Effective Field Theory Approaches to Particle Physics Beyond the Standard Model

246 Pages·2017·6.55 MB·English

Effective Field Theory Approaches to
Particle Physics Beyond the Standard Model
by
Zhengkang Zhang
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Physics)
in the University of Michigan
2018
Doctoral Committee:
Professor James D. Wells, Chair
Professor Fred C. Adams
Professor Aaron T. Pierce
Professor Jianming Qian
Zhengkang Zhang
[email protected]
ORCID iD: 0000-0001-8305-5581
(cid:13)c Zhengkang Zhang 2018
Acknowledgements
First of all, I would like to thank my advisor, James Wells. My development as a scientist
has been greatly influenced by his invaluable guidance. He has always encouraged me to
pursue independent research, to develop new ideas, and to form my own view of the field,
while generously sharing his knowledge, experience and insights to guide my thinking — an
approach I deeply appreciate.
I would also like to thank Aaron Pierce for teaching me a great deal about the field,
especially as my advisor at an early stage of my graduate studies. I am particularly grateful
for his patient guidance through my first project, and his continued support and advice
later on. Additionally, I would like to thank Christophe Grojean for his support and advice,
especially during my stay at DESY Hamburg, where part of this dissertation was completed.
I have greatly benefited from working with my other collaborators as well, including Se-
bastian Ellis, Alexey Petrov, Stefan Pokorski, J´er´emie Quevillon, Bibhushan Shakya, Andrea
Wulzer, Tevong You, and Yue Zhao.
My thanks also go to Fred Adams and Jianming Qian for serving on my committee and
providing valuable feedback.
I am grateful to Ratindranath Akhoury, Henriette Elvang, Finn Larsen, Roberto Merlin,
James Wells, and Kathryn Zurek for their inspiring classes from which I have learned a lot
of interesting physics.
I also would like to thank other (past and current) members of the Leinweber Center
for Theoretical Physics (formerly Michigan Center for Theoretical Physics), especially Arash
Arabi Ardehali, Raymond Co, Josh Foster, Gordy Kane, Jack Kearney, Nick Orlofsky, Sam
Roland, Ben Safdi, and Bob Zheng, for many stimulating conversations.
Special thanks go to Mengxing Ye, my brilliant partner in life, for accompanying me
through this journey (and teaching me interesting condensed matter physics as well).
The work in this dissertation was funded in part by the U.S. Department of Energy grant
DE-SC0007859, the Rackham Summer Award, Rackham Research Grant, and Rackham
Dissertation Fellowship.
ii
Table of Contents
Acknowledgements ii
List of Tables v
List of Figures viii
List of Appendices xii
Chapter 1: Introduction 1
1.1 The Standard Model from an EFT perspective . . . . . . . . . . . . . . . . . 1
1.2 Precision analyses as indirect probes of new physics . . . . . . . . . . . . . . 5
1.3 Bottom-up and top-down EFT approaches . . . . . . . . . . . . . . . . . . . 6
1.4 What’s new? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Outline of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Chapter 2: Precision Electroweak Analyses After the Higgs Boson Discovery 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Standard Model parameters and observables . . . . . . . . . . . . . . . . . . 14
2.3 The formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 New physics examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Chapter 3: Resolving Charm and Bottom Quark Masses in Precision Higgs
Analyses 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Incorporating low-energy observables into a global precision analysis . . . . . 38
3.3 Recasting Higgs observables in terms of low-energy observables . . . . . . . . 39
3.4 Theoretical uncertainties of Higgs partial widths . . . . . . . . . . . . . . . . 44
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
iii
Chapter 4: EFT of Universal Theories and Its RG Evolution 50
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Universal theories at LO and beyond . . . . . . . . . . . . . . . . . . . . . . 53
4.3 RG effects in the electroweak sector . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 RG effects in the Yukawa sector . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Chapter 5: Time to Go Beyond TGC Interpretation of W Pair Production 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Effective operators and anomalous couplings . . . . . . . . . . . . . . . . . . 83
5.3 Triple gauge coupling measurements: from LEP2 to LHC . . . . . . . . . . . 85
5.4 Toward a high energy picture of Standard Model deviations . . . . . . . . . 89
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Chapter 6: Covariant Diagrams for One-Loop Matching 92
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 Gauge-covariant functional matching . . . . . . . . . . . . . . . . . . . . . . 95
6.3 Covariant diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 7: EFT Approach to Trans-TeV Supersymmetry 146
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.2 Matching the MSSM onto the SMEFT . . . . . . . . . . . . . . . . . . . . . 151
7.3 Bottom-tau Yukawa unification . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.4 Higgs couplings in TeV-scale SUSY . . . . . . . . . . . . . . . . . . . . . . . 183
