Dijet Event Shapes at the LHC in SCET Yiannis Makris Duke - - PowerPoint PPT Presentation

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Dijet Event Shapes at the LHC in SCET Yiannis Makris Duke - - PowerPoint PPT Presentation

Aug 12, 2023 182 likes •677 views

Dijet Event Shapes at the LHC in SCET Yiannis Makris Duke University In collaboration with Andrew Hornig (LANL) and Thomas Mehen (Duke U.) [arXiv: 1601.01319] Jets and Heavy Flavor, Jan. 11-13 2016, Santa Fe, NM Outline Problem Setup -

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Dijet Event Shapes at the LHC in SCET

In collaboration with Andrew Hornig (LANL) and Thomas Mehen (Duke U.) Yiannis Makris Duke University Jets and Heavy Flavor, Jan. 11-13 2016, Santa Fe, NM [arXiv: 1601.01319]

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Outline

Problem Setup - Boost Invariant Jet Shapes The Factorization Theorem in SCET (Jet, Hard, Beam and Soft Functions) Scales and R.G. Evolution - Theoretical Uncertainties – Plots Summary - Applications

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Problem Setup

Analytic calculation of diff. Cross sections for Dijet events at proton-proton collisions** Proton Beam Proton Beam Jet 2 (E2, y2 ,τ2)

**Extension of the work on e+e- to N jets by Ellis, Vermilion, Walsh, Hornig and Lee, [arXiv: 1001.0014]

Jet 1 (E1, y1, τ1) Improved P.T. Resumming logarithms at NLL’ accuracy Soft out-of-jet radiation

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Angularities

Rotational invariant Boost invariant

Almeida et al. [arXiv: 0807.0234] Berger, Kucs, and Sterman [hep-ph/ 0303051]

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Angularities

Rotational invariant Boost invariant

Almeida et al. [arXiv: 0807.0234] Berger, Kucs, and Sterman [hep-ph/ 0303051]

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Angularities

Rotational invariant Boost invariant

Almeida et al. [arXiv: 0807.0234] Berger, Kucs, and Sterman [hep-ph/ 0303051]

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The Factorization Theorem in SCET

H S J J B B

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The Factorization Theorem in SCET

Hard Function H S J J B B

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The Factorization Theorem in SCET

Hard Function Soft Function H S J J B B

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The Factorization Theorem in SCET

Hard Function Soft Function Jet Functions H S J J B B

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The Factorization Theorem in SCET

Beam Functions Hard Function Soft Function Jet Functions H S J J B B

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Jet Functions

Quark Jet Function Similarly for Gloun Jets Ellis, Vermilion, Walsh, Hornig and Lee, [arXiv: 1001.0014]

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Hard Function

Wilson Coefficients Kelley and Schwartz [arXiv: 1008.2759]

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Hard Function

Wilson Coefficients Kelley and Schwartz [arXiv: 1008.2759]

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Hard Function

Wilson Coefficients Kelley and Schwartz [arXiv: 1008.2759]

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Beam Function (“Unmeasured”)

Ritzmann and Waalewijn [arXiv:1407.3272] Stewart, Tackmann and Waalewijn [arXiv:0910.0467]

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Beam Function (“Unmeasured”)

Short Distance Matching Coefficients. Procura and Waalewijn, [arXiv: 1111.6605]

Ritzmann and Waalewijn [arXiv:1407.3272] Stewart, Tackmann and Waalewijn [arXiv:0910.0467]

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Beam Function (“Unmeasured”)

Short Distance Matching Coefficients. Parton Distribution Functions (PDF) Procura and Waalewijn, [arXiv: 1111.6605]

Ritzmann and Waalewijn [arXiv:1407.3272] Stewart, Tackmann and Waalewijn [arXiv:0910.0467]

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Beam Function (“Unmeasured”)

Short Distance Matching Coefficients. Parton Distribution Functions (PDF) Procura and Waalewijn, [arXiv: 1111.6605]

Ritzmann and Waalewijn [arXiv:1407.3272] Stewart, Tackmann and Waalewijn [arXiv:0910.0467]

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Soft Function

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Soft Function

Time ordered product

  • f Wilson lines.

Leading Order (LO) contribution Next to Leading Order (NLO) contribution outside Jets Next to Leading Order (NLO) contribution inside Jets

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2-measured 0-unmeasured Jets

Next to Leading Order Form of the Soft Function

1-measured 1-unmeasured Jets 0-measured 2-unmeasured Jets

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Proton Beam Proton Beam Jet 2 (E2, y2 ,τ2) Jet 1 (E1, y1, τ1) Soft out-of-jet radiation

Phase-Space of Integration

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Proton Beam Proton Beam Jet 2 (E2, y2 ,τ2) Jet 1 (E1, y1, τ1) Soft out-of-jet radiation

Phase-Space of Integration

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Unmeasured Evolution

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Unmeasured Evolution

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Unmeasured Evolution

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Unmeasured Evolution

Necessary for the cancellation of μ dependence in the cross section

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Soft-Collinear Refactorization

global-soft scale soft-collinear scale Chien, Hornig, and Lee, [arXiv:1509.04287]

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Scales and R.G. Evolution

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Scales and R.G. Evolution

Appears only in sc- Refactorization

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Theoretical Uncertainties

Variation of the characteristic scales Hard Soft (Unmeasured) Beam Jet (Measured) Soft (Measured)

± 50 % Profile Functions

Ligeti, Stewart and Tackmann [arXiv: 0807.1926]

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Plots

Partonic Channel: qq’ qq’ τa

1 = τa 2 = τa

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Plots - Variation of cone size R

Without S-C Refactorization With S-C Refactorization

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Plots - Variation of a

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Plots - Variation of pT

cut

Increase of pT

cut corresponds to increase of normalization

Peak location and shape independent of pT

cut

Non-Global-Logarithms : not included

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Summary

Establish framework for calculation of dijet events in proton-proton collisions with a veto on out-of-jet transverse momentum radiation and rapidity constrains Calculate differential cross section at NLL’ accuracy Apply s-c refactorization for improved accuracy Use profile functions for measured scale variation

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Future Work

Apply to different partonic channels and compute physically

  • bservable cross section

NNLL calculation Study other jet substructure observables Exclusive cross sections for heavy meson and quarkonium production (In collaboration with Bain, Dai, Hornig, Leibovich, Mehen) Compare to Monte Carlo simulations and experimental data

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Thank you!

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Scales and R.G. Evolution (2/3)

Unmeasured Measured

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Scales and R.G. Evolution (3/3)

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Profile Functions

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Profile Functions (2/2)

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Soft Function (6/6)

Without Refactorization With Refactorization

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Results (1/2)

Soft function after RG Evolution Without s-c Refactorization

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Results (2/2)

With s-c Refactorization

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Applications in heavy meson and quarkonium production

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