Implica(ons of Higgs Boson Mass for New Physics
Nobuchika Okada
University of Alabama, Tuscaloosa, AL
This talk is based on several works in collabora=ons with
Workshop 2012@University of Kobe, March 13-‐14, 2012
Ilia Gogoladze, Naoyuki Haba, Bin He, Shigeki Matsumoto,
Qiasar Shafi, Toshifumi Yamashita
Introduc(on
The Standard Model (SM)
is the best theory in describing the nature of
par(cle physics, which is in excellent agreement with almost of all current experiments
Two basics structures of the SM
Gauge symmetry:
Higgs mechanism:
Mass genera=on mechanism
The Standard Model
Gauge group:
Par=cle contents: leptons & quarks & Higgs doublet QCD int. Electroweak int.
Gauge fields:
gluon
Electroweak Symmetry Breaking & Higgs mechanism
Higgs doublet scalar under
Massive weak gauge bosons & Higgs boson Higgs poten=al:
Electroweak symmetry breaking:
Higgs mechanism:
Fermion masses are also generated
W & Z bosons get masses through gauge coupling
Fermions get masses through Yukawa coupling Ex) top quark mass
Higgs boson mass
The success of the Standard Model
All par=cles have been observed (except Higgs boson)
The nature of the gauge theory has been precisely checked (Ex) LEP Experiment
Z-‐boson produc=on @Z-‐pole Huge number of Z bosons
Very precise measurements
Gauge interac=ons
very precisely checked by experiments Symmetry breaking & Higgs mechanism
Higgs has not yet been observed Need to check
Origin of symmetry breaking & mass genera=on
Current Status of the SM
In addi=on, several experimental results and theore=cal
considera=ons suggest the need of new physics beyond the SM
LHC experiment (ATLAS & CMS) is now hun(ng
Higgs boson & New Physics
Suppose…..
Higgs boson is discovered and Higgs mass is measured
measurement of Higgs quar(c coupling
What is implica=on of Higgs boson mass for New Physics?
New Physics takes place at some high energies Higgs mass measurement
= Higgs quar=c coupling at low energy
Extrapolate the quar=c
coupling to high energies
From the Higgs poten=al in the SM, Higgs quar=c coupling determines
Once Higgs mass is measured, its high energy behavior can be understood via RGE running of
Theore(cal Higgs mass bounds
Ini=al is large is increasing small is decreasing
top Yukawa is important
RGE extrapola(on of the Higgs quaric coupling
What this picture tells us?
Perturba=vity bound:
Vacuum Stability bound:
for
Theore=cal bound on Higgs boson mass
In the SM, if we fix
Higgs mass should be in the range
Cabibbo, Miani, Parisi &Petronsio, NPB 158, 295 (’79)
, …….
If a Higgs mass is found in this rage, the SM can be
extrapolated to the Plank scale without theore(cal
problems for the quar(c coupling
Precision electroweak measurement and direct bounds by LEP &
Tevatron favor a low Higgs mass
Recent LHC results for Higgs boson hun(ng
Combined results via
ATLAS CMS
Observed exclusion at 95% CL:
110-‐117.5, 118.5-‐122.5, 129-‐539 95% CL allowed mass range:
114.4-‐127.5 GeV
An excess of evens has been observed around the Higgs mass
125 GeV with local significance ~ 3 sigma
From the recent LHC results, Higgs mass is likely to be below the vacuum stability bound ~129 GeV
Implica(ons?
Case 1: Cutoff is Planck, but RGE running is altered by some new physics effects
SM running
?
RGE running is
altered by new
physics effects
Case 2: Theory has an effec(ve cutoff < MP
Stability Higgs mass bound as a func(on of an ``effec(ve cutoff’’
LEP bound
Higgs signal at LHC?
In both the case (1) and (2), we need New Physics
What kind of new physics can
account for case (1) and/or (2)?
Oscilla=on data
Neutrinos have masses & mixings Mass =ny!
