Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory

Transcription

1 Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory Raymond Goerke Work completed with Simon Freedman: arxiv: THEP Seminar Feb 2015

2 Outline Punchline: We calculated the anomalous dimensions of subleading dijet operators in Soft- Collinear Effective Theory a step towards improving theoretical precision in the thrust distribution, allowing for an improved determination of The Thrust Observable Factorization/Resummation in General Soft-Collinear Effective Theory (SCET) Applying SCET to Thrust Results

3 Thrust Thrust,, parametrizes the geometry of the energy-momentum flow of an event:

4 Thrust By fitting thrust distributions to LEP data, we can make precise determinations of PRD 83, (2011)

5 Thrust : Centre of mass energy peak : Non-perturbative effects important tail : Perturbation theory + resummation far-tail : Perturbation theory

6 Thrust : Centre of mass energy

7 Factorization

8 Factorization Nonperturbative Perturbative

9 Factorization Factorization Theorem: (inclusive) Nonperturbative Perturbative

10 Factorization An event with thrust Typical relative momentum of particles within a jet:

11 Resummation

12 Effective Field Theory Consider a toy theory with two scales Construct a low-energy effective theory that does not depend on, but get's the IR physics right. Full Effective Match

13 Effective Field Theory Full Effective Match

14 Effective Field Theory By solving the renormalization group equation for :

15 Soft-Collinear Effective Theory Relevant scales that must be factorized in order to sum all large logs for thrust: Typical pattern of scales for observables with double-logs. The correct EFT is Soft-Collinear Effective Theory

16 Soft-Collinear Effective Theory Consider the thrust distribution for collisions:

17 Soft-Collinear Effective Theory Consider a generic feynman diagram: Need to reproduce IR divergences: In massless gauge theory: (soft) ( -collinear) ( -collinear)

18 Soft-Collinear Effective Theory Physical picture:

19 Soft-Collinear Effective Theory Consider a generic feynman diagram: (soft) ( -collinear) ( -collinear)

20 Soft-Collinear Effective Theory Pick an assignment for each propagator as soft, -collinear, or -collinear, sum over graphs:

21 Soft-Collinear Effective Theory Define SCET so that SCET matrix elements equal QCD matrix elements expanded in the soft and collinear limits

22 Soft-Collinear Effective Theory Freedman, Luke (2012)

23 Soft-Collinear Effective Theory

24 Subleading SCET

25 Subleading SCET

26 Subleading SCET New currents that did not appear at leading order:

27 SCET for Thrust Returning to thrust, note: Generally in SCET: For thrust:

28 SCET for Thrust Thrust factorizes in SCET. At leading-order:

29 SCET for Thrust Each matching QCD SCET Anomalous dimension

30 SCET for Thrust To include to subleading operators: Each matching QCD SCET Anomalous dimension Freedman (2013)

31 SCET for Thrust To sum subleading logs we need: This work 1) Anomalous dimensions of the currents 2) Anomalous dimensions of the currents 3) Anomalous dimensions of

32 The Calculation Graphs needed to renormalize the current: There are four independent anomalous dimensions, each requiring a similar number of graphs to compute.

33 The Calculation Non-trivial mixing:

34 Results

35 Conclusion Punchline: We calculated the anomalous dimensions of subleading dijet operators in Soft- Collinear Effective Theory a step towards improving theoretical precision in the thrust distribution, allowing for an improved determination of Still need renormalization. and Renormalization group equations must be solved numerically

36 Bonus Inclusive Drell-Yan: Collins, Soper, Sterman (1985) Sensitive only to Sensitive to low energy, non-perturbative physics

37 Bonus Introducing more scales requires further factorization: Threshold Drell-Yan: new scale

38 Bonus Threshold Drell-Yan: Collins, Soper, Sterman (1987) Sensitive only to Sensitive only to

39 Bonus

40 Factorization Factorization Theorem: (inclusive)

41 EFT's and Factorization Renormalizing sums subleading logs.

42 Soft-Collinear Effective Theory