Limits on anomalous triple and quartic gauge couplings

This page summarizes limits on anomalous triple gauge couplings (aTGCs) and limits on anomalous quartic gauge couplings (aQGCs) from analysis of diboson and triboson final states. Results are included from LHC, Tevatron, and LEP analysis of states involving charged and possible neutral triple gauge couplings. Plots are available as attachments in .png and .pdf formats.

Charged aTGC Results.

Limits on charged aTGC WW$\gamma$ and WWZ couplings are presented. The presence of a possible charged aTGC contribution is parameterized in the so called LEP parametrization which respects SU(2)xU(1) gauge invariance and conserves the charge conjugation, C, and and parity, P, symmetries (LEP parameterization).

This parametrization involves 5 parameters, $\Delta g^Z_1 = g^Z_1 - 1$, $\Delta \kappa_{\gamma} = \kappa_{\gamma} - 1$, $\Delta \kappa_Z = \kappa_Z - 1$, $\lambda_\gamma$, $\lambda_Z$ where all parameters are defined such that they equal zero in the Standard Model and further in the LEP parameterization only three parameters are independent due to the following relationships motivated by SU(2)xU(1) gauge invariance:

$\Delta \kappa_{Z}  = \Delta g^Z_1 - \Delta \kappa_{\gamma} tan^2\theta_W$

and

$\lambda_\gamma = \lambda_Z$

Limits are generally set without the use of form factors or equivalently with the form factor scale set at infinity. In cases where form factors are used limits would be weaker without form factors though not by a large factors since the cut off energy used in the form factors is of the same order and the kinematic limit of the collision energy. Limits are set and 95% C.L. The LEP and D0 experiments also measure the central value of the TGC parameters as shown.

Note: EFT to LEP parameterization conversions have been done using $\alpha$ and $sin^2\theta_W$ evaluated at $m_Z$

Figure 1: Limits on WW$\gamma$ aTGC couplings

Results in figure 1:

ATLAS W$\gamma$ using 4.6 fb-1 of 7 TeV pp collisions Phys. Rev. D 87, 112003 (2013)

CMS W$\gamma$ using 5.0 fb-1 of 7 TeV pp collisions Phys. Rev. D 89 (2014) 092005

CMS WW using 4.9 fb-1 of 7 TeV pp collisions Eur. Phys. J. C 73 (2013) 2610

CMS WW using 19.4 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 76 (2016) 401

CMS VW (V=W,Z) $\rightarrow$jj using 5.0 fb-1 of 7 TeV pp collisions Eur.Phys.J. C73 (2013) 2283

CMS VW (V=W,Z) $\rightarrow$jj using 19 fb-1 of 8 TeV pp collisions Submitted to Phys. Lett. B.

ATLAS WW using 20.3 fb-1 of 8 TeV pp collisions JHEP 09 (2016) 029

ATLAS VW (V=W,Z $\rightarrow$jj) using 4.6 fb-1 of 7 TeV pp collisions JHEP 01 (2015) 049

ATLAS VW (V=W,Z $\rightarrow$jj,J) using 20.3 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 77 (2017) 563 jj (jets from the vector boson decay are resolved) J (single jet analyzed with jet substructure techniques)

D0 Combination of W$\gamma$, WW, WZ and VW using 8.6 fb-1 of 2 TeV $p\bar{p}$ collisions Phys.Lett. B718 (2012) 451-459 (form factor used with $\Lambda = $ 2 TeV)

LEP Combination of WW and single W using 0.7 fb-1 per experiment of $e^+e^-$ collisions at WW pair production energies arXiv:1302.3415

Note: trivial conversion of $\lambda_\gamma = \lambda_Z$ has been done in cases where measurements have direct sensitivity to $\lambda_\gamma$

Figure 2: Limits on WWZ aTGC couplings

Results in figure 2:

ATLAS WW using 4.6 fb-1 of 7 TeV pp collisions Phys. Rev. D 87, 112001 (2013)

ATLAS WW using 20.3 fb-1 of 8 TeV pp collisions JHEP 09 (2016) 029

ATLAS WW using 36.1 fb-1 of 13 TeV pp collisions submitted to EPJC

CMS WW using 4.9 fb-1 of 7 TeV pp collisions Eur. Phys. J. C 73 (2013) 2610

CMS WW using 19.4 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 77 (2017) 236