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Chapter 8: Summary and Outlook 192
Appendices 194
Bibliography 213
iv
List of Tables
2.1 (From [131]) The list of observables, their experimental and reference values,
and percent relative uncertainties. . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 (From [131]) Expansion coefficients, as defined in Eq. (2.20), calculated in the
basis of input observables containing ∆α(5) . These encode the dependence of
had
the output observables on each input observable. . . . . . . . . . . . . . . . 21
2.3 (From [131]) Percent relative uncertainties for the expansion coefficients c ,
ii(cid:48)
with all input observables varied in their 1σ range. . . . . . . . . . . . . . . 24
2.4 (From [131]) The r ’s defined in Eq. (2.25), characterizing the ratios of
ii(cid:48)
second-order vs. first-order terms in the expansion (in units of percentage). . 25
2.5 (From[131])Expansioncoefficientscalculatedinthebasisofinputobservables
containing α(m ), which are derived from the numbers in Table 2.2 by a
Z
change of basis described in Section 2.3.4. . . . . . . . . . . . . . . . . . . . 28
2.6 (From [131]) The b coefficients defined in Eq. (2.68), characterizing the shift in
the output observables due to new physics that shifts vector boson self-energies. 32
4.1 (From [111]) Warsaw basis operator combinations that appear in L
universal
in (4.1), in the notation of [3]. In these expressions, repeated generation
←→
indices i,j,k,l are summed over, H†σaD H = H†σa(D H) − (D H)†σaH,
µ µ µ
←→
H†D H = H†(D H) − (D H)†H. The Yukawa matrices y , y , y should
µ µ µ u d e
not be confused with the hypercharges Y . The SM vector and scalar currents
f
JA , Ja , J , Jα are defined in (4.2). . . . . . . . . . . . . . . . . . . . . . 54
Gµ Wµ Bµ y
4.2 (From [111]) Expressions of the 16 universal parameters in terms of the War-
saw basis Wilson coefficients in (4.1). These parameters completely charac-
terize the indirect BSM effects in universal theories at the dimension-6 level.
More details of the universal parameters, including their definition from the
effective Lagrangian and their expressions in other bases, can be found in [109]. 56
v
4.3 (From [109,111]) Higgs basis couplings in terms of the universal parameters.
ˆ ˆ
∆(cid:15) are independent linear combinations of S,T,W,Y defined in (4.4). c
1,2,3 4f
collectively denotes four-fermion effective couplings, and d stands for the
Vf
dipole-type Vff couplings. Compared with [7], we have written the fractional
W mass shift as δ instead of δm, and defined [δgWq] in the gauge-eigenstate
m L ij
rather than mass-eigenstate basis. . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1 (From [60]) Building blocks of covariant diagrams for integrating out heavy
bosonic fields (and fermionic fields as well if one follows the approach of
Eq. (6.60) to square their quadratic operator), in the absence of mixed heavy-
light contributions and open covariant derivatives in the X matrix, as derived
in Section 6.3.1. All previous universal results in the literature [55,56] can be
easily reproduced by computing one-loop covariant diagrams built from these
elements; see Section 6.4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2 (From [60]) Additional building blocks of covariant diagrams in the presence
of mixed heavy-light contributions to matching, as derived in Section 6.3.2.
Example applications can be found in Sections 6.4.2, 6.4.3 and 6.4.5. . . . . 112
6.3 (From [60]) Additional building blocks of covariant diagrams in the presence
of open covariant derivatives in the X matrix, as derived in Section 6.3.3, up
to one-open-covariant-derivative terms P Zµ +Z†µP . Example applications
µ µ
can be found in Section 6.4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 (From [60]) Additional building blocks of covariant diagrams when Dirac
fermions are involved in matching, as derived in Section 6.3.4. These are
used when the quadratic operator for fermionic fields is not squared like in
Eq. (6.60). Example applications can be found in Sections 6.4.4 and 6.4.5. . 113
6.5 (From [60]) List of universal coefficients in terms of the master integrals de-
fined in Eq. (6.67) (Column 1). The UOLEA master formula for one-loop
matching reported in [56] is reproduced by adding up traces of the operators
in Column 2 with the corresponding universal coefficients, and multiplying
the overall factor −ic ; see Eq. (6.68). The covariant diagrams used to com-
s
pute each universal coefficient are listed in Column 3. See Appendix B for
expressions of the universal coefficients in terms of heavy particle masses. . 122
6.6 (From [60]) Summary of the results in Eq. (6.96) for mixed heavy-light con-
tributions to one-loop matching for the scalar triplet model. The SM gauge
coupling-independent terms for the three operators O ,O ,O in Eq. (6.89)
T H R
are computed (in the MS scheme). . . . . . . . . . . . . . . . . . . . . . . . 127
vi
7.1 (From [132]) Heavy fields ϕ in the MSSM, their gauge quantum numbers,
H
and conjugate fields (which appear on the left side of Q ). . . . . . . . . . 153
UV
7.2 (From [132]) Light fields ϕ in the MSSM, their gauge quantum numbers,
