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Soft Scalars in Effective Field Theory (2403.12142v1)
Published 18 Mar 2024 in hep-th and hep-ph
Abstract: We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.
- S. L. Adler, “Consistency conditions on the strong interactions implied by a partially conserved axial vector current,” Phys. Rev. 137 (1965) B1022–B1033.
- F. E. Low, “Bremsstrahlung of very low-energy quanta in elementary particle collisions,” Phys. Rev. 110 (1958) 974–977.
- S. Weinberg, “Infrared photons and gravitons,” Phys. Rev. 140 (1965) B516–B524.
- T. H. Burnett and N. M. Kroll, “Extension of the low soft photon theorem,” Phys. Rev. Lett. 20 (1968) 86.
- D. Green, Y. Huang, and C.-H. Shen, “Inflationary Adler conditions,” Phys. Rev. D 107 no. 4, (2023) 043534, arXiv:2208.14544 [hep-th].
- C. Cheung, M. Derda, A. Helset, and J. Parra-Martinez, “Soft phonon theorems,” JHEP 08 (2023) 103, arXiv:2301.11363 [hep-th].
- A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory. 3, 2017. arXiv:1703.05448 [hep-th].
- A. Strominger, “On BMS Invariance of Gravitational Scattering,” JHEP 07 (2014) 152, arXiv:1312.2229 [hep-th].
- D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, “Higher-dimensional supertranslations and Weinberg’s soft graviton theorem,” Ann. Math. Sci. Appl. 02 (2017) 69–94, arXiv:1502.07644 [gr-qc].
- M. Campiglia and A. Laddha, “Asymptotic symmetries of QED and Weinberg’s soft photon theorem,” JHEP 07 (2015) 115, arXiv:1505.05346 [hep-th].
- E. Himwich and A. Strominger, “Celestial current algebra from Low’s subleading soft theorem,” Phys. Rev. D 100 no. 6, (2019) 065001, arXiv:1901.01622 [hep-th].
- T. He and P. Mitra, “Asymptotic symmetries and Weinberg’s soft photon theorem in Minkd+2𝑑2{}_{d+2}start_FLOATSUBSCRIPT italic_d + 2 end_FLOATSUBSCRIPT,” JHEP 10 (2019) 213, arXiv:1903.02608 [hep-th].
- D. Kapec and P. Mitra, “Shadows and soft exchange in celestial CFT,” Phys. Rev. D 105 no. 2, (2022) 026009, arXiv:2109.00073 [hep-th].
- D. Kapec, Y. T. A. Law, and S. A. Narayanan, “Soft scalars and the geometry of the space of celestial conformal field theories,” Phys. Rev. D 107 no. 4, (2023) 046024, arXiv:2205.10935 [hep-th].
- D. Kapec, “Soft particles and infinite-dimensional geometry,” Class. Quant. Grav. 41 no. 1, (2024) 015001, arXiv:2210.00606 [hep-th].
- T. Adamo, W. Bu, and B. Zhu, “Infrared structures of scattering on self-dual radiative backgrounds,” arXiv:2309.01810 [hep-th].
- H. Z. Chen, R. C. Myers, and A.-M. Raclariu, “Entanglement, Soft Modes, and Celestial Holography,” arXiv:2308.12341 [hep-th].
- S. Pasterski, M. Pate, and A.-M. Raclariu, “Celestial Holography,” in Snowmass 2021. 11, 2021. arXiv:2111.11392 [hep-th].
- C. Cheung, A. Helset, and J. Parra-Martinez, “Geometric soft theorems,” JHEP 04 (2022) 011, arXiv:2111.03045 [hep-th].
- Y. Wang and X. Yin, “Constraining Higher Derivative Supergravity with Scattering Amplitudes,” Phys. Rev. D 92 no. 4, (2015) 041701, arXiv:1502.03810 [hep-th].
- Y. Wang and X. Yin, “Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories,” arXiv:1505.05861 [hep-th].
- Y.-H. Lin, S.-H. Shao, Y. Wang, and X. Yin, “Supersymmetry Constraints and String Theory on K3,” JHEP 12 (2015) 142, arXiv:1508.07305 [hep-th].
- B. A. Kniehl and M. Spira, “Low-energy theorems in Higgs physics,” Z. Phys. C 69 (1995) 77–88, arXiv:hep-ph/9505225.
- A. Helset, A. Martin, and M. Trott, “The Geometric Standard Model Effective Field Theory,” JHEP 03 (2020) 163, arXiv:2001.01453 [hep-ph].
- K. Meetz, “Realization of chiral symmetry in a curved isospin space,” J. Math. Phys. 10 (1969) 589–593.
- J. Honerkamp, “Chiral multiloops,” Nucl. Phys. B 36 (1972) 130–140.
- G. Ecker and J. Honerkamp, “Application of invariant renormalization to the nonlinear chiral invariant pion lagrangian in the one-loop approximation,” Nucl. Phys. B 35 (1971) 481–492.
- D. V. Volkov, “Phenomenological lagrangians,” Sov. J. Particles Nucl. 4 (1973) 1–17.