ATLAS WZ using 4.6 fb-1 of 7 TeV pp collisions Eur. Phys. J. C72 (2012) 2173

ATLAS WZ using 20.3 fb-1 of 8 TeV pp collisions Phys. Rev. D 93, 092004 (2016)

ATLAS WZ using 33.6 fb-1 of 8 and 13 TeV pp collisions ATLAS CONF 2016-043

CMS WZ using 19.6 fb-1 of 13 TeV pp collisions JHEP 04 (2019) 122

CMS WZ using 35.9 fb-1 of 13 TeV pp collisions JHEP 04 (2019) 122

ATLAS VW (V=W,Z $\rightarrow$jj) using 4.6 fb-1 of 7 TeV pp collisions JHEP 01 (2015) 049

ATLAS VW (V=W,Z $\rightarrow$jj,J) using 20.3 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 77 (2017) 563 jj (jets from the vector boson decay are resolved) J (single jet analyzed with jet substructure techniques)

CMS VW (V=W,Z $\rightarrow$jj) using 5.0 fb-1 of 7 TeV pp collisions Eur. Phys. J. C73 (2013) 2283

CMS VW (V=W,Z $\rightarrow$J) using 19 fb-1 of 8 TeV pp collisions Phys. Lett. B 772 (2017) 21

CMS VW (V=W,Z $\rightarrow$J) using 35.9 fb-1 of 13 TeV pp collisions Submitted to JHEP

ATLAS EWK Z using 20.2 fb-1 of 8 TeV pp collisions JHEP 04 (2014) 031

ATLAS EWK W using 20.2 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 77 (2017) 474

CMS EWK Z using 35.9 fb-1 of 13 TeV pp collisions Eur. Phys. J. C 78 (2018) 589

CMS EWK W using 35.9 fb-1 of 13 TeV pp collisions Submitted to EPJC

D0 Combination of W$\gamma$, WW, WZ and VW using 8.6 fb-1 of 2 TeV $p\bar{p}$ collisions Phys.Lett. B718 (2012) 451-459 (form factor used with $\Lambda = $ 2 TeV)

LEP Combination of WW and single W using 0.7 fb-1 per experiment of $e^+e^-$ collisions at WW pair production energies arXiv:1302.3415

Note: trivial conversion of $\lambda_\gamma = \lambda_Z$ has been done in cases where measurements have direct sensitivity to $\lambda_Z$

Note: Conversion of $\Delta \kappa_{\gamma}$ to $\Delta \kappa_Z$ using $\Delta \kappa_{Z}  = \Delta g^Z_1 - \Delta \kappa_{\gamma} tan^2\theta_W$ has been performed for analysis with direct and competitive sensitivity to $\Delta \kappa_Z$. For the CMS 7 TeV WV analysis $\Delta g^Z_1$ is constrained to the SM values of zero while for the LEP Combined analysis the measured value and limits on $\Delta g^Z_1$ are used.

Figure 3: limits using an effective field theory interpretation

Neutral aTGC Results.

Limits on neutral Z$\gamma\gamma$ ZZ$\gamma$ aTGC couplings are presented. In the Standard Model all neutral triple gauge couplings are zero at tree level. These analyses place limits on the anomalous parameters $h_3$ and $h_4$ .

Figure 4: Limits on neutral aTGC Z$\gamma\gamma$ and ZZ$\gamma$ couplings

Results in figure 4:

ATLAS Z$\gamma$ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 4.6 fb-1 of 7 TeV pp collisions Phys. Rev. D 87, 112003 (2013)

ATLAS Z$\gamma$ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 20.3 fb-1 of 8 TeV pp collisions Phys. Rev. D 93, 112002 (2016)

ATLAS Z$\gamma$ with Z$\rightarrow \nu\bar{\nu}$ using 36.1 fb-1 of 13 TeV pp collisions Submitted to JHEP

CMS Z$\gamma$ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 5.0 fb-1 of 7 TeV pp collisions Phys. Rev. D 89 (2014) 092005 and J. High Energy Phys. 10 (2013) 164

CDF Z$\gamma$ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 5.1 fb-1 of 2 TeV $p\bar{p}$ collisions Phys. Rev. Lett. 107, 051802, 2011 (form factor used with $\Lambda = $ 1.5 TeV)

CMS Z$\gamma$ with Z$\rightarrow \ell^+\ell^-$ using 19.5 fb-1 of 8 TeV pp collisions JHEP 04 (2015) 164

CMS Z$\gamma$ with Z$\rightarrow \nu\bar{\nu}$ using 19.6 fb-1 of 8 TeV pp collisions PLB 760 (2016) 448

Figure 5: Limits on neutral ZZ$\gamma$ and ZZZ aTGC couplings

Limits on neutral aTGC ZZ$\gamma$ and ZZZ couplings are presented. In the Standard Model all neutral triple gauge couplings are zero at tree level. These analyses place limits on the anomalous parameters $f_4$ and $f_5$ .