L
and conjugate fields (which appear on the left side of Q ). Primed Weyl
UV
fermion fields are unphysical auxiliary fields, to be set to zero at the end of
the calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.3 (From [132]) Fields contained in the nonzero entries of the MSSM U matrix,
with the heavy fields ϕ to be set to ϕ (which is nonvanishing only for the
H H,c
heavy Higgs Φ). In this table, ϕ collectively denotes the heavy and light Higgs
fields Φ and φ, e.g. ϕ2 represents Φ2,Φφ,φ2. Also, ψ , the Dirac spinors con-
f
taining SM fermions, are written simply as f for clarity. Detailed expressions
of the U matrix can be found in Appendix C. . . . . . . . . . . . . . . . . . 155
7.4 (From [132]) Dimension-six operators generated at tree level when match-
ing the MSSM onto the SMEFT. p,r,s,t are generation indices. Tree-level
matching alone produces the operator coefficients listed here, but with β(cid:48) in
place of β. As explained in Section 7.2.2, adding the one-loop-generated piece
c (Φ∗φ+φ∗Φ ) to Ltree amounts to replacing β(cid:48) by β in all Ctree. . . . . 158
Φφ c c SMEFT i
7.5 (From [132]) Covariant diagrams contributing to Higgs potential and Yukawa
interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.6 (From [132]) Covariant diagrams contributing to kinetic terms. . . . . . . . . 164
vii
List of Figures
3.1 (From[30])Contoursofm (m )(top-left),Γ (top-right),m (m )(bottom-
c c H→cc¯ b b
left), Γ (bottom-right) in the µ -µ plane. These plots demonstrate
H→b¯b m α
Eqs. (3.18-3.21) with all other inputs fixed. The unlabeled contours represent
decreasing values toward the top-left corner in steps of 0.01 GeV, 0.005 GeV,
0.002 MeV, 0.005 MeV, respectively. . . . . . . . . . . . . . . . . . . . . . . 45
3.2 (From [30]) Percent relative uncertainties in Γ (left) and Γ (right) as
H→cc¯ H→b¯b
functions of µ from: perturbative uncertainty with µc = 4 GeV, µb =
min max max
15 GeV (red solid) or alternatively µc = 3,5 GeV, µb = 13,17 GeV
max max
(red dashed), parametric uncertainties from Mc or Mb (orange), α (m )
1 2 s Z
(cyan solid), Mc,np (blue, for Γ only) and m (purple). The parametric
1 H→cc¯ H
uncertainty from α (m ) incorrectly calculated assuming no correlation with
s Z
m (cyan dotted) is also shown for comparison. The parametric uncertainties
Q
are defined as shifts of the central values of Γ and Γ for µ ≤
H→cc¯ H→b¯b min
µ ,µ ≤ µ caused by varying the input parameters within the errors
m α max
quoted in Eqs. (3.24-3.32), with µc = 4 GeV, µb = 15 GeV (the kinks are
max max
due to the maximum or minimum shifting to a different region in the µ -µ
m α
plane), and are found to be insensitive to µ . . . . . . . . . . . . . . . . . 47
max
viii
4.1 (From [111]) Examples showing how nonuniversal effects can be generated by
universal oblique corrections. Left: effective Wqq(cid:48) and W(cid:96)ν couplings are
renormalized differently, due to the different couplings of quarks and leptons
¯
to neutral gauge bosons. Middle: the Zb b coupling is singled out among
L L
¯
all the Zff couplings probed by Z-pole measurements for relatively large
running effects proportional to y2, via loop corrections involving the charged
t
Goldstone boson (or the longitudinal W± if one uses the unitary gauge).
Right: the Higgs boson couplings to the up- and down-type quarks and
leptons are renormalized differently, due to different gauge interactions of the
fermions. In each example, the interactions generated for the SM fermions
are not in the form of the SM currents, and thus the corresponding operators
cannot be eliminated in favor of bosonic operators. These examples, as well as
many others, can be more rigorously formulated in terms of SU(2) ×U(1)
L Y
invariant operators, but we prefer to give a more intuitive illustration at this
stage. The arguments here will be made concrete in sections 4.3 and 4.4. . . 52
4.2 (From [111]) Theory predictions for R = Γ /Γ(Z → (cid:96)+(cid:96)−) and R =
(cid:96) had b
¯
Γ(Z → bb)/Γ are shifted away from the SM point along the dashed lines,
had
when the universal parameters appearing in (4.40) take the values labeled
beside the dots. The anomalous TGC parameters ∆g¯Z, ∆κ¯ lead to shifts
1 γ
along the same direction as c (green dashed line), with the orange stars
2y
and triangles indicating the maximum shifts allowed by the LEP2 TGC con-
straints (95% C.L.) from single-parameter fits (shown in the bottom-right
corner) [205]. ln Λ = 3 is assumed, as motivated by TeV-scale new physics.
µEW
Agreement between the SM predictions as fitted by the Gfitter group [26] and
the combined measurements by the LEP and SLD collaborations [139] naively
constrains the oblique parameters combination ∆(cid:15) −c2∆(cid:15) (blue) defined in
3 θ 1
(4.41) at the 10−3 level. But even when the oblique parameters are inter-
preted as renormalized at µ following our prescriptions, the neglected LL
EW
terms in such a LO oblique parameters analysis can actually be significant.
ˆ ˆ
The challenge illustrated by this example requires extending the (S,T,W,Y)
parametrization to include additional parameters in a consistent global fit of
universal theories beyond LO. . . . . . . . . . . . . . . . . . . . . . . . . . . 74
ix