model building and collider physics above the weak scale

135 Pages·2011·2.91 MB·English

MODEL BUILDING AND COLLIDER PHYSICS ABOVE THE
WEAK SCALE
A Dissertation
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
by
David Curtin
August 2011
(cid:13)c 2011 David Curtin
ALL RIGHTS RESERVED
MODEL BUILDING AND COLLIDER PHYSICS ABOVE THE WEAK SCALE
David Curtin, Ph.D.
Cornell University 2011
The Standard Model of particle physics, formulated in the 1970s, has been tremendously
successful in explaining almost all experimental results from high-energy colliders. Never-
theless, there are both theoretical and experimental reasons to look for a more fundamental
description of nature. With the Large Hadron Collider finally being online and delivering
data, we might soon be in a position to fathom the solutions to some of the most fundamen-
tal questions in our field, first and foremost the nature of electroweak symmetry breaking
and the solution to the hierarchy problem.
The research presented in this thesis represents the author’s contribution to the ongoing
theoretical effort to develop theories beyond the Standard Model, as well as new methods of
extracting information about the Lagrangian from experimental data.
We start by developing a realistic quark sector for Higgsless Randall-Sundrum models,
which show that this novel way of breaking the electroweak symmetry can be brought into
agreementwithhighlyconstrainingdataonflavorviolatinginteractions. Wethenmoveonto
models involving supersymmetry, and construct a model of metastable SUSY-breaking that
avoids several problems that traditionally plague models of Direct Gauge Mediation: low
gaugino masses and loss of perturbative gauge coupling unification. Finally, we propose new
experimental measurements which could provide a non-trivial consistency check that SUSY
solves the hierarchy problem, and show for the first time how the family of M kinematic
T2
variables can be used in the presence of large combinatorics background.
BIOGRAPHICAL SKETCH
David Curtin was born in Hamburg, Germany, on July 15 1983 as the first child of Richard
and Barbara, two opera singers originally from Australia and Poland, respectively. He was
followed four years later by his brother James, and together they spent their childhood and
early adolescence in Hamburg until 1997, when the family moved to Essen so Richard could
pursue a contract with the Essen Staatsoper.
Less than two years later, when David was in 10thgrade, the family moved again, this
time to Sydney, Australia. It was in Sydney that David graduated from high school and
went on to study Physics and Mathematics at the University of Sydney in 2002. Completing
his Bachelor of Science in 2004, David then moved to Melbourne for one year to pursue his
Honors degree in theoretical physics at the University of Melbourne. There he worked on
the construction of brane-world models with SO(10) grand unification under the supervision
of Professor Raymond Volkas.
He graduated from Melbourne at the end of 2005, and was accepted to start his Ph.D. at
CornellUniversityinIthaca, NY.TragedystruckthefamilywhenRicharddiedunexpectedly
of cancer in June 2006, but with the encouragement of Barbara and James, David moved to
Ithaca in August to begin his studies at Cornell.
In the following year, David was accepted into the research group of Professor Csaba
Csa´ki. He worked on developing theories of physics beyond the Standard Model, concen-
trating on extra dimensions and supersymmetry, as well as the study of collider physics to
verify these theories and determine their parameters. After receiving his degree, he will move
to New York City to join the high energy research group at Stony Brook University as a
postdoctoral research associate.
iii
The research of my Ph.D. is dedicated to the loving memory of my father.
Richard Curtin
27. October 1945 - 26. June 2006
Richard Curtin performing in Bonn, Germany (1996)
My father was born in 1945 in Canberra, Australia, second son of Dr. Pearce Curtin (economist) and Lorna
Curtin (brn. Newman, actress and journalist). Though his true calling was the stage, he was initially
trained as a lawyer in Sydney. Even while finishing his law degree he took singing lessons at the Sydney
Conservatorium, and after working briefly as a solicitor from 1970 - 1973 he moved to Austria in 1974 to
become an opera singer. His beautiful, rich bass voice and his singular dedication to his craft quickly
earned him high acclaim, and it wasn’t long before he started singing in all of Europe’s major venues.
In 1981, while they were both singing in Essen, Germany, he met my mother, the soprano Barbara
Id´zkowska, and married her soon after. Our family life was an extraordinarily happy one. This was in large
part thanks to a father who was always there for his children, and always did the right thing, not the easy
thing, when it came to raising his sons, as well as a husband who showed how much he loved his wife every
single day.
