Aspects of the Stueckelberg Extension

Boris Kors; Pran Nath

REVIEW

Aspects of the Stueckelberg Extension

Boris Kors, Pran Nath

High Energy Physics - Phenomenology · Submitted 21 Mar 2005 · 31 references

Pith's verdict: A solid, honest model-building paper whose collider signal is real but evaluated at an electroweak point the authors never derive — and they say so.

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CitationBoris Kors, Pran Nath. "Aspects of the Stueckelberg Extension." arXiv:hep-ph/0503208 (2005). https://pith.science/paper/LYOAHHY6

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Editor's note

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Worth your time if you work on Z' models or on narrow-resonance searches at a linear collider; less so if you want a model already confronted with precision data. The paper is upfront about the latter, which is why I'd engage rather than set it aside. What's actually new relative to the authors' own earlier letters [5,6] is the supersymmetric sector: the 3x3 CP-even Higgs mass matrix with the Stueckelberg scalar (Eq. 69), the 6x6 neutralino matrix (Eq. 77), and the observation that the LSP flips from an MSSM neutralino to a mostly-Stueckelberg fermion around M ~ 500 GeV (Fig. 1). The vector sector is a clean re-derivation: the mass matrix (17), the explicit angle parametrization (22-23), the sum rule M_rho^2 ~ M_Z'^2 + m_rho^2 (74), and the geometric peak cross section (103) all check out. The A_fb expressions (102, 104) are the usable deliverable. Soft spots, in order of weight. The electroweak-viability question is the big one, and the stress-test lands: a single rho-like number at one point (delta = 0.029, M_Z' = 250 GeV) does not establish it, since Eq. 55 generates a two-parameter contact-operator set that LEP constrains jointly with the Z-pole asymmetries. But the authors say plainly that a global fit is outside scope, so this is a scope gap, not a concealed assumption. Second, the A_fb signal scales steeply with delta (Fig. 4), so the observability claim rides on an upper bound the paper doesn't derive. Third, the collider analysis is leading order with no ISR or beamstrahlung; for an 80 MeV resonance that matters, and Sec. 6 only gestures at beam spread. Fourth, the dark-matter claim is a scenario sketch — relic density is explicitly deferred. One correction to the record: the classifier reports no stated limitations, which is wrong. The paper flags the missing global fit (Secs. 2.1, 4.1.1) and the missing relic-density analysis (Sec. 4.3) in its own words. Who should read it: model builders who want the Stueckelberg Z' coupling pattern and the A_fb template, and anyone thinking about narrow-resonance systematics at the ILC. It deserves a referee.

Referee report

Significance

The paper is a careful and self-contained treatment of a well-motivated alternative to Higgsed U(1)' breaking, and it earns credit for several things a referee should name explicitly. The diagonalization of the neutral mass matrix is given in closed form with the mixing angles expressed in terms of physical inputs (Eqs. 22-23, 29), so the reader can check the result rather than take it on trust. The approximate sum rule M_rho^2 ~ M_Z'^2 + m_rho^2 (Eq. 74) and the geometric peak cross section of Eq. (103) are parameter-free consequences of the construction and are therefore falsifiable. Table 1 gives a qualitative branching-ratio pattern (ll/nunu = 5 versus 0.5 for the Z) that would distinguish a Stueckelberg Z' from a GUT-type Z' at the level of counting, and the observation that the shape of A_fb near the pole encodes the total width, hence the presence of hidden-sector decays, is a genuinely useful diagnostic. The dark-matter remark is more tentative, but the paper is explicit that a relic-density analysis is not performed here.

Major objections (2)

