S-matrix bootstrap for effective field theories: massless pions

We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients (or low energy constants) of the chiral lagrangian controlling the low-energy dynamics of massless pions. This provides a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on massless EFTs in more than two spacetime dimensions.

Testing anomalous $$H-W$$ couplings and Higgs self-couplings via double and triple Higgs production at $$e^+e^-$$ colliders

In the present work we study the implications at the future $$e^+e^-$$ e + e - colliders of the modified interaction vertices WWH, WWHH, HHH and HHHH within the context of the non-linear effective field theory given by the Electroweak Chiral Lagrangian. These vertices are given by four parameters, a, b, $$\kappa _3$$ κ 3 and $$\kappa _4$$ κ 4 , respectively, that are independent and without any constraint from symmetry considerations in this non-linear effective Lagrangian context, given the fact the Higgs field is a singlet. This is in contrast to the Standard Model, where the vertices are related by $$V_{WWH}^\mathrm{SM}=v V_{WWHH}^\mathrm{SM}$$ V WWH SM = v V WWHH SM and $$V_{HHH}^\mathrm{SM}=v V_{HHHH}^\mathrm{SM}$$ V HHH SM = v V HHHH SM , with $$v=246$$ v = 246 GeV. We investigate the implications of the absence of these relations in the Electroweak Chiral Lagrangian case. We explore the sensitivity to these Higgs anomalous couplings in the two main channels at these colliders: double and triple Higgs production (plus neutrinos). Concretely, we study the access to a and b in $$e^+e^- \rightarrow HH \nu {\bar{\nu }}$$ e + e - → H H ν ν ¯ and the access to $$\kappa _3$$ κ 3 and $$\kappa _4$$ κ 4 in $$e^+e^- \rightarrow HHH \nu {\bar{\nu }}$$ e + e - → H H H ν ν ¯ . Our study of the beyond the Standard Model couplings via triple Higgs boson production at $$e^+e^-$$ e + e - colliders is novel and shows for the first time the possible accessibility to the quartic Higgs self-coupling.

2, 12, 117, 1959, 45171, 1170086, …: a Hilbert series for the QCD chiral Lagrangian

We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $$ \mathfrak{su}(n) $$ su n Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

Large $$N_c$$ scaling of meson masses and decay constants

We perform an ab initio calculation of the $$N_c$$Nc scaling of the low-energy couplings of the chiral Lagrangian of low-energy strong interactions, extracted from the mass dependence of meson masses and decay constants. We compute these observables on the lattice with four degenerate fermions, $$N_f=4$$Nf=4, and varying number of colours, $$N_c=3$$Nc=3–6, at a lattice spacing of $$a\simeq 0.075$$a≃0.075 fm. We find good agreement with the expected $$N_c$$Nc scaling and measure the coefficients of the leading and subleading terms in the large $$N_c$$Nc expansion. From the subleading $$N_c$$Nc corrections, we can also infer the $$N_f$$Nf dependence, that we use to extract the value of the low-energy couplings for different values of $$N_f$$Nf. We find agreement with previous determinations at $$N_c=3$$Nc=3 and $$N_f=2, 3$$Nf=2,3 and also, our results support a strong paramagnetic suppression of the chiral condensate in moving from $$N_f=2$$Nf=2 to $$N_f=3$$Nf=3.