Amplitude bases in generic EFTs

De Angelis, Stefano

doi:10.48550/arxiv.2202.02681

Cited by 4 publications

(7 citation statements)

References 76 publications

(114 reference statements)

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“…While our paper was being finalized, Ref. [41] appeared, which presents a similar topic. This work uses a graphic method to construct the massive amplitude bases, which is equivalent to the Young Tableaux method used here.…”

Section: Discussionmentioning

confidence: 82%

“…Nevertheless, some of the assumptions in Ref. [41] are only numerically checked without rigorous proof. On the contrary, our work has a solid mathematical foundation.…”

Section: Discussionmentioning

confidence: 99%

“…1324 [42][31] Zµ Z ν W + µ W − ν 13 24 [43][21] Z µ ZµW +ν W − ν 34 [42][31][21] Źµν Zµν W +ρ W − ρ − i µνρσ ZµγZ γ ν W + ρ W − + µν Z ρ W − ρ − 2W − µ W + ρν Z ρ − 2ZµW + ρν W −ρ ) 23 24 [41][31] Źµν (Zµν W +ρ W − ρ − 2W − µ Zρν W +ρ − 2W + µ Zρν W −ρ ) 14 24 [32][31] Ẃ +µν (W − µν Z ρ Zρ − 4ZµW − ρν Z ρ ) 13 23 [42][41] Ẃ −µν (W + µν Z ρ Zρ − 4ZµW + ρν Z ρ ) 12 24 [43][31] Ẃ +µν (Zµν W −ρ Zρ − 2ZµZρν W −ρ − 2W − µ Zρν Z ρ ) 12 23 [43][41] Ẃ −µν (Zµν W +ρ Zρ − 2ZµZρν W +ρ − 2W + µ Zρν Z ρ ) − µν W +ρ Zρ + 2ZµW − ρν W +ρ − 2W + µ W − ρν Z ρ ) 13 23 24 [41] Ẁ +µν (Zµν W −ρ Zρ + 2ZµZρν W −ρ − 2W + µ Zρν Z ρ ) 12 23 34 [41] Zµν (W + µν W −ρ Zρ + 2ZµW + ρν W −ρ − 2W − µ W + ρν Z ρ ) 12 13 24 [43] Zµν (Zµν W −ρ W + ρ + 2W + µ Zρν W −ρ − 2W − µ Zρν W +ρ ) 323] 24 [41][21] i Źµν W − µ (D ρ Zν )W + ρ 424] 23 [31][21] i Źµν W + µ (D ρ Zν )W − ρ 134] 24 [32][31] iDρ( Ẃ +µρ g νσ + Ẃ +ρσ g µν + Ẃ +ρν g µσ + Ẃ +σµ g νρ + Ẃ +νµ g ρσ )W − µ Zν Zσ 234] 13 [42][31] i Ẃ −µν Zν (DµW + ρ )Z ρ 423] 13 24 [21] i( Ẁ −µρ g νσ + Ẁ −ρσ g µν + Ẁ −ρν g µσ + Ẁ −σµ g νρ + Ẁ −νµ g ρσ + Ẁ −σν g µρ )(DσZν )ZρW + µ 424] 13 23 [21] i Ẁ +µν (DρZµ)Zν W −ρ 234] 13 24 [31] i Zµν W −And for vertex D 2n W + W + W − W − , we have 2 physical dim-4 operators, and 18 dim-6 operators,Amplitude Operator D 2n W + W + W − W − 13 24 [42][31] W +µ W +ν W − µ W − − µν W +ρ W − ρ − 2W − µ W − ρν W +ρ − 2W + µ W − ρν W −ρ ) 23 24 [41][31] Ẃ +µν (W + µν W −ρ W − ρ − 4W − µ W + ρν W −ρ ) 14 24 [32][31] Ẃ −µν (W − µν W +ρ W + ρ − 4W + µ W − ρν W +ρ ) 12 24 [43][31] Ẃ −µν (W + µν W −ρ W + ρ − 2W + µ W + ρν W −ρ − 2W − µ W + ρν W +ρ ) 13 24 34 [21] Ẁ −µν W − µν W +ρ W + ρ 13 24 2 [31] Ẁ −µν W + µν W −ρ W + ρ 12 24 34 [31] Ẁ +µν (W − µν W −ρ W + ρ + 2W + µ W − ρν W −ρ − 2W + µ W − ρν W +ρ ) 12 13 24 [43] Ẁ +µν W + µν W −ρ W − −µρ g νσ + Ẃ −ρσ g µν + Ẃ −ρν g µσ + Ẃ −σµ g νρ + Ẃ −νµ g ρσ )W − µ W + ν W + σ 423] 13 24 [21] i( Ẁ −µρ g νσ + Ẁ −ρσ g µν + Ẁ −ρν g µσ + Ẁ −σµ g νρ + Ẁ −νµ g ρσ + Ẁ −σν g µρ )(DσW + ν )W + ρ W − µ 234] 13 24 [31] i Ẁ +µν W − µ (Dν W − ρ )W +ρ 232] 423] 13[41] (i µνρσ + g µσ g νρ − g µρ g νσ + g µν g ρσ )(D ξ W − µ )W − ρ (Dν W +ξ )W +σ 424] 242] 13 [31] W +ρ W − ρ (DµW −ν )(Dν W +µ )Finally, for vertex D 2n ZZZZ, we only have 1 physical dim-4 operator, and 4 dim-6 operators,…”

