On soft factors and transmutation operators

Fang-Stars Wei; Kang Zhou

arxiv: 2406.04622 · v1 · submitted 2024-06-07 · ✦ hep-th

On soft factors and transmutation operators

Fang-Stars Wei , Kang Zhou This is my paper

Pith reviewed 2026-05-23 23:59 UTC · model grok-4.3

classification ✦ hep-th

keywords soft factorssoft theoremsYang-Mills amplitudesgravity amplitudestransmutation operatorsuniversalityamplitude factorizationtree-level amplitudes

0 comments

The pith

Transformation operators reconstruct known soft factors and prove the absence of higher-order universal soft factors in Yang-Mills and gravity amplitudes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper applies transformation operators to rebuild the established soft factors in tree-level Yang-Mills and gravitational scattering amplitudes. It shows that any soft factor beyond the known orders cannot be universal. A sympathetic reader would care because universal soft factors enable the factorization of complex amplitudes into simpler pieces determined only by the soft particle. The work confirms that the soft theorems stop at their current orders under the universality condition.

Core claim

By employing the transformation operators proposed by Cheung, Shen and Wen, the known soft factors of YM and GR amplitudes are reconstructed, and the nonexistence of higher order soft factor of YM or GR amplitude which satisfies the universality is proved.

What carries the argument

Transformation operators that act on amplitudes to generate or constrain soft factors while preserving universality.

If this is right

Only leading and sub-leading soft factors are universal for Yang-Mills amplitudes.
Leading, sub-leading and sub-sub-leading soft factors are universal for gravitational amplitudes.
Higher-order soft factors in these theories must depend on the hard process if they exist at all.
The known soft theorems give the complete universal factorization behavior at tree level.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Methods based on these operators could be applied to other theories to test whether higher soft factors appear there.
Explicit checks in concrete multi-particle processes could confirm that candidate higher factors fail universality.
The result limits how far soft factorization can simplify amplitude calculations without additional inputs.

Load-bearing premise

The soft factor at any order must be universal, independent of the specific hard process and determined solely by the soft particle's properties and the theory.

What would settle it

An explicit construction of a higher-order soft factor for a Yang-Mills or gravity amplitude that factors out independently of the hard scattering details would falsify the nonexistence result.

read the original abstract

The well known soft theorems state the specific factorizations of tree level gravitational (GR) amplitudes at leading, sub-leading and sub-sub-leading orders, with universal soft factors. For Yang-Mills (YM) amplitudes, similar factorizations and universal soft factors are found at leading and sub-leading orders. Then it is natural to ask if the similar factorizations and soft factors exist at higher orders. In this note, by using transformation operators proposed by Cheung, Shen and Wen, we reconstruct the known soft factors of YM and GR amplitudes, and prove the nonexistence of higher order soft factor of YM or GR amplitude which satisfies the universality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This note reconstructs known soft factors with transmutation operators and claims a nonexistence result for higher-order universal ones, but the argument's reach depends on whether those operators exhaust all possibilities.

read the letter

The paper's main result is that Cheung-Shen-Wen transmutation operators recover the standard leading and subleading soft factors in tree-level Yang-Mills and gravity, while repeated application fails to produce any higher-order factor that remains universal across hard processes. This gives a concrete negative statement on the absence of further universal soft theorems at tree level. The reconstruction step is useful because it makes the action of the operators explicit on the known cases, and the nonexistence claim is the incremental addition to the soft theorem literature. The authors treat universality as the requirement that the soft factor depend only on the soft leg and the theory, not on the specific hard scattering, which matches the usual definition in the field. The derivation appears to rest on direct manipulation within the operator framework rather than new assumptions about the amplitudes themselves. A soft spot is that the nonexistence is shown inside the transmutation construction. The abstract does not indicate an exhaustive classification of every conceivable universal soft factor that might exist outside this operator family, so it remains possible that some other functional form could satisfy universality without arising from repeated transmutation. If the full text closes that gap by showing any universal factor must be reproducible by the operators, the result strengthens; otherwise the claim is narrower than stated. Readers working on scattering amplitudes and soft theorems will get the most from this short note, as it supplies a practical constraint within an established toolkit. It deserves peer review because the negative result is falsifiable once the operators are fixed and the universality condition is accepted.

