Standard Model precision measurements Misure di precisione del modello standard
Lesson 2: Asymmetries at Z pole
Stefano Lacaprara
INFN Padova
Dottorato di ricerca in fisica
Universit` a di Padova, Dipartimento di Fisica e Astronomia
Outline
1 Introduction
2 Z-pole observables
3 Asymmetries
4 W mass and width
5 Top mass
6 Higgs mass and features
7 Global ElectroWeak fit
Outline
1 Introduction
2 Z-pole observables Standard Model Z lineshape
3 Asymmetries
4 W mass and width
5 Top mass
Outline
1 Introduction
2 Z-pole observables
3 Asymmetries
Forward-Backward Asymmetries Left-Right Asymmetries
Tau polarization Results
4 W mass and width
5 Top mass
6
Stefano Lacaprara (INFN Padova)Higgs mass and features
SM precision measurements Padova 07/03/2019 4/54Input to global EWK fit
(in parenthesis the order followed in these lessons)
2) (MZ (5) αhad
∆ mt
b R0 c R0 0,b AFB
0,c AFB
Ab Ac (Tevt.) lept Θeff sin2
) FB lept(Q eff 2Θ sin
(SLD) Al
(LEP) Al
0,l AFB
lep R0
0 σhad ΓZ MZ ΓW MW MH
Global EW fit Indirect determination Measurement GfitterSM
Mar ’18
Higgs mass (5)
I
LHC
W mass and width (3)
I
LEP2, Tevatron, LHC Z-pole observables (1,2)
I
LEP1, SLD
I
M Z , Γ Z
Iσ 0 had
I
sin 2 θ lept eff
I
Asymmetries
I
BR R lep,b,c 0 = Γ had /Γ ``,b ¯ b,c ¯ c
Top mass (4)
Input to global EWK fit
(in parenthesis the order followed in these lessons)
Higgs mass (5)
I
LHC
W mass and width (3)
I
LEP2, Tevatron, LHC Z-pole observables (1,2)
I
LEP1, SLD
I
M Z , Γ Z
Iσ 0 had
I
sin 2 θ lept eff
I
Asymmetries
I
BR R lep,b,c 0 = Γ had /Γ ``,b ¯ b,c ¯ c
Top mass (4)
I
Tevatron, LHC other:
I
α s (M Z 2 ), ∆α had (M Z 2 )
Forward-Backward Asymmetries
Asymmetries [1]
The key features of the SM x-section for ee → f ¯ f production can be fully exploited by looking at the differential x-section d cos θ d σ as well as to effects related to the helicities of the fermions in the initial or final state.
Both are related to the parity violation present in the neutral current of the SM lagrangian.
Possible asymmetries
d σ
d cos θ : Forward-backward asymmetry A FB (LEP);
Helicity state: Left-Right asymmetry A LR (initial state: SLD, final state:LEP [τ ]);
Both: Left-Right Forward-Backward asymmetry A LRFB SLD;
We can differentiate the vector- and axial-vector coupling of the Z, including the measurement
of sin θ eff W
From Z-lineshape we got [2]
σ(s) = 12π Γ
eM Γ
had2 Zs
(s−M
z2)
2+M
Z2Γ
2Z: At peak: σ 0 = 12π M
2 ZΓ
eΓ
hadΓ
ZΓ had = Σ q6=t Γ q ¯ q , and Γ Z = Γ ee + Γ µµ + Γ τ τ + Γ had + Γ inv
So we measure the SM prediction for the total coupling of Z to fermions, but not the actual, inner form of the V-A strucutre
−i g cos θ W γ µ
1 2
c V f − c A f γ 5
, c V f = T 3 − 2Q sin 2 θ W ) , c A f = T 3
fermion Q f T 3 c A f c V f
(ν e , ν µ , ν τ ) L 0 1/2 1/2 1/2 = 0.50 (e, µ, τ ) L -1 -1/2 -1/2 −1/2 + 2 sin 2 θ W = 0.03
(e, µ, τ ) R -1 0 0 +2 sin 2 θ W = 0.47
(u, c, t) L 2/3 1/2 1/2 1/2 + 4/3 sin 2 θ W = 0.19
At √
s = M Z the dominating term is the Z exchange.