Mixing angle large
For case (1): Seesaw extension of the SM
Seesaw Mechanism: mechanism to naturally explain =ny mass
Effec=ve operator:
If the seesaw scale
Naturally,
The seesaw scale lies in intermediate scale or less
Type I Seesaw
Type II Seesaw
origin
origin
SM singlet fermion
SM SU(2) triplet scalar
Type III Seesaw
origin
SM SU(2) triplet fermion
Running mass:
We choose
SM running
In all seesaw scenarios, new par=cles couple to Higgs doublet
contribute to Higgs quar=c RGE for
Contribu=ons
by
: type I
: type II
: type III
Type I seesaw
Modifica=on of RGEs in the presence of 3 singlet fermion with
For simplicity, we assume 3 degenerate Ns:
Light neutrino mass matrix:
SM RGEs
* We employ 2-‐loop SM RGEs + 1-‐loop new RGEs
Casas, Clemente, Ibarra & Quiros, PRD 62, 053005 (2000)
In order to realize the neutrino oscilla=ons data
Assump=on I : is real
: degenerate RH neutrino masses Through the seesaw mechanism,
3 by 3 light neutrino mass matrix:
Assump=on II: MNS mixing matrix = tri-‐bi-‐maximal
Results: red : hierarchical case
blue: inverted-‐hierarchical case
SM result
Perturba=vity bound
Stability bound
Higgs mass window is closed
* Here Higgs mass evalua=on is not so precise
From two-‐loop RGE improved 1-‐loop effec=ve poten=al analysis
Stability bound is s=ll >129 GeV
Not relevant to our case
Type III seesaw
Modifica=on of RGEs in the presence of 3 triplet fermions with
Gogoladze, N.O. &Shafi, Phys. Ler. B 668 (2008) 121
For simplicity, we assume 3 degenerate triplets:
Light neutrino mass matrix:
Type III is similar to Type I, but we introduce
SM RGEs
* We employ 2-‐loop SM RGEs + 1-‐loop new RGEs
We did the same analysis as in Type I case Results: red : hierarchical case
blue: inverted-‐hierarchical case
SM result
Perturba=vity bound
Stability bound
Higgs mass window is closed
Wider than the SM result
Gogoladze, N.O. &Shafi, Phys. Ler. B 668 (2008) 121
Type III seesaw can lower the SM stability bound because the presence of SU(2) triplets alters the SU(2) gauge coupling
running
In order to lower the stability bound, the triplet mass scale should be low Neutrino Dirac Yukawa is small
More detailed analysis in the light of LHC results
We generalize the analysis to the cases with 1, 2 and 3
genera(ons of SU(2) triplet right-‐handed neutrinos
He, N.O. &
Shafi, in prepara=on
Stability bound in SM
Higgs signal at LHC?
1 genera=on
degenerate 2 genera=ons
In Type III seesaw extended SM, the stability bound can be around 125 GeV
For 2 genera=ons case:
For 3 genera=ons case:
Type II seesaw
Gogoladze, N.O. &Shafi, Phys. Rev. D 78 (2008) 085005We introduce a triplet scalar field
Scalar poten=al
Many new couplings:
Neutrino Yukawa coupling:
Tadpole term for the triplet scalar
Neutrino mass:
Aser integra=ng out the heavy triplet, we have
SM Higgs quar=c is defined as
Now we solve RGEs in the presence of Type II seesaw
SM RGEs
* We employ 2-‐loop SM RGEs + 1-‐loop new RGEs Many free parameters:
with the matching condi=on:
RGEs
Fixing the cutoff scale , we inves=gate Higgs mass bounds
Vacuum stability bound: the lowest Higgs boson mass which sa=sfies for any scale between
Perturba=vity bound: the highest Higgs boson mass which sa=sfies for any scale between
Analysis is quite involved…..
