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Dynamical Left-Right Symmetry Breaking

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E. Akhmedov, M. Lindner, E. Schnapka, J.W.F. Valle

High Energy Physics - Phenomenology · Submitted 8 Sep 1995 · 47 references

Pith's verdict: The structural result — triplet composite LR fails, doublet-plus-singlet works because gauge loops force λ2 > λ1 — is real and worth having; the quantitative claims are softer than the abstract implies, and the authors mostly say so themselves.

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arXiv IDhep-ph/9509255 (version 1)
Pith ID4SUF7ICW, Pith's permanent record of this paper and its review
CitationE. Akhmedov, E. Schnapka, J.W.F. Valle, M. Lindner. "Dynamical Left-Right Symmetry Breaking." arXiv:hep-ph/9509255 (1995). https://pith.science/paper/4SUF7ICW
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The paper

The paper claims

A left-right symmetric model with no fundamental Higgs fields can break its own symmetry in the right order, provided a single new neutral fermion is added to the spectrum.

The reading

The paper asks whether the left-right symmetric extension of the Standard Model can work with no elementary scalar fields at all: only gauge bosons, fermions, and a set of attractive four-fermion interactions standing in for unknown heavy physics. The authors argue that it can. If those interactions are strong enough, scalar bound states form dynamically and the symmetry breaks in the required two-step order, first $SU(2)_R times U(1)_{B-L} to U(1)_Y$ at a scale that may be as low as $sim 20$ TeV, then ordinary electroweak breaking near $100$ GeV. The ingredient that makes the chain work is a new electrically neutral, gauge-singlet fermion; without it the composite scalars would be triplets and, as the authors show, parity would never break. With renormalization-group improvement the model accommodates the observed top quark mass for $tanbeta equiv kappa/kappa' approx 1.3$–$4$, and it predicts a spectrum of intermediate-mass scalars with fixed mass ratios, plus lepton-flavour violation close to the present $mu to e gamma$ bound.

What carries the argument

The calculation is a left-right generalization of top-condensation: four-fermion operators are rewritten with static auxiliary scalar fields, which acquire kinetic terms, quartic couplings and negative mass-squared terms through fermion and gauge loops in the bubble (large-$N_c$, cutoff $Lambda$) approximation. The effective potential is obtained by truncating the one-loop Coleman-Weinberg potential at quartic order with an infrared cutoff $mu$, which yields explicit expressions for the mass parameters and quartic couplings in terms of Yukawa and gauge couplings. Compositeness is imposed as a boundary condition at the cutoff: the wave-function renormalization constants $Z_varphi, Z_chi, Z_sigma$ vanish as $mu to Lambda$, equivalent to Landau poles in the Yukawa couplings, and the full one-loop renormalization-group equations are then run down from those poles. The infrared quasi-fixed-point structure makes the low-energy predictions largely insensitive to the precise values chosen at the cutoff.

Extended reading notes

Core claim

The central claim is that a left-right symmetric theory with no elementary scalars can break its own symmetry in the phenomenologically correct order, and that whether parity breaks is decided by the particle content rather than by adjustable couplings in a Higgs potential. Composite scalars arise as bound states of four-fermion interactions: a bi-doublet $varphi$ from top/bottom and $tau$/$nu_tau$ pairs, doublets $chi_L, chi_R$ built from a new singlet fermion $S_L$ together with the lepton doublets, and a singlet $sigma$. Gauge-boson loops make the quartic coupling $lambda_2$ exceed $lambda_1$ automatically, which is precisely the condition for the right-handed doublet to acquire the larger vacuum expectation value; in the triplet version of the same construction the two couplings come out equal and parity stays unbroken. The breaking then tumbles: the parity-breaking condensate at scale $mu_R$ drives the electroweak condensate at $mu_{EW}$ through a negative cross quartic coupling $lambda_5$, so the hierarchy is generated rather than assumed.

Load-bearing premise

The singlet scalar $sigma$ must never condense, which requires the four-fermion coupling $G_8$ to stay sub-critical and the inequality of eq. (III.20) to hold beyond the bubble approximation; the authors state in Section V.1 that they assume this 'although we were unable to prove that', and if $sigma$ condensed first the driving term for $v_R$ would never turn negative and the whole breaking chain would collapse.