Absorbing QED correction into effective coupling, and ignoring fermion masses, QCD ISR/FSR, . . .
d σ
d cos θ = 16πQ f (N c ) 2s |χ(s)| 2
(g Ve 2 + g Ae 2 )(g Vf 2 + g Af 2 )(1 + cos 2 θ) + 8g Ve g Ae g Vf g Af cos θ
Where lineshape is
χ(s) = G F M W 2 8π √
2
s
s − M Z 2 + isΓ Z /M Z g Vf (g Af ) are effective vector (axial) coupling of Z to fermion f . At tree level, in S:
c Af = (T (3) ), c Vf = (T (3) − 2Q f sin 2 θ W )
A FB definition
Definition
Forward-Backward asymmetry as
A FB = σ F − σ B
σ F + σ B = N F − N B N F + N B
where F (B) is the direction of the final state fermion (e − , µ − , τ − , b, c) with respect to the incoming e − beam
σ F (B) = Z 1(0)
0(−1)
d σ
d cos θ d cos θ
Modulo asymmetries in the detector acceptances and efficiencies,
d σ
d cos θ = 16πQ
f(N
c) 2s |χ(s)|
2(g
Ve2+ g
Ae2)(g
Vf2+ g
Af2)(1 + cos
2θ) + 8g
Veg
Aeg
Vfg
Afcos θ
From
d cos θd σ, and integrating over the angles σ
F− σ
B∝ R
10
cos θd cos θ − R
0−1
cos θd cos θ = 1 σ
F+ σ
B∝ R
1−1
(1 + cos
2θ)d cos θ = 8/3
A
fFB= 8g
Veg
Aeg
Vfg
Af8/3(g
Ve2+ g
Ae2)(g
Vf2+ g
Af2)
= 3 4
2g
Veg
Aeg
Ve2+ g
Ae22g
Vfg
Afg
Vf2+ g
Af2= 3
4 A
eA
fAlternative
One can rewrite the x-section as:
d σ
d cos θ = 16πQ f (N c ) 2s |χ(s)| 2
(g Ve 2 + g Ae 2 )(g Vf 2 + g Af 2 )(1 + cos 2 θ) + 8g Ve g Ae g Vf g Af cos θ
∝
(1 + cos 2 θ) + 8 g Ve g Ae g Vf g Af
(g Ve 2 + g Ae 2 )(g Vf 2 + g Af 2 ) cos θ
∝ (1 + cos 2 θ) + 2A e A f cos θ
∝
(1 + cos 2 θ) + 8
3 A FB cos θ
N −N
d σ
d cos θ in µµ channel
On-peak (M Z ) and ±2GeV off-peak
As described before, there are two contributions:
I
∝ (1 + cos 2 θ) symmetical
I
∝ cos θ gives asymmetry the asymmetry is small
I
A FB ∝ g V f which is small for lepton. c V f ≈ 0.03 dependence of d cos θ d σ on √
s
I
at √
s = M Z 2 , resonance function is ≈ s−M s
2Z
I
off-peak, the contribution from γ − Z interference term
does not vanish and so the actual shape changes
d σ
d cos θ in ee channel
Shape is different wrt to µµ due to presence of t-channel in ee final state.
most of asymmetry comes from t-channel
and s/t-channel interference
off-peak
A FB for ee channel wrt s
Interference contribution vanishes (only) on-peak;
it is dominant off-peak
I
A FB ∝ g Ae g Af
s(s−M
Z2) (s−M
Z2)
2+M
Z2Γ
2Zt-channel is important (for ee), s-channel is small;
I
in particular on-peak, since:
F
A
FB∝ g
Veg
Aeg
Vfg
AfF
g
Vfis small, expecially for leptons;
F
g
Ve,µ∼ 0.038;
Corrections
As usual, the measured quantities suffers from large corrections: QED (ISR/FSR), self-energy, etc.
