1. What can we learn from recent anomalies in B Physics
Xiao-Gang He
NTU/SJTU
Seminar at USTC, June 22, 2018

2. 1. Anomalies in B decays 2. Standard Model and beyond for B Physics 3
1. Anomalies in B decays 2. Standard Model and beyond for B Physics 3. Models for R(D(*)) and b->s m+m- anomalies 4. CPT sum rule and SU(3)/U relation Violation 5. Conclusions

3. 1. Anomalies in B decays
– Cambridge Dictionary
B decays that are different from SM predictions and therefore not satisfactory. The B physics anomalies might be some hints of something more that just SM

4. The RK* Anomaly S. Bifani, CERN Seminar, 18th April, 2017
LHCb arXiv:
A. Datta, et al, arXiv: , trying to usi=e light intermediate particle to explain by low q^2is lower than high q^2

5. More B physics anomalies
New data on Bs -> m+m- from LHCb, lowered the differences
LHCb arXiv:
All these processes are induced by b -> s ll interaction.
Consistently lower than SM predictions. Combined effects are now about 4s !

6. More
4s effects!
SM prediction

7. Even more LHCb has been a great job for B physics
Even more LHCb has been a great job for B physics! Confirming other observations and many new discoveries!
LHCb-CONF
CPT sum rule
LHCb data
CPT Sum rule violated!
Fleischer et al, arXiv :
He, Li, Ren, Yuan, arXive:
U-spin symmetry relation
SU(3) or U-spin symmetric: rc = 1
LHCb data:
SU(3)/U-spin relation violation!
He, Li, Ren, Yuan, arXive:

8. 2. Standard Model and beyond for B Physics
Standard Model is based on SU(3)CxSU(2)LxU(1)Y gauge interaction. In SM mis-match of weak and mass eigen-bases, leads to flavor mixing and CP violation, part of the story of flavor physics. The theory for B physics!

9. Number of SM generations
In the SM, only 3 generations of quarks and leptons are allowed.
gg -> Higgs ~ (number of heavy quarks)2, if fourth generation
exist, their mass should be large, 9 times bigger production of
Higgs. LHC data ruled out more than 3 generations of quarks.
LEP already ruled out more than 3 neutrinos with mass less than mZ/2.
Cosmology and astrophysics, number of light neutrinos also less than 4.
SM, triangle anomaly cancellation: equal number of quarks and leptons!
There are only three generations of sequential quarks and leptons!
Why 3 generations? How do they mix with each other?
Beyond SM, conclusions may change, X-G He and G. Valencia, PPLB707 (2012)

10. Quark and Lepton mixing patterns
The mis-match of weak and mass eigen-state bases lead quark and lepton mix within generations.

11. Status of Quark and Lepton
Quark Mixing Neutrino Mixing
PDG

12. b -> s ll induced anomalies
B -> s ll in the SM
New Physics beyond SM,
New operators: Ci = CiSM + CiNP
Ci’= Ci’NP

13. Global fit for Ci(’) before new LHCb data on RK. Descotes-Genon et al
Global fit for Ci(’) before new LHCb data on RK* Descotes-Genon et al., arXiv:

14. Global fit for Ci(’) including new LHCb data on RK*
Capdevila et al., arXiv:
Six dimensional fit

15. 3. Models for R(D(*)) and b->sm+m- anomalies
A lot of model building activities trying to provide solutions to R(D(*)) and b->s m+m- induced anomalies.
Making b->s m+m- smaller or b->s e+e- larger than SM predictions.
Z’ and W’ models, Multi-Higgs models, leptoquark models,
Susy, R-parity violating models,
…..
Solve two types of anomalies separately or solve them simultaneously. Hundreds of papers written on related subjects!
Since the new LHCb RK* data, just to the end of April 2017 papers:
arXiv: , , , , , , , , , , , , , , , , , …

16. Theoretical modeling for b -> s ll anomalies
A Z’ model based on gauge family symmetry
A Variation of each generation has a SU(2)xU(1) , Ernest Ma and X-Y Li
C-W. Chiang, X-G He, G. Valencia,PRD93,
Motivated by the fact that the third generation mass is bigger than the first two generations.)
Lm- Lt model (He, Joshi, Lew and Volkas, 1991; Foot, He, Lew and Volkas,1994) can help to resolve the anomalies too.

17. Very constraining electroweak precision data!
Chiang, Deshpande, He, Jiang, PRD81, (2010). Chiang, He, Valencia, PRD93, (2016)
Updated by Fang Ye, Updated by G. Valencia 2017

18. The B ->D(*) t n anomalies
New Physics modify charged current interaction… in a way that
The first two and third
generations interact differently;
b) Modification for charged current interaction in SM!
If one neglects differences between
(RD*/RD)EXP = 1.3 and (RD* /RD)SM = 1.16,
then modification of the form
Vij – KM matrix element
With D22,3 ~ 0.13 and other Dij,k = 0
will solve the problem.
But if one cares, then needs to have Charged Higgs contribution is not enough
different modifications for RD* and RD Babar collaboration, arXiv

19. A sample model modify RD* and RD differently
X-G He, G. Valencia, PRD87, (2013)
The 3rd generation is differnt than other generations. Motivated by Rb problem in
EW precision test.