[Section 2.1 and Section 4.1.1, Eqs. (55)-(59)] The electroweak viability of the scenario is asserted rather than derived, and this is load-bearing for the collider reach quoted in Sections 5 and 6. Section 2.1 states that fixing the parameters 'requires global fits to the electro-weak data which is outside the scope of this work,' and Section 4.1.1 then checks consistency at a single illustrative point (delta = 0.029, M_Z' = 250 GeV) by quoting 1 - rho_Z/rho_SM = 0.0001 and rho_Z'/rho_SM ~ 0.0025 against an error corridor of order 0.005. A single rho-like number is not the same as a fit: the Z' exchange in Eq. (55) generates a two-parameter set of contact operators (rho_Z', sin^2 theta_Z') that LEP/SLC constrain jointly with the Z-pole asymmetries and M_W, and the Z couplings themselves are shifted at order phi^2 (Eqs. 60-61). Because the A_fb deviation scales steeply with delta (Figure 4 shows the effect shrinking by roughly an order of magnitude between delta = 0.1 and delta = 0.01), the observability statements of Sections 5 and 6 are tied directly to an upper bound on delta that the paper does not establish. I do not ask for a full global fit here, but the manuscript should at minimum use its own Eqs. (57)-(59) to state the range of (M, delta) that survives the existing Z-pole and M_W constraints, and should qualify the reach claims accordingly. As it stands, a reader cannot tell whether Figures 3-6 describe an allowed region or an already-excluded corner.
[Section 6, Eq. (112)] The bin-size dependence in the signal-to-background estimate appears inverted, and this affects the detectability claim that Section 6 is built to support. The text immediately above Eq. (112) defines A_SM(Delta) = 1.8 x 10^-3 Delta nb-GeV as the Standard Model cross section integrated over a bin of width Delta, so the ratio A_St/A_SM(Delta) must fall as 1/Delta: the resonance signal is fixed while the background grows linearly with the bin. Eq. (112) instead prints the ratio as proportional to Delta, and the surrounding text concludes that the effect is significant 'with bin sizes ranging from 1-20 GeV,' which is the opposite of the stated scaling. The numerical prefactor happens to agree with the correct expression at Delta = 1 GeV, which suggests the Delta factor was misplaced rather than the estimate miscomputed. Since the Z' width considered here ranges from 0.08 to 3 GeV, a 20 GeV bin would in any case integrate over the whole resonance and beyond. Please correct the scaling and restate the range of bin widths for which the signal is actually recoverable, ideally with the statistical significance (signal/sqrt(background) at the stated luminosity) made explicit.

Minor objections (7)

[Section 6, Eq. (111)] Eq. (111) is dimensionally inconsistent as printed: A_St carries units of nb-GeV, whereas (45 pi^2/412) alpha_1 tan^2(phi) M_Z' carries units of GeV. The quoted numerical value A_St ~ 1.1 x 10^-2 nb-GeV for M_Z' = 250 GeV and delta = 0.02 is reproduced if M_Z' in the numerator is replaced by 1/M_Z' (with the mu+mu- branching ratio absorbed into the prefactor). Please correct the formula; the scaling with M_Z' in Eq. (112) is then consistent with A_St falling as 1/M_Z'.
[Section 5.2, Eq. (103)] The printed expression for the peak cross section, (15/103)^2 (1/8)^2, evaluates to roughly 0.08 nb for M_Z' = 250 GeV, not the 4.8 nb quoted. The quoted number follows from (15/103)^2 alone, i.e. from B(e+e-) = B(mu+mu-) = 15/103 as lepton universality requires. The extra factor (1/8)^2 appears to be spurious and should be removed or explained.
[Section 3.1 and Section 4.3, Eqs. (49), (77), (79)] The notation for the U(1)_X gaugino soft mass is inconsistent. Eq. (49) introduces mtilde_X for lambda_X and mtilde_Y for lambda_Y, and the text states that there is no soft mass for the chiral fermion psi_S, consistent with the zero (1,1) entry of Eq. (77). The (2,2) entry of Eq. (77) and the eigenvalues of Eq. (79) are however labelled mtilde_S, and the Figure 1 and Figure 2 captions use m_S. Since the 2x2 block in the M_Z -> 0 limit is [[0, M1],[M1, mtilde_X]], the symbol in Eqs. (77) and (79) should presumably be mtilde_X. Please harmonize.
[Section 1.2, Eq. (10)] The Kaluza-Klein Stueckelberg term in Eq. (10) reads n^2 (M A^(n)_mu + n partial_mu sigma^(n))^2, which is not what the stated compactification gives: the nth mode has mass nM = n/R, so the term should be (1/2)(nM A^(n)_mu + partial_mu sigma^(n))^2 up to an overall normalization. Please check the factors of n. In the same paragraph, 'a half circle S^1 of radius R' should presumably read an interval or S^1/Z_2 orbifold.
[Section 4.3 and Abstract] The abstract's phrase 'a possible new superweak candidate for dark matter' is stronger than what Section 4.3 supports. The paper shows that the LSP composition can flip to a Stueckelberg fermion and explicitly states that a relic-density analysis is outside its scope. Since the annihilation rate of a gauge-singlet-dominated LSP is not obviously in the required range, the abstract and conclusion should say 'a candidate LSP whose relic density remains to be computed' rather than implying a viable dark-matter candidate.
[Sections 5.2 and 6, Figures 3-6] The figures show A_fb and cross sections as functions of sqrt(s) but give no indication of the assumed luminosity or of the statistical error bars on the asymmetry. Since the central claim is that the deviation is observable, a statement of the expected statistical precision per point (or a shaded error band) would let the reader judge the significance of the structure shown, particularly for the smallest values of delta in Figure 4.
[Section 3.2 and elsewhere] The name is consistently misspelled 'Fayet-Illiopoulos' (section heading 3.2 and body text); it should be 'Fayet-Iliopoulos'. There is also a typo 'diagnonalize' in Section 7, and the reference list entry [7] is listed as 'to appear' in the PASCOS04 proceedings, which should be updated to its published form if available.

