Probing Neutral Triple Gauge Couplings at the LHC and Future Hadron Colliders

We study probes of neutral triple gauge couplings (nTGCs) at the LHC and the proposed 100 TeV <math display="inline"><mi>p</mi><mi>p</mi></math> colliders, and compare their sensitivity reaches with those of proposed <math display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></math> colliders. The nTGCs provide a unique window to the new physics beyond the Standard Model (SM) because they can arise from SM effective field theory operators that respect the full electroweak gauge group <math display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">L</mi></mrow></msub><mo stretchy="false">⊗</mo><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Y</mi></mrow></msub></mrow></math> of the SM only at the level of dimension-8 or higher. We derive the neutral triple gauge vertices (nTGVs) generated by these dimension-8 operators in the broken phase and map them onto a newly generalized form factor formulation, which takes into account only the residual <math display="inline"><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>em</mi></mrow></msub></mrow></math> gauge symmetry. Using this mapping, we derive new nontrivial relations between the form factors that guarantee a truly consistent form factor formulation of the nTGVs and remove large unphysical energy-dependent terms. We then analyze the sensitivity reaches of the LHC and future 100 TeV hadron colliders for probing the nTGCs via both the dimension-8 nTGC operators and the corresponding nTGC form factors in the reaction <math display="inline"><mrow><mi>p</mi><mi>p</mi><mo stretchy="false">(</mo><mi>q</mi><mover accent="true"><mrow><mi>q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>Z</mi><mi>γ</mi></mrow></math> with <math display="inline"><mrow><mi>Z</mi><mo stretchy="false">→</mo><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>-</mo></mrow></msup></mrow></math>, <math display="inline"><mrow><mi>ν</mi><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>. We compare their sensitivities with the existing LHC measurements of nTGCs and with those of the high-energy <math display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> colliders. In general, we find that the prospective LHC sensitivities are comparable to those of an <math display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></math> collider with center-of-mass energy <math display="inline"><mrow><mo>≤</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>, whereas an <math display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></math> collider with center-of-mass energy (3–5) TeV would have greater sensitivities, and a 100 TeV <math display="inline"><mi>p</mi><mi>p</mi></math> collider could provide the most sensitive probes of the nTGCs.