Use pseudo-observable A 0 FB (QED correction accounted for)
Other correction (QCD, top, Higgs, . . . ) still
there.
A f in Standard Model
A f depends on the vector- and axial-vector coupling of fermion to the Z.
A f = 2g Vf g Af
g Vf 2 + g Af 2 = 2 g Vf /g Af
1 + (g Vf /g Af ) 2
In particular, it is strictly null if no axial/vector coupling exists for the neutral current.
Coupling SM: c Vf = (T 3 − 2Q f sin 2 θ W ) and c Af = (T 3 )
Using effective SM quantities, the radiative correction are re-absorbed sin θ W ,eff f = (1 + ∆ρ) sin θ f W with ∆ρ = α(M π
Z) M m
2t2Z
− α(M 4π
Z) ln m M
H22 Zg Vf /g Af = 1 − 2 2Q f
T f 3 sin θ f W ,eff
So A f is directly related to sin θ f W ,eff
A f for different fermions
The actual A f dependence on sin θ W ,eff f varies with the fermion charge and weak-isospin
A FB results
A ` FB : testing lepton universality
A 0,e FB =0.0145 ± 0.025 A 0,µ FB =0.0169 ± 0.013 A 0,τ FB =0.0188 ± 0.017 A 0,` FB =0.0171 ± 0.010
A 0,e FB suffers from uncertainties related to
t-channel, as well as to s-t interference.
A FB for quarks
Need to tag also the flavour and distinguish bc from ¯ b ¯ c, not only bc from q Done only for A c ¯ FB c and A b ¯ FB b with different techniques:
lifetime tagging;
I
cτ for b is ∼ 450µm (in lab ×γ)
I
cτ for c is ∼ 150µm (in lab ×γ)
I
detect displaced secondary vertex by impact parameter or decay lenght measurements Exclusive decays:
I
leptonic decay;
I
decay with D mesons;
additional techniques:
I
jet charge;
I
vertex charge;
I
kaons;
Correction to asymmetries from QCD (gluon radiation from final state quarks), in addition to QED
correction and LEP energy scale.
lifetime tagging
d 0 significance L significance and NN
b ↔ c separation via M vtx
b-tagging performance
Lepton tagging
A lepton inside a jet is a stong indication of a b or c flavour.
To distinguish from b to ¯ b use semileptonic decay of b quarks.
b → ` − ; ≈ 10%
c → ` + ; ≈ 13%
b → c → ` + cascade decay ;
Distinguish between direct and cascade decay using lepton p T and p
lower purity and efficiency wrt lifetime tagger
D-Meson Tags
Tagging via reconstruction of charmed meson and barions in jet:
direct evidence of a jet originated by an heavy quark.
low B ∼ O(%)
b → c fragmentation is small
distinguish c from b decay by charmed mesons momentum;
I
D 0 → K − π +
I
D + → K − π + π +
I
D s → K + K − π +
I
Λ + c → pK − π +
Jet charge, vertex charge and kaons
Consider ee → q ¯ q → jet + jet events.
The average charge of all particles within a jet retains some info about initial q charge.
Q h = Σ i q i p i k k Σ i p i k k
where p i k k is the p parallel to trust axis of the event (corresponding to jets’ directions)
Likewise, the sum can run over all the charged particles from a secondary (displaced) vertex.
Tag efficieny is rather small: data driven estimation from fraction of same-sign double tag in pure sample of q quarks.
Kaons: deduce the q flavour via decay chain b → c → s and c → s
A FB for b and c
A 0,c FB = 0.0707 ± 0.0035 A 0,b FB = 0.0992 ± 0.0016
A FB for b and c vs √ s
Note larger error off-peak: contribution from s/t interference term
Inclusive Hadronic Charge Asymmetry
Do not try to distinguish between quark flavour, but rather measure an “average” asymmetry based on charge asymmetries.
hQ FB had i = hQ F − Q B i = X
q=udcsb
R f A f FB δ q
δ q = hQ q − Q q ¯ i jet charge diff for q ¯ q
hQ FB had i can be interpreted as a function of sin 2 θ lept eff (in A f FB )
δ q from Z → bb/cc and MC for udc
(large syst uncert)
Left-Right Asymmetries
The forward-backward asymmetry is due to the presence of axial and vector couplig of fermions in the neutral current, introducing a dependence on cos θ which can be measured.
