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Top Quark Polarizationand New Physics

Qing-Hong Cao

Peking University

理论物理前沿研讨会 @ 中科院理论物理研究所2011年12月27日

Qing-Hong Cao 理论物理前沿研讨会 @ 中科院理论物理研所 / 31

• Large mass： 173 GeV ~ VEV (246GeV) Yt ~ O(1)• Short lifetime:

• “bare” quark： spin info well kept among its decay products

Top-quark: king of the SM

Top

Wb

5⇥ 10�27 s

2

hadronization


Top-quark leptonic decay• Charged lepton: top-quark spin analyzer

FIG. 6: top quark spin correlation.

FIG. 7: R distribution.

Otherwise, it yields R ≤ 0.5. Figure 7 displays the R distributions for mφ = 500GeV and

1000GeV. For comparison we also plot the SM contribution ignoring the lepton charges.

9

The charged-lepton tends to follow the top-quark spin direction.

3


Charged lepton distribution

• In top-quark rest frame1

�

d�

d cos ✓hel=

1 + �t cos ✓hel2

�t = +

�t = �right-handedleft-handed

`+

t~pt (cms)

helcos-1 -0.5 0 0.5 1

hel

/dcos

d-1

00.10.20.30.40.50.60.70.80.91

RtLt

(a)

tRtL

✓hel

4


Top-quark Polarization:A powerful discriminator of NP models

1. Color sextet scalars and vectors Same-sign top-quark pair production

2. Stop-quarks in MSSM and T-odd top-partners in LHT Top-antitop quark pair plus missing energy

5


New Physics Models(1) Color sextet scalar/vector

Pheno 2010May. 10, 2010

๏ Signal topology

same sign di-muons with 2 b-jets

๏ Much better reconstruction than electron

๏ Prominent backgrounds (ALPGEN):

6

b

ν

"+

ν

"+

b

t

tφ

u

u

pp� ⇥� tt� bb̄W+W+, W+ � ⇤+�

pp� tt̄� bb̄W+W�, W+ � ⇥+�, W� � jj, b� ⇥+

pp� ZW+W�, Z � ⇥+⇥�, W+ � ⇥+�, W� � jjpp�W+W+W,W+ � ⇥+�, W � jjpp�W+W+jj, W+ � ⇥+�

{

Dominant

b

b

�

u

u

`+

`+

⌫

⌫

t

t�6/V6

Berger, QHC, Chen, Shaughnessy, Zhang, Phys Rev Lett 105 (2010) 181802

Zhang, Berger, QHC, Chen, Shaughnessy, Phys Lett B 696 (2001) 68Berger, QHC, Chen, Li, Zhang, Phys Rev Lett 106 (2011) 201801

6


The Models

Measuring polarizations of

both top quarks

• Effective Lagrangian ( SU(3)C x SU(2)L x U(1)Y )

Spin and gauge quantum numbers of

heavy resonances

7

Atag, Cakir, Sultansoy, PRD59 (1999) 015008


Discovery potential

8

400 500 600 700 800 900 1000mΦ

(GeV)10-3

10-2

10-1

100

λ2uu

× Br

(Φ→

tt)

5σ discove

ry30 ev

ents

CDF: σ(tt+tt)

CDF:

m tt 95

% C.L

.

100 events

1000 even

ts

Hadronization region (ΓΦ

< 300 MeV)

★ Simple cuts to extract signal:✴ Same sign di-muons✴ Two jets and leptons with

PT>50GeV

✴ Shown are numbers of signal events;✴ about 1 background events

7 TeV


Collider signature: same-sign charged leptons

Need full event reconstruction

Difficulty: identical muons and b jets

Pheno 2010May. 10, 2010

๏ Signal topology

same sign di-muons with 2 b-jets

๏ Much better reconstruction than electron

๏ Prominent backgrounds (ALPGEN):

6

b

ν

"+

ν

"+

b

t

tφ

u

u

pp� ⇥� tt� bb̄W+W+, W+ � ⇤+�

pp� tt̄� bb̄W+W�, W+ � ⇥+�, W� � jj, b� ⇥+

pp� ZW+W�, Z � ⇥+⇥�, W+ � ⇥+�, W� � jjpp�W+W+W,W+ � ⇥+�, W � jjpp�W+W+jj, W+ � ⇥+�

{

Dominant

b

b

(1) Do the pairs of jet+lepton each reconstruct a top quark?

�

(4) Are the top quarks from a scalar/vector decay?

(3) What is top quark polarization?

