Transcript Slide 1

Does Nature respect (gauge)
Symmetry?
DISCOVERY and beyond:
What’s next in Higgs physics
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REGINA DEMINA (UNIVERSITY OF ROCHESTER)
PHASE OF THE WAVE FUNCTION
• First lecture on quantum mechanics – introduce wave
function, but only define (Wave function Y)2 dV=probability
to find particle in volume dV.
• While probability is a real number, wave function is a
complex number. It has a phase.
• When two matter waves meet we add wave functions, not
probabilities! Interference can be observed phase is
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important!
GAUGE INVARIANCE = NONOBSERVABILITY OF THE PHASE
For some reason Nature goes to great length to hide the phase of
the wave function from us Preserve gauge invariance
• Gauge invariance - Fundamental symmetry of nature, so
Langrangian must be invariant under gauge (phase)
transformation:
y (x) ® eiay (x)
• According to Noether’s theorem, symmetry (==nonobservability) leads to conserving quantity
• If a is the same everywhere – global gauge invariance (leads
to e.g. baryon number conservation)
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LOCAL GAUGE INVARIANCE
• Local gauge invariance:
a(x) –– phase depends
on 4 dimensional spacetime coordinate x
• Demanding local gauge
invariance leads to
interactions via gauge
fields
• E.g. U(1) gauge group,
leads to EM
interactions and
charge conservation
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ELECTRO-WEAK INTERACTIONS
Transformation
group
Conserved
quantity
Gauge field
Group properties
Fermion masses
U(1) – QED
SU(2)L –Weak
Q (scalar) electric
charge
EM interaction
T (doublet) weak isospin
Photons M(g)=0
W-boson M(W)=80GeV
Z-boson M(Z)=91 GeV
Abelian (commutative)
group – photons do not
interact with each other
added by hand without
breaking gauge
invariance
Weak interactions
Non-Abelian group – W
and Z do interact with
each other
cannot be added by
hand without breaking
gauge invariance 5
ELECTROWEAK SYMMETRY BREAKING
F. ENGLERT AND R. BROUT, PHYS. REV. LETT. 13 (1964) 321
P.W. HIGGS,, PHYS. REV. LETT. 13(1964) 508,
G. S. GURALNIK, C. R. HAGEN, AND T.W. B. KIBBLE, PHYS. REV. LETT. 13 (1964) 585
Problem #1: W and Z boson masses violate SU(2)L gauge
invariance
Solution: Postulate #1
There exists a scalar complex field doublet f
•Mexican hat (bottle’s bottom) potential
V (f )   (v f f  (f f ) )
2 *
*
2
•The Universe chose to roll into a minimum at fmin
•Non-zero v generates masses for W and Z-bosons
 v/ 2
• Absorb 3/ 4 degrees of freedom
• Given W mass (muon decay rate) v is constrained to be 246 GeV
• Predict ratio between W and Z masses - verified in experiment
•One remaining d.o.f. – H (aka Higgs) boson (s=0, P=+)
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H BOSON
• Expand f near its minimumf
 [v  h( x)] / 2 v constrained by MW
- free parameter
• Lagrangian
1 m
L  [(  igAm )(v  h)( m  igAm )(v  h)] 
2
1 2
1
1 m
2
4
 m (v  h)   (v  h)  F Fm
2
4
4
•
•
•
•
(g2v2/2)AmAm – mass term for gauge bosons
v2h2 – mass term for the scalar boson itself
h3,h4 –self interaction terms
hAA, h2AA – interaction with gauge fields terms
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Higgs mass is not
predicted
This is what we
were after
Byproducts
Strength of these
terms is predicted
given  (MH)
HIGGS MECHANISM OF FERMION
MASS GENERATION
Problem #2: fermion masses violate SU(2)L gauge invariance
Solution: Postulate #2
• Yukawa-like couplings to fermions – generate fermion
masses in a gauge invariant way through interaction with
Higgs field
• This mechanism does not reduce the number of free
parameters in the model, masses are traded for the
strength of interaction with the Higgs field (gf)
1
mf 
gfv
2
1
g f v( f L f R  f R f L )
2
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TESTABLE PREDICTIONS
• Existence of a true scalar boson (s=0, P=+1)
• Find the resonance
• measure its spin, parity
• Couplings to gauge bosons
• Probing custodial symmetry (between W and Z-bosons) – one of best
motivated symmetries given that the new state is responsible for breaking
the EW symmetry
• Couplings to fermions
• New state can be responsible for EW symmetry breaking but NOT for
generation of fermionic masses – fermiophobic Higgs
• Self coupling
• h3,h4 –self interaction terms arise from the same assumption as
couplings to gauge fields. Interesting to test their absolute and
relative strength
• Require large statistics to observe
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HIGGS PRODUCTION @ LHC
