Download Quantum measurements and chiral magnetic effect

Quantum measurements
and
chiral magnetic effect
V.Shevchenko
Kurchatov Institute, Moscow
based on arXiv: 1008.4977 (with V.Orlovsky); 1208.0777
Workshop on QCD in strong magnetic field
Trento, Italy, 15 November 2012
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
General purpose experiments
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.
New state of matter
Chiral symmetry of strong
interactions: pattern of restoration?
Deconfinement. P-parity violation?
Theoretical view:
SM = EW + QCD
P-invariance is 100% broken
at 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 Ttransformations.
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...
+
≠ 0
no Furry
theorem at
µ≠0
or, magnetic catalysis of CSB at finite B…
Closer look at P-parity
•
Electroweak sector
M.Giovannini, M.E.Shaposhnikov, ‘97
Hypercharge magnetic fields. At T>Tc : U(1)em → U(1)Y
•
Strong sector
T.D.Lee, G.C.Wick, ’66
:
P-odd bubbles
A.B.Migdal, ’71
:
Pion condensate
M.Dey, V.L.Eletsky, B.L.Ioffe, ’90 :
ρ-π mixing at T ≠ 0
L. McLerran, E.Mottola, M.E.Shaposhnikov, ‘91
Sphalerons and axions at high-T QCD
A seminal suggestion for QCD: chiral magnetic effect
Vilenkin, ‘80 (not in heavy ion collision context);
Kharzeev, Pisarski, Tytgat, ’98; Halperin, Zhitnitsky, ‘98;
Kharzeev, ’04; Kharzeev, McLerran, Warringa ’07;
Kharzeev, Fukushima, Warringa ’08
Energy
µR
µL
Left-handed
Right-handed
Many complementary ways
to derive (Chern-Simons,
linear response, triangle loop
etc). At effective Lagrangian

level
5 ~ 
Robust theoretical result
Possible experimental manifestations of
chiral magnetic effect ?
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. …
One general comment about chiral current
Not all currents of the form
results from the physics of massless degrees of freedom:
with the “chiral current”
The crucial point is time dependence, not masslessness
Another general comment
CME can be seen as a consequence of correlation between
the vector and (divergence of the) axial current
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.
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 abelian
field 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 …
…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
Hamiltonian with P-even potential
Measuring coordinate in a single experiment (“event”) one
gets sequence of generally nonzero values with zero mean
Device itself is P-odd!
Event-by-event P-parity violation?
In QM individual outcome has no meaning
Law of Nature, not inefficiency of our apparatus
To consider less trivial example, lets us take
for
but not invariant
under reflections of only one coordinate.
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
If the measuring device is switched off
Measurement is a story about interaction between quantum
and classical objects.
Interaction with the medium provides decoherence and
transition from quantum to classical fluctuations in the
process of continuous measurement.
Quantum fluctuations:
Classical fluctuations
all histories (field
(statistical, thermal etc):
configurations) coexist
one random position
together and simultaneously
(field configuration) at
any given time
Quantum fluctuations of magnetic field in the vacuum
do not force a freely moving charge to radiate
Measurement of the electric current fluctuations in
external magnetic field for free massless fermions.
Standard Unruh – DeWitt detector coupled to vector current:
Amplitude to click:
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
Asymmetry:
The result:
• 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
The asymmetry is small:
At large magnetic fields
B≠0
T≠0
Fluctuations enhancement along the field and
suppression perpendicular to it by the same amount
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 the
direction of gradient
of the magnetic field
Qualitative outcome of the above
analysis:
(stronger current fluctuations along
the field B than in reaction plane)
(if the asymmetry is caused by B)
Data clearly indicate
presence of both terms
ALICE, arXiv: 1207.0900
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 is given by
Maximal effective µ5 in the model:
•
•
•
•
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 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 parallel
with common wisdom about importance of (quasi)classical
degrees of freedom in heavy ion collisions.
Superfluidity → macroscopically coherent quantum phase →
non-dissipative (superconducting) current. Compare with
non-dissipative CME current flowing in decohered media.
Classical pattern for strongly interacting
many-body quantum system
Instead of conclusion…
Thank you for attention!