Editorial extensions

If this is right

  • Low-energy parity violation becomes a consequence of the fermion content rather than of tuning: one gauge-singlet fermion per generation is enough to make spontaneous parity breaking automatic, while the triplet version of the same construction cannot break parity at all.
  • Vacuum stability requires the right-handed scale to exceed roughly $17$–$20$ TeV, and with only mild cancellation in the relation between the two VEVs the scale can sit just above that bound, bringing the new physics within reach of the LHC rather than only of GUT-scale probes.
  • The scalar spectrum carries fixed ratios: a heavy CP-even state near $2M$ (a bound state of heavy Majorana neutrinos), a Standard-Model-like Higgs near $2m_t$, charged scalars $varphi^pm_2$ suppressed by $m_tau/m_t$, and pseudo-Goldstone $chi_L$ states at about a tenth of the parity scale from an accidental global $SU(4)$ symmetry.
  • With flavour off-diagonal $Y_5$ couplings of order one, $mathrm{BR}(mu to e gamma)$ reaches the present experimental upper bound for $M approx 20$ TeV, so the model predicts lepton-flavour violation just around the corner.
  • Neutral scalars $varphi^0_{2r}$ and $varphi^0_{2i}$ may be as light as $60$–$100$ GeV when the parity scale is near its lower bound, possibly visible at LEP2 and able to supply a positive contribution to $R_b = Gamma(Z to bar b b)/Gamma(Z to text{hadrons})$.

Reading between the lines

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

  • The claim that particle content, not parameter choice, decides whether parity breaks can be read as a selection rule for model building: any left-right composite-Higgs construction whose spectrum lacks a gauge-singlet fermion is excluded on structural grounds, which turns the singlet into a prediction rather than an optional extra.
  • Because the same singlet fermion supplies both the parity-breaking condensate and the modified seesaw that keeps neutrinos light, the parity scale and the size of lepton-flavour-violating rates are tied together; a measurement of either would constrain the other, giving a consistency check that does not require reaching the new gauge bosons directly.
  • The accidental $SU(4)$ symmetry of the $chi$ sector arises whenever two doublets are generated by four-fermion operators with equal Yukawa strength, so pseudo-Goldstone scalars at roughly a tenth of the parity scale may be a generic signature of dynamical left-right breaking rather than a feature of this particular parameter point.
  • The unproven decoupling of the singlet scalar $sigma$ is the natural target for a dedicated gap-equation or lattice study: whether $G_8$ stays sub-critical is a statement about the ultraviolet completion, which the paper explicitly leaves to future work.
Original abstract

We study a left--right symmetric model which contains only elementary gauge boson and fermion fields and no scalars. The phenomenologically required symmetry breaking emerges dynamically leading to a composite Higgs sector with a renormalizable effective Lagrangian. We discuss the pattern of symmetry breaking and phenomenological consequences of this scenario. It is shown that a viable top quark mass can be achieved for the ratio of the VEVs of the bi--doublet $\tan\beta\equiv\kappa/\kappa'$ =~ 1.3--4. For a theoretically plausible choice of the parameters the right--handed scale can be as low as $\sim 20 TeV$; in this case one expects several intermediate and low--scale scalars in addition to the \SM Higgs boson. These may lead to observable lepton flavour violation effects including $\mu\to e\gamma$ decay with the rate close to its present experimental upper bound.

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, 4,990 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study a left--right symmetric model which contains only elementary gauge boson and fermion fields and no scalars. The phenomenologically required symmetry breaking emerges dynamically leading to a composite Higgs sector with a renormalizable effective Lagrangian. We discuss the pattern of symmetry breaking and phenomenological consequences of this scenario. It is shown that a viable top quark mass can be achieved for the ratio of the VEVs of the bi--doublet $\tan\beta\equiv\kappa/\kappa'$ =~ 1.3--4. For a theoretically plausible choice of the parameters the right--handed scale can be as low as $\sim 20 TeV$; in this case one expects several intermediate and low--scale scalars in addition to the \SM Higgs boson. These may lead to observable lepton flavour violation effects including $\mu\to e\gamma$ decay with the rate close to its present experimental upper bound.