Gluon Fusion
- dominant process
Vector Boson Fusion
20% of gg @ 120GeV
Associated Production
W or Z (1-10% of gg)
Associated Production
ttbar or bbbar (1-5% of gg)
4 production mechanism
key to measure H-boson parameters
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LHC AT CERN
Alps
7/17/2015
• Large Hadron Collider located in Europe (France and
Switzerland)
• Circumference 27 km;
• 7TeV(2010-2011)8TeV (now)14 Tev(2014)
• LHC has uncovered the mechanism behind mass - 2012
• Discovery of a particle that might be known as Higgs boson
Lecture I
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APPARATUS: LHC
7/17/2015
Lecture I
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APPARATUS: CMS
7/17/2015
Lecture I
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4 JULY, 2012
F. Englert, P.W. Higgs, C. R. Hagen, G. S. Guralnik
J. Incandela
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HIGGS TO TWO PHOTONS
CMS COLLABORATION: PHYS. LETT. B 716 (2012) 30-61
ATLAS COLLABORATION: PHYS. LETT. B 716 (2012) 1-29
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DI-PHOTON SPECTRUM
7/17/2015
Lecture XII
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HZZ*4L
7/17/2015
Lecture XII
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HZZ*4L
7/17/2015
Lecture XII
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COMBINED P-VALUE
7/17/2015
Lecture XII
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PROJECTED SIGNAL
Current status: signal observed in ZZ, gg and WW modes
There is some evidence (Tevatron) for bbbar coupling
Projected signal by the end of
the run
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OBSERVABLES
• the framework to probe the Higgs couplings issued by the “low
mass” LHCXS WG and endorsed by both CMS and ATLAS:
arXiv:1209.0040
• Overall signal strength m
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DISENTANGLING COUPLING FROM
PRODUCTION AND DECAY
VBF production – sensitive to vector boson couplings
ggH – sensitive to quark loops;
Hgg – fermion+W loop
HWW, ZZ – vector boson coupling at decay
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DISENTANGLING COUPLING FROM
PRODUCTION AND DECAY
kVkF - scale vector and fermion
coupling
Kg(kV, kF) – coupling to g, depends on
W and fermion loops (Hgg)
ggH – sensitive to quark loops;
HWW, ZZ – vector boson coupling
No direct Higgs to fermion couplings observed
yet, limits on Htt, Hbb
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CURRENT STATUS: TESTING
CUSTODIAL SYMMETRY
• WZ: ratio of scale factors for W and Z
• The measurement of the HWW/HZZ ratio is
mostly driven by the ratio of the Higgs couplings to
WW and ZZ, which is protected by custodial
symmetry
• Combination of “inclusive” WW and ZZ yields gives
Rww/zz=0.9+1.1-0.6
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MORE TESTS TO COME
• lq: ratio of scale factors for leptons and quarks
• kV left floating in the fit
• du: ratio of scale factors for down and up type of fermions
• kV left floating in the fit
• kg- kg: contour of loop scale factors
• BRInv,Undet: same as kg- kg but with a scale factor in the total
width accounting for invisible or undetectable decay modes
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SPIN MEASUREMENT
ARXIV:1208.4018
• Xgg excludes s=1 option
(Landau-1948, Yang -1950)
• XZZ4l system is described by
5 non-trivial angles
Different scenarios result in distinct
angular distributions
2+m
02+h
0+m
0+m
2+h
2+m
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COMPARING SPIN-PARITY
HYPOTHESES
• Matrix Element Likelihood Analysis (MELA) allows for
optimal separation of different sP hypotheses
XZZ4l
0+(SM) vs 0- hypothesis
Expected significance of hypotheses
separation based on 35 fb-1
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MELA – was already used to separate
signal from bg
SM H(125 GeV)
Bg:ZZ
Data w.r.t 126 GeV Higgs
Expectation
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SUMMARY
• Observed narrow resonance at 125.3+-0.6 GeV couples
to weak gauge bosons, hence it is potentially responsible
for the EW symmetry breaking
• To verify this hypothesis it is necessary to show that its
properties are consistent with the predictions:
• Spin=0, Parity =+
• An angular based analysis is developed that has a potential to
exclude pseudoscalar and tensor hypotheses based on 35 fb-1
• The framework is developed to independently measure
• Vector and fermion couplings
• W and Z boson couplings
• Lepton and quark couplings
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