Results in figure 5:

ATLAS ZZ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 4.6 fb-1 of 7 TeV pp collisions JHEP 03 (2013) 128

ATLAS ZZ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 20.3 fb-1 of 8 TeV pp collisions JHEP 01 (2019) 99

ATLAS ZZ with Z$\rightarrow \ell^+\ell^-$ using 36.1 fb-1 of 13 TeV pp collisions Phys. Rev. D 97, 032005 (2018)

ATLAS ZZ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 36.1 fb-1 of 13 TeV pp collisions Submitted to JHEP

CMS ZZ with Z$\rightarrow \ell^+\ell^-$ using 19.6 fb-1 of 8 TeV pp collisions, Phys. Lett. B 740 (2015) 250

CMS ZZ with Z$\rightarrow \ell^+\ell^-$ and Z$\rightarrow \nu\bar{\nu}$ using 5.1 fb-1 of 7 TeV and 19.6 fb-1 of 8 TeV pp collisions and ZZ combination, Eur. Phys. J. C 75 (2015) 511

CMS ZZ with Z$\rightarrow \ell^+\ell^-$ using 35.9 fb-1 of 13 TeV pp collisions, Submitted to EPJC

Combination of CMS and ATLAS results at 7 TeV CMS PAS SMP-15-001 and ATLAS note ATLAS-CONF-2016-036

aQGC Results.

Diboson final states in scattering topologies and triboson final states can be used to set limits on quartic gauge couplings (aQGCs). Limites on D8 effective field theory parameters

Figure 6: limits on dimension scalar/longitudinal parameters $f_{S,i}$

aQGC_fs.png

Figure 7: limits on dimension 8 mixed transverse and longitudinal parameters $f_{M,i}$

aQGC_fm.png

Figure 8: limits on dimension 8 transverse parameters $f_{T,i}$

aQGC_ft.png

Results in figures 6-8:
D8 limits are set using the convention followed in Madgraph.

Older figures are located here.

CMS EWK ss WW $\rightarrow \ell^{+/-}\ell^{+/-}$qq: using 19.4 fb-1 of 8 TeV pp collisions Phys. Rev. Lett. 114, 051801 (2015)

ATLAS V $\rightarrow VW\gamma \rightarrow jj\ell\bar{\nu}\gamma$ triboson production with 20.1 fb-1 of 8 TeV pp collisions Eur. Phys. J. C 77, 646 (2017

CMS $VW\gamma \rightarrow jj\ell\bar{\nu}\gamma$ triboson production with 19.3 fb-1 of 8 TeV pp collisions Phys. Rev. D 90, 032008 (2014)

CMS $\gamma\gamma \rightarrow W^+W^- \rightarrow e^+\mu^-$ scattering with 5.0 fb-1 of 7 TeV and 19.7 fb-1 of 8 TeV pp collisions JHEP 08 (2016) 119

CMS EWK qq $\rightarrow Z\gamma qq \rightarrow \ell^+\ell^-\gamma$qq: using 19.7 fb-1 of 8 TeV pp collisions Phys. Lett. B 770 (2017) 380

CMS EWK qq $\rightarrow Z\gamma qq \rightarrow \ell^+\ell^-\gamma$qq: using 35.9 fb-1 of 13 TeV pp collisions CMS-PAS-SMP-18-007

CMS EWK qq $\rightarrow W\gamma qq \rightarrow \ell^+\nu\gamma$qq: using 19.7 fb-1 of 8 TeV pp collisions JHEP 06 (2017) 106

CMS EWK qq $\rightarrow WZ qq \rightarrow \ell^+\ell^-\ell \nu$qq: using 35.9 fb-1 of 13 TeV pp collisions Phys. Lett. B 795 (2019) 281