Referee Report

1 major / 0 minor

Summary. The paper uses transmutation operators proposed by Cheung, Shen and Wen to reconstruct the known leading and sub-leading soft factors of tree-level Yang-Mills and gravity amplitudes. It then argues that repeated application of these operators cannot produce higher-order universal soft factors (independent of the hard process), thereby proving their nonexistence.

Significance. If the nonexistence argument holds rigorously, the result would confirm that universality in soft theorems for YM and GR is restricted to the known orders, providing a unified operator-based derivation of existing soft factors. The reconstruction itself is a useful technical contribution.

major comments (1)

[Main argument (following the reconstruction)] The nonexistence claim for higher-order universal soft factors rests on the transmutation operators. The argument shows that these operators fail to generate such factors but does not demonstrate that every possible universal soft factor (i.e., one independent of the hard scattering) must arise from this specific operator construction. Without an exhaustive classification or a separate consistency argument that rules out other functional forms, the proof only excludes factors generated by the given operators rather than all universal ones.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of the reconstruction of the known soft factors. We address the major comment below.

read point-by-point responses

Referee: [Main argument (following the reconstruction)] The nonexistence claim for higher-order universal soft factors rests on the transmutation operators. The argument shows that these operators fail to generate such factors but does not demonstrate that every possible universal soft factor (i.e., one independent of the hard scattering) must arise from this specific operator construction. Without an exhaustive classification or a separate consistency argument that rules out other functional forms, the proof only excludes factors generated by the given operators rather than all universal ones.

Authors: We agree that the nonexistence result is demonstrated specifically within the framework of repeated applications of the transmutation operators of Cheung, Shen and Wen. The manuscript reconstructs the known leading and sub-leading factors using these operators and shows that further applications do not produce additional universal (hard-process-independent) factors. However, the argument does not include an exhaustive classification of all conceivable functional forms that could satisfy universality, nor a separate consistency proof that every possible universal soft factor must be generated by this operator construction. We will revise the manuscript to clarify the scope of the claim, explicitly noting that the nonexistence holds for factors obtainable via the given operators, and we will add a brief discussion of why this operator approach is expected to be complete for universal soft theorems in YM and GR. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies external operators

full rationale

The paper cites transmutation operators from Cheung, Shen and Wen (distinct authors) as an external construction, then applies them to reconstruct known YM/GR soft factors and argue nonexistence of higher-order universal ones. No self-citation load-bearing, self-definitional reduction, or fitted-input-called-prediction is present in the abstract or described chain. The nonexistence claim is an application within the cited framework rather than a redefinition of inputs, leaving the central result with independent content from the operator application. This is the common case of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard domain assumptions from soft theorem literature and the definition of universality; no free parameters or invented entities are indicated in the abstract.

axioms (2)

domain assumption Soft theorems with universal factors hold at leading and sub-leading orders for YM and up to sub-sub-leading for GR at tree level.
Described as well known in the abstract.
domain assumption Transmutation operators from Cheung, Shen and Wen can reconstruct soft factors.
Used as the method in the abstract.

pith-pipeline@v0.9.0 · 5619 in / 1105 out tokens · 24207 ms · 2026-05-23T23:59:51.636101+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 32 internal anchors

[1]

F. E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions , Phys. Rev. 110 (1958) 974–977

work page 1958
[2]

Weinberg, Infrared photons and gravitons, Phys

S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516–B524

work page 1965
[3]

Evidence for a New Soft Graviton Theorem

F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem , arXiv:1404.4091

work page internal anchor Pith review Pith/arXiv arXiv
[4]

Soft sub-leading divergences in Yang-Mills amplitudes

E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes , JHEP 08 (2014) 077, [ arXiv:1404.5551]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[5]

B. U. W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014), no. 10 101601, [ arXiv:1404.7749]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[6]

Soft Graviton Theorem in Arbitrary Dimensions

N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions , arXiv:1405.3533. – 25 –

work page internal anchor Pith review Pith/arXiv arXiv
[7]

Sub-sub-leading soft-graviton theorem in arbitrary dimension

M. Zlotnikov, Sub-sub-leading soft-graviton theorem in arbitrary dimension , JHEP 10 (2014) 148, [arXiv:1407.5936]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[8]

New Recursion Relations for Tree Amplitudes of Gluons

R. Britto, F. Cachazo, and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl. Phys. B 715 (2005) 499–522, [ hep-th/0412308]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[9]

Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory

R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602, [ hep-th/0501052]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[10]