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The paper

The paper claims

A Stueckelberg extension of the electroweak gauge group gives an extra U(1) whose Z-prime mass comes from eating a pseudo-scalar, not from a Higgs, and whose fermion couplings are fixed by just two new parameters.

The reading

The paper asks whether the Standard Model's electroweak gauge group can be enlarged by one extra abelian factor, $U(1)_X$, whose gauge boson acquires its mass the Stueckelberg way: a massless pseudo-scalar $sigma$ shifts under the new gauge symmetry and is absorbed as the longitudinal mode, with no Higgs field required. The authors show that after electroweak symmetry breaking the neutral gauge bosons $C_ mu$, $B_ mu$ and $A^3_ mu$ mix in a $3 times 3$ mass matrix with one exactly massless eigenvalue, so the photon stays massless while the other two eigenstates are the $Z$ and a new $Z'$. What makes the construction worth taking seriously is that the $Z'$ couplings to quarks and leptons are not free: they follow from the same two parameters, an overall mass scale $M$ and the ratio $delta = M_2/M_1$, that set the masses. The paper then argues that this produces a resonance whose leptonic and quark branching ratios differ qualitatively from conventional GUT-type $Z'$ bosons, and that the forward-backward asymmetry in $e^+e^- to mu^+mu^-$, $u bar u$ and $d bar d$ near the pole swings sharply away from the Standard Model prediction, with the shape of the swing recording the total width and therefore whether the $Z'$ also decays into unseen matter.

What carries the argument

The load-bearing device is the Stueckelberg mass term $-tfrac{1}{2}(partial_ mu sigma + M_1 C_ mu + M_2 B_ mu)^2$, made gauge invariant by having $sigma$ shift under both abelian factors. Diagonalising the resulting mass matrix gives an orthogonal rotation parametrised by three angles $theta$, $phi$, $psi$ with $tan phi = M_2/M_1 = delta$ and $tan theta = (g_Y/g_2) cos phi$, so the entire modification of neutral-current physics is carried by two numbers. The second piece of machinery is the forward-backward asymmetry $A_{fb}$ near the $Z'$ pole: because the $Z'$ pole term and the photon-$Z'$ interference term both vary rapidly across the resonance while the Standard Model $gamma$-$Z$ background does not, $A_{fb}$ becomes a sensitive discriminator, and the integrated cross section over the resonance, following the technique used for the $J/psi$, separates the partial width into a given final state from the total width.

Extended reading notes

Core claim

The central claim is that a Stueckelberg extension of the electroweak sector by a single extra $U(1)_X$ yields a calculable, sharply predictive $Z'$ rather than a generic one. The mass matrix for $(C_ mu, B_ mu, A^3_ mu)$ has determinant zero, so one state remains the massless photon, and the two nonzero eigenvalues are identified with the $Z$ and the $Z'$; in the limit where the electroweak scale is small compared with $M$, only one mixing angle vanishes, so deviations from Standard-Model couplings are not suppressed by a high new-physics scale. Because $U(1)_X$ charges are assigned to be zero for all Standard Model fields (otherwise neutron charge neutrality and electric charges would be spoiled), the $Z'$ couples to ordinary matter only through mixing, while it couples with normal strength to any hidden sector charged under $U(1)_X$. The supersymmetric version adds a chiral multiplet containing the Stueckelberg scalar $rho$ and fermion $psi_S$, giving a $6 times 6$ neutralino mass matrix with two extra states and a $3 times 3$ CP-even scalar mass matrix; the paper reports that the extra scalar is heavier than the $Z'$, with the approximate relation $M_rho^2 simeq M_{Z'}^2 + m_rho^2$. One consequence the authors highlight is that the lightest supersymmetric particle can become dominantly a Stueckelberg fermion, which would make the ordinary lightest neutralino unstable and offer a different dark-matter candidate.

