quantum measurements and chiral magnetic effect v.shevchenko kurchatov institute, moscow workshop on...
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Quantum measurements and
chiral magnetic effect
V.Shevchenko
Kurchatov Institute, Moscow
Workshop on QCD in strong magnetic fieldTrento, Italy, 15 November 2012
based on arXiv: 1008.4977 (with V.Orlovsky); 1208.0777
Vacuum of any QFT (and the SM in particular) is
often described as a special (relativistic etc) medium
There are two main approaches to study properties of this (and actually of any) media:
• Send test particles and look how they move and interact• Put external conditions and study response
Of particular interest is a question about the fate of symmetries
under this or that choice of external conditions
Experimental view: LHC as a tester of symmetries
Electroweak gauge symmetry breaking pattern: Higgs boson and/or New Physics?Space-time symmetries: extra dimensions, black holes?Supersymmetry: particles – superpartners? Dark matter?
Enigma of flavor
CP-violation: new sources?Baryon asymmetry.Indirect search of superpartners.
Chiral symmetry of strong interactions: pattern of restoration? Deconfinement. P-parity violation?
New state of matter
General purpose experiments
Theoretical view:
SM = EW + QCD
P-invariance is 100% brokenat Lagrangian level (lefts are doublets, rights are singlets).
CP-invariance (and hence T) gets broken by CKM mechanism (complex phase)
Without θ-term QCD Lagrangian is invariant under P-, C- and T-transformations.
Moreover, vacuum expectation value of any local P-odd observable has to vanish in vector-like theories such as QCD (C.Vafa, E.Witten, ’84).
There can however be surprises at finite T/B/µ/..
For example, C-invariance is intact at finite temperature, but gets broken at finite density...
+ ≠ 0no Furry
theorem atµ ≠ 0
or, magnetic catalysis of CSB at finite B…
A.B.Migdal, ’71 :
M.Giovannini, M.E.Shaposhnikov, ‘97
• Electroweak sector
• Strong sector
Pion condensate
T.D.Lee, G.C.Wick, ’66 : P-odd bubbles
M.Dey, V.L.Eletsky, B.L.Ioffe, ’90 : ρ-π mixing at T ≠ 0
L. McLerran, E.Mottola, M.E.Shaposhnikov, ‘91
Hypercharge magnetic fields. At T>Tc : U(1)em → U(1)Y
Sphalerons and axions at high-T QCD
Closer look at P-parity
A seminal suggestion for QCD: chiral magnetic effectVilenkin, ‘80 (not in heavy ion collision context);Kharzeev, Pisarski, Tytgat, ’98; Halperin, Zhitnitsky, ‘98;Kharzeev, ’04; Kharzeev, McLerran, Warringa ’07;Kharzeev, Fukushima, Warringa ’08
Possible experimental manifestations of chiral magnetic effect ?
µR
µL
Energy
Right-handedLeft-handed
Many complementary ways to derive (Chern-Simons,linear response, triangle loopetc). At effective Lagrangian level
Robust theoretical result
~5
Questions worth to explore:(the list is by definition subjective and incomplete)
1. How to proceed in a reliable way from nice qualitative picture of CME to quantitative predictions for charge particle correlations measured in experiments?
2. How to disentangle the genuine nonabelian physics from just dynamics of free massless fermions in magnetic field?
3. How is the fact of quantum, anomalous and microscopic current non-conservation encoded in equations for macroscopic, effective currents?
4. What is quantum dynamics behind µ5 ?5. …
with the “chiral current”
The crucial point is time dependence, not masslessness
One general comment about chiral current
Not all currents of the form
results from the physics of massless degrees of freedom:
CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current
Another general comment
vanishing in the vacuum.
Another general comment CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current
vanishing in the vacuum. Not the case if external abelianfield is applied:
and the coefficient is fixed by triangle (abelian) anomaly.
The correlator is the same regardless the physics behind quantum fluctuations of the currents.
Far from being intuitively clear …
Another general comment CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current
…and one more comment It could be interesting to look on the lattice at nonlocal“order parameters” like
vanishing without external magnetic field. With nonzero field one would expect (for free fermions)
where there are no higher powers of magnetic field.
(Non)renormalization, temperature dependence etc.
Measurement can induce symmetry violation
Event-by-event P-parity violation?
In QM individual outcome has no meaning
Hamiltonian with P-even potential
Measuring coordinate in a single experiment (“event”) onegets sequence of generally nonzero values with zero mean
Law of Nature, not inefficiency of our apparatus
Device itself is P-odd!
If one is monitoring P-odd observable, e.g.
where the corridor width is given by
the result for another (correlated) P-odd observable is
To consider less trivial example, lets us take for but not invariant under reflections of only one coordinate.
If the measuring device is switched off
Measurement is a story about interaction between quantumand classical objects.
Quantum fluctuations:all histories (fieldconfigurations) coexisttogether and simultaneously
Classical fluctuations(statistical, thermal etc):one random position (field configuration) at any given time
Interaction with the medium provides decoherence andtransition from quantum to classical fluctuations in the process of continuous measurement.
Quantum fluctuations of magnetic field in the vacuum do not force a freely moving charge to radiate
Standard Unruh – DeWitt detector coupled to vector current:
Amplitude to click:
Measurement of the electric current fluctuations in external magnetic field for free massless fermions.
Response function:
Usually one is interested in detector excitation rate in unit time. For infinite observation time range it is determined by the power spectrum of the corresponding Wightman function:
where
The detector is supposed to be at rest. Explicitly one gets
Usually one is interested in detector excitation rate in unit time. For infinite observation time range it is determined by the power spectrum of the corresponding Wightman function:
where
The detector is supposed to be at rest. Explicitly one gets
The result:
Asymmetry:
• positive, i.e. detector measuring currents along the field clicks more often than the one in perpendicular direction• caused by the same term in the Green’s function which is responsible for triangle anomaly• no higher orders in magnetic field, the asymmetry is quadratic in В for whatever field, weak or strong • inversion of statistics from FD for elementary excitations to BE for the observable being measured
T≠0
B≠0
The asymmetry is small:
Fluctuations enhancement along the field and suppression perpendicular to it by the same amount
At large magnetic fields
Same physics in the language of energy-momentum tensor:
B = 0
Strong magnetic field:
If the magnetic field is strong but slowly varied:
Magnetic Arkhimedes law
B≠0
T≠0
Buoyancy force in thedirection of gradientof the magnetic field
ALICE, arXiv: 1207.0900
Qualitative outcome of the aboveanalysis:
Data clearly indicate presence of both terms
(stronger current fluctuations alongthe field B than in reaction plane)
(if the asymmetry is caused by B)
Measurement in the language of decoherence functionals and filter functions
one can define distribution amplitude for the vector current and some P-odd quantity
CTP functional
Mean field current
In Gaussian approximation
Fluctuations are correlated due to
For the model Gaussian Ansatz
• the current flows only inside decoherence volume• it is odd in κ and linear in B• it has a maximum value (as a function of κ)• subtle interplay of abelian and nonabelian anomalies
the current is given by
Maximal effective µ5 in the model:
The filter field κ describes classicalization of some P-parity odd degrees of freedom in the problem.
It is this classicalization that leads to electric current.
Classicalization is caused by decoherence: clear parallelwith common wisdom about importance of (quasi)classical degrees of freedom in heavy ion collisions.
Superfluidity → macroscopically coherent quantum phase →non-dissipative (superconducting) current. Compare withnon-dissipative CME current flowing in decohered media.
Classical pattern for strongly interacting many-body quantum system
Instead of conclusion…
Thank you for attention!