Precision QCD Event Shapes at Hadron Colliders: The Transverse Energy-Energy Correlator in the Back-to-Back Limit

Abstract

We present an operator based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-nextto-leading logarithm (NNLL) matched to fixed order at the LHC. Our results constitute the first NNLL resummation for a dijet event shape observable at a hadron collider, and the first analytic result for a hadron collider dijet soft function at NNLO. We anticipate that the theoretical simplicity of the TEEC observable will make it indispensable for precision studies of QCD at the LHC, and as a playground for theoretical studies of factorization and its violation.

Transverse momentum dependent PDFs at N3LO

“…Our results are also the last missing ingredient for TMD resummation at N 3 LL accuracy. They also arise in q T -dependent event shapes at hadron colliders such as the Transverse Energy-Energy Correlator (TEEC) [54], and for the azimuthal angle in vector boson +j production in the back-to-back limit [55,56].…”

Transverse parton distribution and fragmentation functions at NNLO: the gluon case

“…The gluon TMDFFs can be used to calculate the gluon jet function for the back-to-back resummation of the EEC in the Higgs gluonic decay [87]. Such jet functions also appear in the back-to-back resummation for TEEC [36]. The gluon jet function can be expanded as…”

“…Recently, EEC in the back-to-back limit has also been studied at hadron collider, the so-called TEEC. Due to the special geometry at hadron colliders, the linearly polarized gluon does not contribute to TEEC [36]. In that case, the gluon jet function is simply given by…”

“…Analytical calculations, phenomenological applications, and experimental determinations of the TMD distributions play important role in understanding the structure of hadrons [1,2]. TMDPDFs and TMDFFs have important applications in collider processes, such as Drell-Yan [3][4][5][6][7][8][9][10][11] and Higgs production [12][13][14][15][16][17][18][19], top quark pair production [20][21][22][23], hadronic J/ψ production, semi-inclusive deep-inelastic scattering [24][25][26][27][28], hadron or jet production in electron-positron annihilation [29][30][31][32][33][34], and energy correlators in both e + e − and hadron colliders [29,35,36]. The TMDPDFs and TMDFFs are intrinsically non-perturbative objects.…”

Transverse parton distribution and fragmentation functions at NNLO: the quark case

“…However, in certain regions of phase space, the transverse momenta of the partons become relevant, and one needs the transverse momentum dependent PDFs (TMDPDFs) and FFs (TMDFFs) in the corresponding factorization formulas. This is case for the small transverse momentum (Q T ) region in the Drell-Yan process [3][4][5][6][7][8][9][10][11], and also for similar regions in, e.g., semi-inclusive deep-inelastic scattering (SIDIS) [12][13][14][15][16], electron-positron annihilation to hadrons and jets [17][18][19][20][21][22], Higgs boson production [23][24][25][26][27][28][29][30], top quark pair production [31][32][33][34], as well as Energy-Energy Correlator (EEC) in the back-to-back limit at both lepton and hadron colliders [35,36]. To improve the theoretical predictions for these observables, it is desirable to have precise knowledges about these basic objects.…”