Scattering Equations and KLT Orthogonality

F. Cachazo, S. He, and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality , Phys. Rev. D90 (2014), no. 6 065001, [ arXiv:1306.6575]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[11]

Scattering of Massless Particles in Arbitrary Dimension

F. Cachazo, S. He, and E. Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions , Phys. Rev. Lett. 113 (2014), no. 17 171601, [ arXiv:1307.2199]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[12]

Scattering of Massless Particles: Scalars, Gluons and Gravitons

F. Cachazo, S. He, and E. Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons , JHEP 07 (2014) 033, [ arXiv:1309.0885]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[13]

Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

F. Cachazo, S. He, and E. Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations , JHEP 01 (2015) 121, [ arXiv:1409.8256]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[14]

Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM

F. Cachazo, S. He, and E. Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149, [ arXiv:1412.3479]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[15]

Z. Bern, S. Davies, and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons , Phys. Rev. D 90 (2014), no. 8 085015, [ arXiv:1405.1015]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[16]

Loop Corrections to Soft Theorems in Gauge Theories and Gravity

S. He, Y.-t. Huang, and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity , JHEP 12 (2014) 115, [ arXiv:1405.1410]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[17]

Are Soft Theorems Renormalized?

F. Cachazo and E. Y. Yuan, Are Soft Theorems Renormalized?, arXiv:1405.3413

work page internal anchor Pith review Pith/arXiv arXiv
[18]

More on Soft Theorems: Trees, Loops and Strings

M. Bianchi, S. He, Y.-t. Huang, and C. Wen, More on Soft Theorems: Trees, Loops and Strings , Phys. Rev. D 92 (2015), no. 6 065022, [ arXiv:1406.5155]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[19]

Subleading Soft Graviton Theorem for Loop Amplitudes

A. Sen, Subleading Soft Graviton Theorem for Loop Amplitudes , JHEP 11 (2017) 123, [ arXiv:1703.00024]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[20]

The Tree Formula for MHV Graviton Amplitudes

D. Nguyen, M. Spradlin, A. Volovich, and C. Wen, The Tree Formula for MHV Graviton Amplitudes , JHEP 07 (2010) 045, [ arXiv:0907.2276]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[21]

Constructing Amplitudes from Their Soft Limits

C. Boucher-Veronneau and A. J. Larkoski, Constructing Amplitudes from Their Soft Limits , JHEP 09 (2011) 130, [arXiv:1108.5385]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[22]

Scattering Amplitudes from Soft Theorems and Infrared Behavior

L. Rodina, Scattering Amplitudes from Soft Theorems and Infrared Behavior , Phys. Rev. Lett. 122 (2019), no. 7 071601, [ arXiv:1807.09738]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[23]

S. Ma, R. Dong, and Y.-J. Du, Constructing EYM amplitudes by inverse soft limit , JHEP 05 (2023) 196, [arXiv:2211.10047]

work page arXiv 2023
[24]

Effective Field Theories from Soft Limits

C. Cheung, K. Kampf, J. Novotny, and J. Trnka, Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett. 114 (2015), no. 22 221602, [ arXiv:1412.4095]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[25]

Cheung, K

C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, and J. Trnka, On-Shell Recursion Relations for Effective Field Theories, Phys. Rev. Lett. 116 (2016), no. 4 041601. – 26 –

work page 2016
[26]

Recursion relations from soft theorems

H. Luo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088, [ arXiv:1512.06801]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[27]

Soft Bootstrap and Supersymmetry

H. Elvang, M. Hadjiantonis, C. R. T. Jones, and S. Paranjape, Soft Bootstrap and Supersymmetry , JHEP 01 (2019) 195, [ arXiv:1806.06079]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[28]

Tree level amplitudes from soft theorems

K. Zhou, Tree level amplitudes from soft theorems , JHEP 03 (2023) 021, [ arXiv:2212.12892]

work page internal anchor Pith review Pith/arXiv arXiv 2023
[29]

Expanding single trace YMS amplitudes with gauge invariant coefficients

F.-S. Wei and K. Zhou, Expanding single-trace YMS amplitudes with gauge-invariant coefficients , Eur. Phys. J. C 84 (2024), no. 1 29, [ arXiv:2306.14774]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[30]

Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem

C. Hu and K. Zhou, Recursive construction for expansions of tree Yang–Mills amplitudes from soft theorem , Eur. Phys. J. C 84 (2024), no. 3 221, [ arXiv:2311.03112]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[31]