20. R(D(*)) anomalies can be solved.

21. He and Valencia, arXiv:1711.09525, PLB779, 52(2018)

23. Bring R(D(*)) and b -> s mu mu anomalies together A role of a leptoquark scalar
Leptoquark interaction, Bauer&Neubert, arXiv: Yes
R-parity violating interaction, N. Deshpande&X-G He, arXiv: No
Leptoquark, D. Becirevic et al., arXiv: No. A different one
A. Crivellin et al., arXiv: Also a different one
Y. Cai et al, arXiv: Yes …
Which leptoquark scalar?

24. Leptoquark scalars

25. Exchange leptoquark at tree and one loop level
D->mm, pmm
K-> p nn, B-> K(*) nn
R(D(*)), B->D(*) (r,p) ln, Bc -> t n
D->mm, p mm
R(D(*)), B->D(*) (r,p) ln, Bc -> t n
Solution to R(D(*)) Solution to b-> sm+m- induced anomalies Solution to (g-2)m If R-parity violating interaction, exchange sd-quark, the last line is absent. That is the reason why R-parity cannot solve R(D(*)) and b -> s m+m- anomalies (Deshpande and He) Also why Baur&Neubert, and Becrivic et al could not work, neglect last term contributions to R(D(*)) and lead to conflict for b -> s m+m- when other constraints are included, important one B -> K(*) nn! (R = B(B -> K(*) nn)exp/ B(B -> K(*) nn)SM < 4.3! (Becirevic et al.)

26. Solution to R(D(*)) anomalies
Y. Cai et al, arXiv:
Significant contribution needed from coupling! Can also solve (g-2)m anomaly!

27. nnn Solution to and b -> s m+m- induced anomalies
Y. Cai et al, arXiv:

28. Without coupling (R-parity violating model) Satisfying B -> K(
Without coupling (R-parity violating model) Satisfying B -> K(*) nn constraints
N. Deshpande&X-G He, arXiv:

29. Bs -> m+m- Higgs Yukawa couplings precision test
Chiang, He, Ye and Yuan, arXiv:

30. Higgs contribution to Bs -> m+m-

31. Constraint from Bs – anti-Bs mixing

33. 4. CPT sum rule and SU(3)/U relation Violation
He, Li, Ren and Yuan, arXiv:
Effective Hamiltonian for B to PP decays in SM

34. CPT sum rule in time dependent B decays
A(B -> PP) = <PP|Heff|B>
CPT invariance imply anti-B decay to be given by
Time dependent CP violation
CPT sum rule

35. Violation of CPT sum rule
LHCb-CONF
CPT sum rule
LHCb data
Sum rule violated!

36. Further tests of CPT sum rule
CPT symmetry tested to great precision. Not attempt to build a theoretical model to explain violation of CPT rum rule. If there is a mixing with some other sector (or sectors) with the correct quantum numbers, the sum rule may change. Do not have a good candidate to choose from because the mass of the candidate system should have a mass very close to BsL and BsH. Further tests time-dependent CP violation

37. SU(3)/U relations in B -> PP Decays
SU(3)/U symmetric, Td = Ts and Pd = Ps rc = 1

38. Violation of SU(3)/U relation
LHCb-CONF
SU(3) or U-spin symmetric: rc = 1
LHCb data:
SU(3)/U-spin relation violation!

39. Test SU(3)/U relations with several other B decays
For P1 ~ P6, theoretical calculations 1 ~ 2 rc for P1 experimental data: (expected with SU(3) breaking) Why for P5, rc = , so much different?

40. Large FSI phases?!
For P1, both B0 → K+p− and Bs0 → p+K−, the final states are K± p ± and are CP conjugate of each other. Their final state phase spaces are the same and also FSI should be similar. But for B0 → p+π− and Bs0 → K+K− decays, Support from D -> KK, Kp, pp data the final state π+π− are very much different than the final state K+K−. The phases of T and P caused the difference!

41. Further tests: pattern of SU(3)/U relation breaking

42. 5. Conclusions
Anomalies exist in R(D(*)) and b -> s m+m- anomalies at about 4s. R(D(*)) : NP constructively add to tree SM contributions. b -> s m+m- : NP destructively contributes to loop SM contributions. Models exist for solve the above two types of anomalies separately. Can also have model to solve both simultaneously. LHCb and CMS data on Bs -> m+m- can provide precision test for Higgs Yukawa couplings. LHCb data on time-dependent CP violation in Bs -> K+K- show hint of violation of CPT sum rule. Data on B0-> p+p- and Bs -> K+K- show violation of SU(3)/U-spin symmetry. Indication of large FSI phase differences. Rich B physics ahead of us with future new data from LHCb and Belle II. Still need data to confirm whether the anomalies are really there. Also a lot to do for theorists!