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 We study a left--right symmetric model which contains only elementary gauge boson and fermion fields and no scalars. contribution 0.82 0.59 0.05 asserted 0.98
s1 The phenomenologically required symmetry breaking emerges dynamically leading to a composite Higgs sector with a renormalizable effective Lagrangian. result 0.86 0.84 0.64 asserted 1.00
s2 We discuss the pattern of symmetry breaking and phenomenological consequences of this scenario. contribution 0.98 0.76 0.06 unclear 0.56
s3 It is shown that a viable top quark mass can be achieved for the ratio of the VEVs of the bi--doublet $\tan\beta\equiv\kappa/\kappa'$ =~ 1.3--4. result 1.00 0.88 0.15 asserted 0.97
s4 For a theoretically plausible choice of the parameters the right--handed scale can be as low as $\sim 20 TeV$; in this case one expects several intermediate and low--scale scalars in addition to the \SM Higgs boson. result 0.96 0.81 0.13 hedged possibility 0.83
s5 These may lead to observable lepton flavour violation effects including $\mu\to e\gamma$ decay with the rate close to its present experimental upper bound. interpretation 0.77 0.61 0.12 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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. Fermion loop diagrams contributing to the quartic couplings λ1 (Fig. 1a) and λ2 (Fig. 1b) for Higgs triplets. viable scenario), this would not save the situation since the diagram of Fig. 1b is finite whereas the one of Fig. 1a is logarithmically divergent and so the inequality λ2 > λ1 cannot be satisfied. We also checked that using the full one–loop Coleman–Weinberg [23] effective potential instead of the truncated one which includes up to the quartic terms in the fields does not save the situation. Therefore we will consider a model with a different composite Higgs content. As we…
Figure 2. Fermion loop diagrams contributing to the quartic couplings λ1 (Fig. 2a) and λ2 (Fig. 2b) for the Higgs doublets χL/R. given by similar diagrams. Since the Yukawa couplings of χL and χR coincide (which is just the consequence of the discrete parity symmetry), Figs. 2a and 2b yield λ1 = λ2. Recall that one needs λ2 > λ1 for spontaneous parity breakdown. As we shall see, taking into account the gauge–boson loop contributions to λ1 and λ2 shown in
Figure 3. Gauge boson loop diagrams contributing to the quartic couplings λ1 (Fig. 3a) and λ2 (Fig. 3b) for the Higgs doublets χL/R in Landau gauge. minus sign compared to those from the fermion loops, one finds λ2 > λ1 irrespective of the values of the Yukawa or gauge couplings or any other parameter of the model, provided that the SU(2) gauge coupling g2 6= 0 [compare the expressions for λ1 and λ2 in (B.9)]. Thus the condition for spontaneous parity breaking is automatically satisfied in our model. We have a very interesting situation here. In a model with composite triplets ∆L and ∆R…
Figure 4. Diagrams contributing to the effective scalar mass terms Mf2 0 . . . Mf2 3 in Landau gauge
Figure 5. Diagrams contributing to the quartic terms in the Higgs potential in Landau gauge. 12
Figure 6. Renormalization Group evolution of the Y5 Yukawa coupling for various compositeness scales Λ, t = ln(µ/mZ). small difference between (9/2) Y 3 1 in the Standard Model and 5 Y 3 1 in the LR symmetric model with a bi–doublet. For the same reason our top quark mass prediction in the κ ′ = 0 case is very similar to the one of the BHL model [6], which is too high compared to the recent experimental results [28, 29]. We also conclude that the renormalization group analysis for the minimal left–right symmetric model in Ref. [32], which predicted a lower top quark mass, is wrong due to the…
Figure 7. Renormalization Group evolution of the Y1 Yukawa coupling for various parity breaking scales µR (indicated by little ticks) and compositeness scales Λ; t = ln(µ/mZ). V.2 The general case κ, κ′ 6= 0 In the preceding discussion we assumed for simplicity that only one of the two neutral com￾ponents of the bi–doublet φ acquires a VEV (κ 6= 0, κ ′ = 0). Apparently the resulting fixed–point value of the top quark Yukawa coupling is in this limit outside the phenomeno￾logically acceptable region [28, 29], and moreover the assumption κ ′ = 0 implies a zero bottom quark mass. Evidently a…
Figure 8. Renormalization Group evolution of the Y4 Yukawa coupling with the boundary condi￾tion Y4 = 0.005Y1 at Λ. remains. On the other hand, to obtain mt ≫ mb for κ ∼ κ ′ one requires the condition Y2 Y1 ≈ − κ ′ κ (V.13) to be satisfied. From eq. (V.12) it is seen that the ratio of κ ′/κ is determined by the low energy values of Y3 and Y4. Since these values are not governed by infrared quasi–fixed points and depend on the boundary conditions at the cutoff, the ratio tan β ≡ κ κ ′ (V.14) is a free parameter in our model. Unfortunately, the renormalization group evolution of the Y
Figure 9. Values of tan β for mt = 180 GeV and various magnitudes of the cutoff Λ and right– handed scale µR. In

Figures reproduced from arXiv:hep-ph/9509255 by the authors.

References
How the literature uses it

118 arXiv papers cite this in 160 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 · 76 sentences without a confident label

Builds on it 1 paper
  • More explicitly, the standard model fermions are written in component form as [equation] Notice that we have extended the fermion sector of the original Pati-Salam model [ref] by introducing three fermion singlets $S_i$, in order to implement inverse and/or linear seesaw mechanisms for the generation of light active neutrino masses [ref] .

    Predictive Pati-Salam theory of fermion masses and mixing · The model · 0.85

Uses its method or tool 1 paper
Compares with it 4 papers
Cites it as background 67 papers

Discussion

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