He is my role model; a man of towering intellect, deep wisdom and iron-clad integrity, whose wonderfully
gentle sense of humor nevertheless prevented him from taking himself too seriously. Growing up as a child
in Hamburg I hardly remember him being gone, because no matter how high his workload he always made
time for us. He passed away unexpectedly from cancer in June 2006, just before I moved to Cornell. Even
though the emptiness his early death has left behind can never be filled, I am always thankful to have had
a father like him, and to feel so loved. This is to you Dad.
iv
ACKNOWLEDGEMENTS
I thank my mother Barbara, my late father Richard and my brother James for always
being there for me with love and support. It was hard for the three of us after Dad died
and I had to move to the United States, but we got each other through it. You are the most
important people in my life.
Thank you Csaba for believing in me and giving the chance to prove myself to you.
Thanks for all the time you patiently spent teaching me, and for always being there when I
needed help or advice. I couldn’t have gotten a better advisor.
Thank you Maxim for working with me and teaching me collider physics. Thank you
Peter for always making time to talk to me, and providing a valuable window into the
experimental world. Thank you Yuval and Liam and everybody in the theory group for
creating such a wonderful atmosphere for everyone to work and thrive together.
Thank you Yuhsin for being a wonderful friend and esteemed collaborator. Thank you
Praveen and Sohang for the great conversation and company. Thank you Flip for always
organizing things, it is much appreciated. Thank you Naresh and Mario for teaching me how
to play ping pong while putting up with my overly-competitive half-serious temper-tantrums
and distinct lack of talent. Thank you Bibhushan, Greg, Sumiran, Mike, Thomas, Johannes,
Dan, Gang, Josh, Dean, David, Itay, Julian, Yang, Mathieu and Ben for making the last few
years so much more enjoyable and interesting.
Thank you to the administrative staff, to Katerina, Kasey, Monica, Cindy, Deb and John,
they kept all the wheels turning smoothly and put up with many last-minute requests and
changes.
Thank you to all my friends back home in Germany and Australia, who kept in contact
with me despite my sporadic correspondence and always make me feel welcome when I visit.
These are the friends I have for a lifetime.
v
TABLE OF CONTENTS
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
1.1 Opening Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 The LHC Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 A Realistic Quark Sector for Higgsless RS Models 20
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Gauge Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2 The Fermion Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 The NMFV Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.2 Going to 4D Mass Basis . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.3 Satisfying Electroweak Precision Data and CDF Bounds . . . . . . . 34
2.3.4 Counting Physical Parameters and the Meaning of Large UV Kinetic
Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.5 The Zero Mode Calculation . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Flavor Matching and Protection in the NMFV Model . . . . . . . . . . . . . 40
2.4.1 Matching in the Zero Mode Approximation . . . . . . . . . . . . . . . 41
2.4.2 Flavor Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Estimating FCNCs for the NMFV Model . . . . . . . . . . . . . . . . . . . . 44
2.5.1 4-Fermi Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5.2 G(cid:48) contributions to FCNCs . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5.3 Z contribution to FCNCs . . . . . . . . . . . . . . . . . . . . . . . . 47
2.5.4 Contribution to FCNCs from Higher-Dimensional Operators in the 5D
Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.6 Numerical Results and Mixing Constraints . . . . . . . . . . . . . . . . . . . 49
2.6.1 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.6.2 Angle Scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
vi
3 Singlet-Stabilized Minimal Gauge Mediation 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Overview of the SSMGM Model . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Reviewing the ISS Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3.1 The necessity of metastable SUSY-breaking . . . . . . . . . . . . . . 67
3.3.2 The ISS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.3 Uplifting the ISS Model . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4 The Adjoint Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4.1 The messenger contribution to V (Z) . . . . . . . . . . . . . . . . . 76
eff
3.4.2 Model Building Requirements for Stabilizing Z . . . . . . . . . . . . 78
3.5 Vacuum Structure & Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5.1 The Uplifted Vacuum (k = 0) . . . . . . . . . . . . . . . . . . . . . . 79
3.5.2 The ISS Vacuum (k = 1) . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 Direct Gauge Mediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.7 Stabilizing the Uplifted Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.7.1 Organizing the Spectrum & Contributions to V . . . . . . . . . . . 89
CW
3.7.2 Conditions for local minimum . . . . . . . . . . . . . . . . . . . . . . 91
3.7.3 Validity of 1-loop calculation . . . . . . . . . . . . . . . . . . . . . . . 94
3.7.4 Lifetime Constraints on Uplifted Vacuum Stabilization . . . . . . . . 95
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4 The SUSY-Yukawa Sum Rule and M Combinatorics 99
T2
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 SUSY-Yukawa Sum Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Prospects at the LHC: a Case Study . . . . . . . . . . . . . . . . . . . . . . 107
4.3.1 Measuring the ˜b ,g˜,χ˜0 masses . . . . . . . . . . . . . . . . . . . . . . 108
1 1
4.3.2 Measuring the t˜-mass . . . . . . . . . . . . . . . . . . . . . . . . . . 112
1
4.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5 Conclusion 115
Bibliography 117
vii
LIST OF TABLES
2.1 We compare lower bounds on the NP flavor scale Λ (all in TeV) for arbi-
F
trary NP flavor structure from the UTFit collaboration [42] to the effective
suppression scale in RS-GIM [29] and our Higgsless NMFV model, see eq.