- L. Tataru, “One Loop Divergences of the Nonlinear Chiral Theory,” Phys. Rev. D 12 (1975) 3351–3352.
- R. Alonso, E. E. Jenkins, and A. V. Manohar, “A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space,” Phys. Lett. B 754 (2016) 335–342, arXiv:1511.00724 [hep-ph].
- R. Alonso, E. E. Jenkins, and A. V. Manohar, “Geometry of the Scalar Sector,” JHEP 08 (2016) 101, arXiv:1605.03602 [hep-ph].
- R. Alonso, K. Kanshin, and S. Saa, “Renormalization group evolution of Higgs effective field theory,” Phys. Rev. D 97 no. 3, (2018) 035010, arXiv:1710.06848 [hep-ph].
- A. Helset, M. Paraskevas, and M. Trott, “Gauge fixing the Standard Model Effective Field Theory,” Phys. Rev. Lett. 120 no. 25, (2018) 251801, arXiv:1803.08001 [hep-ph].
- K. Finn, S. Karamitsos, and A. Pilaftsis, “Frame Covariance in Quantum Gravity,” Phys. Rev. D 102 no. 4, (2020) 045014, arXiv:1910.06661 [hep-th].
- T. Cohen, N. Craig, X. Lu, and D. Sutherland, “Is SMEFT Enough?,” JHEP 03 (2021) 237, arXiv:2008.08597 [hep-ph].
- T. Cohen, N. Craig, X. Lu, and D. Sutherland, “Unitarity violation and the geometry of Higgs EFTs,” JHEP 12 (2021) 003, arXiv:2108.03240 [hep-ph].
- A. Helset, E. E. Jenkins, and A. V. Manohar, “Renormalization of the Standard Model Effective Field Theory from geometry,” JHEP 02 (2023) 063, arXiv:2212.03253 [hep-ph].
- R. Alonso and M. West, “On the effective action for scalars in a general manifold to any loop order,” Phys. Lett. B 841 (2023) 137937, arXiv:2207.02050 [hep-th].
- R. Alonso, “A primer on Higgs Effective Field Theory with Geometry,” arXiv:2307.14301 [hep-ph].
- E. E. Jenkins, A. V. Manohar, L. Naterop, and J. Pagès, “Two Loop Renormalization of Scalar Theories using a Geometric Approach,” arXiv:2310.19883 [hep-ph].
- K. Finn, S. Karamitsos, and A. Pilaftsis, “Frame covariant formalism for fermionic theories,” Eur. Phys. J. C 81 no. 7, (2021) 572, arXiv:2006.05831 [hep-th].
- C. Cheung, A. Helset, and J. Parra-Martinez, “Geometry-kinematics duality,” Phys. Rev. D 106 no. 4, (2022) 045016, arXiv:2202.06972 [hep-th].
- A. Helset, E. E. Jenkins, and A. V. Manohar, “Geometry in scattering amplitudes,” Phys. Rev. D 106 no. 11, (2022) 116018, arXiv:2210.08000 [hep-ph].
- B. Assi, A. Helset, A. V. Manohar, J. Pagès, and C.-H. Shen, “Fermion geometry and the renormalization of the Standard Model Effective Field Theory,” JHEP 11 (2023) 201, arXiv:2307.03187 [hep-ph].
- T. Cohen, N. Craig, X. Lu, and D. Sutherland, “On-Shell Covariance of Quantum Field Theory Amplitudes,” Phys. Rev. Lett. 130 no. 4, (2023) 041603, arXiv:2202.06965 [hep-th].
- N. Craig, Y.-T. Lee, X. Lu, and D. Sutherland, “Effective Field Theories as Lagrange Spaces,” arXiv:2305.09722 [hep-th].
- N. Craig, Yu-Tse, and Lee, “Effective Field Theories on the Jet Bundle,” arXiv:2307.15742 [hep-th].
- M. Alminawi, I. Brivio, and J. Davighi, “Jet Bundle Geometry of Scalar Field Theories,” arXiv:2308.00017 [hep-ph].
- T. Cohen, X. Lu, and D. Sutherland, “On Amplitudes and Field Redefinitions,” arXiv:2312.06748 [hep-th].
- V. Gattus and A. Pilaftsis, “Minimal supergeometric quantum field theories,” Phys. Lett. B 846 (2023) 138234, arXiv:2307.01126 [hep-th].
- B. S. DeWitt, Supermanifolds. Cambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, UK, 5, 2012.
- L. J. Dixon, “Calculating scattering amplitudes efficiently,” in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95): QCD and Beyond, pp. 539–584. 1, 1996. arXiv:hep-ph/9601359.
- K. Kampf, J. Novotny, M. Shifman, and J. Trnka, “New Soft Theorems for Goldstone Boson Amplitudes,” Phys. Rev. Lett. 124 no. 11, (2020) 111601, arXiv:1910.04766 [hep-th].
- C. G. Callan, Jr., “Broken scale invariance in scalar field theory,” Phys. Rev. D 2 (1970) 1541–1547.
- R. H. Boels and W. Wormsbecher, “Spontaneously broken conformal invariance in observables,” arXiv:1507.08162 [hep-th].
