A
bstract
We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, ...commonly referred to as “Warsaw basis”. We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear
R
ξ
-gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this
mass basis
we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available
Mathematica
code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.
We present SUSY_FLAVOR version 2.5—a program that calculates over 30 low-energy flavor observables in the general R-parity conserving MSSM. Compared to previous versions, in SUSY_FLAVOR v2.5 ...parameter initialization in SLHA2 formats has been significantly generalized, so that the program accepts most of the output files produced by other libraries analyzing the MSSM phenomenology. A number of bugs and inconsistencies have been fixed, based on users feedback. Calculations of several processes implemented in the earlier version have been corrected. New processes of rare decays of the top quark to Higgs boson have been included. Variables controlling contributions from various MSSM sectors have been added.
Program title: SUSY FLAVOR v2.5
Catalogue identifier: AEGV_v2_5
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGV_v2_5.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 22623
No. of bytes in distributed program, including test data, etc.: 614938
Distribution format: tar.gz
Programming language: Fortran 77.
Computer: Any.
Operating system: Any, tested on Linux.
Classification: 11.6.
Catalogue identifier of previous version: AEGV_v2_0
Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 1004
Does the new version supersede the previous version?: Yes
Nature of problem: Predicting CP-violating observables, meson mixing parameters and branching ratios for a set of rare processes in the general R-parity conserving MSSM.
Solution method: We use standard quantum theoretical methods to calculate Wilson coefficients in MSSM at one loop and including QCD corrections at higher orders when this is necessary and possible.
Reasons for new version: The input/output routines have been rewritten to make them more flexible and compatible with the SLHA2 standard 1. Calculations of the several processes implemented in earlier SUSY_FLAVOR versions have been corrected. New observables have been added. A number of bugs have been corrected.
Summary of revisions:1.Modified initialization routines. Currently the program should be able to read without modifications most of the SLHA2-compatible output files produced by other publicly available libraries calculating observables related to the MSSM phenomenology. In addition, new optional input block SFLAV_HADRON has been defined to facilitate modifications of the parameters related to the hadronic and QCD sector.The initialization sequence now goes through the following steps: •Before reading the file, all parameters are set to some initial values (which can be changed by editing the values given in the subroutine sflav_defaults in file sflav_io.f).•Subsequently, the user-defined data are read from the file with the default name susy_flavor.in. Data are grouped in Blocks following the SLHA2 specification or extensions described in 2. Blocks are read in the following order: SOFTINP, SMINPUTS, VCKMIN, MINPAR (tanβ only, other entries are ignored), EXTPAR, IMEXTPAR, MSL2IN, IMMSL2IN, MSE2IN, IMMSE2IN, TEIN, IMTEIN, TEINH, IMTEINH, MSQ2IN, IMMSQ2IN, MSU2IN, IMMSU2IN, MSD2IN, IMMSD2IN, TUIN, IMTUIN, TUINH, IMTUINH, TDIN, IMTDIN, TDINH, IMTDINH, SFLAV_HADRON.•The presence of any Block is optional—if some Block is absent, the program falls back to the default parameter values. At least flavor-diagonal SUSY mass parameters have to be defined, otherwise the vanishing default values cause the program to crash.•If a parameter is multiply defined in several Blocks, the value from Block read as latest in the list above overwrites (without warning!) the values from preceding Blocks.•Blocks do not need to be complete and to contain all the entries described in the SLHA2 specification—it is sufficient to define a minimal set of the parameters relevant for a given problem, others are filled with the default values.