Z coupling to left and right fermions are different as well, since L and R fermions belongs to different multiplet in the SM, with different quantum numbers.
This feature can be measured studing the Z production with polarized e ± beam, or by looking at the polarization of the decay product of the Z .
I
SLD produces Z with polarized e ± beams;
F
Most precise determination of A
eI
LEP measure the polarization of τ in Z → τ τ decay, studing subsequent τ decays;
Differential x-section for polarized beam
For unpolarized beam
d σ
d cos θ ∝ (1 + cos 2 θ) + A e A f 2 cos θ
Differential cross section (born-level) in case of initial- or final-state fermion helicity are:
d σ Ll
d cos θ ∝ g Le 2 g lf 2 (1 + cos θ) 2 + f (A e,f ) cos θ d σ Rr
d cos θ ∝ g Re 2 g rf 2 (1 + cos θ) 2 + . . . d σ Lr
d cos θ ∝ g Le 2 g rf 2 (1 − cos θ) 2 + . . . d σ Rl
d cos θ ∝ g Re 2 g lf 2 (1 − cos θ) 2 + . . .
For e − with partial polarization P e and e + unpolarized (SLC), summing over final-state polarization
d σ f ¯ f d cos θ = 3
8 σ f ¯ tot f (1 − P e A e )(1 + cos 2 θ) + 2(A e − P e )A f cos θ P e is positive for right-handed beam helicity, negative for left.
Measurements (see also next slides)
if we look at total x-section for left/right-polarized e − beam:
I
σ tot L/R sensitive to (1 + cos 2 ) term:
I
A LR sensitive to A e
if we look at forward/backward x-section for left/right-polarized e − beam:
I
σ F /B L/R sensitive to cos θ term:
I
A LRFB sensitive to A f
A FB sensitive to A e A f
Measure the x-section for e L − e + → f ¯ f (σ f L ) and e R − e + → f ¯ f (σ R f ).
I
Note: only e − beam is polarized;
I
the polarization is not complete P e ∼ 0.8
I
P e > 0 for Left, P e < 0 for Right electrons;
I
Final state is inclusive, no flavour determation needed;
A LR = σ L f − σ R f σ L f + σ R f From A LR get A e from (1 + cos 2 θ) term integration:
σ L/R f = Z +1
−1
d σ L
d cos θ d cos θ ∝ 1 ± P e A e
N f − N f 1
It is also possible to combine the two techniques: FB and LR.
A LRFB = (σ F − σ B ) L − (σ F − σ B ) R
(σ F + σ B ) L + (σ F + σ B ) R
The integration to get F and B drop the (1 + cos 2 θ) term and keep the cos θ one.
σ F /B ∝ (A e ∓ P e )A f , (σ F − σ B ) L/R ∝ (P e )A f
A LRFB = (N F − N B ) L − (N F − N B ) R (N F + N B ) L + (N F + N B ) R
1 h|P e |i = 3
4 A f
Possible to measure directly A f for identified final state (f = e, µ, τ, b, c)
In both case, the precise knowledge of P e is critical
SLC: beam polarization [3]
First e ± linear collider e − source
I
polarized by shining circ. polarized light on a ArGa photo-cathode (P e ∼ 22%)
SLC: beam polarization [3]
linear acceleration;
I
e + produced by e − on a target, and collected, squized and accelerated;
two damping rings to reduce size and energy spread of e ± bunches;
final arch to single interaction region 1 GeV lost for sync. rad.
