TY - JOUR

T1 - Fragmentation of a jet with small radius

AU - Dai, Lin

AU - Kim, Chul

AU - Leibovich, Adam K.

N1 - Funding Information:
C.K. was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, Information & Communication Technology, and Future Planning (Grant No. NRF-2014R1A2A1A11052687). A.L. and L.D. were supported in part by NSF Grant No. PHY-1519175.
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/12/21

Y1 - 2016/12/21

N2 - In this paper, we consider the fragmentation of a parton into a jet with small jet radius R. Perturbatively, logarithms of R can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we introduce the fragmentation function to a jet (FFJ), which describes the fragmentation of a parton into a jet. We discuss how these objects are related to the standard jet functions. Calculating the FFJ to next-to-leading order, we show that these objects satisfy the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, with a natural scale that depends upon R. By using the standard renormalization group evolution, we can therefore resum logarithms of R. We further use the soft-collinear effective theory to prove a factorization theorem where the FFJs naturally appear, for the fragmentation of a hadron within a jet with small R. Finally, we also show how this formalism can be used to resum the ratio of jet radii for a subjet to be emitted from within a fat jet.

AB - In this paper, we consider the fragmentation of a parton into a jet with small jet radius R. Perturbatively, logarithms of R can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we introduce the fragmentation function to a jet (FFJ), which describes the fragmentation of a parton into a jet. We discuss how these objects are related to the standard jet functions. Calculating the FFJ to next-to-leading order, we show that these objects satisfy the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, with a natural scale that depends upon R. By using the standard renormalization group evolution, we can therefore resum logarithms of R. We further use the soft-collinear effective theory to prove a factorization theorem where the FFJs naturally appear, for the fragmentation of a hadron within a jet with small R. Finally, we also show how this formalism can be used to resum the ratio of jet radii for a subjet to be emitted from within a fat jet.

UR - http://www.scopus.com/inward/record.url?scp=85012005931&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.94.114023

DO - 10.1103/PhysRevD.94.114023

M3 - Article

AN - SCOPUS:85012005931

SN - 1550-7998

VL - 94

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 11

M1 - 114023

ER -