Structure functions at small 
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 from worldlines: Unpolarized distributions

Tarasov, Andrey; Venugopalan, Raju

doi:10.1103/physrevd.100.054007

Cited by 10 publications

(13 citation statements)

References 88 publications

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“…Even numbers of insertions of scalar, pseudoscalar and axial vector fields contribute to the real part of W while odd numbers contribute to the imaginary part. The map between the worldline and Feynman diagram computations of these was discussed previously in [50,55]; for DIS specifically, it was discussed in [53]. The (Euclidean) fermion effective action in the presence of these sources can in general be written as…”

Section: Wzw η Term From the Imaginary Part Of The Worldline Effectiv...mentioning

confidence: 99%

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The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Tarasov,

Venugopalan

2021

Preprint

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In [1], we demonstrated that structure function g1(xB, Q 2 ) measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both Bjorken (Q 2 → 0) and Regge (xB → 0) asymptotics. In the worldline formulation of quantum field theory, the triangle anomaly arises from the imaginary part of the worldline effective action. We show explicitly how a Wess-Zumino-Witten term coupling the topological charge density to a primordial isosinglet η arises in this framework. We demonstrate the fundamental role played by this contribution both in topological mass generation of the η and in the cancellation of the off-forward pole arising from the triangle anomaly in the proton's helicity Σ(Q 2 ). We recover the striking result by Shore and Veneziano that Σ ∝ χ (0), where χ is the slope of the QCD topological susceptibility in the forward limit. We construct an axion-like effective action for g1 at small xB that describes the interplay between gluon saturation and the topology of the QCD vacuum. In particular, we outline the role of "over-thebarrier" sphaleron-like transitions in spin diffusion at small xB. Such topological transitions can be measured in polarized DIS at a future Electron-Ion Collider., with the ≈ sign denoting that a term needs to be added on the l.h.s corresponding to a linear combination of the isotriplet and isooctet axial vector charges of the proton. These contributions are weakly dependent on Q 2 and we will ignore them henceforth to focus on isosinglet contributions to g 1 (x B , Q 2 ).

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Section: Wzw η Term From the Imaginary Part Of The Worldline Effectiv...mentioning

confidence: 99%

“…The evaluation of the functional integrals over x and ξ, as well as the integral over zero mode ψ 0 , is straightforward and discussed at length in [1,53]. We obtain,…”

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confidence: 99%

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Tarasov,

Venugopalan

2021

Preprint

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“…This argument is quantified in the color glass condensate effective field theory (CGC EFT) [58], wherein an emergent scale proportional to the density of color sources grows through a Wilsonian renormalization group evolution of the separation between sources and fields with decreasing x Bj [59][60][61][62]. In Regge asymptotics, this scale is larger than intrinsic nonperturbative QCD scales and therefore the hadron tensor in the CGC EFT can be written as [63,64] W μν ðq; P; SÞ ¼ P þ…”

Section: Dis In the Regge Limitmentioning

confidence: 99%

“…Further technical details of the worldline computation of this "dipole model" can be found in Ref. [64].…”

Section: Dis In the Regge Limitmentioning

confidence: 99%

Deeply inelastic scattering structure functions on a hybrid quantum computer

2020

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We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical path integral over 0 þ 1-dimensional fermionic and bosonic worldlines. The proper time evolution of these worldlines can be determined on a quantum computer. While extremely challenging in general, the problem simplifies in the Regge limit of QCD, where the interaction of the worldlines with gauge fields is strongly localized in proper time and the corresponding quantum circuits can be written down. As a first application, we employ the color glass condensate effective theory to construct the quantum algorithm for a simple dipole model of the F 2 structure function. We outline further how this computation scales up in complexity and extends in scope to other real-time correlation functions.

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“…Mata, U. Müller and C. Schubert ground field [76], as well as for obtaining tensor decompositions of off-shell gluon amplitudes [8]. Very recently it has also been shown how to apply it to the computation of deeply inelastic structure functions [68,77]. Yukawa and axial couplings have been included using dimensional reduction [41,42,66,67] as well as direct approaches [65].…”

Section: Introductionmentioning

confidence: 99%

New Techniques for Worldline Integration

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Mata²,

ller³

et al. 2021

SIGMA

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The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining the contributions of large classes of Feynman diagrams of different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding to individual diagrams poses a formidable mathematical challenge. We summarize the history and state of the art of this problem, including some natural connections to the theory of Bernoulli numbers and polynomials and multiple zeta values.

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Structure functions at small x from worldlines: Unpolarized distributions

Cited by 10 publications

References 88 publications

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Deeply inelastic scattering structure functions on a hybrid quantum computer

New Techniques for Worldline Integration

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