scholarly journals Sum rules in the standard model effective field theory from helicity amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Jiayin Gu ◽  
Lian-Tao Wang
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Sum Rules ◽  
High Energy ◽  
Effective Field ◽  
Low Energy ◽  
Tree Level ◽  
The Standard Model ◽  
Helicity Amplitudes

Abstract The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.

scholarly journals Extending low energy effective field theory with a complete set of dimension-7 operators

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma ◽  
Quan-Yu Wang
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Cross Sections ◽  
Effective Field Theory ◽  
Degrees Of Freedom ◽  
Independent Set ◽  
Effective Field ◽  
Low Energy ◽  
Tree Level ◽  
The Standard Model

Abstract We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon (∆B) and lepton (∆L) numbers violated. Including Hermitian-conjugated operators, there are in total 3168, 750, 588, 712 operators with (∆B, ∆L) = (0, 0), (0, ±2), (±1, ∓1), (±1, ±1) respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare various neutrino-photon scattering cross sections with their counterparts in the standard model and highlight the new features. Finally, we illustrate how these effective interactions could arise from ultraviolet completion.

scholarly journals General non-leptonic ∆F = 1 WET at the NLO in QCD

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jason Aebischer ◽  
Christoph Bobeth ◽  
Andrzej J. Buras ◽  
Jacky Kumar ◽  
Mikołaj Misiak
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
High Energy ◽  
Effective Field ◽  
Effective Theory ◽  
Leading Order ◽  
The Standard Model ◽  
Complete Set ◽  
The One

Abstract We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic ∆F = 1 decays that govern s → d and b → d, s transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers Nf of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of K → ππ and non-leptonic B-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

scholarly journals Bottom-flavored mono-tau tails at the LHC

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
David Marzocca ◽  
Ui Min ◽  
Minho Son
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Low Energy ◽  
Final State ◽  
Lepton Flavor ◽  
The Standard Model ◽  
The Impact ◽  
Integrated Luminosity

Abstract We study the effective field theory sensitivity of an LHC analysis for the τν final state with an associated b-jet. To illustrate the improvement due to the b-tagging, we first recast the recent CMS analysis in the τν channel, using an integrated luminosity of 35.9 fb−1 at $$ \sqrt{s} $$ s = 13 TeV, and provide limits on all the dimension-six effective operators which contribute to the process. The expected limits from the b-tagged analysis are then derived and compared. We find an improvement of approximately ∼ 30% in the bounds for operators with a b quark. We also discuss in detail possible angular observables to be used as a discriminator between dimension-six operators with different Lorentz structure. Finally, we study the impact of these limits on some simplified scenarios aimed at addressing the observed deviations from the Standard Model in lepton flavor universality ratios of semileptonic B-meson decays. In particular, we compare the collider limits on those scenarios set by our analysis either with or without the b-tagging, assuming an integrated luminosity of 300 fb−1, with relevant low-energy flavor measurements.

scholarly journals Low-Energy Effective Field Theory below the Electroweak Scale: dimension-8 operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher W. Murphy
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Low Energy ◽  
Electroweak Scale ◽  
Left Handed ◽  
The Standard Model ◽  
Two Generations ◽  
Charged Leptons

Abstract We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals Complete set of dimension-eight operators in the standard model effective field theory

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Hao-Lin Li ◽  
Zhe Ren ◽  
Jing Shu ◽  
Ming-Lei Xiao ◽  
Jiang-Hao Yu ◽  
...  
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
The Standard Model ◽  
Complete Set

scholarly journals Complete set of dimension-nine operators in the standard model effective field theory

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Hao-Lin Li ◽  
Zhe Ren ◽  
Ming-Lei Xiao ◽  
Jiang-Hao Yu ◽  
Yu-Hui Zheng
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
The Standard Model ◽  
Complete Set

scholarly journals An explicit construction of the dimension-9 operator basis in the standard model effective field theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Explicit Construction ◽  
Effective Field ◽  
Starting Point ◽  
The Standard Model ◽  
Symmetry Relations

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

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