I
spin further rotated, and collision with longitudinal pol.
repetition rate 120 Hz (45 o 90 kHz at LEP)
Polarization randomly rotated every pulse (120 Hz) by changing the laser circ pol
P e measured continously via a downstream Compton polarimeter [4, 5]
Compton scattering is senstitive to P e and P γ (σ(j = 3/2) > σ(j = 1/2))
maximum for “head-on” γ − e collisions
High intensity laser (25MW), lead to 1000 compton interaction per pulse
Compton-scattered e − are bent by a magnet and
analyzed by multichannel cherenkov detector
Compton-scattered γ are analyzed by a quarz-fiber
calorimeter for cross-check
Electron polarization durin data-taking
σ P
e∼ 0.5% (initial 2.7%)
Energy calibration
√ s at SLC was measured and monitored downstream of the beams;
precise vertical bending dipole to bend the beam;
two horizontal bending magnets to produce synchrotron radiation before and after dipole;
syncrotron light monitor to measure the bending;
Expected precision 20 MeV
Absolute calibration from Z peak mass and
comparing with LEP results
SLDetector
Beam pipe (and beam) smaller than LEP, closer vertex detector;
Slow repetition rate, use slow but high resolution CCD arrays;
Central Drift Chamber LAr calorimeter
Event selection as at LEP,
better b/c tagging.
Results
A 0 LR = 0.1514 ± 0.0022 syst. uncert:
I
δP e /P e ∼ 0.5%
I
interference correction (0.39%)
I
√
s (0.15%)
Additional asymmetries (arc spin trasport, e + polarization, lumi) negligible
A 0 LR = 2(1 − 4 sin 2 θ lept eff )
1 + (1 − 4 sin 2 θ lept eff )
sin 2 θ lept eff = 0.23097 ± 0.00027
at LEP
A LRFB
Computed for ` = e, µ, τ
I
15k Z → ee, 12k → µµ, 11k → τ τ
I
via likelihood fit to d cos θ d
I
uncertainties dominated by statistics
I
then radiative corrections, polarization, background larger for τ due to τ decay ID
smaller for e: from A LR and A LRFB
A e =0.1544 ± 0.0060 A µ =0.142 ± 0.015 A τ =0.136 ± 0.025
A ` = 0.1513 ± 0.0021, sin 2 θ eff lept = 0.23098 ± 0.00026
τ polarization
At LEP e ± not polarized, but it is possible to look at the polarization of final state in Z → τ τ decays, by using the τ → ν τ + X decay.
P τ = σ + − σ − σ + + σ −
where σ + is the x-sec to produce positive helicity τ − etc.
Must take care that τ have mass, so helicity state do not correspond to chirality state (the one involved directly in the SM coupling).
I
However at LEP, p τ ≈ M Z /2 m τ , so helicity ≈ chirality
P τ = − A τ (1 + cos 2 θ τ
−) + 2A e cos θ τ
−(1 + cos 2 θ ) + 8/3A τ cos θ
Experimental method
Consider τ → πν decay.
It is purely V-A charged weak current, and obviously conserve angular momentum. In the τ rest frame, the neutrino (LH) is emitted opposite to τ spin, and so the π is emitted
backward, namely along the τ spin.
If the τ has positive helicity (spin k to momentum) then the π is emitted in the p τ direction (left configuration), and so, in the LAB (LEP CM), has larger momentum.
If helicity is negative (spin antik), π is emitted in opposite direction and has smaller momentum.