Load-bearing premise

The load-bearing premise is that the model survives electroweak precision data over a usable region of its two parameters, which the paper illustrates with a single chosen point and explicitly leaves to a global fit it does not perform.

Editorial extensions

If this is right

The $Z'$ branching ratios into leptons, quarks and neutrinos differ qualitatively from those of GUT-type extra abelian bosons, so a observed resonance's decay pattern would itself identify a Stueckelberg origin.
In the supersymmetric version the neutralino sector grows from four to six states, and over part of parameter space the lightest state is mostly a Stueckelberg fermion, changing missing-energy supersymmetry signals into cascades that end in a superweak particle.
The total width of the $Z'$ is a direct probe of a hidden sector: a GeV-scale invisible width would visibly flatten the peak in the cross section and the forward-backward asymmetry, while an MeV-scale visible-only width would leave a sharp spike.
Extending the construction to several extra $U(1)$ factors and several axions relaxes the constraints on mixing, since each axion absorbs one linear combination of gauge fields and the surviving massless directions are set by the kernel of the coupling matrix.

Reading between the lines

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

If the $Z'$ couplings really are fixed by only $M$ and $delta$, a single measurement of the resonance peak cross section plus one off-peak asymmetry point would over-determine the model, giving a consistency test rather than a parameter fit.
The same mixing that lets the $Z'$ talk to hidden matter gives the photon a small irrational charge under $U(1)_X$, so minicharged-particle searches and stellar-cooling bounds become an independent, non-collider handle on $delta$.
Because the extra CP-even scalar is tied to the $Z'$ mass by $M_rho^2 simeq M_{Z'}^2 + m_rho^2$, a $Z'$ discovery at a fixed mass would come with a predicted scalar resonance nearby, decaying mainly to third-generation quarks.
The paper's collider study assumes a parameter point rather than a globally fitted region, so an electroweak-precision global fit would either sharpen the predicted asymmetry swing into a definite target or move the whole signal out of reach.

Original abstract

A detailed analysis of a Stueckelberg extension of the electro-weak gauge group with an extra U(1) factor is presented for the Standard Model as well as for the MSSM. The extra gauge boson gets massive through a Stueckelberg type coupling to a pseudo-scalar, instead of a Higgs effect. This new massive neutral gauge boson Z' has vector and axial vector couplings uniquely different from those of conventional extra abelian gauge bosons, such as appear e.g. in GUT models. The extended MSSM furthermore contains two extra neutralinos and one extra neutral CP-even scalar, the latter with a mass larger than that of the Z'. One interesting scenario that emerges is an LSP that is dominantly composed out of the new neutralinos, leading to a possible new superweak candidate for dark matter. We investigate signatures of the Stueckelberg extension at a linear collider and discuss techniques for the detection of the expected sharp Z' resonance. It turns out that the substantially modified forward-backward asymmetry around the Z' pole provides an important signal. Furthermore, we also elaborate on generalizations of the minimal Stueckelberg extension to an arbitrary number of extra U(1) gauge factors.

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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.53 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A detailed analysis of a Stueckelberg extension of the electro-weak gauge group with an extra U(1) factor is presented for the Standard Model as well as for the MSSM. The extra gauge boson gets massive through a Stueckelberg type coupling to a pseudo-scalar, instead of a Higgs effect. This new massive neutral gauge boson Z' has vector and axial vector couplings uniquely different from those of conventional extra abelian gauge bosons, such as appear e.g. in GUT models. The extended MSSM furthermore contains two extra neutralinos and one extra neutral CP-even scalar, the latter with a mass larger than that of the Z'. One interesting scenario that emerges is an LSP that is dominantly composed out of the new neutralinos, leading to a possible new superweak candidate for dark matter. We investigate signatures of the Stueckelberg extension at a linear collider and discuss techniques for the detection of the expected sharp Z' resonance. It turns out that the substantially modified forward-backward asymmetry around the Z' pole provides an important signal. Furthermore, we also elaborate on generalizations of the minimal Stueckelberg extension to an arbitrary number of extra U(1) gauge factors.

