. On the calculational side, the machinery is the string torus amplitude with two different U(1) current insertions, giving $|chi|/(g_a g_b) = (b_{ab}/16pi^2)ln(M_X^2/mu^2) + Delta_{ab}/16pi^2$ (Eq. 3.10), where $b_{ab} = -Str_{massless} Q_H^2 Q_a Q_b$ and $Delta_{ab}$ sums the massive tower. The normalization $k_{ab}$ defined by the OPE $J_a(z)J_b(w) = (k_{ab}/2)/(z-w)^2 + dots$ (Eq. 3.13) is the switch that turns the universal contribution off for orthogonal gauge factors.

Extended reading notes

Core claim

The central claim is that kinetic mixing between a hidden U(1) and hypercharge is a supersymmetry-communication channel in its own right, distinct from supergravity and gauge mediation, and that it is generically large enough to matter. The authors derive it cleanly: shifting $V_a$ to $V_a - |chi| V_b$ diagonalizes the gauge kinetic terms but moves the mixing into the matter interactions, giving visible fields hidden charges $g_b Q_b + g_a |chi| Q_a$ (Eq. 2.6), a coupling of visible matter to hidden gauginos (Eq. 2.7), and a hidden D-term $D_b = -g_b sum Q_b |Phi_i|^2 - |chi| g_a sum Q_a |phi_i|^2$ (Eq. 2.8). Solving for the D-terms then yields the soft-mass shift $(m_i^2)_{KM} = g_a |chi| Q_{ai} langle D_b angle$ (Eq. 2.9), which combines with the ordinary visible D-term into a single hypercharge-proportional contribution governed by $eta equiv |chi| langle D_b angle / M_Z^2$ (Eq. 2.13). For $eta gg 1$ the hierarchy is destroyed and, because anomaly cancellation requires both signs of hypercharge, some state is driven to negative mass-squared; for $eta sim 1$ the effect is a flavor-independent correction to the soft masses and a new measurable parameter; for $eta ll 1$ it is negligible. The authors are explicit that the last case is reachable either by small $|chi|$ or by a hidden D-term much below the intrinsic supersymmetry-breaking scale, and they note a symmetry escape as well: a discrete charge-conjugation-like symmetry acting on the hidden U(1) alone forces hidden states into degenerate conjugate pairs and forbids the operator outright. Having stated the danger, they estimate $|chi|$ in two settings. In field theory, a loop of states charged under both U(1)s gives $|chi| = -(g_a g_b/16pi^2) Q_a Q_b log(m^2/m'^2)$ (Eq. 3.4), typically $10^{-2}$ to $10^{-3}$ for order-one charges and couplings in the $1/60$ to $1/25$ range. In string theory, they set up the torus amplitude with two distinct current insertions, show the universal term cancels because orthogonal U(1)s have $k_{ab}=0$, and reduce the whole effect to a threshold correction $Delta_{ab}$ from the massive string tower (Eq. 3.12).

Load-bearing premise

The sharp hierarchy-destabilization bound rests on the hidden U(1) D-term being of order the fundamental supersymmetry-breaking scale, $langle D_b angle sim Lambda^2$; if that D-term is naturally much smaller, or the hidden U(1) is not coupled to the source of supersymmetry breaking, the effect shrinks to a correction and the $10^{-16}$ and $10^{-6}$ bounds dissolve.

Editorial extensions

If this is right

  • Any model with a supersymmetry-breaking hidden sector containing a U(1) whose D-term is of order the fundamental scale must either suppress $|chi|$ below about $10^{-16}$ (supergravity mediation) or $10^{-6}$ (gauge mediation), or explain why the hidden D-term is small.
  • Kinetic mixing adds a flavor-independent, hypercharge-proportional shift to the soft scalar masses, so precision sparticle spectroscopy becomes a probe of the hidden sector, not just of the mediation mechanism.
  • The mixing induces a coupling of visible matter to hidden gauginos (Eq. 2.7), so hidden-sector F-terms can feed visible masses through loops even when the D-term contribution is arranged to be small.
  • Model builders get a sharp selection rule: a discrete symmetry that acts as charge conjugation on the hidden U(1) alone forbids the operator, and the same class of symmetries forbids a Fayet-Iliopoulos term.
  • String models do not automatically escape: even where the tree-level spectrum cancels the mixing level by level, symmetry breaking, vacuum shifts, and renormalization-group flow split the degenerate pairs and regenerate it.