- Y.-t. Huang and C. Wen, “Soft theorems from anomalous symmetries,” JHEP 12 (2015) 143, arXiv:1509.07840 [hep-th].
- P. Di Vecchia, R. Marotta, M. Mojaza, and J. Nohle, “New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order,” Phys. Rev. D 93 no. 8, (2016) 085015, arXiv:1512.03316 [hep-th].
- S. L. Adler, “Consistency conditions on the strong interactions implied by a partially conserved axial-vector current. II,” Phys. Rev. 139 (1965) B1638–B1643.
- Y. Nambu and E. Shrauner, “Soft pion emission induced by electromagnetic and weak interactions,” Phys. Rev. 128 (1962) 862–868.
- Y. Nambu and D. Lurie, “Chirality conservation and soft pion production,” Phys. Rev. 125 (1962) 1429–1436.
- Cambridge University Press, 1985.
- E. Witten, “Current Algebra Theorems for the U(1) Goldstone Boson,” Nucl. Phys. B 156 (1979) 269–283.
- M. Campiglia, L. Coito, and S. Mizera, “Can scalars have asymptotic symmetries?,” Phys. Rev. D 97 no. 4, (2018) 046002, arXiv:1703.07885 [hep-th].
- S. Biswas and G. W. Semenoff, “Soft scalars do not decouple,” Phys. Rev. D 106 no. 10, (2022) 105023, arXiv:2208.05023 [hep-th].
- S. Weinberg, “Pion scattering lengths,” Phys. Rev. Lett. 17 (1966) 616–621.
- W.-M. Chen, Y.-t. Huang, and C. Wen, “New Fermionic Soft Theorems for Supergravity Amplitudes,” Phys. Rev. Lett. 115 no. 2, (2015) 021603, arXiv:1412.1809 [hep-th].
- T. Uematsu and C. K. Zachos, “Structure of Phenomenological Lagrangians for Broken Supersymmetry,” Nucl. Phys. B 201 (1982) 250–268.
- T. T. Dumitrescu, T. He, P. Mitra, and A. Strominger, “Infinite-dimensional fermionic symmetry in supersymmetric gauge theories,” JHEP 08 (2021) 051, arXiv:1511.07429 [hep-th].
- N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, “Scattering amplitudes for all masses and spins,” JHEP 11 (2021) 070, arXiv:1709.04891 [hep-th].
- G. Durieux, T. Kitahara, Y. Shadmi, and Y. Weiss, “The electroweak effective field theory from on-shell amplitudes,” JHEP 01 (2020) 119, arXiv:1909.10551 [hep-ph].
- A. Falkowski and C. S. Machado, “Soft Matters, or the Recursions with Massive Spinors,” JHEP 05 (2021) 238, arXiv:2005.08981 [hep-th].
- C. Cheung, K. Kampf, J. Novotny, and J. Trnka, “Effective Field Theories from Soft Limits of Scattering Amplitudes,” Phys. Rev. Lett. 114 no. 22, (2015) 221602, arXiv:1412.4095 [hep-th].
- C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, and J. Trnka, “On-Shell Recursion Relations for Effective Field Theories,” Phys. Rev. Lett. 116 no. 4, (2016) 041601, arXiv:1509.03309 [hep-th].
- C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, and J. Trnka, “A Periodic Table of Effective Field Theories,” JHEP 02 (2017) 020, arXiv:1611.03137 [hep-th].
- K. Kampf, J. Novotny, and J. Trnka, “Tree-level Amplitudes in the Nonlinear Sigma Model,” JHEP 05 (2013) 032, arXiv:1304.3048 [hep-th].
- H. Luo and C. Wen, “Recursion relations from soft theorems,” JHEP 03 (2016) 088, arXiv:1512.06801 [hep-th].
- H. Elvang, M. Hadjiantonis, C. R. T. Jones, and S. Paranjape, “On the Supersymmetrization of Galileon Theories in Four Dimensions,” Phys. Lett. B 781 (2018) 656–663, arXiv:1712.09937 [hep-th].
- H. Elvang, M. Hadjiantonis, C. R. T. Jones, and S. Paranjape, “Soft Bootstrap and Supersymmetry,” JHEP 01 (2019) 195, arXiv:1806.06079 [hep-th].
- C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, J. Trnka, and C. Wen, “Vector Effective Field Theories from Soft Limits,” Phys. Rev. Lett. 120 no. 26, (2018) 261602, arXiv:1801.01496 [hep-th].
- I. Low and Z. Yin, “Soft Bootstrap and Effective Field Theories,” JHEP 11 (2019) 078, arXiv:1904.12859 [hep-th].
- K. Kampf, J. Novotny, F. Preucil, and J. Trnka, “Multi-spin soft bootstrap and scalar-vector Galileon,” JHEP 07 (2021) 153, arXiv:2104.10693 [hep-th].
- K. Kampf, J. Novotny, and P. Vasko, “Extended DBI and its generalizations from graded soft theorems,” JHEP 10 (2021) 101, arXiv:2107.04587 [hep-th].