•The “non-holomorphic” LR mixing terms are not included in the SLHA2 specification and by default are set to 0. They can be initialized to the non-trivial values in the blocks TXINH and IMTXINH (X=E,D,U)•The new input block SFLAV_HADRON allows the modification of the hadronic- and QCD-related quantities used by SUSY_FLAVOR. The structure of this block and the default values of the hadronic parameters are shown at the end of the sample input file susy_flavor.in attached to the SUSY_FLAVOR distribution.2.New control variables have been added, allowing the separate switching of contributions from various MSSM sectors on or off. They can be set by the following statement at the beginning of the driver program: call set_active_sector(ih,ic,in,ig) where the variables ih, ic, in, ig can take values 0 or 1 and they control, respectively, the inclusion in the total result of the diagrams with gauge and Higgs bosons, charginos, neutralinos and gluinos exchanged in the loops. Note that diagrams with Higgs and gauge bosons are always added together and currently cannot be disentangled, so setting ih=1, ic=in=ig=0 does not reproduce the SM result. By default, if no call to set_active_sector is made, all control variables are assumed to be equal to 1, so that all contributions are included.3.Added or modified processes: •The expressions used to calculate the neutron Electric Dipole Moment have been modified.•The branching ratios for the radiative decays of the heavy lepton into the lighter lepton and the photon, μ→eγ and τ→eγ, μγ, are now normalized to the total heavy lepton decay width (previously they were normalized to the decay width into leptonic channels).•The routines calculating branching ratios of B→τν and B→Dτν decays have been generalized to include more general structure of the effective Higgs boson–fermion couplings. In addition the routine calculating Br(B→D∗τν) has been added.•The routines for rare decays of the top quark to the CP-even Higgs boson and the light quarks, t→ch, uh, have been added, based on Ref. 3 (program can calculate also the decay rates of the top quark to the heavier CP-even Higgs boson H, assuming that such decays are allowed kinematically).•The routine calculating the approximate 2-loop estimate of the neutral CP-even Higgs mass mh has been added, based on Ref. 4. Note that for the more precise calculations of this mass other publicly available SUSY codes should be used.•Default values of numerous quantities which are treated by SUSY_FLAVOR as the external parameters, mainly the values of hadronic parameters obtained from lattice calculations and results of experimental measurements, have been updated to accommodate the latest published results.4.SUSY_FLAVOR’s output is now written to the file named susy_flavor.out. It has ”SLHA-like” structure, i.e. it is divided into “data blocks”, however these blocks are SUSY_FLAVOR specific and do not follow the common SLHA2 standards. The output file contains the following data blocks: •SFLAV_CONTROL: control variables and error code status.•SFLAV_MASS: MSSM mass spectrum after mass matrix diagonalization.•SFLAV_CHIRAL_YUKAWA: relative size of the resummed chiral corrections to the Yukawa couplings.•SFLAV_CHIRAL_CKM: relative size of the resummed chiral corrections to the CKM matrix elements.•SFLAV_DELTA_F0: ΔF=0 observables: leptonic EDMs and g−2 anomalies, neutron EDM.•SFLAV_DELTA_F1: ΔF=1 observables: decay rates of l→l′γ, K→πν̄ν, B+→τ+ν, B→Dτν, B→D∗τν, B→Xsγ, Bd,s→li+lj−, t→uh, t→ch.•SFLAV_DELTA_F2: ΔF=2 observables: εK, ΔmK, ΔmD, ΔmBd, ΔmBs.Blocks SFLAV_CHIRAL_YUKAWA and SFLAV_CHIRAL_CKM show the relative differences of bare and physical Yukawa couplings and CKM matrix elements after the resummation of chiral corrections. If they are large, ≥O(1), the perturbation expansion is not reliable and the remaining program output may not be correct.5.The new integrated manual for SUSY_FLAVOR_v2.5 has been created, including the detailed description of the modifications listed above. It is attached to the SUSY_FLAVOR distribution. Regular code distribution updates and bug fixes (between the major revisions submitted to Computer Physics Communications) can be found on the program web page www.fuw.edu.pl/susy_flavor.
Restrictions:
The results apply only to the case of MSSM with R-parity conservation and without heavy right neutrino sector 5.
Additional comments:
This program has been cataloged as AEGV_v2_5 to conform to the manuscript version number. There are no programs cataloged as, AEGV_v2_1, AEGV_v2_2, AEGV_v2_3, AEGV_v2_4, in the CPC Program Library.
Running time:
For a single parameter set, under 1s on a personal computer.
References:
1 B. Allanach et al., Comput. Phys. Commun. 180 (2009) 8 arXiv:0801.0045 hep-ph.
2 J. Rosiek, P Chankowski, A. Dedes, S. Jager and P. Tanedo, Comput. Phys. Commun. 181 (2010) 2180 arXiv:1003.4260 hep-ph; A. Crivellin, J. Rosiek et. al., Comput. Phys. Commun. 184 (2013) 1004, arXiv:1203.5023” hep-ph.
3 A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho and K. Tamvakis, arXiv:1409.6546 hep-ph.
4 S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Lett. B455 (1999) 179–191 hep-ph/9903404
5 A. Dedes, H. Haber and J. Rosiek, JHEP 0711 (2007) 059, arXiv:0707.3718 hep-ph.
When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical ...article by Buchmüller and Wyler
3
. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in ref.
3
. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 5 new operators arise in the four-fermion sector.