(2.5.5). In this RS-GIM model, |Y | ∼ 3, f = 0.3 and r = m /g , with
∗ q3 G s∗
a KK scale of ∼ 3TeV. For the Higgsless model L ≈ 13 determines a KK
scale m ≈ 700GeV. Setting ρ = 10 gives M = 110GeV ∼ 1/R(cid:48), and
G c D
(c ,c ) = (0.48,−0.44) matches the couplings for the first two genera-
QL QR
tions to the SM. A third generation EWPD match is most easily obtained for
ρ = 1 and (c ,c ,c ) = (0.1,−0.73,0). To satisfy the flavor bounds, we
b,t L bR tR
needtopushmoremixingintotheup-sectorbysettingλ−1U13 ∼ U13 ∼ λ3
L(d) L(u)
and λ−1U32 ∼ U32 ∼ λ2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
L(d) L(u)
4.1 Mass measurements (all in GeV), assuming Gaussian edge measurement un-
certainties. We imposed the lower bound m > 45GeV, which generically
χ˜0
1
follows from the LEP invisible Z decay width measurement [98]. . . . . . . . 112
viii
LIST OF FIGURES
2.1 (a) shows the region of bulk masses that reproduces the SM couplings for the
first quark generation with varying magnitudes of the IR brane mass. The
threebandsareforthreevaluesofρ = M /Mmin, whereMmin isthesmallest
d D D D
possibleIRbraneDiracmasswhichcanreproducethefirstgenerationmasses.
Darker(lighter)regionsindicatethatthecouplingisupto0.6%below(above)
SM value. The blue (horizontal) band for ρ = 1 is reproduced by the zero
d
mode approximation, and shows that Q must be almost flat and near the
L
IR brane as expected. The green and red bands (successively more curved
upwards)correspondtoρ = 600and1000, andweseesignificantshiftswhich
d
allow the quarks to be UV localized. (b) shows Mmin for the first generation
D
in MeV. It is clear that increasing those brane terms by a factor of 1000 is
not necessarily unreasonable, since it corresponds to a TeV scale M . . . . . 39
D
2.2 Lefttoright: PointsinU anglespaceforscans1, 2and3thatsatisfyFCNC
Ld
constraints in the zero mode calculation, where s = asCKM,s = bsCKM
12 12 23 23
and s = csCKM. Red (darker) points are found to violate the bounds when
13 13
taking into account KK mixing. . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 Slices of thickness 0.1 in the (a,c)-plane at different points along the b-axis,
from b = −0.5 to b = 0.5, for scan 2 (scans 1 and 3 are similar). Green (light)
points satisfy FCNC constraints in the zero mode calculation, and red (dark)
points fail bounds when KK mixing is taken into account. The points which
fail FCNC bounds in the zero mode calculation are not shown, but they fill
up the entire remaining volume of angle space. There is no overlap between
points satisfying FCNC bounds and points that do not – they occupy well
defined, mutually exclusive volumes. . . . . . . . . . . . . . . . . . . . . . . 54
3.1 (a)Thetree-levelpotentialwithouttheinstantontermasafunctionof|M |
sing
and S, where we have enforced tree-level VEVs |S¯| = |S| and Z = Z¯ =
(cid:112)
−d N M S/m(cid:48). The valley marked with a green band is perfectly flat
f sing
in the |M | direction and shows that the potential has a SUSY-breaking
sing
minimum for S2 = hf2 − m(cid:48)2 . Note that the messengers are tachyonic for
√ d d2Nf
|M | < m(cid:48)/ dh. (b) The same potential with the instanton term added.
sing
The minimum along the S-direction is approximately unchanged close to
the origin but is significantly shifted as we move outwards along the |M |
sing
direction. As we walk along the the valley in the |M | direction (which now
sing
tilts slightly away from the origin) we eventually reach the SUSY-minimum
√
at |M | ∼ Λf and S,Z = 0. (c) We compute quantum corrections to the
sing
potential along the pseudomodulus direction, i.e. the green band in (b), by
setting all fields to their VEVs in terms of |M |. The vacuum is stabilized
sing
(cid:112) (cid:112)
at |M | ∼ h/d f −→ Z,Z¯ ∼ h/d f2/m(cid:48). The parameters used
sing
for these plots in units of m(cid:48) were N = 5, Λ = 3.8 × 109, f = 63 and
f
(g,d,h) = (0.02513,0.02,1). . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
ix