tracing the qcd pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-peshier.pdf ·...
TRANSCRIPT
![Page 1: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/1.jpg)
Tracing the QCD pressure
André Peshier w/ G Jackson
University of Cape Town
•
– Goethe University Frankfurt • 161201 –
![Page 2: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/2.jpg)
Tracing the QCD pressure
André Peshier w/ G Jackson
University of Cape Town
•
– Goethe University Frankfurt • 161201 –
![Page 3: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/3.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 3
Why this talk may be relevant – or not ;) Why this talk may be relevant – or not ;)
idea relevant for many lattice-QCD calculations at T>0
understand QCD where we think it is simple
revisit first non-perturbativecoefficient
![Page 4: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/4.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 4
Why this talk may be relevant – or not ;) Why this talk may be relevant – or not ;)
here: only quenched limit of QCD (no quarks)
hard work done by others, we only interpret their results
only 1% effect … for quenched QCD
idea relevant for many lattice-QCD calculations at T>0
understand QCD where we think it is simple
revisit first non-perturbativecoefficient
![Page 5: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/5.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 5
Why this talk may be relevant – or not ;) Why this talk may be relevant – or not ;)
here: only quenched limit of QCD (no quarks)
hard work done by others, we only interpret their results
only 1% effect … for quenched QCD
idea relevant for many lattice-QCD calculations at T>0
understand QCD where we think it is simple
revisit first non-perturbativecoefficient
![Page 7: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/7.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 7
Methods Methods
Perturbation theory
![Page 8: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/8.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 8
Methods Methods
Perturbation theory Lattice QCD
![Page 9: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/9.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 9
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
[Shuryak 1978] ⁞[Kajantie et al 2003]
![Page 10: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/10.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 10
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
[Shuryak 1978] ⁞[Kajantie et al 2003]
![Page 11: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/11.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 11
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
convergence …?[Shuryak 1978] ⁞[Kajantie et al 2003]
![Page 12: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/12.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 12
Perturbation theory “diverges” Perturbation theory “diverges”
toy model: scalar “QFT” in d=0 dimensions
• “Lagrangian” → “partition fnc”
• perturbative expansion
![Page 13: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/13.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 13
Perturbation theory “diverges” Perturbation theory “diverges”
toy model: scalar “QFT” in d=0 dimensions
• “Lagrangian” → “partition fnc”
• perturbative expansion
lower order better for larger coupling
![Page 14: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/14.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 14
Perturbation theory “diverges” Perturbation theory “diverges”
toy model: scalar “QFT” in d=0 dimensions
• “Lagrangian” → “partition fnc”
• perturbative expansion
cut plane: convergence radius = 0
lower order better for larger coupling
![Page 15: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/15.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 15
Lattice QCD CHALLENGES Lattice QCD CHALLENGES
[Borsanyi et al, 2012]
![Page 16: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/16.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 16
Lattice QCD CHALLENGES Lattice QCD CHALLENGES
finite-size artefacts in particular around TC: correlations
[Borsanyi et al, 2012]
![Page 17: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/17.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 17
Lattice QCD Lattice QCD
integral method: pressure from interaction measure
![Page 18: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/18.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 18
Lattice QCD Lattice QCD
integral method: pressure from interaction measure
region around TC
“contributes most”
![Page 19: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/19.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 19
Scrutinize existing results [Borsanyi et al, 2012] Scrutinize existing results [Borsanyi et al, 2012]
compare to pQCD known
→ fit:
![Page 20: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/20.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 20
Scrutinize existing results [Borsanyi et al, 2012] Scrutinize existing results [Borsanyi et al, 2012]
compare to pQCD known
→ fit:
![Page 21: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/21.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 21
Scrutinize existing results [Borsanyi et al, 2012] Scrutinize existing results [Borsanyi et al, 2012]
compare to pQCD known
→ fit:
pQCD should be “better” at large T ...
![Page 22: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/22.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 22
Scrutinize existing results [Borsanyi et al, 2012] Scrutinize existing results [Borsanyi et al, 2012]
compare to pQCD known
→ fit:
pQCD should be “better” at large T ...
![Page 23: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/23.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 23
Scrutinize existing results [Borsanyi et al, 2012] Scrutinize existing results [Borsanyi et al, 2012]
compare to pQCD known
→ fit:
pQCD should be “better” at large T ...
