Abstract
Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present the most accurate calculation of the transverse-energy-energy correlation event shape variable in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section is factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. We report the resummed transverse-energy-energy correlation distributions up to N3LL accuracy matched with the NLO cross section for the production of a lepton and two jets. Our work provides a new way to precisely study TMD physics at the future Electron-Ion Collider.
Highlights
Where Ei is the energy of hadron i and θab is the opening angle between hadrons a and b
A close connection to transverse-momentum dependent (TMD) factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient
We report the resummed transverse-energy-energy correlation distributions up to N3LL accuracy matched with the NLO cross section for the production of a lepton and two jets
Summary
The underlying partonic Born process considered in this work is e(k1) + q(k2) → e(k3) + q(k4). In the back-to-back limit it is convenient to introduce the variable τ = (1 + cos φ)/2, related to the non-zero momentum balance along y-direction of the event due to soft and/or collinear radiations. The resummed cross section is obtained by evolving the hard function from μh to μc and the soft function from (μs, νs) to (μc, νc) It can be written as dσR(0E)S = dτ f. The prediction away from the back-to-back limit is obtained through matching the resummed calculations with the fixed-order ones, which can be written as dσNlLL+NkLO = dσNlLL + dσNkLO − dσNkLO dτ dτ sing. Leading power of SCET, which captures the singular behavior of the QCD fixed-order predictions in the leading power in the back-to-back limit
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