Transverse vetoes with rapidity cutoff in SCET

Journal of High Energy Physics, Dec 2017

We consider di-jet production in hadron collisions where a transverse veto is imposed on radiation for (pseudo-)rapidities in the central region only, where this central region is defined with rapidity cutoff. For the case where the transverse measurement (e.g., transverse energy or min p T for jet veto) is parametrically larger relative to the typical transverse momentum beyond the cutoff, the cross section is insensitive to the cutoff parameter and is factorized in terms of collinear and soft degrees of freedom. The virtuality for these degrees of freedom is set by the transverse measurement, as in typical transverse-momentum dependent observables such as Drell-Yan, Higgs production, and the event shape broadening. This paper focuses on the other region, where the typical transverse momentum below and beyond the cutoff is of similar size. In this region the rapidity cutoff further resolves soft radiation into (u)soft and soft-collinear radiation with different rapidities but identical virtuality. This gives rise to rapidity logarithms of the rapidity cutoff parameter which we resum using renormalization group methods. We factorize the cross section in this region in terms of soft and collinear functions in the framework of soft-collinear effective theory, then further refactorize the soft function as a convolution of the (u)soft and soft-collinear functions. All these functions are calculated at one-loop order. As an example, we calculate a differential cross section for a specific partonic channel, qq ′ → qq ′ , for the jet shape angularities and show that the refactorization allows us to resum the rapidity logarithms and significantly reduce theoretical uncertainties in the jet shape spectrum.

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Transverse vetoes with rapidity cutoff in SCET

HJE Transverse vetoes with rapidity cuto in SCET Andrew Hornig 0 1 2 4 5 Daekyoung Kang 0 1 2 4 5 Yiannis Makris 0 1 2 3 4 5 Thomas Mehen 0 1 2 3 5 0 Shanghai , 200433 , China 1 and Institute of Modern Physics, Fudan University 2 Los Alamos, NM , 87545 , U.S.A 3 Department of Physics, Duke University 4 Theoretical Division T-2, Los Alamos National Laboratory 5 Durham , NC 27708 , U.K We consider di-jet production in hadron collisions where a transverse veto is imposed on radiation for (pseudo-)rapidities in the central region only, where this central region is de ned with rapidity cuto . For the case where the transverse measurement (e.g., transverse energy or min pT for jet veto) is parametrically larger relative to the typical transverse momentum beyond the cuto , the cross section is insensitive to the cuto parameter and is factorized in terms of collinear and soft degrees of freedom. The virtuality for these degrees of freedom is set by the transverse measurement, as in typical transversemomentum dependent observables such as Drell-Yan, Higgs production, and the event shape broadening. This paper focuses on the other region, where the typical transverse momentum below and beyond the cuto is of similar size. In this region the rapidity cuto further resolves soft radiation into (u)soft and soft-collinear radiation with di erent rapidities but identical virtuality. This gives rise to rapidity logarithms of the rapidity ArXiv ePrint: 1708.08467 - cuto parameter which we resum using renormalization group methods. We factorize the cross section in this region in terms of soft and collinear functions in the framework of softcollinear e ective theory, then further refactorize the soft function as a convolution of the (u)soft and soft-collinear functions. All these functions are calculated at one-loop order. As an example, we calculate a di erential cross section for a speci c partonic channel, qq0 ! qq0, for the jet shape angularities and show that the refactorization allows us to resum the rapidity logarithms and signi cantly reduce theoretical uncertainties in the jet shape spectrum. 1 Introduction 2 Two jets with an E? veto in electron-positron annihilation 2.1 2.2 3.1 3.2 2.3 Jet function corrections for E bosons [1{12]. This is essential for expanding our understanding of quantum chromodynamics (QCD) as well as testing the standard model (SM) or searching for beyond SM physics. { 1 { In experimental studies of exclusive N -jet production, it is common to impose a veto on the out-of-jet radiation in order to control soft emissions. Additionally, due to detector limitations these vetoes are imposed within a speci c (pseudo-)rapidity region and the veto is not imposed outside this region. These constraints can induce large logarithms of the cuto parameter, e problem (e.g., the hard scale H p cut , and ratios of the veto parameter, pcTut, to other scales in the t, where t is the usual Mandelstam variable). These logarithmic enhancements could potentially ruin the e ectiveness of the ordinary perturbative expansion. In this work we propose a factorization theorem for resumming logarithms of e where cut and pcTut= within the framework of soft-collinear e ective theory (SCET) [13{16], is the factorization scale. SCET was extensively used in the past decade for factorization of observables with sensitivity to soft and collinear radiation, such as jet substructure measurements in hadronic colliders. Some other interesting applications of SCET include cross sections for event shapes in the collinear limit, jet production rates [17, 18], and identi ed hadrons within jets [19{26]. In this paper, we study rapidity cuto resummation and develop the necessary ingredients for di-jet cross sections with transverse energy, ET , and jet-veto measurements in hadronic collisions. Our results can easily be extended to zero and one-jet cross sections as well. The transverse energy is de ned as the sum of the scalar transverse momentum of all the particles that do not belong to a jet and have rapidity, , in the range j j < cut, X i2=jet ET = jpT j ( cut i by imposing the constraint ET < pcTut. Due to the nature of the observable one expects that such a measurement is sensitive to the underlying event (UE). Measurements of the UE activity have been performed by ATLAS and CMS in inclusive charged particle production [27], Drell-Yan [28{30], and exclusive dijet events [31]. The e ect of UE in transverse energy resummed distributions was studied in refs. [32, 33] for cut = 4:5 in the case of Higgs and vector-boson production using montecarlo simulation. In contrast to the work in this paper, in refs. [32, 33] the rapidity cuto was introduced only during the simulation and not in the resummed distribution. However, as will be discussed below, for the large values of rapidity cuto ( cut & 4:5) the e ect of the cuto on the resummed distribution is expected to be small. In this work we ignore e ects of multiparton int (...truncated)


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Andrew Hornig, Daekyoung Kang, Yiannis Makris, Thomas Mehen. Transverse vetoes with rapidity cutoff in SCET, Journal of High Energy Physics, 2017, pp. 43, Volume 2017, Issue 12, DOI: 10.1007/JHEP12(2017)043