Multi-trace YMS amplitudes from soft behavior

Y.-J. Du and K. Zhou, Multi-trace YMS amplitudes from soft behavior , JHEP 03 (2024) 081, [arXiv:2401.03879]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[32]

Unifying Relations for Scattering Amplitudes

C. Cheung, C.-H. Shen, and C. Wen, Unifying Relations for Scattering Amplitudes , JHEP 02 (2018) 095, [arXiv:1705.03025]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[33]

Note on differential operators, CHY integrands, and unifying relations for amplitudes

K. Zhou and B. Feng, Note on differential operators, CHY integrands, and unifying relations for amplitudes , JHEP 09 (2018) 160, [ arXiv:1808.06835]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[34]

Transmuting CHY formulae

M. Bollmann and L. Ferro, Transmuting CHY formulae, JHEP 01 (2019) 180, [ arXiv:1808.07451]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[35]

On BMS Invariance of Gravitational Scattering

A. Strominger, On BMS Invariance of Gravitational Scattering , JHEP 07 (2014) 152, [ arXiv:1312.2229]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[36]

T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem , JHEP 05 (2015) 151, [ arXiv:1401.7026]. – 27 –

work page internal anchor Pith review Pith/arXiv arXiv 2015

[1] [1]

F. E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions , Phys. Rev. 110 (1958) 974–977

work page 1958

[2] [2]

Weinberg, Infrared photons and gravitons, Phys

S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516–B524

work page 1965

[3] [3]

Evidence for a New Soft Graviton Theorem

F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem , arXiv:1404.4091

work page internal anchor Pith review Pith/arXiv arXiv

[4] [4]

Soft sub-leading divergences in Yang-Mills amplitudes

E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes , JHEP 08 (2014) 077, [ arXiv:1404.5551]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[5] [5]

B. U. W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014), no. 10 101601, [ arXiv:1404.7749]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[6] [6]

Soft Graviton Theorem in Arbitrary Dimensions

N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions , arXiv:1405.3533. – 25 –

work page internal anchor Pith review Pith/arXiv arXiv

[7] [7]

Sub-sub-leading soft-graviton theorem in arbitrary dimension

M. Zlotnikov, Sub-sub-leading soft-graviton theorem in arbitrary dimension , JHEP 10 (2014) 148, [arXiv:1407.5936]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[8] [8]

New Recursion Relations for Tree Amplitudes of Gluons

R. Britto, F. Cachazo, and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl. Phys. B 715 (2005) 499–522, [ hep-th/0412308]

work page internal anchor Pith review Pith/arXiv arXiv 2005

[9] [9]

Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory

R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602, [ hep-th/0501052]

work page internal anchor Pith review Pith/arXiv arXiv 2005

[10] [10]

Scattering Equations and KLT Orthogonality

F. Cachazo, S. He, and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality , Phys. Rev. D90 (2014), no. 6 065001, [ arXiv:1306.6575]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[11] [11]

Scattering of Massless Particles in Arbitrary Dimension

F. Cachazo, S. He, and E. Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions , Phys. Rev. Lett. 113 (2014), no. 17 171601, [ arXiv:1307.2199]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[12] [12]

Scattering of Massless Particles: Scalars, Gluons and Gravitons

F. Cachazo, S. He, and E. Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons , JHEP 07 (2014) 033, [ arXiv:1309.0885]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[13] [13]

Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

F. Cachazo, S. He, and E. Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations , JHEP 01 (2015) 121, [ arXiv:1409.8256]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[14] [14]

Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM

F. Cachazo, S. He, and E. Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149, [ arXiv:1412.3479]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[15] [15]

Z. Bern, S. Davies, and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons , Phys. Rev. D 90 (2014), no. 8 085015, [ arXiv:1405.1015]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[16] [16]

Loop Corrections to Soft Theorems in Gauge Theories and Gravity

S. He, Y.-t. Huang, and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity , JHEP 12 (2014) 115, [ arXiv:1405.1410]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[17] [17]

Are Soft Theorems Renormalized?