A
bstract
Assuming that new physics effects are parametrized by the Standard-Model Effective Field Theory (SMEFT) written in a complete basis of up to dimension-6 operators, we calculate the ...CP-conserving one-loop amplitude for the decay
h
→
γγ
in general
R
ξ
- gauges. We employ a simple renormalisation scheme that is hybrid between on-shell
S
M
¯
-like renormalised parameters and running MS Wilson coefficients. The resulting amplitude is then finite, renormalisation scale invariant, independent of the gauge choice (
ξ
) and respects SM Ward identities. Remarkably, the
S
-matrix amplitude calculation resembles very closely the one usually known from renormalisable theories and can be automatised to a high degree. We use this gauge invariant amplitude and recent LHC data to check upon sensitivity to various Wilson coefficients entering from a more complete theory at the matching energy scale. We present a closed expression for the ratio ℛ
h
→
γγ
, of the Beyond the SM versus the SM contributions as appeared in LHC
h
→
γγ
searches. The most important contributions arise at tree level from the operators
Q
φB
, Q
φW
, Q
φW B
, and at one-loop level from the dipole operators
Q
uB
, Q
uW
. Our calculation shows also that, for operators that appear at tree level in SMEFT, one-loop corrections can modify their contributions by less than 10%. Wilson coefficients corresponding to these five operators are bounded from current LHC
h
→
γγ
data — in some cases an order of magnitude stronger than from other searches. Finally, we correct results that appeared previously in the literature.
A
bstract
We study lepton flavor observables in the Standard Model (SM) extended with all dimension-6 operators which are invariant under the SM gauge group. We calculate the complete one-loop ...predictions to the radiative lepton decays
μ
→
e
γ,
τ
→
μ
γ and
τ
→
e
γ as well as to the closely related anomalous magnetic moments and electric dipole moments of charged leptons, taking into account all dimension-6 operators which can generate lepton flavor violation. Also the 3-body flavor violating charged lepton decays
τ
±
→
μ
±
μ
+
μ
−
,
τ
±
→
e
±
e
+
e
−
,
τ
±
→
e
±
μ
+
μ
−
,
τ
±
→
μ
±
e
+
e
−
,
τ
±
→
e
∓
μ
±
μ
±
,
τ
±
→
μ
∓
e
±
e
±
and
μ
±
→
e
±
e
+
e
−
and the
Z
0
decays
Z
0
→
are considered, taking into account all tree-level contributions.
Effective field theories in Rξ gauges Misiak, M.; Paraskevas, M.; Rosiek, J. ...
The journal of high energy physics,
02/2019, Letnik:
2019, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
In effective quantum field theories, higher dimensional operators can affect the canonical normalization of kinetic terms at tree level. These contributions for scalars and gauge bosons ...should be carefully included in the gauge fixing procedure, in order to end up with a convenient set of Feynman rules. We develop such a setup for the linear
R
ξ
-gauges. It involves a suitable reduction of the operator basis, a generalized gauge fixing term, and a corresponding ghost sector. Our approach extends previous results for the dimension-six Standard Model Effective Field Theory to a generic class of effective theories with operators of arbitrary dimension.
A
bstract
In full one-loop generality and in next-to-leading order in QCD, we study rare top to Higgs boson flavour changing decay processes
t
→
qh
with
q
=
u, c
quarks, in the general MSSM with ...R-parity conservation. Our primary goal is to search for enhanced effects on
ℬ
t
→
q
h
that could be visible at current and high luminosity LHC running. To this end, we perform an analytical expansion of the amplitude in terms of flavour changing squark mass insertions that treats both cases of hierarchical and degenerate squark masses in a unified way. We identify two enhanced effects allowed by various constraints: one from holomorphic trilinear soft SUSY breaking terms and/or right handed up squark mass insertions and another from non-holomorphic trilinear soft SUSY breaking terms and light Higgs boson masses. Interestingly, even with
O
1
flavour violating effects in the, presently unconstrained, up-squark sector, SUSY effects on
ℬ
t
→
q
h
come out to be unobservable at LHC mainly due to leading order cancellations between penguin and self energy diagrams and the constraints from charge- and colour-breaking minima (CCB) of the MSSM vacuum. An exception to this conclusion may be effects arising from non-holomorphic soft SUSY breaking terms in the region where the CP-odd Higgs mass is smaller than the top-quark mass but this scenario is disfavoured by recent LHC searches. Our calculations for
t
→
qh
decay are made available in SUSY FLAVOUR numerical library.
We present SUSY_FLAVOR version 2 — a Fortran 77 program that calculates low-energy flavor observables in the general R-parity conserving MSSM. For a set of MSSM parameters as input, the code gives ...predictions for: 1.Electric dipole moments of the leptons and the neutron.2.Anomalous magnetic moments (i.e. g−2) of the leptons.3.Radiative lepton decays (μ→eγ and τ→μγ,eγ).4.Rare Kaon decays (KL0→π0ν̄ν and K+→π+ν̄ν).5.Leptonic B decays (Bs,d→l+l−, B→τν and B→Dτν).6.Radiative B decays (B→X̄sγ).7.ΔF=2 processes (K̄0–K0, D̄–D, B̄d–Bd and B̄s–Bs mixing). Comparing to SUSY_FLAVOR v1, where the matching conditions were calculated strictly at one-loop level, SUSY_FLAVOR v2 performs the resummation of all chirally enhanced corrections, i.e. takes into account the enhanced effects from tanβ and/or large trilinear soft mixing terms to all orders in perturbation theory. Also, in SUSY_FLAVOR v2 new routines calculation of B→(D)τν, g−2, radiative lepton decays and Br(l→l′γ) were added. All calculations are done using exact diagonalization of the sfermion mass matrices. The program can be obtained from http://www.fuw.edu.pl/susy_flavor.