We focus on parameters:
appear in Higgs quar=c RGE
shiss Higgs quar=c coupling @ by the matching condi=on We analyze RGEs for various at the cutoff with others fixed
Higgs mass bounds versus for various
Window is closed
Perturba=vity bound
Stability bound
Example of results
Even the perturba(vity bound can be < 114.4 GeV
Gogoladze, N.O. &Shafi, Phys. Rev. D 78 (2008) 085005
For case (2): lowering the cutoff
Examples: Randall-‐Sundrum type model:
with the warp factor
non-‐minimal gravita(onal coupling:
He, N.O. & Shafi, Phys. Ler. B (2011) 219
More interes(ng example: 5D gauge-‐Higgs unifica(on
Gauge-‐Higgs Unifica(on (GHU) model in flat 5D
Bulk Standard Model
5-‐dim. theory compac=fied on orbifold
y SM
All SM fields reside in the bulk
Crucial difference is Higgs boson is unified into 5th component of gauge fields in higher dimension
Basic structure 5 dim SU(3) gauge theory (toy model)
adj doublet doublet singlet SU(3) gauge =
Impose non-‐trivial boundary condi=ons (parity assignment)
are Z2 even fields, others odd fields Zero modes for odd fields are project out,
So SU(3) is broken to SU(2) =mes U(1) by this parity assignment
Proper(es
(1) The SM Higgs doublet is iden(fied as the 5
thcomponent of 5D bulk gauge field
(2) Mass term and Higgs self-‐coupling are protected to be zero by the 5D gauge invariance
(3) 5D gauge invariance is broken by the boundary
condi(ons and as a result, Higgs mass and self-‐coupling are induced through quantum correc(ons at low energies (4) However, there is no quadra(c divergence in the theory
(5) Low energy effec(ve theory of the model is equivalent to the SM with a certain boundary condi(on
Gauge-‐Higgs condi=on:
Haba, Matsumoto, N.O. &Yamashita, JHEP 02 (2006) 073
5D flat GHU at low energies = SM + GH condi(on
for Higgs self-‐coupling
Higgs boson mass from GHU
in effec(ve theore(cal point of view
* We do not care about the fine-‐tuning of Higgs mass^2 for the moment
Gogoladze, N.O. & Shafi, Phys. Ler. B 655 (2007) 257
We impose the Gauge-‐Higgs condi(on for the Higgs quar(c coupling and predict Higgs mass as a func(on of the compac(fica(on scale
Equivalent to the stability bound
Stability Higgs mass bound as a func(on of an ``effec(ve cutoff’’
LEP bound
Higgs signal at LHC?
Predic(on of Higgs mass in the GHU as UV comple(on of SM
Update of Gogoladze, N.O. &
Shafi, Phys. Ler. B 655 (2007) 257
We may fix the compac(fica(on by considering the unifica(on of gauge coupling and top Yukawa coupling
Higgs mass predic=on: 121 GeV for
Original mo(va(on of GHU is to solve the gauge hierarchy problem
Compac(fica(on scale ~ 1-‐10 TeV Predicted Higgs boson mass is too low
SU(3) (mes U(1) GHU with SU(3) an adjoint fermion in the bulk
Haba, Matsumoto, N.O. &
Yamashita, JHEP 02 (2006) 073
SU(3) (mes U(1) GHU with SU(3) adjoint
fermions in the bulk
Haba, Matsumoto, N.O. &
Yamashita, JHEP 02 (2006) 073
The discovery of the mechanism for the electroweak symmetry
breaking and mass genera(on is a major goal of the physics program at the LHC
Higgs boson (and also new physics) is being intensively hunted The allowed mass range for the Higgs boson to hide is being
squeezed drama(cally, and Higgs boson will be discovered soon Higgs mass has an very important implica(on for new physics in the view point of the stability bound because the LHC results constrain Higgs mass below the SM stability bound with Planck mass cutoff
In order to change the cutoff or RGE evolu(ons, we need to consider new physics, even though it has not been discovered
Conclusions
