Rigorous bounds on the Analytic $S$-matrix

Guerrieri, Andrea; Sever, Amit

doi:10.48550/arxiv.2106.10257

Cited by 4 publications

(11 citation statements)

References 43 publications

(99 reference statements)

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“…By combining our primal data and the dual bound in ref. [64], we obtain the best estimate to date: − 8.02 min λ −7.0 .…”

Section: Properties Of the Amplitudes In The Boundarymentioning

confidence: 78%

“…Formulating the dual S-matrix Bootstrap in higher dimensions d > 2 has turned out to be a challenging mathematical problem. Recently, it has been solved assuming either maximal analyticity [63], or in [64] by employing the rigorous analyticity domain derived by Martin [65] 5 .…”

Section: S-matrix Bootstrap In D = 3 +mentioning

confidence: 99%

“…Instead, the dual approach excludes those values of c i that cannot be attained by a unitarity, analytic and crossing-symmetric amplitude, and therefore produces bounds on the values of c i 's. A number of problems have been studied with both the primal and the dual [60][61][62][63][64]40], finding that both approaches lead to the same optimal values for the objectives (i.e. the values for the min/max(c i ) values in our example above).…”

Section: S-matrix Bootstrap In D = 3 +mentioning

confidence: 99%

See 2 more Smart Citations

Bridging Positivity and S-matrix Bootstrap Bounds

Miro¹,

Guerrieri²,

Gumus³

2022

Preprint

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The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. Moreover, we discuss the notion of Spin-Zero and UV dominance along the boundary of the allowed amplitude space by introducing suitable observables. Finally, we show that this construction also leads to novel bounds on operators of dimension less than or equal to six.

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“…By combining our primal data and the dual bound in ref. [64], we obtain the best estimate to date: − 8.02 min λ −7.0 .…”

Section: Properties Of the Amplitudes In The Boundarymentioning

confidence: 78%

Section: S-matrix Bootstrap In D = 3 +mentioning

confidence: 99%

Section: S-matrix Bootstrap In D = 3 +mentioning

confidence: 99%

See 1 more Smart Citation

Bridging Positivity and S-matrix Bootstrap Bounds

Miro¹,

Guerrieri²,

Gumus³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In this section, we assume the amplitude to be analytic for large negative t (within the EFT validity), outside Martin's domain. Although not rigorously proven, it is believed that this assumption holds at least for scattering of the lightest particles in the spectrum, and it is often (though not always [56]) assumed in the modern S-matrix bootstrap approach [57][58][59].…”

Section: Dispersion Relations At Finite T mentioning

confidence: 99%

The IR-Side of Positivity Bounds

Bellazzini,

Riembau,

Riva

2021

Preprint

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“…The basic idea of the model independent approach we explore is to work directly with the measured particles, and constrain the S-matrix of the minimum bias events. This philosophy aligns with a bootstrap approach to QCD which is actively being pursued for low-multiplicity processes in quantum field theory [16][17][18][19][20][21][22][23][24][25][26][27][28]. The nature and high-multiplicity of minimum bias events offers some simplifications by appealing to the principle of ergodicity: a given particle is representative of any particle in the event.…”

Section: Introductionmentioning

confidence: 98%

A Large-$N$ Expansion for Minimum Bias

Larkoski,

Melia

2021

Preprint

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Despite being the overwhelming majority of events produced in hadron or heavy ion collisions, minimum bias events do not enjoy a robust first-principles theoretical description as their dynamics are dominated by low-energy quantum chromodynamics. In this paper, we present a novel expansion scheme of the cross section for minimum bias events that exploits an ergodic hypothesis for particles in the events and events in an ensemble of data. We identify power counting rules and symmetries of minimum bias from which the form of the squared matrix element can be expanded in symmetric polynomials of the phase space coordinates. This expansion is entirely defined in terms of observable quantities, in contrast to models of heavy ion collisions that rely on unmeasurable quantities like the number of nucleons participating in the collision, or tunes of parton shower parameters to describe the underlying event in proton collisions. The expansion parameter that we identify from our power counting is the number of detected particles N and as N → ∞ the variance of the squared matrix element about its mean, constant value on phase space vanishes. With this expansion, we show that the transverse momentum distribution of particles takes a universal form that only depends on a single parameter, has a fractional dispersion relation, and agrees with data in its realm of validity. We show that the constraint of positivity of the squared matrix element requires that all azimuthal correlations vanish in the N → ∞ limit at fixed center-of-mass energy, as observed in data. The approach we follow allows for a unified treatment of small and large system collective behavior, being equally applicable to describe, e.g., elliptic flow in PbPb collisions and the "ridge" in pp collisions. We also briefly comment on power counting and symmetries for minimum bias events in other collider environments and show that a possible ridge in e + e − collisions is highly suppressed as a consequence of its symmetries.

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Rigorous bounds on the Analytic $S$-matrix

Cited by 4 publications

References 43 publications

Bridging Positivity and S-matrix Bootstrap Bounds

Bridging Positivity and S-matrix Bootstrap Bounds

The IR-Side of Positivity Bounds

A Large-$N$ Expansion for Minimum Bias

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