Program title:SUSY_FLAVOR v2
Catalogue identifier: AEGV_v2_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGV_v2_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 15683
No. of bytes in distributed program, including test data, etc.: 89130
Distribution format: tar.gz
Programming language: Fortran 77.
Computer: Any.
Operating system: Any, tested on Linux.
Classification: 11.6.
Does the new version supersede the previous version?: Yes
Catalogue identifier of previous version: AEGV_v1_0
Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 2180
Nature of problem:
Predicting CP-violating observables, meson mixing parameters and branching ratios for set of rare processes in the general R-parity conserving MSSM.
Solution method:
We use standard quantum theoretical methods to calculate Wilson coefficients in MSSM and at one loop including QCD corrections at higher orders when this is necessary and possible. The input parameters can be read from an external file in SLHA format.
Reasons for new version:
A major rewrite of the internal code structure to accommodate higher order corrections; new observables added.
Summary of revisions:1.SUSY_FLAVOR v2.0 is able to perform resummation of chirally enhanced corrections to all orders of perturbation expansion (v1.0 included 1-loop terms only).2.Routines calculating new observables are added: g-2 lepton magnetic moment anomaly, μ to eγ and τ to eγ,μγ decays, B to Dτν decays, B to μe,τe,τμ decays.3.Parameter initialization in the sfermion sector is simplified and follows, by default, the SLHA2 conventions.Restrictions: The results apply only to the case of MSSM with R-parity conservation.
Running time: For a single parameter set approximately 1 s in double precision on a PowerBook Mac G4.
A
bstract
We present and prove a theorem of matrix analysis, the Flavour Expansion Theorem (or FET), according to which, an analytic function of a Hermitian matrix can be expanded polynomially in ...terms of its off-diagonal elements with coefficients being the divided differences of the analytic function and arguments the diagonal elements of the Hermitian matrix. The theorem is applicable in case of flavour changing amplitudes. At one-loop level this procedure is particularly natural due to the observation that every loop function in the Passarino-Veltman basis can be recursively expressed in terms of divided differences. FET helps to algebraically translate an amplitude written in mass eigenbasis into flavour mass insertions, without performing diagrammatic calculations in flavour basis. As a non-trivial application of FET up to a third order, we demonstrate its use in calculating strong bounds on the real parts of flavour changing mass insertions in the up- squark sector of the MSSM from neutron Electric Dipole Moment (nEDM) measurements, assuming that CP-violation arises only from the CKM matrix.
We present SUSY_FLAVOR – a Fortran 77 program that calculates important leptonic and semi-leptonic low-energy observables in the general
R-parity conserving MSSM. For a set of input MSSM parameters, ...the code gives predictions for the
K
¯
0
K
0
,
D
¯
D
,
B
¯
d
B
d
and
B
¯
s
B
s
mixing parameters;
B
→
X
s
γ
,
B
s
,
d
→
l
+
l
−
,
K
L
0
→
π
0
ν
¯
ν
and
K
+
→
π
+
ν
¯
ν
decay branching ratios; and the electric dipole moments of the leptons and the neutron. All these quantities are calculated at one-loop level (with some higher-order QCD corrections included) in the exact sfermion mass eigenbasis, without resorting to mass insertion approximations. The program can be obtained from
http://www.fuw.edu.pl/susy_flavor.
Program title: SUSY_FLAVOR
Catalogue identifier: AEGV_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEGV_v1_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 14 603
No. of bytes in distributed program, including test data, etc.: 82 126
Distribution format: tar.gz
Programming language: Fortran 77
Computer: PCs and workstations
Operating system: Any, tested on Linux
Classification: 11.6
Nature of problem: Predicting CP-violating observables, meson mixing parameters and branching ratios for a set of rare processes in the general
R-parity conserving MSSM.
Solution method: We use standard quantum theoretical methods to calculate Wilson coefficients in MSSM and at one loop including QCD corrections at higher orders when this is necessary and possible. The input parameters can be read from an external file in SLHA format.
Restrictions: The results apply only to the case of MSSM with
R-parity conservation.
Running time: For single parameter set approximately 1 s in double precision on a PowerBook Mac G4.
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