gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/ppp2017/slides/yamada.pdfgauge...
TRANSCRIPT
![Page 1: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/1.jpg)
Gauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism
Masatoshi Yamada (Ruprecht-Karls-Universität Heidelberg)
with Christof Wetterich
PPP2017@Yukawa Institute Based on C. Wetterich and M.Y., Phys. Lett. B 770, 268
![Page 2: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/2.jpg)
First of all…
The “resurgence” mechanism
differs from
a method to resume perturbative series. (Misumi san’s talk)
![Page 3: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/3.jpg)
What’s resurgence?According to “Oxford Dictionary of English”,
an increase or revival after a period of little activity, popularity
![Page 4: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/4.jpg)
Plan• Revisit gauge hierarchy problem
• Asymptotically safe gravity
• The resurgence mechanism
![Page 5: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/5.jpg)
Gauge hierarchy problem • Renormalized Higgs mass
• O(102 GeV)2 = -O(1019 GeV)2 +O(1019 GeV)2
✖ ✖= + +・・・�
Z ⇤
d4p1
p2⇠ ⇤2
m2⇤
m2R = m2
⇤ +⇤2
16⇡2(�+ · · · )
m2R ⌧ m2
⇤
![Page 6: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/6.jpg)
In viewpoint of Wilson RG�k =
Zd
4x
1
2(@µ�)
2 � m
2k
2�
2 � �k
4�
4
�
�k
m2k
k2
m2k < 0 m2
k > 0
0
m2k
k2= � C
8⇡2�k
![Page 7: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/7.jpg)
In viewpoint of Wilson RG�k
m2k
k2
m2R = m2
⇤ +C⇤2
8⇡2�k=0
m2R
(m2⇤,�⇤)
0
�⇤ ' �k=0
m2k
k2= � C
8⇡2�k
![Page 8: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/8.jpg)
In viewpoint of Wilson RG�k
m2k
k2
m2R = m2
⇤ +C⇤2
8⇡2�k=0
(m2⇤,�⇤)
0
�⇤ ' �k=0= 0
m2k
k2= � C
8⇡2�k
m2⇤ = �C⇤2
8⇡2�⇤
m2R
![Page 9: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/9.jpg)
In viewpoint of Wilson RG
• Λ2 determines the position of phase boundary (critical line).
• The phase boundary corresponds to the massless (critical) theory.
• To obtain small mR, put the bare parameters close to the phase boundary.
�k
m2k
k2
m2k < 0 m2
k > 0
0
m2k
k2= � C
8⇡2�k
![Page 10: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/10.jpg)
In viewpoint of Wilson RGGauge hierarchy problem
= Criticality problem
Why is the Higgs close to critical?
Picture from web
![Page 11: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/11.jpg)
Discussion• Λ
2 is spurious?
• The position of phase boundary is physically meaningless.
• The distance between the flow and the boundary is physically meaningful.
• In perturbation theory, Λ2 is always subtracted by the counter term or
dimensional regularization.
• Rotation of coordinate. ➡
• Choice of renormalization scheme ⇔ Choice of coordinate of theory space
• Gauge hierarchy problem ⇄ The bare theory of Higgs is almost scale (conformally) invariant.
C = 0
�k
m2k
k2
m2k0
k2= 0
�0k
m2k0
k2
W. A. Bardeen, FERMILAB-CONF-95-391-T H. Aoki, S, Iso, Phys. Rev. D86, 013001
m2k
k2= � C
8⇡2�k
m2k
k2= � C
8⇡2�k
m2k0
k2= 0
K-I Aoki et. al., hep-th/0002231
![Page 12: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/12.jpg)
Gauge hierarchy problem• RG equation for dimensionless scalar mass (deviation from phase boundary)
anomalous dim.canonical dim. effective dim.
From observations
![Page 13: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/13.jpg)
RG flow of scalar mass
![Page 14: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/14.jpg)
Comment• If m0=0, mR=0 is realized.
• The theory exactly on the phase boundary.
• Idea of classical scale (conformal) invariance
• How to generate the EW scale? (scalegenesis)
• Dimensional transmutation or Dynamical symmetry breaking with TeV scale. (Next Matsuzaki san’s talk)
![Page 15: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/15.jpg)
Summary so far• Gauge hierarchy problem is criticality problem.
• Why is Higgs close to the phase boundary?
• Λ2 may be not physically meaningful.
• The deviation from the phase boundary is physical.
• The positive canonical dimension 2 causes gauge hierarchy problem.
![Page 16: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/16.jpg)
Plan• Revisit gauge hierarchy problem
• Asymptotically safe gravity
• The resurgence mechanism
![Page 17: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/17.jpg)
Asymptotic safety• Suggested by S. Weinberg
• Existence of UV fixed point
• Continuum limit k→∞.
• UV critical surface (UV complete theory) is defined by relevant operators.
• Dimension of UV critical surface = number of free parameters.