?

(2) Is there a resonance? (s- or t-channel?)

`+

`+

⌫

⌫

t

t

9


Full kinematics reconstruction★ Four unknowns and four on-shell conditions

6 unknowns-2 from MET

Quartic equation (correct l-b pairing is necessary)

Two complex, two real solutions

m2W1 = (pµ1 + p⌫1)2

m2W2 = (pµ2 + p⌫2)2

m2t2 = (pW2 + pb2)2

m2t1 = (pW1 + pb1)2 p4

x

(⌫1) + a p3x

(⌫1) + b p2x

(⌫1) + c px(⌫1) + d = 0

10


- pairing: MT2

11

★ Question: how can one measure the mass of heavy particles if they are produced in pairs and then decay into visible and invisible particles?

★ The MT2 variable is a function of the momenta of visible particles ( , ) and missing transverse momentum. Its upper bound yields the mass of the parent particle ( ) .

Lester and Summers, hep-ph/9906349


- pairing: MT2

12

Choose smaller MT2 (correct combination found with nearly 100% probability)

P

P

t

t

★ MT2 of lepton-b clusters and MET

Two combinations of lepton-b clusters


Full kinematics reconstruction★ Four unknowns and four on-shell conditions

6 unknowns-2 from MET

Quartic equation (correct l-b pairing is necessary)

Two complex, two real solutions

m2W1 = (pµ1 + p⌫1)2

m2W2 = (pµ2 + p⌫2)2

m2t2 = (pW2 + pb2)2

m2t1 = (pW1 + pb1)2 p4

x

(⌫1) + a p3x

(⌫1) + b p2x

(⌫1) + c px(⌫1) + d = 0

13


Neutrino momentum reconstruction

14

True

Reconstructed (GeV)

★ Strong correlation between the true and reconstructed

s-channel 700GeV resonance

★The mass of the heavy resonance can be determined:


Top-polarization: color sextet scalar

15

★ Polarization correlates with angle between top quark spin and charged lepton momenta

Roughly 30 events required to distinguish from unpolarized case

+ : right-handed- : left-handed

?


Difficulty in color sextet vector

16

★ The vector sextet must be a SU(2) doublet. It couples to a left-handed quark and a right-handed quark according to:

★ Top quarks are oppositely polarized, but the net polarization distribution of the two identical top quarks exhibits a flat profile (i.e. like unpolarized top quarks).

★ Even though the flat profile of sextet vectors is different from the one for scalars, it is interesting to see if we could determine that the top quarks have L and R polarizations.

★ Can we measure the polarizations of the top quarks to distinguish the color sextet vector and scalar mesons?

YES!!!


Lepton energy and top-quark polarization★ Lepton energy distribution is sensitive to top quark polarization.

17

Leptons from right-handed top quark decay are more energetic than those from left-handed top quark decay.

FIG. 6: top quark spin correlation.

FIG. 7: R distribution.

Otherwise, it yields R ≤ 0.5. Figure 7 displays the R distributions for mφ = 500GeV and

1000GeV. For comparison we also plot the SM contribution ignoring the lepton charges.

9



18

C. R. Schmidt and M. E. Peskin, Phys Rev Lett 69 (1992) 410


Top-polarization: color sextet vector

19

★ Before lepton energy selection ★ After lepton energy selection

Flat profile is distorted by kinematic cuts.

✴ Roughly 98 (67) events required to distinguish vector lesser (greater) from vector unpolarized case


Top-polarization: color sextet vector

20

★ Apply the same analysis to sextet scalar (gauge singlet)

The shape of sextet scalar still remains with a moderate distortion.1

2

(1 + cos ✓)


Interim summary

21

★ Color sextet scalar and vector mesons may be a long shot they offer good discovery potential in early LHC running at 7 TeV

✴ Enhanced cross sections relative to EW scale new physics✴ 30 events (scalar) and 100 events (vector) sufficient✴ Naturally large same-sign dilepton rates allow background rejection

★ Search strategy

MT2

combinationtop quark

polarization

tripletsinglet

gauge #

doubletvectorscalarscalar

spin


New Physics Models(2) with DM candidates

P

DM

DM

P

t

t̄

?