Bottomline: if τ has positive (negative) helicity, the π momentum is higher (lower)
(a) Measure the direction of π in the τ rest frame cos θ π
1 Γ
d Γ
d cos θ pi = 1
2 (1 + P τ cos θ π )
boosted in the LAB (x π = E π /E τ = E π /E beam ) 1
Γ d Γ
dx pi = 1 + P τ (2x π − 1)
Similar, but more complex, and less sensitive, for
(b) τ → ρν
(c) τ → a 1 ν
P τ results
A τ =0.1439 ± 0.0043 A e =0.1498 ± 0.0049
A ` =0.1465 ± 0.0033
sin 2 θ eff lept =0.23159 ± 0.00041
Results on axial and vector coupling
g V −A f scale from σ ff ∝ g Vf 2 + g Af 2 g V −A f ratio from A f = 2 1+(g g
Vf/g
AfVf
/g
Af)
2A 0 FB = 3 4 A e A f A 0 LR =A e A 0 LRFB = 3
4 A f
P τ = − A τ
Results on axial and vector coupling
g V −A f scale from σ ff ∝ g Vf 2 + g Af 2 g V −A f ratio from A f = 2 1+(g g
Vf/g
AfVf
/g
Af)
2A 0 FB = 3 4 A e A f A 0 LR =A e
A 0 LRFB = 3
4 A f
P τ = − A τ
Results on axial and vector coupling
g V −A f scale from σ ff ∝ g Vf 2 + g Af 2 g V −A f ratio from A f = 2 1+(g g
Vf/g
AfVf
/g
Af)
2A 0 FB = 3 4 A e A f A 0 LR =A e
A 0 LRFB = 3
4 A f
P τ = − A τ
C and B quarks coupling
A q vs A `
vert band: A ` , horiz: A q , diagonal: A 0,q FB
sin 2 θ lept eff
Input to global EWK fit
(in parenthesis the order followed in these lessons)
3
− −2 −1 0 1 2 3
tot
O) / σ
−
indirect
(O
2) (MZ αs
2) (MZ (5) αhad
∆ mt
b R0 c R0 0,b AFB
0,c AFB
Ab Ac (Tevt.) lept Θeff sin2
) FB lept(Q eff 2Θ sin
(SLD) Al
(LEP) Al
0,l AFB
lep R0
0 σhad ΓZ MZ ΓW MW MH
Global EW fit Indirect determination Measurement GfitterSM
Mar ’18
Higgs mass (4)
I
LHC
W mass and width (2)
I
LEP2, Tevatron, LHC Z-pole observables (1)
I
LEP1, SLD
I
M Z , Γ Z
Iσ 0 had
I
sin 2 θ lept eff
I
Asymmetries
I
BR R lep,b,c 0 = Γ had /Γ ``,b ¯ b,c ¯ c Top mass (3)
I
Tevatron, LHC other:
I
α s (M Z 2 ), ∆α had (M Z 2 )
Input to global EWK fit
(in parenthesis the order followed in these lessons)
Higgs mass (4)
I
LHC
W mass and width (2)
I
LEP2, Tevatron, LHC Z-pole observables (1)
I
LEP1, SLD
I
M Z , Γ Z
Iσ 0 had
I
sin 2 θ lept eff
I
Asymmetries
I
BR R lep,b,c 0 = Γ had /Γ ``,b ¯ b,c ¯ c
Top mass (3)
ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group Collaboration, S. Schael et al., “Precision electroweak measurements on the Z resonance,” Phys.Rept. 427 (2006) 257–454, arXiv:hep-ex/0509008 [hep-ex].
F. Halzen and A. D. Martin, Quarks and Leptons: an introductory course in modern particle physics.
Wiley, New York, USA, 1984.
G. A. Loew, “The slac linear collider and a few ideas on future linear colliders,” Proceedings of the 1984 Linear Accelerator Conference (1984) . https://inis.iaea.org/search/search.aspx?orig_q=RN:16018252.
G. Shapiro, S. Bethke, O. Chamberlain, R. Fuzesy, M. Kowitt, D. Pripstein, B. Schumm, H. Steiner, M. Zolotorev, P. Rowson, D. Blockus, H. Ogren, M. Settles, M. Fero, A. Lath, D. Calloway, R. Elia, E. Hughes, T. Junk, and G. Zapalac, “The compton polarimeter at the slc,”.
https://escholarship.org/uc/item/78t2f6wp.
SLD Collaboration, M. J. Fero, “The Compton polarimeter for SLC,” in Frontiers of high energy spin physics. Proceedings, 10th International Symposium, 35th Yamada Conference, SPIN’92, Nagoya, Japan, November 9-14, 1992, pp. 899–904.
1992.
http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx?slacPubNumber=SLAC-PUB- 6026.