![Page 24: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/24.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 24
Theory & models Theory & models
phenomena, observables
ADJUSTparams VERIFY PREDICT
theory
in practice, we always use models/approximations
validity check is crucial
in QFT
adjusting parameters = renormalization
![Page 25: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/25.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 25
Theory & models Theory & models
phenomena, observables
ADJUSTparams VERIFY PREDICT
theory
in practice, we always use models/approximations
validity check is crucial
in QFT
adjusting parameters = renormalization
![Page 26: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/26.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 26
Theory & models Theory & models
phenomena, observables
ADJUSTparams VERIFY PREDICT
theory
in practice, we always use models/approximations
validity check is crucial
in QFT
adjusting parameters = renormalization
![Page 27: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/27.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 27
Our approach Our approach
thermodynamic renormalization: match perturbative resultsto lattice data at sufficiently large “renormalization temperature”to specify model parameter(s)
use interaction measure (being the actual lattice “observable”)
check range of applicability of adjusted model by comparison with lattice data (not by vague arguments “coupling small”)
make predictions for other observables in applicability range
![Page 28: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/28.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 28
Our approach Our approach
thermodynamic renormalization: match perturbative resultsto lattice data at sufficiently large “renormalization temperature”to specify model parameter(s)
use interaction measure (being the actual lattice “observable”)
check range of applicability of adjusted model by comparison with lattice data (not by vague arguments “coupling small”)
make predictions for other observables in applicability range
![Page 29: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/29.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 29
Our approach Our approach
thermodynamic renormalization: match perturbative resultsto lattice data at sufficiently large “renormalization temperature”to specify model parameter(s)
use interaction measure (being the actual lattice “observable”)
check range of applicability of adjusted model by comparison with lattice data (not by vague arguments “coupling small”)
make predictions for other observables in applicability range
![Page 30: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/30.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 30
(n|l) models (nf=0) (n|l) models (n
f=0)
pressure (= thermodynamic potential) to order n:
running coupling to order l:
![Page 31: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/31.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 31
Running coupling Running coupling
fairly similar for l=2 and l=3 (and l=1 after rescaling)
![Page 32: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/32.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 32
(5|2)-model … how NOT to: p-scheme (5|2)-model … how NOT to: p-scheme
![Page 33: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/33.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 33
(5|2)-model … how NOT to: p-scheme (5|2)-model … how NOT to: p-scheme
![Page 34: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/34.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 34
(5|2)-model … how NOT to: p-scheme (5|2)-model … how NOT to: p-scheme
small applicability range, not to T → ∞
![Page 35: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/35.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 35
(5|2)-model … how NOT to: p-scheme (5|2)-model … how NOT to: p-scheme
systematic discrepancy forinteraction measure asactual lattice “observable”
small applicability range, not to T → ∞
![Page 36: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/36.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 36
(5|2)-model (5|2)-model
![Page 37: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/37.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 37
(5|2)-model (5|2)-model
![Page 38: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/38.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 38
(5|2)-model (5|2)-model
![Page 39: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/39.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 39
(5|2)-model (5|2)-model
![Page 40: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/40.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 40
(5|2)-model (5|2)-model
applicability range: T > 40TC
![Page 41: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/41.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 41
(5|2)-model (5|2)-model
applicability range: T > 40TC
![Page 42: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/42.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 42
(5|2)-model (5|2)-model
applicability range: T > 40TC
![Page 43: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/43.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 43
(5|2)-model (5|2)-model
applicability range: T > 40TC
![Page 44: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/44.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 44
(5|2)-model (5|2)-model
applicability range: T > 40TC
in applicability range:
discrepancy = constant shift
![Page 45: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/45.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 45
(5|2)-model (5|2)-model
applicability range: T > 40TC
in applicability range:
discrepancy = constant shift
![Page 46: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/46.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 46
(5|2) model (5|2) model
breakdown at T* ~ 40Tc because “coupling too large” …?
![Page 47: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/47.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 47
(5|2) model (5|2) model
breakdown at T* ~ 40Tc because “coupling too large” …?
![Page 48: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/48.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 48
(5|2) model (5|2) model
breakdown at T* ~ 40Tc because “coupling too large” …?
similar properties asasymptotic series
![Page 49: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/49.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 49
(6|3) model (6|3) model
more difficult 2 parameters
expect smaller
applicability range
![Page 50: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/50.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 50
(6|3) model (6|3) model
more difficult 2 parameters
expect smaller
applicability range
fit over interval [Tf, Tmax]
![Page 51: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/51.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 51
(6|3) model (6|3) model
more difficult 2 parameters
expect smaller
applicability range
fit over interval [Tf, Tmax]
applicability range: T > 300TC
![Page 53: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/53.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 53
Results Results
matching interaction measure at large T
↓
“re-calibration” of pressure at T > 4TC
slower approach to free limit
![Page 54: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/54.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 54
Results Results
matching interaction measure at large T
↓
“re-calibration” of pressure at T > 4TC
slower approach to free limit
non-perturbative coefficient
![Page 55: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/55.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 55
Results Results
matching interaction measure at large T
↓
“re-calibration” of pressure at T > 4TC
slower approach to free limit
non-perturbative coefficient
![Page 57: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/57.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 57
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 58: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/58.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 58
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 59: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/59.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 59
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 60: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/60.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 60
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 61: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/61.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 61
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 62: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/62.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 62
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 63: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/63.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 63
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case
![Page 64: Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf · Andre.Peshier@uct.ac.za • Tracing the QCD pressure • Frankfurt University, Dec 2016 27 Our](https://reader035.vdocuments.net/reader035/viewer/2022062415/5fda89c9d5b4d04198436a9a/html5/thumbnails/64.jpg)
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 64
Resumé [arXiv:1610.08530] Resumé [arXiv:1610.08530]
● new approach to deal with lattice artefacts (which have physics reasons):combine integral method with perturbative QCD
● 1% modification of pressure, slower approach to asymptotic freedom ~ relevant to benchmark improved analytical methods
● impoved value of 1st nonperturbative coefficient
● outlook: phenomenological implications for physical case