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	A detailed analysis of a Stueckelberg extension of the electro-weak gauge group with an extra U(1) factor is presented for the Standard Model as well as for the MSSM.	contribution 1.00	0.89	0.08	asserted 0.99
s1	The extra gauge boson gets massive through a Stueckelberg type coupling to a pseudo-scalar, instead of a Higgs effect.	contribution 0.49	0.43	0.11	asserted 1.00
s2	This new massive neutral gauge boson Z' has vector and axial vector couplings uniquely different from those of conventional extra abelian gauge bosons, such as appear e.g. in GUT models.	result 0.89	0.67	0.22	asserted 1.00
s3	The extended MSSM furthermore contains two extra neutralinos and one extra neutral CP-even scalar, the latter with a mass larger than that of the Z'.	result 0.84	0.75	0.07	asserted 1.00
s4	One interesting scenario that emerges is an LSP that is dominantly composed out of the new neutralinos, leading to a possible new superweak candidate for dark matter.	interpretation 0.58	0.71	0.12	hedged possibility 0.98
s5	We investigate signatures of the Stueckelberg extension at a linear collider and discuss techniques for the detection of the expected sharp Z' resonance.	contribution 0.87	0.89	0.08	asserted 0.81
s6	It turns out that the substantially modified forward-backward asymmetry around the Z' pole provides an important signal.	result 0.98	0.90	0.20	asserted 1.00
s7	Furthermore, we also elaborate on generalizations of the minimal Stueckelberg extension to an arbitrary number of extra U(1) gauge factors.	contribution 0.97	0.88	0.07	asserted 0.92

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

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arXiv listing abstract v2

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.** Plot of the neutralino mass spectrum as a function of

**Figure 2.** The mass of the LSP as function of M and δ. Plot of the lowest eigenvalues of the neutralino mass matrix for values tan(β) = 3, µ = 500, m2 = 400, m1 = 300, mS = 500 as a function of M and δ. of decays channels such as χ 0 1 → qiq¯iχ 0 St , li ¯liχ 0 St , Zχ 0 St . (81) We estimate the lifetime for this decay to lie in the range 10−19±2 sec. Thus χ 0 1 will decay in the detection chamber. In this case the detection signals will change drastically. Thus, for example, the decay of the chargino χ − 1 → l − + {χ 0 1 + νl} will be changed into χ − 1 → l − 1 l − 2 l

**Figure 3.** Plot of the total cross-section σ(e +e − → µ +µ −) (left) and the forwardbackward asymmetry Afb in e +e − → µ +µ − (right) in the vicinity of the Z′ resonance for MZ′ = 250 GeV, φ = 0.029. The values of ΓZ′ are 3 GeV (black line), 0.5 GeV (blue line), 0.2 GeV (green line), 0.08 GeV (red line). 249.98 250 250.02 GeV 2 4 nb 249 250 251 GeV 0.4 0.5 0.6 0.7

**Figure 4.** Plot of the total cross-section σ(e +e − → µ +µ −) (left) and the forwardbackward asymmetry Afb in e +e − → µ +µ − (right) in the vicinity of the Z′ resonance for MZ′ = 250 GeV. The values of δ are 0.1 (black line), 0.05 (blue line), 0.01 (green line), 0.001 (red line). In

**Figure 5.** Plot of the total cross-section σ(e +e − → uu¯) (left) and the forwardbackward asymmetry Afb in e +e − → uu¯ (right) in the vicinity of the Z′ resonance for MZ′ = 250 GeV, φ = 0.029. The values of ΓZ′ are 3 GeV (black line), 0.5 GeV (blue line), 0.2 GeV (green line), 0.08 GeV (red line). 249 250 251 GeV 0.002 0.003 0.004 nb 249 250 251 GeV 0.2 0.4 0.6

**Figure 6.** Plot of the total cross-section σ(e +e − → d ¯d) (left) and the forwardbackward asymmetry Afb in e +e − → d ¯d (right) in the vicinity of the Z′ resonance for MZ′ = 250 GeV, φ = 0.029. The values of ΓZ′ are 3 GeV (black line), 0.5 GeV (blue line), 0.2 GeV (green line), 0.08 GeV (red line). presence of a hidden sector to which the Z′ can decay will be provided by the visible width versus the total width of the Z′ . 6 Detection of a sharp Z ′ resonance As mentioned already the Z′ is expected to be a sharp resonance, and determination of the Γ(Z′ → e +e −) is a difficult pr

**Figure 7.** Plot of the mass of the Z, as a function of

Figures reproduced from arXiv:hep-ph/0503208 by the authors.