mentioning

confidence: 99%

“…µ (Dν W + ρ )Z ρ 434] 12 23 [31] i Zµν Zµ(DρW + ν )W −ρ 232] 423] 13 [41] (i µνρσ + g µσ g νρ − g µρ g νσ + g µν g ρσ )(D ξ W + µ )W − ρ (Dν Z ξ )Z σ 424] 242] 13 [31] Z ρ W + ρ (DµW −ν )(Dν Z µ ) ρ 323] 24 [41][21] i Ẃ +µν W − µ (D ρ W + ν )W − ρ 134] 24 [32][31] iDρ( Ẃ ρ Zρ − 4ZµZρν Z ρ )1324 34 [21] Zµν Zµν Z ρ Zρ 232] 423] 13[41] (DµZ ν )(Dν Z µ )ZρZ ρ…”

mentioning

confidence: 99%

See 3 more Smart Citations

Constructing Generic Effective Field Theory for All Masses and Spins

Dong¹,

Ma²,

Shu³

et al. 2022

Preprint

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We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude bases at any given dimension through semi-standard Young tableaus of Lorentz subgroup SU (2)r and global symmetry U (N ) (N is the number of external legs), which can be directly mapped into physical operator bases. We first construct a complete set of monomial bases whose dimension is not the lowest and a redundant set of bases that always contains a complete set of amplitude bases with the lowest dimension. Then we decompose the bases of the redundant set into the monomial bases from low to high dimension and eliminate the linear correlation bases. Finally, the bases with the lowest dimension can be picked up. We also propose a matrix projection method to construct the massive amplitude bases involving identical particles. The operator bases of a generic massive effective field theory can be efficiently constructed by the computer programs. A complete set of four-vector operators at dimensions up to six is presented.

show abstract

Section: Discussionmentioning

confidence: 82%

“…Nevertheless, some of the assumptions in Ref. [41] are only numerically checked without rigorous proof. On the contrary, our work has a solid mathematical foundation.…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Constructing Generic Effective Field Theory for All Masses and Spins

Dong¹,

Ma²,

Shu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, a systematic construction of three and four-point non-factorizable amplitudes was presented in [76]. Systematic algorithms for the construction of independent massive amplitudes were further in [77][78][79], while their derivation from the Higgsing of massless amplitudes was studied in [80]. This approach also yields all-order results in v/Λ, whose powers are all absorbed in constant amplitude coefficients.…”

Section: Renormalization Group Running and Implications For Positivitymentioning

confidence: 99%

Theoretical developments in the SMEFT at dimension-8 and beyond

Alioli¹,

Boughezal²,

Cao³

et al. 2022

Preprint

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In this contribution to the Snowmass 2021 process we review theoretical developments in the Standard Model Effective Field Theory (SMEFT) with a focus on effects at the dimension-8 level and beyond. We review the theoretical advances that led to the complete construction of the operator bases for the dimension-8 and dimension-9 SMEFT Lagrangians. We discuss the possibility of obtaining all-orders results in the 1/Λ expansion for certain SMEFT observables as well as the current status of renormalization group running and implications for positivity, and briefly present the on-shell approach to constructing SMEFT amplitudes. Finally we present several new phenomenological effects that first arise at dimension-8 and discuss the impact of these terms on experimental analyses.

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Factorizing hidden particle production rates

Klose

2022

J. High Energ. Phys.

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A method is proposed to streamline the computation of hidden particle production rates by factorizing them into i) a model-independent SM contribution, and ii) a observable-independent hidden sector contribution. The SM contribution can be computed once for each observable and re-used for a wide array of hidden sector models, while the hidden sector contribution can be computed once for each model, and re-used for a wide array of observables. The SM contribution also facilitates extracting model independent constraints on hidden particle production. The method is compatible with effective field theory (EFT) and simplified model approaches. It is illustrated by factorizing the rate of charged kaon decays into a charged lepton and a number of hidden particles, and a single form factor Fℓ is found to parametrize the impact of general hidden sectors. We derive model-independent constraints for the form factor Fe that governs decays into positrons and hidden particles.

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Amplitude bases in generic EFTs

Cited by 4 publications

References 76 publications

Constructing Generic Effective Field Theory for All Masses and Spins

Constructing Generic Effective Field Theory for All Masses and Spins

Theoretical developments in the SMEFT at dimension-8 and beyond

Factorizing hidden particle production rates

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