Reading between the lines

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

  • If $eta$ is measured to be nonzero, the natural interpretation is that the messenger of supersymmetry breaking is not supergravity or gauge mediation but a hidden U(1), which would make the soft-mass pattern a direct window on hidden-sector dynamics rather than on Planck-scale physics.
  • The same operator should exist between two visible U(1)s, for instance hypercharge and a would-be $B-L$ or $L_i - L_j$ factor, where it would shift the interpretation of precision electroweak and $Z'$ searches without any hidden sector at all.
  • Because the effect is hypercharge-proportional and flavor-blind, it can be partially absorbed into a redefinition of the standard $M_Z^2 cos 2eta$ D-term contribution; disentangling the two would require a mass relation such as Eq. 2.14 measured in more than one channel, which is a concrete target for a future lepton collider.
  • The paper's own escape hatch, a discrete charge-conjugation symmetry on the hidden U(1), suggests a model-building principle: hidden sectors with exact conjugate pairing are the ones where the messenger is guaranteed to be something other than kinetic mixing.
Original abstract

The most general Lagrangian for a model with two U(1) gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. In models whose supersymmetry (SUSY)-breaking hidden sectors contain U(1) gauge factors, we show that such terms will generically arise and communicate SUSY-breaking to the visible sector through mixing with hypercharge. In the context of the usual supergravity- or gauge-mediated communication scenarios with D-terms of order the fundamental scale of SUSY-breaking, this effect can destabilize the gauge hierarchy. Even in models for which kinetic mixing is suppressed or the D-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. We conclude that the possibility of kinetic mixing effects cannot be ignored in model-building and in phenomenological studies of the low-energy SUSY spectra.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,706 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The most general Lagrangian for a model with two U(1) gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. In models whose supersymmetry (SUSY)-breaking hidden sectors contain U(1) gauge factors, we show that such terms will generically arise and communicate SUSY-breaking to the visible sector through mixing with hypercharge. In the context of the usual supergravity- or gauge-mediated communication scenarios with D-terms of order the fundamental scale of SUSY-breaking, this effect can destabilize the gauge hierarchy. Even in models for which kinetic mixing is suppressed or the D-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. We conclude that the possibility of kinetic mixing effects cannot be ignored in model-building and in phenomenological studies of the low-energy SUSY spectra.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The most general Lagrangian for a model with two U(1) gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. background 1.00 0.10 0.04 asserted 1.00
s1 Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. result 0.49 0.24 0.06 asserted 0.97
s2 In models whose supersymmetry (SUSY)-breaking hidden sectors contain U(1) gauge factors, we show that such terms will generically arise and communicate SUSY-breaking to the visible sector through mixing with hypercharge. result 0.61 0.88 0.16 asserted 1.00
s3 In the context of the usual supergravity- or gauge-mediated communication scenarios with D-terms of order the fundamental scale of SUSY-breaking, this effect can destabilize the gauge hierarchy. interpretation 0.59 0.46 0.12 hedged possibility 0.84
s4 Even in models for which kinetic mixing is suppressed or the D-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. result 0.63 0.52 0.11 hedged possibility 0.67
s5 We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. contribution 0.58 0.93 0.08 asserted 0.78
s6 We conclude that the possibility of kinetic mixing effects cannot be ignored in model-building and in phenomenological studies of the low-energy SUSY spectra. interpretation 0.88 0.47 0.93 hedged possibility 0.54

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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. (a) The one-loop diagram which contributes to kine

Figures reproduced from arXiv:hep-ph/9610479 by the authors.

References
How later papers used it

141 later papers cite it

Evidence: some. 136 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 182 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 2 papers with this label
How the literature uses it

139 arXiv papers cite this in 179 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 · 102 sentences without a confident label

Uses its method or tool 2 papers
  • Following Ref. [ref] , this kinetic mixing can be written as a cross term between the $D$ terms associated with the two $U(1)$'s as [equation] where $Q_Y^i$ is the $U(1)_Y$ charge of the scalar $ϕ_i$, $Q^j$ is the $U(1)$ charge, and $e$ is the $U(1)$ electric charge.

    Cosmologically Viable Low-energy Supersymmetry Breaking · The Models · 0.92

  • This regulator is essentially the one used in Ref. [ref] and later in Ref. [ref] .

    Calculating the Higgs Mass in String Theory · Pulling it all together: Discussion, top-down perspectives, and future directions · 0.84

Compares with it 1 paper
  • Indeed, this explicit subtraction of the contributions from massless states is similar to what occurs in the calculation of string-theoretic gauge threshold corrections in Ref. [ref] and in the calculation of string-theoretic kinetic mixing in Ref. [ref] .

    Calculating the Higgs Mass in String Theory · Results using the minimal regulator · 0.95

Cites it as background 68 papers
  • At low energies, their interactions with the visible sector occur primarily via kinetic mixing [ref] (studied in string theory in [ref] ) with the electromagnetic[Of course, the mixing is originally with the hypercharge $U(1)$ but after electroweak symmetry breaking this mixing is inherited by the electromagnetic $U(1)$.][A massive hidden photon behaves very similar to a $Z^'$.

    Testing String Vacua in the Lab: From a Hidden CMB to Dark Forces in Flux Compactifications · Introduction · 0.95

  • To see this, let us first recall the relation between field-theory loop and string loop calculations [ref] : We focus on type IIB, where gauge theories live on D-branes and the relevant string loop diagram is the cylinder shown in fig.

    Small Kinetic Mixing in String Theory · Small kinetic mixing in type IIB string compactifications · 0.89

  • Well-motivated scenarios include photon mixing into low-mass bosonic states like axions [ref] and dark photons [ref] , photon decay via Lorentz invariance violation [ref] , etc.

    Axion and dark photon limits from Crab Nebula high energy gamma-rays · Introduction · 0.85

Discussion

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