F. Cachazo and E. Y. Yuan, Are Soft Theorems Renormalized?, arXiv:1405.3413

work page internal anchor Pith review Pith/arXiv arXiv

[18] [18]

More on Soft Theorems: Trees, Loops and Strings

M. Bianchi, S. He, Y.-t. Huang, and C. Wen, More on Soft Theorems: Trees, Loops and Strings , Phys. Rev. D 92 (2015), no. 6 065022, [ arXiv:1406.5155]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[19] [19]

Subleading Soft Graviton Theorem for Loop Amplitudes

A. Sen, Subleading Soft Graviton Theorem for Loop Amplitudes , JHEP 11 (2017) 123, [ arXiv:1703.00024]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[20] [20]

The Tree Formula for MHV Graviton Amplitudes

D. Nguyen, M. Spradlin, A. Volovich, and C. Wen, The Tree Formula for MHV Graviton Amplitudes , JHEP 07 (2010) 045, [ arXiv:0907.2276]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[21] [21]

Constructing Amplitudes from Their Soft Limits

C. Boucher-Veronneau and A. J. Larkoski, Constructing Amplitudes from Their Soft Limits , JHEP 09 (2011) 130, [arXiv:1108.5385]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[22] [22]

Scattering Amplitudes from Soft Theorems and Infrared Behavior

L. Rodina, Scattering Amplitudes from Soft Theorems and Infrared Behavior , Phys. Rev. Lett. 122 (2019), no. 7 071601, [ arXiv:1807.09738]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[23] [23]

S. Ma, R. Dong, and Y.-J. Du, Constructing EYM amplitudes by inverse soft limit , JHEP 05 (2023) 196, [arXiv:2211.10047]

work page arXiv 2023

[24] [24]

Effective Field Theories from Soft Limits

C. Cheung, K. Kampf, J. Novotny, and J. Trnka, Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett. 114 (2015), no. 22 221602, [ arXiv:1412.4095]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[25] [25]

Cheung, K

C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, and J. Trnka, On-Shell Recursion Relations for Effective Field Theories, Phys. Rev. Lett. 116 (2016), no. 4 041601. – 26 –

work page 2016

[26] [26]

Recursion relations from soft theorems

H. Luo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088, [ arXiv:1512.06801]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[27] [27]

Soft Bootstrap and Supersymmetry

H. Elvang, M. Hadjiantonis, C. R. T. Jones, and S. Paranjape, Soft Bootstrap and Supersymmetry , JHEP 01 (2019) 195, [ arXiv:1806.06079]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[28] [28]

Tree level amplitudes from soft theorems

K. Zhou, Tree level amplitudes from soft theorems , JHEP 03 (2023) 021, [ arXiv:2212.12892]

work page internal anchor Pith review Pith/arXiv arXiv 2023

[29] [29]

Expanding single trace YMS amplitudes with gauge invariant coefficients

F.-S. Wei and K. Zhou, Expanding single-trace YMS amplitudes with gauge-invariant coefficients , Eur. Phys. J. C 84 (2024), no. 1 29, [ arXiv:2306.14774]

work page internal anchor Pith review Pith/arXiv arXiv 2024

[30] [30]

Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem

C. Hu and K. Zhou, Recursive construction for expansions of tree Yang–Mills amplitudes from soft theorem , Eur. Phys. J. C 84 (2024), no. 3 221, [ arXiv:2311.03112]

work page internal anchor Pith review Pith/arXiv arXiv 2024

[31] [31]

Multi-trace YMS amplitudes from soft behavior

Y.-J. Du and K. Zhou, Multi-trace YMS amplitudes from soft behavior , JHEP 03 (2024) 081, [arXiv:2401.03879]

work page internal anchor Pith review Pith/arXiv arXiv 2024

[32] [32]

Unifying Relations for Scattering Amplitudes

C. Cheung, C.-H. Shen, and C. Wen, Unifying Relations for Scattering Amplitudes , JHEP 02 (2018) 095, [arXiv:1705.03025]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[33] [33]

Note on differential operators, CHY integrands, and unifying relations for amplitudes

K. Zhou and B. Feng, Note on differential operators, CHY integrands, and unifying relations for amplitudes , JHEP 09 (2018) 160, [ arXiv:1808.06835]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[34] [34]

Transmuting CHY formulae

M. Bollmann and L. Ferro, Transmuting CHY formulae, JHEP 01 (2019) 180, [ arXiv:1808.07451]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[35] [35]

On BMS Invariance of Gravitational Scattering

A. Strominger, On BMS Invariance of Gravitational Scattering , JHEP 07 (2014) 152, [ arXiv:1312.2229]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[36] [36]

T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem , JHEP 05 (2015) 151, [ arXiv:1401.7026]. – 27 –

work page internal anchor Pith review Pith/arXiv arXiv 2015