References

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[18]

A. H. Chamseddine, R. Arnowitt and P. Nath, Locally Supersymmetric Grand Uniﬁcation, Phys. Rev. Lett. 49 (1982) 970; R. Barbieri, S. Ferrara and C. A. Savoy, Gauge Models with Spontaneously Broken Local Supersymmetr y, Phys. Lett. B 119 (1982) 343; P. Nath, R. Arnowitt and A. H. Chamsed- dine, Gauge Hierarchy in Supergravity Guts , Nucl. Phys. B 227 (1983...

View on Pith 1982
[19]

P. Nath and R. Arnowitt, Supersymmetric Signals at the Tevatron , Mod. Phys. Lett. A 2 (1987) 331; H. Baer, T. Krupovnickas and X. Tata, Reach of the Fermilab Tevatron for Minimal Supergravity in the Reg ion of Large Scalar Masses , JHEP 0307 (2003) 020 [hep-ph/0305325]

View on Pith Pith review arXiv 1987
[20]

B. Holdom, Two U(1)’s and Epsilon Charge Shifts , Phys. Lett. B 166 (1986) 196

View on Pith 1986
[21]

R. N. Mohapatra and I. Z. Rothstein, Astrophysical Constraints on Minicharged Particles, Phys. Lett. B 247 (1990) 593

View on Pith 1990
[22]

H. Goldberg and L. J. Hall, A New Candidate for Dark Matter , Phys. Lett. B 174 (1986) 151. 48

View on Pith 1986
[23]

K. Hagiwara, A. D. Martin, D. Nomura and T. Teubner, Predictions for g-2 of the Muon and alpha(QED)(M(Z**2)) , Phys. Rev. D 69 (2004) 093003 [hep-ph/0312250]

View on Pith Pith review arXiv 2004
[24]

M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Updated Estimate of the Muon Magnetic Moment using Revised Results from e+e- Annihi lation, Eur. Phys. J. C 31 (2003) 503 [hep-ph/0308213]

View on Pith Pith review arXiv 2003
[25]

H. Deng [Muon g-2 Collaboration], Experimental Results and Theoretical Developments of Muon g-2 , hep-ex/0408148

View on Pith Pith review arXiv
[26]

T. Behnke et.al., DESY-TESLA-2001-23; M. N. Danielson et al. , Supersym- metry at the NLC , eConf C960625 (1996) SUP117; NLC Collaboration, 2001 Report on the Next Linear Collider: A Report submitted to Sno wmass’01, in Proc. of the APS/DPF/DPB Summer Study on the Future of Partic le Physics (Snowmass 2001) ed. N. Graf, SLAC-R-571; CLIC Physics Working Gr...

View on Pith Pith review arXiv 1996
[27]

E. Accomando et al. [ECF A/DESY LC Physics Working Group],Physics with e+e- Linear Colliders , Phys. Rept. 299 (1998) 1 [hep-ph/9705442]; G. Wei- glein et al. [LHC/LC Study Group], Physics Interplay of the LHC and the ILC, hep-ph/0410364

View on Pith Pith review arXiv 1998
[28]

R. N. Cahn and G. Goldhaber, The Experimental Foundations of Particle Physics, Cambridge University Press

View on Pith
[29]

B. Abbott et al. [D0 Collaboration], Measurement of the High-mass Drell- Yan Cross Section and Limits on quark-electron Compositene ss Scales, Phys. Rev. Lett. 82 (1999) 4769 [hep-ex/9812010]; T. Behnke, J. D. Wells and P. M. Zerwas, Physics with e+ e- Linear Colliders , Prog. Part. Nucl. Phys. 48 (2002) 363

View on Pith Pith review arXiv 1999
[30]

See e.g.: G. Rodrigo, H. Czyz, J. H. Kuhn and M. Szopa, Radiative Re- turn at NLO and the Measurement of the Hadronic Cross-sectio n in Electron Positron Annihilation , Eur. Phys. J. C 24 (2002) 71 [hep-ph/0112184]; and the references therein

View on Pith Pith review arXiv 2002
[31]

R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected Compactiﬁ- cations of the Heterotic String with Line Bundles , hep-th/0504232. 49

View on Pith Pith review arXiv

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

(In)direct Detection of Boosted Dark Matter
hep-ph 2014-05 conditional novelty 7.0 of 10