CMS EWK qq $\rightarrow ZZ qq \rightarrow \ell^+\ell^-\ell^+\ell^-$qq: using 35.9 fb-1 of 13 TeV pp collisions Phys. Lett. B 774 (2017) 682

CMS $W\gamma\gamma \rightarrow \ell\bar{\nu}\gamma\gamma$ and $Z\gamma\gamma \rightarrow \ell^+\ell^-\gamma\gamma$triboson production with 19.4 fb-1 of 8 TeV pp collisions JHEP 10 (2017) 072

ATLAS EWK qq $\rightarrow Z\gamma qq \rightarrow \ell^+\ell^-\gamma$qq: using 20.2 fb-1 of 8 TeV pp collisions JHEP 07 (2017) 107

ATLAS $W\gamma\gamma \rightarrow \ell\bar{\nu}\gamma\gamma$ triboson production with 19.3 fb-1 of 8 TeV pp collisions Phys.Rev.Lett. 115 (2015) 3, 031802

CMS EWK qq $\rightarrow (W,Z)V qq \rightarrow ( \ell^+\nu,\ell^+\ell^-)$qqbar qq: using 35.9 fb-1 of 13 TeV pp collisions Submitted to Phys. Lett. B.

CMS WWW using 35.9 fb-1 of 13 TeV pp collisions Submitted to PRD

Anomalous gauge coupling plotting scripts

Scripts for the anomalous gauge coupling summary plots are available here.

Topic attachments
I Attachment History Action Size Date Who Comment
PDFpdf aQGC_fm.pdf r10 r9 r8 r7 r6 manage 17.6 K 2019-07-31 - 22:10 MattHerndon Dim 8 aQGC fm parameters
PNGpng aQGC_fm.png r10 r9 r8 r7 r6 manage 305.2 K 2019-07-31 - 22:11 MattHerndon dim 8 aQGC fm paramters
PDFpdf aQGC_fs.pdf r2 r1 manage 13.9 K 2019-05-21 - 17:43 MattHerndon D8 aQGC fs parameter limits
PNGpng aQGC_fs.png r2 r1 manage 85.1 K 2019-05-21 - 17:43 MattHerndon D8 aQGC fs parameter limits
PDFpdf aQGC_ft.pdf r10 r9 r8 r7 r6 manage 17.3 K 2019-07-31 - 22:11 MattHerndon dim 8 aQGC ft paramters
PNGpng aQGC_ft.png r10 r9 r8 r7 r6 manage 298.3 K 2019-07-31 - 22:12 MattHerndon dim 8 aQGC ft paramters
PDFpdf aTGC_ceft.pdf r2 r1 manage 18.5 K 2019-09-22 - 16:54 MattHerndon Charged aTGC using EFT
PNGpng aTGC_ceft.png r2 r1 manage 341.0 K 2019-09-22 - 16:54 MattHerndon Charged aTGC using EFT
PDFpdf aTGC_cg.pdf r6 r5 r4 r3 r2 manage 16.3 K 2019-09-22 - 16:52 MattHerndon Charged aTGC with gamma
PNGpng aTGC_cg.png r6 r5 r4 r3 r2 manage 201.4 K 2019-09-22 - 16:53 MattHerndon Charged aTGC with gamma
PDFpdf aTGC_cz.pdf r15 r14 r13 r12 r11 manage 18.0 K 2019-09-22 - 16:53 MattHerndon Charged aTGC with Z bosons
PNGpng aTGC_cz.png r15 r14 r13 r12 r11 manage 319.6 K 2019-09-22 - 16:53 MattHerndon Charged aTGC with Z bosons
PDFpdf aTGC_ng.pdf r3 r2 r1 manage 15.8 K 2018-10-21 - 19:08 MattHerndon Neutral aTGC with Zgg and ZZg
PNGpng aTGC_ng.png r3 r2 r1 manage 164.0 K 2018-10-21 - 19:08 MattHerndon Neutral aTGC with Zgg and ZZg
PDFpdf aTGC_nz.pdf r7 r6 r5 r4 r3 manage 16.5 K 2019-05-21 - 18:07 MattHerndon Neutral aTGC ZZg and ZZZ
PNGpng aTGC_nz.png r7 r6 r5 r4 r3 manage 268.7 K 2019-05-21 - 18:06 MattHerndon Neutral aTGC ZZg and ZZZ
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