• Generalization of asymptotic free
S. Weinberg, Chap 16 in General Relativity
Picture from Wiki
![Page 18: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/18.jpg)
Asymptotic safety• Asymptotic free
![Page 19: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/19.jpg)
Asymptotic safety• Asymptotic safety
![Page 20: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/20.jpg)
Functional renormalization group
k@k�k =1
2Str[(�(2)
k +Rk)�1k@kRk]
g1
g2
gi
�k =
Zd
4x[g1O1 + g2O2 + · · ·+ giOi + · · · ]
�k 'Z
d
4x[g1O1 + g2O2]
S = �⇤
� = �k=0
exact flow
truncated flow
projection
Wetterich equation
![Page 21: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/21.jpg)
Critical exponent• Classification of flow around FP
• RG eq. around FP g*
• Solution of RG eq.
✓i > 0
✓i < 0
relevant
irrelevant
eigenvaluek ! 0
![Page 22: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/22.jpg)
Earlier studies• Pure gravity
• Truncation:
• There exists a UV fixed point in gravity sector
• Number of relevant operators: 3 ⇔ 3 free parameters
• With matters
• stability of FP
• scalar-gravity system
• Higgs-Yukawa system
• gauge field system
• Fermionic system
f(R), ↵R+ �R2 + �Rµ⌫Rµ⌫ , etc.
Cf. O. Lauscher, M. Reuter, Phys. Rev. D66, 025016 K. Falls, et. al., arXiv: 1301.4191 D. Benedeti, et. al,. Mod. Phys. Lett. A24, 2233
Cf. R. Percacci, D. Perini, Phys. Rev. D67, 081503 P. Dona, et. al., Phys. Rev. D89, 084035 J. Meibohm, et. al., Phys.Rev. D93, 084035 R. Percacci, D. Perini, Phys. Rev. D68, 044018 G. Narain, R. Percacci, CQG 27, 075001 R. Percalli et. al, Phys. Lett. B689, 90 G. P. Vacca, O. Zanusso, Rhys. Rev. Lett. 105, 231601 J. Daum et. al., JHEP 01, 084 U. Harst, M. Reuter, JHEP 05, 119 A. Eichhorn, H. Gies, New Phys. J., 113, 125012 A. Eichhorn, Phys. Rev. D86, 105021 etc.
![Page 23: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/23.jpg)
Many possibilities• Prediction of Higgs mass
• Prediction of top-quark mass
• U(1) Landau pole problem
• Cosmological constant problem
• Gauge hierarchy problem
M. Shaposhinikov, C. Wetterich, Phys. Lett. B683 (2010), 196
A. Eichhorn, A Held, arXiv:1707.01107
C. Wetterich, arXiv:1704.08040
N. Christiansen, A. Eichhorn, Phys.Lett. B770 (2017) 154
C. Wetterich, M.Y., Phys. Lett. B 770 (2017), 268
![Page 24: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/24.jpg)
Plan• Revisit gauge hierarchy problem
• Asymptotically safe gravity
• The resurgence mechanism
![Page 25: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/25.jpg)
Corrections to scalar mass• RG equation for scalar mass
• Contributions from graviton fluctuation
graviton loop
![Page 26: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/26.jpg)
Quantum Scaling of scalar mass
• Critical exponent (effective dimension)
• At Gaussian-matter fixed point:
![Page 27: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/27.jpg)
Quantum Scaling of scalar mass
• Critical exponent
• If we have a large anomalous dimension
![Page 28: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/28.jpg)
RG flow of scalar mass
![Page 29: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/29.jpg)
RG flow of scalar massresurgence mechanism
self-tune criticality
![Page 30: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/30.jpg)
Possibility of θ<0• Higgs-Yukawa model
• We find which yields . K. oda and M.Y., Class.Quant.Grav. 33 (2016) no.12, 125011
![Page 31: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/31.jpg)
Comment on “Classical” scale invariance
• Gaussian-matter fixed point: Matter’s FP is trivial.
• In continuum limit k→∞, matter coupling constants converge to the trivial fixed point.
• The scalar couplings keep vanishing up to below the Planck scale.
• The “classical” scale invariance is realized at the Planck scale. In particular, the flatland is realized.
• What is the origin of the EW scale?
![Page 32: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/32.jpg)
Summary• Gauge hierarchy problem is criticality problem.
• Asymptotically safe gravity is one of strong candidates of quantum gravity.
• Graviton fluctuation could induce large anomalous dimension.
• Gauge hierarchy problem could be solved by the resurgence mechanism.
• We need new physics.
![Page 33: Gauge hierarchy problem in asymptotically safe gravity ...ppp.ws/PPP2017/slides/Yamada.pdfGauge hierarchy problem in asymptotically safe gravity ‒the resurgence mechanism Masatoshi](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecdf6babfc69535540164b0/html5/thumbnails/33.jpg)
Prospects• Dependence of critical exponent of scalar mass on number of particles.
• Higgs portal dark matter
• Neutrino mass (Majorana mass)
• Strong CP problem?
• Weak gravity conjecture
• Relation with string theory
Working with A. Eichhorn, A. Held. S. Lippold, Y. Hamada
Working with A. Eichhorn, Y. Hamada, J. Lumma
Working with T. Denz, A. Eichhorn, S. Lippold, J. M. Pawlowski, M. Reichert, F. Versteegen
Working with J. M. Pawlowski, M. Reichert, C. Wetterich