Present-day annihilation of a heavy dark matter species into a lighter dark-sector partner yields a relativistic flux that should appear as a directional electron excess in Super-K, Hyper-K, PINGU and MICA.
Baryon-dark matter coincidence in Randall-Sundrum Model
hep-ph 2026-01 conditional novelty 6.0 of 10

Graviton- and radion-mediated freeze-in in a Randall-Sundrum model can match the observed dark matter relic abundance, and TeV-scale resonant leptogenesis through the same portals can match the observed baryon asymmet...
Self-interacting asymmetric dark matter coupled to a light massive dark photon
hep-ph 2014-03 conditional novelty 6.0 of 10

Asymmetric dark matter coupled to a light massive dark photon stays multi-component and partly atomic across most of the parameter space where self-interaction matters, and the resulting halo scattering is bounded by ...
Intersecting branes and a standard model realization in matrix models
hep-th 2011-07 conditional novelty 6.0 of 10

Intersecting noncommutative branes in the IKKT matrix model produce localized chiral fermions, and a four-D7-brane configuration reproduces the Standard Model chiral spectrum with generation number set by fluxes.
Did LZ see modified gravity?
hep-ph 2026-09 conditional novelty 5.0 of 10

A freeze-in dark matter scenario with a modified cosmological expansion rate can accommodate the LZ 248 keV nuclear recoil event while satisfying relic abundance and experimental constraints.

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CDF W mass anomaly from a dark sector with a Stueckelberg-Higgs portal
hep-ph 2022-04 conditional novelty 5.0 of 10

A Stueckelberg Z-prime heavier than about 300 GeV can reconcile the CDF W mass excess with LEP Z-pole data and ATLAS dilepton limits by generating a negative tree-level shift in the Z mass.
Implications of unitarity and gauge invariance for simplified dark matter models
hep-ph 2015-10 accept novelty 5.0 of 10

Requiring gauge invariance and perturbative unitarity in a fermionic dark matter model with a vector mediator forces a dark Higgs sector, and the resulting dilepton, electroweak precision and Higgs constraints are str...
Hidden fermion as milli-charged dark matter in Stueckelberg Z' model
hep-ph 2007-01 conditional novelty 5.0 of 10

A hidden Dirac fermion in the Stueckelberg Z' model can be milli-charged dark matter with the observed relic density, yielding monochromatic Galactic-center gamma rays and an invisible Z' width at colliders.
Extra-weakly Interacting Dark Matter
hep-ph 2006-10 conditional novelty 5.0 of 10

A hidden-sector particle with couplings an order of magnitude weaker than the weak force can still reproduce the observed dark matter abundance, provided it is nearly mass-degenerate with the lightest MSSM neutralino ...
Explaining the $W$ boson mass anomaly and dark matter with a $U(1)$ dark sector
hep-ph 2022-04 conditional novelty 4.0 of 10

A U(1) extension mixing with the Standard Model through hypercharge can produce the 77 MeV CDF W boson mass shift and a fermionic dark matter candidate, whereas kinetic mixing alone yields at most 10 MeV.

How the literature uses it

45 arXiv papers cite this in 63 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 · 34 sentences without a confident label

Uses its method or tool 2 papers

In order to accomplish this we use the Stueckelberg mechanism [ref] where by the dark particles that are thermally produced can annihilate into the Standard Model particles via a direct channel $Z'$ pole.

Perspectives on Higgs Boson and Supersymmetry · Supersymmetry and asymmetric dark matter · 0.81
We use the Stueckelberg mechanism [ref] to provide mass to the three $U(1)$ gauge bosons; the new Lagrangian is given by ΔL = - ∑_i=1,2,3 14 X_i μν X_i^μν + χ̅(iγ^μ∂_μ- m_χ) χ+ g^χ_2 X_2^μ χ̅γ^μχ+ g^χ_3 X_3^μ χ̅γ^μχ

Two-component millicharged dark matter and the EDGES 21cm signal · The model · 0.98

Compares with it 1 paper

These formulas agree with those in the literature [ref] .

Probing Leptonic Interactions of a Family-Nonuniversal Z' Boson · Cross sections of $e^+e^-→l^+l^-$ · 0.91

Cites it as background 25 papers

We refer to the literature for such an extension [ref] .

Generalized Landau Yang Theorem · Stueckelberg extension of SUSY · 0.82
The mixing of the $U(1)$ dark sector with the SM can be generated through either the gauge kinetic terms [ref] or the mass terms [ref] .