Berger, QHC, Jianghao Yu and Hao Zhang, in preparation

22

Measuring top-quark polarization without reconstructing top-quark kinematics


NP signature: Top-antitop plus MET

• Stop-quark pair production in the MSSM

23

g

g

t̃

˜̄t

t

t̄

χ̃0

χ̃01000500200 2000300 30001500700

90

100

110

120

130

140

mt1é @GeVD

mh@Ge

VD

MSSM Higgs Mass

Xt = 0

Xt = Xtmax

SuspectFeynHiggs

Figure 1: The Higgs mass in the MSSM as a function of the lightest top squark mass, m˜t1 , with

red/blue solid lines computed using Suspect/FeynHiggs. The two upper lines are for maximaltop squark mixing assuming degenerate stop soft masses and yield a 126 GeV Higgs mass form

˜t1 in the range of 500–800 GeV, while the two lower lines are for zero top squark mixing anddo not yield a 126 GeV Higgs mass for m

˜t1 below 3 TeV. Here we have taken tan � = 20. Theshaded regions highlight the di↵erence between the Suspect and FeynHiggs results, and may betaken as an estimate of the uncertainties in the two-loop calculation.

the Higgs doublets, �SHuHd, that is perturbative to unified scales, thereby constraining � . 0.7(everywhere in this paper � refers to the weak scale value of the coupling). The maximum mass

of the lightest Higgs boson is

m2h = M2

Z cos2 2� + �2v2 sin2 2� + �2t , (2)

where here and throughout the paper we use v = 174 GeV. For �v > MZ , the tree-level

contributions to mh are maximized for tan � = 1, as shown by the solid lines in Figure 2,

rather than by large values of tan � as in the MSSM. However, even for � taking its maximal

value of 0.7, these tree-level contributions cannot raise the Higgs mass above 122 GeV, and

�t & 32 GeV is required. Adding the top loop contributions allows the Higgs mass to reach126 GeV, as shown by the shaded bands of Figure 2, at least for low values of tan � in the region

of 1 – 2. In this case, unlike the MSSM, maximal stop mixing is not required to get the Higgs

heavy enough. In section 3 we demonstrate that, for a 126 GeV Higgs mass, the fine-tuning of

the NMSSM is significantly improved relative to the MSSM, but is still of concern.

2

tan� = 20

‣ A light stop-quark is preferred to rise mh to 125 GeV in the maximal mixing scenario.

‣ Top-polarization could shed lights on the stop-quark mixing matrix.

Hall, Pinner and Ruderman, 1112.2703


NP signature: Top-antitop plus MET

• T-odd top-quark partner pair production in the LHT

24

g

g

T−

T−

t

t̄

AH

AH

QHC, Li, Yuan, Phys.Lett. B668 (2008) 24

EWPTHubisz et al

2005

allowed


Difficulty in NP signature of ttbar plus MET

• It is impossible to reconstruct a top-quark in the leptonic-decay mode.

25

g

g

T−

T−

t

t̄

AH

AH

b ν

"+

Angular distribution of the charged-lepton cannot be used.

Can we measure top-quark polarization? Yes !!!

10 unknowns

-2 from MET

No enoughconstraints

assuming is known


0 0.5 1 1.5 2xl

0

1

2

3

1/d

/xl

Et = 250 GeV (tL)Et = 250 GeV (tR)Et = 500 GeV (tL)Et = 500 GeV (tR)Et = 1000 GeV (tL)Et = 1000 GeV (tR)


26

x` = 2E`/Et



27

g

g

T−

T−

t

t̄

AH

AH

bν

"+

b̄

j

j

x

0` = 2E`+/Et̄


• Define a useful variable :

28

Lepton energy and top-quark polarization

0 0.5 1 1.5 2xl

0

1

2

3

1/d

/xl



Toy models mimicking MSSM and LHT

★ MSSM like: Purely left-handed or Purely right-handed

29

★ LHT like:

• Preliminary study of collider simulation

Minimal- theme is used to pick up three jets from top-quark hadronic decay.


Preliminary results

30

cutx0 0.2 0.4 0.6 0.8 1

rati

o o

f e

ve

nt

#

0

0.5

1

1.5

2

2.5

3

The lepton energy fraction ratioThe lepton energy fraction ratio

0 0.5 1 1.5 2xl

0

1

2

3

1/d

/xl


SPIN before MASS

heavy particle’smass increases

heavy particle’smass increases

Stat. & Sys. uncertainties

and background study is needed


Summary• Top-quark polarization provides much richer info of

new physics beyond the Standard Model.

• MT2 variable is good at solving the combinatory of multiple indistinguishable particles in the final state.

• Lepton energy (long ignored) could also be used to measure top-quark polarization, especially in NP models consisting of dark matter candidates.

31

THANK YOU !