Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf ·...
64
Tracing the QCD pressure André Peshier w/ G Jackson University of Cape Town • – Goethe University Frankfurt • 161201 –
Transcript of Tracing the QCD pressure - uni-frankfurt.dehees/np-colloquium/ws16/talk-Peshier.pdf ·...
Tracing the QCD pressure
André Peshier w/ G Jackson
University of Cape Town
•
– Goethe University Frankfurt • 161201 –
Tracing the QCD pressure
André Peshier w/ G Jackson
University of Cape Town
•
– Goethe University Frankfurt • 161201 –
[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
[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
[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
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 7
Methods Methods
Perturbation theory
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 8
Methods Methods
Perturbation theory Lattice QCD
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 9
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
[Shuryak 1978] ⁞[Kajantie et al 2003]
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 10
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
[Shuryak 1978] ⁞[Kajantie et al 2003]
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 11
Perturbation theory CHALLENGES Perturbation theory CHALLENGES
convergence …?[Shuryak 1978] ⁞[Kajantie et al 2003]
[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
[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
[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
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 15
Lattice QCD CHALLENGES Lattice QCD CHALLENGES
[Borsanyi et al, 2012]
[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]
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 17
Lattice QCD Lattice QCD
integral method: pressure from interaction measure
[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”
[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:
[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:
[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 ...
[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 ...
[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 ...
[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
[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
[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
[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
[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
[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
[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:
[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)
[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
[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
[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 → ∞
[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 → ∞
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 36
(5|2)-model (5|2)-model
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 37
(5|2)-model (5|2)-model
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 38
(5|2)-model (5|2)-model
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 39
(5|2)-model (5|2)-model
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 40
(5|2)-model (5|2)-model
applicability range: T > 40TC
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 41
(5|2)-model (5|2)-model
applicability range: T > 40TC
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 42
(5|2)-model (5|2)-model
applicability range: T > 40TC
[email protected] • Tracing the QCD pressure • Frankfurt University, Dec 2016 43
(5|2)-model (5|2)-model
applicability range: T > 40TC
[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
[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
[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” …?
[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” …?
[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
[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
[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]
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