Explaining the $W$ boson mass anomaly and dark matter with a $U(1)$ dark sector · The $U(1)_x$ extension of the SM with kinetic mixing · 0.87
The LSP is then an XWIMP (Extra Weakly Interacting Massive Particle), a class of particles which have already been studied in literature [ref] .

Dark Matter in Anomalous $U(1)'$ Models with neutral mixing · Introduction · 0.90

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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A. H. Chamseddine, R. Arnowitt and P. Nath, Locally Supersymmetric Grand Uniﬁcation, Phys. Rev. Lett. 49 (1982) 970; R. Barbieri, S. Ferrara and C. A. Savoy, Gauge Models with Spontaneously Broken Local Supersymmetr y, Phys. Lett. B 119 (1982) 343; P. Nath, R. Arnowitt and A. H. Chamsed- dine, Gauge Hierarchy in Supergravity Guts , Nucl. Phys. B 227 (1983...

View on Pith 1982

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P. Nath and R. Arnowitt, Supersymmetric Signals at the Tevatron , Mod. Phys. Lett. A 2 (1987) 331; H. Baer, T. Krupovnickas and X. Tata, Reach of the Fermilab Tevatron for Minimal Supergravity in the Reg ion of Large Scalar Masses , JHEP 0307 (2003) 020 [hep-ph/0305325]

View on Pith Pith review arXiv 1987

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B. Holdom, Two U(1)’s and Epsilon Charge Shifts , Phys. Lett. B 166 (1986) 196

View on Pith 1986

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R. N. Mohapatra and I. Z. Rothstein, Astrophysical Constraints on Minicharged Particles, Phys. Lett. B 247 (1990) 593

View on Pith 1990

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H. Goldberg and L. J. Hall, A New Candidate for Dark Matter , Phys. Lett. B 174 (1986) 151. 48

View on Pith 1986

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K. Hagiwara, A. D. Martin, D. Nomura and T. Teubner, Predictions for g-2 of the Muon and alpha(QED)(M(Z**2)) , Phys. Rev. D 69 (2004) 093003 [hep-ph/0312250]

View on Pith Pith review arXiv 2004

[24] [24]

M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Updated Estimate of the Muon Magnetic Moment using Revised Results from e+e- Annihi lation, Eur. Phys. J. C 31 (2003) 503 [hep-ph/0308213]

View on Pith Pith review arXiv 2003

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H. Deng [Muon g-2 Collaboration], Experimental Results and Theoretical Developments of Muon g-2 , hep-ex/0408148

View on Pith Pith review arXiv

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T. Behnke et.al., DESY-TESLA-2001-23; M. N. Danielson et al. , Supersym- metry at the NLC , eConf C960625 (1996) SUP117; NLC Collaboration, 2001 Report on the Next Linear Collider: A Report submitted to Sno wmass’01, in Proc. of the APS/DPF/DPB Summer Study on the Future of Partic le Physics (Snowmass 2001) ed. N. Graf, SLAC-R-571; CLIC Physics Working Gr...

View on Pith Pith review arXiv 1996

[27] [27]

E. Accomando et al. [ECF A/DESY LC Physics Working Group],Physics with e+e- Linear Colliders , Phys. Rept. 299 (1998) 1 [hep-ph/9705442]; G. Wei- glein et al. [LHC/LC Study Group], Physics Interplay of the LHC and the ILC, hep-ph/0410364

View on Pith Pith review arXiv 1998

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R. N. Cahn and G. Goldhaber, The Experimental Foundations of Particle Physics, Cambridge University Press

View on Pith

[29] [29]

B. Abbott et al. [D0 Collaboration], Measurement of the High-mass Drell- Yan Cross Section and Limits on quark-electron Compositene ss Scales, Phys. Rev. Lett. 82 (1999) 4769 [hep-ex/9812010]; T. Behnke, J. D. Wells and P. M. Zerwas, Physics with e+ e- Linear Colliders , Prog. Part. Nucl. Phys. 48 (2002) 363

View on Pith Pith review arXiv 1999

[30] [30]

See e.g.: G. Rodrigo, H. Czyz, J. H. Kuhn and M. Szopa, Radiative Re- turn at NLO and the Measurement of the Hadronic Cross-sectio n in Electron Positron Annihilation , Eur. Phys. J. C 24 (2002) 71 [hep-ph/0112184]; and the references therein

View on Pith Pith review arXiv 2002

[31] [31]

R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected Compactiﬁ- cations of the Heterotic String with Line Bundles , hep-th/0504232. 49

View on Pith Pith review arXiv